i
CONTENTS ABOUT THIS MANUAL ..................................................................................................ii COURSE OUTLINE .................................................................................................... v PART ONE: IN LIEU OF FUNDAMENTALS ...........................................................01 1 ASSORTED PRELIMINARIES ...................................................................................02 2 INTERVALS ................................................................................................................08 PART TWO: DIATONIC HARMONY.........................................................................16 3 BASIC HARMONIC STRUCTURES ...........................................................................17 4 MUSICAL SHORTHAND: LEAD SHEETS AND FIGURED BASS ............................26 5 HARMONIES OF THE MAJOR AND MINOR SCALES .............................................34 6 CADENCES/HARMONIC RHYTHM..........................................................................45 PART THREE: MELODY .............................................................................................53 7 MELODIC PITCH AND RHYTHM ............................................................................54 8 EMBELLISHING TONES ...........................................................................................67 9 MELODIC FORM .......................................................................................................81 PART FOUR: VOICE LEADING .................................................................................95 10 MELODIC PRINCIPLES OF PART WRITING/THE OUTER VOICE FRAMEWORK .............................................................................................................96 11 THE MELODIC FACTOR IN FOUR-VOICE PART WRITING/VOICING AND CONNECTING CHORDS..................................................................................102 12 PART WRITING WITH ROOT-POSITION TRIADS/ THE CHORALE .....................113 13 PART WRITING WITH TRIADS IN INVERSION ......................................................123 14 PART WRITING SEVENTH CHORDS .......................................................................140 PART FIVE: BASIC CHROMATIC HARMONY .....................................................154 15 SECONDARY FUNCTION I .......................................................................................155 16 SECONDARY FUNCTION II .....................................................................................168 17 MODULATION I ........................................................................................................177 PART SIX: COUNTERPOINT .....................................................................................188 18 THE ART OF COUNTERMELODY ...........................................................................189 19 THE FUGUE ..............................................................................................................202
PART SEVEN: ADVANCED CHROMATIC HARMONY ......................................211 20 MIXING MODES ........................................................................................................212
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21 22 23 24
ALTERED PRE-DOMINANTS ...................................................................................226 OTHER CHROMATIC HARMONIES ........................................................................238 MODULATION II .......................................................................................................248 HARMONIC EXTENSIONS AND CHROMATIC TECHNIQUES .............................257
PART EIGHT: FORM ..................................................................................................269 25 BINARY AND TERNARY FORMS ..............................................................................269 26 INTRODUCTION TO SONATA FORM......................................................................284 27 INTRODUCTION TO THE RONDO ..........................................................................287 PART NINE: MUSIC IN THE TWENTIETH CENTURY AND BEYOND............291 28 SYNTAX AND VOCABULARY ...................................................................................291 29 NEW TONAL METHODS ...........................................................................................300 30 ATONALITY AND SERIALISM ..................................................................................309 31 HARMONIC PRINCIPLES IN JAZZ ..........................................................................323 32 THE BLUES ................................................................................................................338 33 SHAPING A SONG .....................................................................................................350 APPENDIX A....................................................................................................................A-1 APPENDIX B....................................................................................................................B-1 ABOUT THIS MANUAL This manual is a teaching aid for Theory for Today’s Musician, Second Edition. In it, we have attempted: to provide some insight into the philosophy governing the organization of the text and the assumptions underlying the presentation of the topics; to give practical suggestions that we’ve found to work well in the classroom; to provide references to supplemental books or music, where appropriate; to include supplementary information and drill material; and to provide answers to those assignments in the Workbook that lend themselves to definitive answers. In short, this manual can be a convenience and time-saver for the more experienced teacher and an instructional guide for the less experienced teacher or the instructor whose specialization lies outside the area of music theory. FORMAT A consistent format is followed throughout the manual. General comments are followed by notes pertaining to specific items in the text. In many cases, we offer suggestions concerning additional ways to use the assignments, thereby increasing their usefulness. Solutions to the workbook assignments follow. In most cases, a chapter quiz is included. For certain exercises, particularly those dealing with part writing, numerous solutions are possible. Generally speaking, no
iii
solutions are included in the manual for such assignments, although in some cases, general commentary regarding the range of possibilities may be given. ORGANIZATION Important information concerning the organization of the text is furnished in the two prefaces (“To the Instructor” and “To the Student”). Please read that material carefully. The 33 chapters are organized in this way: PART ONE: IN LIEU OF FUNDAMENTALS Chapters 1–2 PART TWO: DIATONIC HARMONY Chapters 3–6 PART THREE: MELODY Chapters 7–9 PART FOUR: VOICE LEADING Chapters 10–14 PART FIVE: BASIC CHROMATIC HARMONY Chapters 15–17 PART SIX: COUNTERPOINT Chapters 18–19 PART SEVEN: ADVANCED CHROMATIC HARMONY Chapters 20–24 PART EIGHT: FORM Chapters 25-27 PART NINE: MUSIC IN THE TWENTIETH CENTURY AND BEYOND Chapters 28–33 APPENDIX A: APPENDIX B: APPENDIX C: APPENDIX D:
PITCH RHYTHM BASIC LEAD-SHEET SYMBOLS PART-WRITING GUIDELINES
iv
SYLLABUS Course outlines for two-, three-, and four-semester plans are given below. You’ll no doubt need to fine tune these based on your students’ level of preparation and your own preferences. Flexibility is inherent in the text. We’ve explained in the prefatory notes our rationale for placing the fundamentals in appendices. You may wish to start there. If so, that’s no problem. They are formatted and presented just like chapters, complete with assignments. In addition to the assignments, there are callouts in the margin to Back to Basics exercises, which are remediation exercises that can be completed on the website (www.routledge.com/cw/turek ). Exercises linked to the Routledge Music Theory Trainer can be completed by students online and their results emailed or printed out, should you wish to use them as homework assignments. Back to Basics appear throughout the early chapters offering students the opportunity to review key music fundamentals on their own time, in the hopes that by completing these exercises it will prevent the need for additional lecture time on these topics. Students with adequate high school preparation may be able to move quickly through this material or bypass it altogether. If so, so much the better. Otherwise, you’ll need to cut back in other areas to fit all topics into the syllabus. The chapters of Parts Two and Three should be presented in order. However, Part Four—Part Writing—can be tailored to suit your needs. Chapters 10 and 11 contain all the information required in a more circumscribed study. From there, you may wish to move to the sections of Chapters 12 and 13 that deal with suspensions and then to Chapter 14 (Part Writing Seventh Chords). Doing this will make more time available for the newer topics later in the text. Part Six—Counterpoint—contains more-or-less self-contained chapters. Chapter 18 (The Art of Countermelody) can suffice for an abbreviated look at the topic. Chapter 19 can be included in your syllabus or omitted from it, depending perhaps on whether your degree program includes a later course on counterpoint. Part Seven is a fairly hefty look at harmonic chromaticism and generally is a good foundation for the jazz harmony chapters that follow later. Part Eight is a threechapter introduction to form. Part Nine contains much of the newer material that we consider indispensable to today’s musician and that makes this text different from others. The two chapters relating to jazz and blues and the chapter on song writing probably played a big role in your decision to adopt this book. Thus, you are not likely to omit any of this material. Again, if your degree includes a course on form, you may opt to omit Chapters 26 and 27. If you prefer to include an introduction to the topic, Chapter 25 alone can do it. It looks at form in a way that we believe students today can understand and appreciate.
v 4-SEMESTER COURSE OUTLINE (Tailor to Suit)
SEMESTER ONE Appendix A and B 0-2 weeks Part One: In Lieu of Fundamentals Chapter One: Assorted Preliminaries Chapter Two: Intervals
1 week 2 weeks
Part Two: Diatonic Harmony Chapter Three: Basic Harmonic Structures Chapter Four: Musical Shorthand: Lead Sheets and Figured Bass Chapter Five: Harmonies of the Major and Minor Scales Chapter Six: Cadences/Harmonic Rhythm
1 week 2 weeks 2 weeks 1 week
Part Three: Melody Chapter Seven: Melodic Pitch and Rhythm Chapter Eight: Embellishing Tones Chapter Nine: Melodic Form
1 week 2 weeks 2 weeks
SEMESTER TWO Part Four: Voice Leading Chapter Ten: Melodic Principles of part Writing/The Outer Voice Framework 1 week Chapter Eleven: The Melodic Factor in Four-Voice Part Writing/ Voicing and Connecting Chords 2 weeks Chapter Twelve: Part Writing with Root-Position Triads/ The Chorale 2 weeks Chapter Thirteen: Part Writing with Triads in Inversion 2 weeks Chapter Fourteen: Part Writing Seventh Chords 2 weeks Part Five: Basic Chromatic Harmony Chapter Fifteen: Secondary Function I Chapter Sixteen: Secondary Function II Chapter Seventeen: Modulation I
2 weeks 2 weeks 2 weeks
SEMESTER THREE Part Six: Counterpoint Chapter Eighteen: The Art of Countermelody Chapter Nineteen: The Fugue
2 weeks 2 weeks
Part Seven: Advanced Chromatic Harmony Chapter Twenty: Mixing Modes Chapter Twenty-One: Altered Pre-Dominants
2 weeks 2 weeks
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Chapter Twenty-Two: Other Chromatic Harmonies Chapter Twenty-Three: Modulation II Chapter Twenty-Four: Harmonic Extensions and Techniques
2 weeks 2 weeks 1 week
Part Eight: Form Chapter Twenty-Five: Binary and Ternary Forms
2 weeks
SEMESTER FOUR Chapter Twenty-Six: Introduction to Sonata Form Chapter Twenty-Seven: Introduction to the Rondo
2 weeks 1 week
Part Nine: Music in the Twentieth Century and Beyond Chapter Twenty-Eight: Syntax and Vocabulary Chapter Twenty-Nine: New Tonal Methods Chapter Thirty: Atonality and Serialism Chapter Thirty-One: Harmonic Principles in Jazz Chapter Thirty-Two: The Blues Chapter Thirty-Three: Shaping a Song
2 weeks 2 weeks 2 weeks 2 weeks 2 weeks 2 weeks
2-SEMESTER COURSE OUTLINE Use Semester One and Two material only.
3-SEMESTER COURSE OUTLINE OPTIONS Note: 3-semester theory courses are rather unusual. These plans could be used by schools who wish to offer a different final semester of theory (i.e. Schenker analysis, set theory, etc.) Option 1: Counterpoint, Form, Twentieth Century but excluding chapters on vernacular music. Part Six: Counterpoint Chapter Eighteen: The Art of Countermelody Chapter Nineteen: The Fugue
2 weeks 2 weeks
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Part Eight: Form Chapter Twenty-Five: Binary and Ternary Forms Chapter Twenty-Six: Introduction to Sonata Form Chapter Twenty-Seven: Introduction to the Rondo
2 weeks 2 weeks 1 week
Part Nine: Music in the Twentieth Century and Beyond Chapter Twenty-Eight: Syntax and Vocabulary Chapter Twenty-Nine: New Tonal Methods Chapter Thirty: Atonality and Serialism
2 weeks 2 weeks 2 weeks
Option 2: Same basic plan as Option 1 but replacing sonata form and rondo chapters with chapters on blues and song composition. Part Six: Counterpoint Chapter Eighteen: The Art of Countermelody Chapter Nineteen: The Fugue
2 weeks 2 weeks
Part Eight: Form Chapter Twenty-Five: Binary and Ternary Forms
2 weeks
Part Nine: Music in the Twentieth Century and Beyond Chapter Twenty-Eight: Syntax and Vocabulary Chapter Twenty-Nine: New Tonal Methods Chapter Thirty: Atonality and Serialism Chapter Thirty-Two: The Blues Chapter Thirty-Three: Shaping a Song
2 weeks 2 weeks 2 weeks 2 weeks 2 weeks
Option 3: Same basic plan as Option 2 but eliminating chapter on fugue in favor of chapter on jazz harmony. Provides a limited dose of form with full dose of vernacular music. Part Six: Counterpoint Chapter Eighteen: The Art of Countermelody
2 weeks
Part Eight: Form Chapter Twenty-Five: Binary and Ternary Forms
2 weeks
Part Nine: Music in the Twentieth Century and Beyond Chapter Twenty-Eight: Syntax and Vocabulary Chapter Twenty-Nine: New Tonal Methods
2 weeks 2 weeks
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Chapter Thirty: Atonality and Serialism Chapter Thirty-One: Harmonic Principles in Jazz Chapter Thirty-Two: The Blues Chapter Thirty-Three: Shaping a Song
2 weeks 2 weeks 2 weeks 2 weeks
Option 4: Advanced Chromatic Harmony and Music in the Twentieth Century, omitting chapters on The Blues and Song Composition (This might be an option for schools that require an upper-level form or counterpoint course for all music majors.) Part Seven: Advanced Chromatic Harmony Chapter Twenty: Mixing Modes Chapter Twenty-One: Altered Pre-Dominants Chapter Twenty-Two: Other Chromatic Harmonies Chapter Twenty-Three: Modulation II
2 weeks 2 weeks 2 weeks 2 weeks
Part Nine: Music in the Twentieth Century and Beyond Chapter Twenty-Eight: Syntax and Vocabulary Chapter Twenty-Nine: New Tonal Methods Chapter Thirty: Atonality and Serialism Chapter Thirty-One: Harmonic Principles in Jazz
2 weeks 2 weeks 2 weeks 2 weeks
Option 5: Advanced Chromatic Harmony and final three chapters on vernacular music (this might be usable by schools offering majors in jazz studies, music business, and commercial music.) Part Seven: Advanced Chromatic Harmony Chapter Twenty: Mixing Modes Chapter Twenty-One: Altered Pre-Dominants Chapter Twenty-Two: Other Chromatic Harmonies Chapter Twenty-Three: Modulation II Chapter Twenty-Four: Harmonic Extensions and Techniques
2 weeks 2 weeks 2 weeks 2 weeks 1 week
Part Nine: Music in the Twentieth Century and Beyond Chapter Thirty-One: Harmonic Principles in Jazz Chapter Thirty-Two: The Blues Chapter Thirty-Three: Shaping a Song
2 weeks 2 weeks 2 weeks
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ASSIGNMENTS There are more assignments than can possibly be given in a single course. Pick and choose which you’ll use for in-class work and which you’ll assign. In general, you will probably want to make many short assignments in the earlier chapters and fewer but longer assignments as the course progresses. QUIZZES Quizzes are included in the manual for most of the chapters. These can be photocopied and given at the completion of each chapter, they can be combined to form larger tests that cover several chapters, or you may simply use parts of the quizzes in devising your own exams. At any rate, most of the questions are of the objective sort, requiring very specific and concise answers. This has the advantage of being easy to grade. In later chapters, you may wish to supplement these objective questions with musical excerpts for analysis. Anthologies are available which will supply a wealth of material for this purpose. SOME THOUGHTS ON TEACHING MUSIC THEORY Learning music theory involves, in part, the acquisition of a set of skills. Fluency in music reading, the ability to recognize at an intellectual level the processes at work in a musical passage, and the ability to hear in one’s mind a musical passage by viewing the score page are skills which are cultivated only with time and practice. Learning music theory does not equate with memorizing a long list of technical terms, even though a technical vocabulary is essential to meaningful discourse about a musical work. It is only when a vocabulary has been assimilated to the point that it becomes a means, rather than an obstacle, to the expression of one’s views about music and the communication of one’s understanding of it that it has value. Because proficiency in music theory is a skill, it cannot be acquired overnight. The knowledge is cumulative, and it must therefore rest on a solid foundation. Intensive in-class work, student-instructor interaction, and regular homework assignments are essential. Students must understand this and must realize that daily class attendance and diligent, careful preparation of homework are every bit as important as one’s performance on examinations. In fact, they constitute the best method of preparing for exams. Music theory is difficult to teach in a mass lecture format. The ideal class size perhaps numbers from twelve to fifteen students. This size permits enough one-to-one interaction between student and teacher while providing a large enough class so that ideas can be cross-generated and so that classroom performance of the music under discussion can be an occasional reality.
x
It is very important that the students listen to the music under study. Most of the examples in the text are easily playable at the keyboard. Instructors with limited pianistic skills can overcome this problem by requesting a piano major to prepare examples for a given chapter or section (one class period should be sufficient notice). Generally, students (especially the better ones) welcome the opportunity for such participation. CD ROMs accompany both the text and workbook. These contain hundreds of the musical examples—almost all that are over four measures in length. While students can access these on their computers, it is always good to have a fresh aural impression in their minds when discussing a passage. Then, too, taking the few minutes necessary to play the excerpts in class will help to prevent students from developing the attitude that music theory is only theory, and not relevant to actual practice. The time has long passed when theory could focus only on the standard classical repertoire. Students must be able work and communicate in the world of vernacular music, and so our mix of examples is fairly ecumenical. Sight singing and ear training (“aural theory”) are critically important skills that must be cultivated. In some schools, they form a part of the theory course and at others, they are taught under separate course numbers. Either way, we believe that these skills are most effectively taught and learned in correlation with “written theory.” To this end, we have included Suggestions for Aural Drill in this manual. If you teach in an integrated program (which unites written and aural theory in a single course structure), then we suggest that you spend time at the beginning or end of each and every class on these and other aural drills. To do so may mean covering a given topic in somewhat less depth than you might otherwise prefer, but the benefits will probably be worth it. If you teach in a program where the two disciplines are separated, coordination is a bit more difficult but not impossible. Again, we believe that the effort is worthwhile. RT and DM
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PART ONE IN LIEU OF FUNDAMENTALS (CHAPTERS 1–2) Students enter their freshman year of music study with diverse backgrounds in theory, ranging from little or no knowledge of the fundamentals to two or more years’ study in high school. Because of this, instructors will inevitably cover the material of these first chapters in different ways. This text presumes no prior knowledge. The fundamentals are presented in full detail, with sufficient exercises to bring even students with the least preparation “up to speed.” However, most of that material has been placed in two appendices, to be accessed as necessary. We've opted to begin the text proper in a different way, one that we hope will make a more ingratiating first impression, provide a little perspective on both music and theory, and serve notice that music theory is brimming with fascinating subtopics—that it’s not just about scales, key signatures, meter signatures, and the like. Bottom line here: We’re hoping to pique students’ interest at the outset. Chapter One—Assorted Preliminaries—provides historical perspective regarding the origin of the staff and clefs, the evolution of the major and minor scales, the origins of meter, and the acoustic foundations of musical sound and temperament. Chapter Two—Intervals—is a complete presentation of that topic. Although those students fortunate enough to have had extensive high-school theory may feel they already know all there is to know about intervals, we've found very few freshman music majors who are entirely fluent in their spelling and recognition. That’s why we've deemed it necessary to separate this topic from the other fundamentals covered in Appendices A and B and give it an honored spot in the front of the book.
Recommended time allocation: 3 weeks
2
CHAPTER ONE Assorted Preliminaries MATTERS OF PITCH (pages 5–8) The history of our pitch notation system is a fascinating portal to the study of music theory. We’ve given a synopsis here. A convenient source of additional information is The New Harvard Dictionary of Music (ed. Don Randel). We’ve adopted the practice of starting every (or nearly every) class with a singing of the “Ut Queant Laxis”—a bow to tradition and a musical beginning. Students seem to appreciate knowing whence come the syllables with which we torment them for two years. MODES, SCALES, AND EVOLUTION (pages 8-10) This discussion is meaningful only if students are familiar with major and minor scales. Jazz students are typically taught the modes in a different manner, and we encourage students to use whatever works for them. The modes are encountered again in the discussion of cadences in Chapter 6 and in the discussion of early twentieth-century tonal materials in Chapter 28. METRIC MATTERS (pages 11-14) This discussion presupposes understanding of the material presented in Appendix B. The origin of the dot and the early meter signatures are topics that students find fascinating. The inclusion of hypermeter here is the first of many past-present comparisons in the text. SOUND (pages 15-19) Again, the discussion is just enough to whet students’ appetite for more. The experiment on page 15 is a good introduction to overtones, because students can actually hear their contribution to the overall piano sound. You can recall this experiment later in the text to explain the frequent omission of the chord fifth from a root-position triad or seventh chord. Equal temperament is given a necessarily simplistic presentation. We like to give students a pitch on the piano, divide them into groups, and ask them to sing the most “in-tune” major triad they can produce. When they finally get close, we’ll play that triad on the piano and let them hear the difference. We hope instructors will pardon our reference to Pythagoras as “the old boy.” No irreverence is intended. It’s just part of our attempt to inject a colloquial tone into a subject (theory) that often comes across as dry and pedantic. It’s probably unnecessary to test on this first chapter, although some drill on modes is worthwhile.
3
****************************************************************** SOLUTIONS TO ASSIGNMENTS A. 1 Phrygian 2 Lydian 3 Mixolydian 4 Dorian 5 Aeolian B. 1
2
3
4
5
6
7
8
9
10
(white keys E to E) (white keys F to F) (white keys G to G) (white keys D to D) (white keys A to A)
6 Lydian 7 Mixolydian 8 Phrygian 9 Dorian 10 Aeolian
(white keys F to F) (white keys G to G) (white keys E to E) (white keys D to D) (white keys A to A)
4
C. 1
2
3
4
5
6
7
8
9
10
5
D. 1
Lydian
2
Dorian
3
Phrygian
4
Mixolydian
6
E.
Lydian
Mixolydian
Aeolian
Dorian
Phrygian
F. 1
"Scarborough Fair” (English folk song): Dorian on E
2
Adkins: ”Set Fire to the Rain”: Aeolian on D
3
Debussy: String Quartet, op. 10 (first movement): Phrygian on G
4
Elfman: “Simpsons” Theme: Lydian on Db
5
Mann, Weil, Lieber, and Stollar: "On Broadway": Mixolydian on E
6
Kabalevsky: Sonatina: Aeolian on A
No. 2 displays a duple hypermeter, with every other measure accented by a change of harmony. You might tell students to think of every two measures as a single 4-beat measure (the half note being the beat).
7
G. 1
Traditional: “Drink to Me Only with Thine Eyes” Division of beat: 3 Grouping of beats (division of measure): 2 Meter classification: Compound duple Grouping of measures (Hypermeter): Quadruple
2
Ed Haley: “While Strolling through the Park” Division of beat: 2 Grouping of beats (division of measure): 4 Meter classification: Simple quadruple Grouping of measures (Hypermeter): Quadruple
8
CHAPTER TWO Intervals At no other point in this text are students’ varying backgrounds in theory likely to be more obvious than in this chapter. The time spent here is typically a necessary period of “equalization,” in which a more-or-less level playing field is established. It is difficult to overstate the importance of interval recognition and spelling. Students must be able to work with intervals quickly and accurately to be successful with the more advanced topics that follow. Therefore, the timed quiz at the conclusion of this chapter is appropriate. WHITE-KEY INTERVALS (pages 21-24) We think it useful to provide alternative methods for spelling intervals and let students choose the one that works best for them. The white-key approach might also be called the “letter-name” approach because it is based first on counting the number of letter names spanned by an interval. The second step is to determine the number of black keys spanned. A M7 spans 5, a m7 spans 4; a M6 spans 4, a m6 spans 3; and so on. This approach is independent of any other musical knowledge. All that students need are eight fingers to count the number of letter names, noting black keys on the way. Applying the guidelines on page 21 gives the quality of the white-key interval. All that remains is to factor in the effect flats or sharps when the white-key interval is altered. The ability to visualize the piano keyboard helps a great deal. INTERVALS OF THE MAJOR SCALE (pages 25-26) For us, the most generally successful method for spelling intervals has been the major scale approach. This approach gives intervals a tonal context and thus seems more musical than the more abstract white-key approach. The disadvantage is the extra step of injecting a scale into the mix. Trying to figure out the interval Ab-C, for example, requires students to spell either the Ab major scale or C major scale, either upward or downward. RELATED MATTERS (pages 27-30) Once inversion is introduced (page 27), it can be a useful tool for recognizing the wider intervals (students can simply invert sixths and sevenths to the more easily reckoned thirds and seconds). Enharmonic intervals take a couple forms—either intervals of identical numerical value and quality that are spelled differently (Example 2-10) or intervals with different numerical values and qualities that nevertheless contain the same number of half steps (Example 2-9).
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Some instructors consider only the second type to be a true enharmonic interval, regarding the first as an enharmonic spelling. This is perhaps a matter of semantics. At the end of the chapter, we’ve included one additional way to measure intervals–the “additive” or building-block method. Students will gravitate toward the method that works best for them, which could end up being none of these or some combination. Suggested Aural Quiz An aural quiz on scales, modes, and intervals is appropriate at this point. A suggested format follows: • 10 intervals (melodic) • 10 intervals (harmonic) • 5 scales • 5 modes NOTE: The intervals may include all diatonic intervals or, more practically, a set of intervals, such as: all consonances; all dissonances; thirds and sixths only; minor second through the tritone; and so on.
SOLUTIONS TO ASSIGNMENTS 1. Identifying and Spelling Intervals 1A. 1 2; P4
2 4; M6
3 4: M6
4 4; m7
5 1; m3
6 2; P4
7 4; m7
8 4; M6
9 3; P5
10 0; m2
11 4; m7
12 3; +4
13 4; m7
14 5; P8
15 2; o5
1 P4, +4
2 P8, +8
3 +4, P4
4 P5, o5
5 P4, +4
6 P4, +4
7 o5, P5
8 P8, o8
9 P4, o4
10 P4, +4
1B.
10
1C. 1 m3, o3
2 M6, m6
3 m7, M7
4 m3, o3
5 M2, m2
6 M3, +3
7 m7, o7
8 M6, m6
9 m3, o3
10 m2, M2
1D. 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1E. P4
M3
m3
P5
P4
M3
m3
m3
M2
m3
m2
m3
P5
m7
m2
M3
P4
M6
P4
M2
M2
11
1F. 1
2
3
4
5
6
7
8
9
10
1G. 1 2 3 4 5 6 7
A B C B A G F Eb D C Bb Ab F G A Bb C D E Ab Bb C Db Eb F Bb A G F EbD C E F G A B C
(M3) (P4) (P5) (M7) (M6) (m7) (M6)
12
8 9 10 11 12 13 14 15
B CD Eb D C Bb Ab G-Gb C D E F G A B D E F G A B-Bb Bb C D Eb D C B A F E D CB A F E D C B A-A
(M3) (M6) (M7) (m6) (P4) (P4) (m6) (M6)
2. Related Matters 2A. 1 and 7
2 and 4
3 and 11
5 and 8
6 and 10
9 and 12
2B. Other enharmonic spellings besides the ones shown are possible. 1
2
3
4
5
6
7
10
8
9
13
2C. 1
2
6
7
2D. 1
2
3
8
4
9
5
5
3
4
5
6
7
8
9
10
2E. 1
2
3
4
5
6
7
8
9
10
14
2F. 1
2
6
7
3
8
4
5
9
10
2G. Melodic intervals in “Silver Threads among the Gold”: m2 m2 M6 M2 M6 |
M2 m6 | m3 M2 M2 o5 m6 m6 | m2
15
QUIZ FOR CHAPTER TWO Suggested time: 15 minutes 1.
Write the specified intervals.
1
&
2
w m3 above
6
&
w
M6 above 7
M2 above
4
m7 below 8
w
bw
#w
3
+6 above
5
bw P5 above
m6 below 10
9
#w
w w
bw
P4 below
M7 above
o7 below
2. Identify the following intervals. Then indicate the type of interval formed by the inversion. 1
2
Interval: ____ Inversion: ____
____ ____
6
3.
6
&
8
____ ____
5
____ ____
____ ____
9
____ ____
10
____ ____
____ ____
Match the measures containing intervals of the same size.
___ and ___
&
4
____ ____
7
Interval: ____ Inversion: ____
1
3
bw w #w
bw
___ and ___ 2
7
w #w
___ and ___
#w
3
bw
8
bw
bw
w bw
___ and ___ 4
9
bw bw
#w bw
___ and ___ 5
10
w
w
bw #w
16
PART TWO DIATONIC HARMONY (CHAPTERS 3–6) Students should thoroughly understand the principles of functional harmony before attempting to part-write music based on those principles. Part Two introduces the diatonic harmonic vocabulary and the analytical tools that are used to describe it. Chapter Three describes the structure of the basic triads and seventh chords. The five diatonic seventh chord types are introduced. While this introduction occurs earlier than is typical, it is necessary given one of the prime intentions of this text—to show the connections between popular-based styles and art music. The seventh chord is rampant in popular music and jazz. Chapter Four introduces lead-sheet and figured-bass notation. Consistent with the idea of moving from more-familiar to less so, lead-sheet notation is presented first. Chapter Five considers the manner in which the triads of a key relate to each other—i.e., harmonic function. The replacement of lead-sheet symbols with the more informative Roman numerals at this point is but a small step. Chapter Six completes Part Two with the introduction of the standard harmonic cadences (along with some popular-music variants) and a look at harmonic rhythm.
Recommended time allocation: 6 weeks
17
CHAPTER THREE Basic Harmonic Structures A major goal of this text is to make students aware that “vernacular” and “art” music are part of a continuum. Example 3-1 makes the triadic connection. TRIADS (pages 35–39) Example 3-3 is the basic reference point for this part of the chapter. It can be helpful to students to point out the following similarities and differences among the four basic triad types: • The shared major third at the bottom of the major and augmented triads • The shared minor third at the bottom of the minor and diminished triads • The shared perfect fifth in the major and minor triads It’s a good idea to incorporate classroom drill spelling the four triad types as soon as they are introduced. It is not necessary to use text exercises for this purpose. Calling upon students randomly to spell a given triad type upward from a given root or downward from a given fifth is efficient and helps to keep and focus their attention. You’ll probably wish to reinforce the presentation of triad types with aural drill, using root-position triads. These drills can take various forms, such as the following: 1. Discrimination: Play a random selection of all four triad types in root position but with various voicings, and ask students to signal by raising their hands when they hear a designated type. 2. Identification: Play a random selection of major, minor, diminished and augmented triads in root position at the piano, using different voicings, and ask students to identify each triad type. On page 38, invoking the overtone series helps to explain the primacy of the major triad over all others (including the minor triad) as a musical endpoint and as a chord of maximum stability. CHORD INVERSION (pages 39–41) Although presenting inversion as a by-product of the linear-contrapuntal process is an attractive concept that has the advantage of historical accuracy, we’ve found it to be less pedagogically successful than the more vertical (less historically accurate) method. However, aural comparison of Examples 3-5 and 36 is an effective way to convince students of the contrapuntal value of inversion. Although Example 3-7 specifically addresses the point, you may wish to
18
emphasize the fact that inversion is determined solely by the lowest pitch of the chord. Aural reinforcement can be used in comparing the relative stability and “harmonic weight” of the various triad positions. Immediate drill on the spelling and recognition of inversions is advisable. SEVENTH CHORDS (pages 42–47) All five diatonic seventh chords are introduced here. Almost every triadic harmony found in jazz and popular music is reducible to one of the four basic triads or one of the seventh chord types shown in Example 3-14. The subject is given fuller treatment in Chapters Thirteen and Fourteen. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT1B on page 21: Students can be asked how to change the given triad into one of the other basic triad types. For aural reinforcement, have the class sing each triad, upward and downward from the root, as follows: 1-3-5-3-1. • ASSIGNMENT 1C on page 21: Obviously, students can be asked to alter the chords to form other triad types. • ASSIGNMENT 1D on page 22: Each of the given pitches can be treated as the chord third or the chord fifth as well. Spelling a triad from all three chord members helps solidify students’ understanding of triadic structure. • ASSIGNMENT 3A on page 27: As with Assignment 1B on page 21, students can be asked how to change the given seventh chord into a different type. • ASSIGNMENT 3C on page 28: As with Assignment 1D on page 22, each of the given pitches can be treated not only as the root, but as the third, fifth or seventh of the chord. Suggested Aural Quiz An aural quiz on triad and seventh-chord types and inversions is appropriate at this point. A suggested format follows: • 10 triads in root position (5 arpeggiated and 5 played as chords) Note: You may wish to require students to identify among the four types or to distinguish between major and minor, and between augmented and diminished. • 10 triads in root position, first inversion or second inversion Note: You may wish to restrict the triad types to major and minor only, since inversions of diminished triads are typically more difficult to distinguish and inversions of augmented triads are aurally indistinguishable.
19
•
10 seventh chords Note: Identification of the type of chord is probably sufficient at this point. ****************************************************************** SOLUTIONS TO ASSIGNMENTS 1. Triads 1A. 1
2
3
4
5
6
7
8
9
10
No. 12 ia actually an error in the Workbook. The intended triad was to be 1B. E#m. Still theoretical, yes, but not as pointlessly so as E o. 1 GM 6 Cm 11 Go
2 Dbm 3 Bo 4 A+ 7 Db+ 8 Fo 12 E o 13 F m
5 Gb+ 9 EM 10 Am b b 14 A o 15 B +
1C. Following are the changes needed to created the requested triad: 1 A n 2 D 3 Bb
4 Cb
5 Ebb
6 E n 7 Db 8 E n 9 Bb 10 Bb
20
1D. 1
2
3
6
7
8
11
12
13
16
17
4
9
10
14
18
15
19
1E. 1
2
3
4
5
6
7
8
9
10
5
20
21
2. Chord Inversion 2A. 1 B-D-F (1) 2 Ab-C-Eb (2) 3 C-E-G (R) 4 F-A-C (1) 5 E-G-Bb (R) 6 D-F-A (1) 7 G-B-D (2) 8 C-E-G (1) 9 Eb-G-Bb (2) 10 C-E-G (2) 2B. 1 1 m 2 1 m 3 2 M 4 R m 5 2 M 6 1 + 7 R o 8 2 o 9 2 m 10 1 + 2C. 1
2
3
4
5
6
7
8
9
10
2D. 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
22
2E.
X
Bb M 1
Bb M 1
Eb M R
Eb Bb M M 2 R
F m 1
Eb Bb X M M 2 R
F m 1
Eb X M R
D o R
X
Bb M R
3. Seventh Chords 3A. 1 mm7 2 MM7 3 ø7 4 o7 5 o7 6 ø7 7 MM7 8 Mm7 9 mm7 10 ø7 11 o7 12 MM7 13 Mm7 14 Mm7 15 o7
3B. 1 o7 1
2 ø7 1
3 o7 3
4 MM7 2
5 mm7 2
6 MM7 1
7 mm7 1
8 ø7 1
9 Mm7 1
10 MM7 2
23
3C. 1
2
3
4
5
9
10
6
7
8
11
12
13
16
17
18
14
15
20
19
3D. 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
24
3E. 1
2
3
4
5
11
12
13
14
15
6
16
7
8
9
10
17
18
19
20
3F. Root: D C D Bb C D E F G F D G C A D G Type: oo oo oo MM Mm mm om MM mm MM mm mm Mm Mm Mm Mm Inv: 1 2 2 R R R R R R 1 R R R 1 3 1
Root: C A D B E A Type: Mm Mm mm Mm Mm M Inv: 3 R R R R 1
3G.
25
QUIZ FOR CHAPTER THREE Suggested time: 30 minutes 1.
Indicate the triad type (M, m, +, or o) and the inversion (R, 1, or 2) beneath each chord:
Type Inversion 2.
___ ___
___ ___
2
mm7
oo7
2
MM7
4
5
om7
MM7
Mm7
3
Mm7
4
5
oo7
mm7
om7
Identify both the type and inversion of the following seventh chords. 1
Type: Inv:
3
Spell the indicated root-position seventh type below the given pitches. 1
4.
___ ___ ___ ___ ___ ___ ___ ___
Spell the indicated seventh chord type above the given roots. 1
3.
___ ___ ___ ___ ___ ___ ___ ___
2
___ ___
3
___ ___
4
___ ___
5
___ ___
___ ___
26
CHAPTER FOUR Musical Shorthand: Lead Sheets and Figured Bass In keeping with the present-past focus of the text, lead-sheet chord symbology and figured-bass notation occupy the same chapter. Lead-sheet symbols serve the needs of today’s musician in the same way the figured bass did for the Baroque musician. Roman-numerals, introduced in Chapter Five, are a synthesis of the two systems. LEAD-SHEET NOTATION (pages 48-52) Example 4-2 shows the more common symbols for basic triads and seventh chords. Fake books and sheet music are flush with variants. This textbook employs those variants in order to familiarize students with multiple ways of expressing the chords. Around the 1970s, the slash symbol began to appear regularly, reflecting the growing importance of the bass line to the harmonic structure in many popular songs. The method is capsulized in Example 4-4. The discussion builds on the topic of inversion from page 39. You may wish to refer back. MORE ON CHORD INVERSION: THE NUMBERS GAME (page 52-54) Between the chord member names (root, third, fifth and seventh) and the figured bass symbols for inversion, students often go into “numbers overload,” and confusion is rampant. This section is intended to clarify what all these numbers mean. FIGURED-BASS NOTATION (pages 54-60) The need to indicate a bass line in a lead-sheet symbol provides a natural segue to the figured bass. You might begin by pointing out the parallel nature of the two systems. In lead-sheet notation, symbols instruct the performer how to realize the harmonies and bass line beneath a given melody. In figured-bass notation, symbols instructed the performer how to realize the harmonic structure and create a melody above a given bass line. Both systems served a music in which the performer was accorded major responsibility for the creation of the final product. The music separating these two styles—Classical, Romantic, and twentieth-century art music—required ever-increasing fidelity to the written score, which became increasingly encumbered with notational directions regarding dynamics, expression, articulation, and tempo. As with lead-sheet notation, variations abound in the figured-bass system. This is especially true regarding the indication of accidentals (point 7 on page 56) and the extent to which a bass line was actually figured. The ten rules of figured
27
bass (pages 55-57) can be intimidating. Dispense in small doses. You might bring students to the chalkboard to symbolize simple triads in various inversions (points 1–6) before considering chromatic alteration (point 7) and seventh chords (point 8). You can recycle some earlier examples here. Ask your students to represent by a figured bass Examples 3-8 and 3-16. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1H on page 36: Once figured-bass notation is covered, you can ask students to return to this song and show the figured bass that would represent it. • ASSIGNMENT 2C on page 39: Conversely, students can be asked to show the expanded lead-sheet symbols that would represent these figured-bass passages. ****************************************************************** SOLUTIONS TO ASSIGNMENTS 1. Lead-Sheet Notation 1A. 1
2
3
4
5
6
7
8
9
10
5 Em 6 Co
7 A+ 8 D
9 Ebm 10 Bb
1B. 1 Abm
2 C+ 3 B
4 F o
1C. 1
2
3
4
5
6
7
8
9
10
28
1D. 1 FMaj7
2 Bm7-5
3 Eo
6 AMaj7
7 Bdim7 8 G
9 Emin7
10 B+
1 Eø7
2 C7
4 GM7
6 F7
5 Cm7-5
7 BMaj7
4 Cø7
5 D-7
IE.
1F.
3 Bm7 8 Co7
9 Ab7
10 DbM7
Notes of the right hand can be disposed in any manner.
1
2
3
4
5
6
7
8
9
10
1G. 1 F/G Em/G | Dm7/G C/G | Gb/Ab Fm/Bb | F/B DbM7 | CM7/D D/E | EbM7/F Fm/G | GbM7/Ab ||
2 Gm7/C | Am7/C | DbM7/Bb Cm7/Bb | Cm7 |
DMaj7/A | Cm7/B CM7 | CbM7/Db | DMaj7 Bbm7/Eb |
29
1H. F F/E | Dm Dm/C BbMaj7 | F/A Am7/D D | G7 Gm/F | C7/E C7 A/C | Dm Dm/C Bm7-5 | Gm/C C7 | F ||
1I. Eb/G Eb+/G Ab Fm7 Fo7 | Gm7 Cm Fm/Ab | Eb/G Eb+/G Ab Gm7 | F7 Bb7 | Eb Eb7 Fm7/Eb Fo7/Eb | Eb G/D Cm Aø7 Fø7/Ab |
Gm7 Cm7 F7 Bb7 | Ab/Eb Eb || 2. Figured Bass Notation 2A. 1
2
6
7
11
12
3
4
8
13
2B. 1 6+
2 3
3 b6 4
6 4n 3
6 3
7 6 n3
8 n 6 3
9 n3
5
9
10
14
15
5
6 3
10 6 3
30
2C. 1
2
3
4
31
2D. 1
2
3
4
5
2E. (x = no figure needed under bass note) 1 2
x 6 | x 6 6 | x 6 x | x | x ||
n x 6 x 6 | x x x | x 6 x | x 5
x ||
32
2F. G| G D Em Bm | Em D G G | Em Bm D Em | C G D Em | x
x
x
D G D x
x
x
x
x
x
x
x
x
G/B | C D Em D/F | 6
x
x
x
6
x
x
x
x
x x
x
G Em D Am | G/B D G x
x
x
x
6
x
x
x
33
QUIZ FOR CHAPTER FOUR (Suggested time: 30 minutes) 1.
Write the indicated chords. 2 AMA7/D
1 Cm 7-5
3 Eo /F
5 Db+/A
4 Em7/D
2.
Give the lead-sheet symbol that represents each chord.
1
___
3.
Spell the triads and seventh chords indicated by the figured-bass notes.
2
___
3
___
4
___
5
1
2
3
4
5
6
7
8
9
10
4.
___
Add lead-sheet symbols above and figured-bass symbols beneath.
___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___
___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___
___
34
CHAPTER FIVE Harmonies of the Major and Minor Scales THE DIATONIC CHORDS (pages 61-68) The arrangement of “Amazing Grace” sacrifices simplicity on the altar of musical interest. However, the triads and the couple seventh chords are clearly shown on the extra staff. Again, it’s a way of beginning with a tune familiar to most students. Example 5-2 is laid out to show the logic behind the functional names given to triads (and scale degrees). For example, students sometimes ask why the submediant is not under the mediant but in fact above it in the scale. The illustration shows that the chord is named to reflect its position as a midpoint (median) between the tonic and subdominant, just as the mediant is named to reflect its midpoint position between the tonic and dominant. Example 5-4 (page 66 Of the alternative minor-key triads, v and VII are the most common. Still, students should understand that the most common of all minor-key triads are those shown in the Example 5-4a, i.e. those of the harmonic minor scale but with the major triad on the mediant (III). Once the functional names and symbols have been introduced, immediate drill can be undertaken. Calling upon students at random to “spell the mediant in Bb,” or to “spell the iv chord in E minor” is efficient and effective. Showing Inversion (page 66) The figured-bass numbers are now plugged in to complete the Roman numeral symbol. Complete symbols for the diatonic seventh chords and their inversions are given at this point as well. The Diatonic Seventh Chords The diatonic seventh chords were introduced by type in Chapter 3 following triads (early by some standards but necessary in keeping with our goal of presenting vernacular music throughout the text in renditions that are not simplified to the point of sounding silly or even being unrecognizable. Here, the Roman numeral designations, including inversion, are given, again following the symbology for triads. Seventh chords return in a big way in Part Four (part writing).
35
FUNCTIONAL TONALITY (pages 68-74) The statement on page 68 concerning the effect of a particular triad related to its position (function) within the key is reinforced aurally in Example 5-8. Students can readily hear the different effect of the G major triad in a and b. Functional tonality eludes succinct description because of the number of factors at work. Who would deny the importance of the descending fifth motion? Yet scalar bass lines frequently support harmonizations that run counter to the descending circle. Are these patterns “anti-functional”? Progression, Retrogression, Repetition (page 72) The concept of three basic harmonic motions—progression, retrogression, and repetition—is still valid and easily explained. We’ve tried to convey the following ideas: 1) one type of motion is not inherently better than another; 2) most music based on functional tonal principles employs all three types of motion; 3) the three types of motion rarely occur with equal frequency in a piece of music. Example 5-12 (page 73) shows the “tonal planetary system”–an apt analogy. It provides a sense of the relative “pull” that the tonic exerts on the other chords more graphically than the “straight-line” diagram in Example 5-11. If you like, you can boil this down further for your students into three “orbits” (basic functions)–tonic, dominant, and pre-dominant. Example 5-13 demonstrates the harmonic cul de sac found in so many popular songs from the fifties and sixties You might skip ahead to Example 5-19a for a Baroque work that begins with essentially the same progression or Example 9-16 for another popular song. Ground bass patterns (page 74) The scalar bass is as important in popular music today as it was in the music of the Baroque era. This is shown in Examples 5-16 through 5-19. Other examples you might use for past-present comparisons: Bach’s Cantata 156 (Example 4-6 on page 54) and Reid and Brooker’s “A Whiter Shade of Pale” (Workbook page 53); Mozart’s Piano Sonata, K.332, second movement (Example 20-2 on page 339) and Michel Legrand’s “The Hands of Time” (Example 33-6 on page 603). Well-known examples of the chromatic-descending bass include Purcell’s “When I am Laid to Rest” from Dido and Aeneas and Bach’s Cantata 78 (opening chorus). These might be compared with Legrand’s Theme from Summer of ’42 (Example 7-5 on page 105). Suggested Additional Uses of Drills and Assignments (Workbook): • The assignments on Diatonic Chords can be performed by students either at the chalkboard or at their seats. Varying the format helps to
36
maintain interest. For example, ASSIGNMENT 1A might simply be done verbally; ASSIGNMENT 1B might be done by students at their seats while you casually check their work; and ASSIGNMENT 1D might be done at the chalkboard (getting students out of their seats is a way to keep the interest level high). • ASSIGNMENT 1E on page 45: This is one way to develop students’ familiarity with the diatonic triads. Another approach is to select a function—for example the supertonic—and ask students to spell this harmony in randomly selected keys. Students who can visualize all the scales are at a distinct advantage. Again, the keyboard is a valuable tool. ****************************************************************** SOLUTIONS TO ASSIGNMENTS 1. The Diatonic Chords 1A. 1
2
3
4
5
6
7
8
9
10
1B. 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
37
1C. 1 F: IV d: VI g: III 6 c: i A: iii E: vi
2 Db: vi Gb: iii Eb: X 7 e: iv F: iii G: ii
1D. 1
2
6
7
1E. 1
5 G: ii C: vi F: iii
9 Gb: V Ab: IV f: VI
10 c: X Ab: viio f: iio
8 E: IV B: X c: VI
3
8
2
3
5
9
4 f: iv A: ii D: vi
3 c: X g: iio Bb: viio
6
10
4
5
9
10
4
7
8
11
12
38
1F. 1
2
3
4
5
6
7
8
9
10
39
1G. 7
1 iii
7
2 V
3 vi
7
4 viio
7
7
7
5 ii
6 IV
7 iiø
7
7
8 VI
7
9 V
10 iv
1H. 1 ii 4 2 4 6 iv 2
6
7 V5
1I. 1
3 vi 5
4 VI 3
8 iv7
9 IV3
7
4
8
ii
7
2. Functional Tonality 2A.
6
10 IV 5
3
7
vi
6
5 viio 5
4
2
6
1J. 7 iii
4
6
4
2 V2
7
V
5
9
I
V
IV
10
7
V
I
7
40
1
2
3
4
5
2B. Key: G Motion:
I | I V vi iii | vi V I I | vi iii V vi | IV I V R R P P P S R P R P P
2C. 1 Key: D Motion:
I vi | ii V P P
6
7
6 | I ii | I 64 V P P S
2 6 7 6 Key Bb: I IV iii vi | viio I V V | I viio6 iii vi | ii 6 V I || 5 Motion: R P P P S P R P P P P 3 Key Ab: Motion:
I
7
7
| IV | ii | V | V | I 6 | V | I || 4 S P S P P (S S)*
41
* If you prefer your students regard the cadential six-four chord as a dominant, use this analysis of the harmonic motion . 2D. 1 2 3 4 5 6 7 8
bb d G F Eb b E f
PSPP XPXR SPRPPP XPPRPP XSPRPP PXPPXP XPPPXP RPSPXP
2E. Other possible answers are shown in parentheses. 1 1 2 3 4 5 b D: ii V A : ii V F: V IV g: VI iv e: iv iio (viio) (viio) (ii, vi, iii) (ii, V, viio) 2 1 2 3 4 5 b b b B : iii vi g : V iv G : viio V b: V I G: vi iii 2F. 1
Reid and Brooker: “A Whiter Shade of Pale” 6
6
2
6
4
V 3 | I IV | V
Pachelbel: Canon in D I V | vi
3
4
| vi I 64 | IV I | ii ii 4 | V V 2 | I 2
I V
iii | IV
I
| IV
V |
Joel: “Piano Man” 6
6
6
I | V | vi | I 4 | IV | I | II
| V |
The patterns are similar. They resemble the patterns that support a descending bass such as the one shown in Example 5-14 and elsewhere.
42
QUIZ FOR CHAPTER FIVE Suggested time: 30 minutes 1. Classify the type of motion between each chord in the following succession. P = progression; R = retrogression; S = repetition; X = motion from the tonic to any other chord. IV V vi iii IV ii viio I IV I ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___
I
vi ii V I ___ ___ ___
2. Write the indicated triads on the staff below, adding flats or sharps as necessary.
F: ii
3.
A: V
D: vi
Db: iii
Bb: viio
Provide a clear and concise definition for each of the following terms: a.
Retrogression:
b.
Ground bass:
c.
Progression:
d.
Harmonic function:
43
4.
Provide harmonic analysis of the following passage:
Ab:
___
___
___
___
___ ___
5. Show both the lead-sheet symbol and Roman-numeral symbol that describe each chord. Lead-sheet:
RN:
6.
___ ___
___ ___
___ ___
___ ___
___ ___ ___ ___ ___ ___
___ ___ ___
___ ___ ___
___
___
Notate the following seventh chords:
1
2
Eb: IV 5 6
Ab: viio 43
3
4
Bb: vi 2 4
5
4
g: III 2
6
f: VI 5
45
CHAPTER SIX Cadences/Harmonic Rhythm CADENCES (pages 80-91) The traditional order of presentation (authentic followed by plagal, half, deceptive, and Phrygian half) is a bit misleading, as the two most common cadences by far are the authentic and half. Students should understand that probably 90% of all cadences in the traditional common-practice repertoire fall into one or the other of these two categories. Still, the plagal has enjoyed a twentieth-century renaissance in gospel and blues-based music. Students should also understand that the half cadence comes in many varieties and that any chord leading to a pause on the dominant chord is a half cadence. Standard Cadences (page 83) Feel free to delay introducing the perfect/imperfect distinction at this time. Practically speaking, the need to distinguish degrees of conclusiveness does not arise until Chapter 9, where discussion of periods and phrase groups necessitates it. You’ll probably want to reinforce the presentation of harmonic cadences with aural drill. Root movement (or bass motion, which amounts to the same thing except in the Phrygian cadence) and chord quality are good keys to identification, since each of the standard cadences presents a unique combination of these features. Using the Summary of Standard Cadences on page 90, you might ask students to develop a chart showing the bass motion and chord type for each. They can glean the necessary information from Example 6-13, as well. Alternatively, you may wish to photocopy and hand out the chart on Cadence Identification on page 47 of this manual. The three points on page 91 of the text are worth stressing. For the last forty or so years, self-trained popular musicians have unknowingly assailed (or at least ignored) many long-held-sacred practices. One such practice involves cadences. Popular and rock songs contain some that conform to none of the traditional types, and today’s musicians should be aware of these departures. By whatever harmonic means, a pause in the musical flow can usually be called a cadence. Examples 6-11 and 6-12, though by classically trained composers, contain cadences that defy traditional classification. And that’s okay. Music evolves. HARMONIC RHYTHM (pages 91-96) Although harmonic rhythm is usually presented as if it’s governed by meter, the more accurate approach might be to look at meter as a by-product of
46
harmonic rhythm. Certainly, when early music publishers first began to add barlines for clarity, they did so based on a feeling for accentuation, which was in large measure created by harmonic change. For aural reinforcement, you might play excerpts and ask students to notate the harmonic rhythm in the manner suggested in the “experiment” involving Examples 6-18, 6-19, and 6-20. This is a good predecessor to harmonic dictation since recognizing harmonic change is not as difficult as recognizing harmonies per se. Some of the Bach chorale harmonizations in Chapters 12 and 13 can be used to hone students’ understanding of the importance of harmonic rhythm to meter. Try playing Example 12-2 with no feeling of accent and ask students to determine aurally the location of the strong beats. They might well decide the passage begins with beat one. Next, show them the passage and play it again. Chances are they’ll hear it differently now. Discuss the reasons why, starting with the cadence on beat three (not beat four). HOWEVER: Note how Chopin turns the harmonic rhythm completely around in Example 6-21, which actually sounds like it should begin with an anacrusis. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1A: These cadences can be used for aural identification drills. ASSIGNMENT 1E: You might use some of these excerpts to reinforce students’ understanding of figured bass. Ask students to show the figured bass that would represent the passage. • ASSIGNMENT 1F: Alternatively, students might be asked to show the figured bass that represents each cadence. Suggested Aural Quiz •
•
10 cadences in various keys (authentic, plagal, half, deceptive, and Phrygian half) Students to identify cadence type and mode (major or minor) A simple homorhythmic passage such as: Example 5-16b, 7-1b, 7-4b, 76, or 9-3b Students to notate the durations of the harmonies.
47
KEYS TO IDENTIFICATION OF STANDARD CADENCES
M A
CADENCE TYPE
BASS MOTION
TRIAD QUALITIES
Authentic
Perfect 5 down
Major to Major
Plagal
Perfect 4 down
Major to Major
Half
Major 2 up
Major to Major
Deceptive
Major 2 up
Major to Minor
Authentic
Perfect 5 down
Major to Minor
Plagal
Perfect 4 down
Minor to Minor
Half
Major 2 up
Minor to Major
Phrygian
Minor 2 down
Minor to Major
Deceptive
Minor 2 up
Major to Major
J O R
M I N O R
******************************************************************
48
SOLUTIONS TO ASSIGNMENTS 1. Cadences 6
1 iv -V Phrygian 2 IV-I PC 3 V-I AC 4 V-vi DC 5 IV-V HC
1A.
6
6 V-VI DC 7 iv-i PC 8 V-i AC 9 IV-V HC 10 iv -V Phrygian 1 C: PC OR F: HC 2 Ab: AC 3 G: DC 4 Bb: DC 5 Eb: AC 6. b: PC 7 d: DC 8 c: Phrygian 9 E: PC or A: HC 10 f: AC
1B.
1C. 1 AC d: V i
2 PC Db: IV I
6 PC 7 HC A: IV I Bb: IV V
3 PH b: iv6
V
8 DC Ab: V vi
4 HC G: IV V 9 PC c: iv i
5 DC a: V VI 10 PH g: iv6
V
1D. 1. 2. 3. 4. 5.
Deceptive Half Plagal Authentic Phrygian
1E. 1 Eb: I V vi V6
AC |
I I6 V7 | I V6 I
AC |
IV6
I IV I6
| V V7 I
||
49
2
PC
f: i i | i i | iv
iv |
3
PC
G: I 4 g: i
|
X
6 | I IV 4
| I
AC
i i | iv iv | i i | V7 HC 6 V6 | vi iii 4
AC 6 6 i i | V | V V V | i
1F. 1
2
6
V7 | i i ||
| i
| v6 | VI
i
3
7
| I X | V ||
4
8
PHC iv |V ||
5
9
10
2. Harmonic Rhythm 2A. Meter is
9 , the harmonies change once a measure until the last measure. 8
F: I | I | iii | IV | X | AbMaj | GbMaj | X D | GMaj | X | V | V 7 I IV V | 7
2B. 1
7
7
7
Bach: Was Gott tut, das ist wohlgetan”
7
7
7
7
50
2
Brahms: Symphony no. 1, op. 67 (fourth movement)
3
Traditional: “Old Colony Times”
51
4
Brahms: Romance, op. 118, no. 5
5
Tyler, Perry and Rhodes: “Cryin’”
52
QUIZ ON CADENCES 1. Identify the cadences suggested by the following figured basses. 1 2 3 4 5
Cadence: _______
_______
_______
_______
_______
2.
Name the standard cadence and mode (major or minor):
1. 2. 3.
This cadence ends on an E major triad in a key of five sharps. _______ This cadence involves A bass motion from F to E. _______ This cadence involves bass motion from F to the root of a G-major triad. ________ This cadence involves two minor triads. ________ This cadence involves an upward leap of a fourth to a major triad _______
4. 5. 3.
Name the cadences possible (AC, PC, HC, DC, PHC) at each fermata. _____ _____ _____ _____
Bb:
g: ______ ______
______
_____ _____
Bb: 4.
Add the key signature, and notate the two chords that would produce the cadences. 1 2 3 4 5
G: Plagal
D: Deceptive
E: Half
c: Phrygian
f#: Authentic
53
53
PART THREE MELODY (CHAPTERS 7–9) Few students show up in the theory classroom packing an inspired melodic gift. If the primary goal of this part of the book were to teach students to write inspired melodies, that goal would be doomed to failure, because inspired melody writing involves an elusive intuitive element that is difficult to teach. The mission here, then, is to promote an understanding of the melodic dimension in both its general and specific aspects and develop sufficient skill to write passable melodies when the occasion requires it. Melody writing cannot be easily learned by applying a succinct set of guidelines such as those given later in the book for part writing. For one thing, the factors governing effective melody writing do not lend themselves readily to a recipe approach. For another, rhythm—inherent and indispensible in all melodies—is an aspect difficult to quantify. Tonal melodies are so bound up with functional harmonic principles that students will need to draw upon their newly acquired harmonic understanding in order to write effective tonal melodies.
Recommended time allocation: 6 weeks
54
CHAPTER SEVEN Melodic Pitch and Rhythm
Freshman music students may hold rather narrow attitudes concerning the nature of melody. Chances are that they think of melodies only in tonal and lyrical contexts. You may wish to begin the chapter by playing a variety of melodies— from Mozart to Webern—stressing that each is, in fact, a melody and that the differences are matters of style. RANGE, INTERVAL STRUCTURE, AND GESTURE (pages 99-105) The melodic features discussed in this section should not be taken for granted. You may wish to provide aural reinforcement by playing a number of melodies and asking students to draw a general contour diagram, to make note of the location of high and low points, to make general observations regarding the interval structure, and to notate any recurring rhythmic patterns. REPETITION (pages 105-111) Melodies without repetition in some form are exceedingly rare. Example 7-5, however, is loaded. It contains repetition in all its forms—exact (in m. 7), varied (in mm. 1–2), sequential (mm. 5–6 vis a vis mm. 1–2), and (although not mentioned in the chapter) imitation (in the left-hand part). You may wish to have students identify the various forms of repetition in the melodies of Example 7-4. Others that might be examined include Example 4-7 (page 58), Example 9-17 (page 159), Example 17-1c (page 280), and Example 17-12b (page 292). It’s up to you to decide how specifically your students are to describe sequences. We’ve chosen not to belabor the sometimes elusive distinctions between real and tonal, partial and modified. These additional classifications strike us as unnecessary analytical baggage. There are perhaps more important things for students to consider. MELODIC TONALITY (pages 112-119) We’re amazed by the number of students who apparently do not realize the true value in practicing scales and arpeggios—that it’s an indirect but highly concentrated (and admittedly tedious) way of practicing their repertoire. This part of the chapter pairs those familiar concepts (scales and arpeggios) with their larger but less familiar counterparts—step progressions and large-scale arpeggiations. It’s a logical pairing, but the latter require that students be able to
55
recognize the important pitches in a melody. Does a clearer example of the step progression exist than Harold Arlen’s “Over the Rainbow” (Example 7-16)? Harmonic implication in tonal melody is one of the less tangible concepts. The term tonic-dominant axis has an off-putting, academic sound to it. Yet it’s easy to demonstrate, and students seem to pick up on it quickly. Handel’s “Alla Hornpipe” from Water Music (Example 7-17 illustrates this concept as effectively as “Over the Rainbow” shows the step progression. Other good examples include the Chopin Mazurka op. 7, no. 1 (page 151) and the Mozart Piano Sonata, K. 309 (page 159). Suggested Additional Uses of Drills and Assignments (Workbook): You can get higher mileage from the melodic vehicles in the Workbook by interchanging the instructions preceding them. For example: • ASSIGNMENT 1A on page 65: No. 1 can be re-examined from the standpoint of sequence. Nos. 2, 3, and 5 can be examined for their tonicdominant axis. • ASSIGNMENT 2B on page 70: This melody can be analyzed for its contours, interval structure, and step progressions. • ASSIGNMENT 2D on page 72: Nos. 1, 2, and 4 contain step progressions. • ASSIGNMENT 3B on page 76: These melodies can be studied for their contours and interval structure. Aural Drill Aural reinforcement of the concepts presented in this chapter may be accomplished through melodic dictation. Following is a suggested procedure: Ask students to draw the number of bar lines needed for each melody and to number the beats beneath each measure. Then play the melody and ask students to do any or all of the following: 1. Place a T or D above each beat on which a tonic or dominant occurs. 2. Notate under the numbered beats the rhythm of the passage. 3. Bracket the beats in which sequential passages are present and identify the sequences as real or tonal. 4. Indicate the general contour of the passage. 5. Notate the melody on staff paper.
56
SOLUTIONS TO ASSIGNMENTS 1. Range, Interval Structure, and Gesture 1A. Student opinion may differ slightly, as may yours. Ask them to justify theirs. 1
Descending; arch Prevailingly disjunct C major
2
Arch; arch; arch Prevailingly disjunct B minor
3
Ascending; descending Evenly balanced F major
4
Decending; ascending Prevailingly disjunct G major
5
Arch; ascending Evenly balanced G major
1B.
No solutions are given for this assignment.
1C.
Comparison of the Boccherini (1) and Dvorak (2) melodies. 1. 2. 3. 4. 5.
The ranges are similar, 1 with the slightly wider range. 1 contains the larger leaps. 2 is the more motivic melody. 1 contains more varied gestures. 2 rises once to the F5 that is its high point.
57
2. Repetition 2A. No. 1 is neither a precise real nor tonal sequence. However, it is more tonal than real, remaining completely diatonic in the key. 1
You may wish to point out that the exact manner of variation in the repetition of mm. 20-21. Augmentation is introduced later in the book (Chapter 18) in the context of contrapuntal devices.
58
2
59
2B.
2C. 1
2
3
4
60
2D. 1
2
3
4
61
2E. 1 Measures 0-4 are repeated in a real sequence a P4 higher. Measures 8 (beat 3)-12 are repeated in a real sequence a P4 higher. Measures 9-16 are a varied repetition of mm. 0-8. 2 Measures 11, 12, and 13 are a tonal sequence a step higher at each repetition. Measures 15, 16, and 17 are a tonal sequence a step lower at each repetition. Measure 17 is modified. 3. Melodic Tonality 3A. 1
2
3
62
4
3B. 1
2
3
4
63
3C. For all their surface differences, the two melodies are remarkably similar in certain ways. They both contain a step progression that descends in this manner: 3ˆ - 2ˆ - 1ˆ - 7ˆ - 6ˆ , the first concluding on 5ˆ , the second on 1ˆ . They both reach a high point on the dominant on the first beat of their second measure. They both have a strong tonic-dominant axis, with those pitches appearing in important metric positions. Both feature gestures that are repeated in tonal sequence at a lower pitch level, the first in mm. 47-50 and mm. 51-54, and the second in mm. 14. Neither melody contains a large-scale arpeggiation. 3D. 1
2
3
64
4
65
QUIZ FOR CHAPTER SEVEN 1.
Provide the correct answers to the questions concerning the following melody.
1. This melody’s overall contour might be described as: a) ascending; b) descending; c) arch; d) inverted arch; e) stationary 2. On what scale is this melody based? ____________ 3. A step progression is formed by important pitches in the first four measures. Name the pitches that constitute this step progression. ___________ 4. The melodic pattern of mm. ______ is stated in sequence in mm. ______. The pitch level of the repetition is ______. The sequence is ____________. 5. Describe the repetition present in mm. 5–6. 6. Circle four pitches that are important in establishing the tonicdominant axis in this melody. 2.
Classify the following sequences as: a) real; b) tonal; c) modified real; d) modified tonal; e) partial real; f) partial tonal
66
3 In the melodies that follow, bracket the step progressions or indicate by arrows the large-scale arpeggiations that are present.
67
CHAPTER EIGHT Embellishing Tones Back when embellishing tones were in their formative stages, most composers were involved with choirs. They handled dissonance with special care partly out of concern for the ease with which it could be sung. Because of this, all the standard embellishing tones are either preceded or followed by a step, and the most conservative ones are conjunct on both sides. We present embellishing tones in groups based on their approach and resolution—step-step combinations, step-leap combinations, and step-“rep” combinations. The summary chart on page 139 is organized in this manner. STEP-STEP COMBINATIONS (pages 122–124) Passing tones and neighbor tones compose this group. The former involves a step between different pitches, the latter a step above or below a repeated pitch. The group has its own dedicated set of assignments. STEP-LEAP COMBINATIONS (pages 125–127) This is a three-member group. The appoggiatura and escape tone can be characterized as opposites, in terms of both approach/resolution and accentuation. The changing tone (now commonly called a “double neighbor”) adds an extra step to the configuration; the steps must be in the opposition direction of the leap so that the original pitch returns. A relative, which we’ve chosen to omit from discussion, is the cambiata—a step-leap-step combination in which the first step and leap are in the same direction. It occurs often in Palestrinian counterpoint but is less common in later styles. STEP-REPETITION COMBINATIONS (pages 127–130) This is also a three-member club. It’s helpful to characterize the suspension and anticipation as opposites, both in terms of approach/resolution and accentuation. In the anticipation, one tone arrives at the next chord before the others, while in the suspension, one tone arrives at the next chord after the others. Although this is a bit simplistic, it emphasizes an important and fundamental difference. The retardation is simply an upward-resolving suspension. Suspensions are usually the most difficult of the embellishing tones for students, who can often see how they work readily enough but have trouble writing them. Stress the idea of suspending the tone into the next harmony.
68
Regarding Example 8-12: The metric relationship of the suspension dissonance to its resolution (strong-weak) has much to do with harmonic rhythm. The suspension dissonance occurs at the point at which the harmony changes. Since harmonies typically change at metrically strong points (harmonic change in fact defines the metric strong points), the dissonance must be metrically strong. “Turning the suspension figure around” leads to a syncopated harmonic rhythm, which, while not unheard of, is not the norm. Other ways of designating suspensions (page 130) Measuring both the dissonance and resolution over the point of initial dissonant impact limits suspension designations to 9-8, 7-6, 4-3, and 2-3, even when they occur over a change of bass or change of chord. Suspension designations such as 7-3 and 9-6 only litter the landscape. EMBELLISHING TONES AND STYLE (pages 132-139) This section looks as a few ways that embellishing tones have been used by particular composers and in certain styles. It can be stated generally that embellishing tones have been used more liberally and more prominently in each ensuing style period. Included also are the large-scale embellishing tone (bracketed in Example 8-21) and the embellishing chord tone (Example 8-22). This latter concept can be invoked later in the text to distinguish embellishing tones in atonal music, where harmonic context is not an issue. A riddle for students: Question: When is a nonchord tone not an embellishing tone? Answer: When it’s a pedal point! Although the pedal point is traditionally introduced with the embellishing tones because it frequently disagrees with the harmonies that occur above, below or around it, the pedal point is usually of structural significance and thus the most important pitch in the passage. You may wish to add some aural reinforcement to the material presented in this section. This may be done by playing two-voice passages of note-againstnote counterpoint, adding various types of embellishing tones, which students can then identify. Material from the following workbook assignments may be used for this purpose: Ass. 3C on page 90 Ass. 1B on page 114 Ch. 10 Ass. 2D on page 121
69
Suggested Additional Uses for Drills and Assignments (Workbook): • ASSIGNMENT 1A on page 79: Students can be asked to supply additional embellishing tones in this exercise once they’ve been introduced. Examples: in no. 1, a 4-3 SUS in the alto; in no. 2, a 9-8 SUS in the tenor or an additional PT, either in the soprano or the alto; in no. 3, a 4-3 SUS in the soprano; in no. 4, a PT in the bass or a 4-3 SUS in the alto; and in no. 5, an APP in the tenor. • ASSIGNMENT 1C on page 80: Students can be asked to supply additional embellishing tones, as in Assignment 14A. • ASSIGNMENT 4A on page 93: It is instructive to photocopy and hand out Bach’s harmonizations of these chorales, comparing the embellishing tones he added to the students’ versions. Students can see the dramatic difference embellishing tones make. ****************************************************************** SOLUTIONS TO ASSIGNMENTS
1. Step-Step Combinations 1A. Multiple answers exist for several of these. We’ve indicated a few possibilities. 1
4
2
3
5
70
1B.
1C. In no. 5, a NT is not possible. A PT is only possible as a chromatic PT, and even so, the resulting tone is not a dissonance. 1
2
4
5
3
1D. Both possibilities are shown for Nos. 2, 3, and 4. 1
2
3
4
5
71
1E. 1
2
3
72
1F 1
73
2
*
Students are not asked to identify the two appoggiature present, as they’ve not been covered at this point in the chapter.
74
2. Step-Leap Combinations 2A.
1
6
2B.
2
3
7
4
8
5
9
10
1
2
3
4
5
6
7
8
9
10
75
2C. 1
Kuhlau: Sonatina, op. 59, no. 1 (Rondo)
2
Tchaikovsky: Piano Concerto No. 1, op. 23 (first movement)
76
2D. Student responses will vary. Harmonic analysis follows: 1 2
6
6
6
g: i | IV viio i iv | V V | i viio D: I | vi iii | IV ii iii | vi V | I ||
6
6
i iio | V ||
3. Step-Repetition Combinations 3A.
1
2
3
4
5
6
3B. 1
2
3
4
5
6
7
8
9
10
77
3C. 1
2
3
4
78
3D. 1
2
3
79
4
NCTs are rather loosely interpreted here.
4. Embellishing Tones and Style 4A. Student solutions will vary. None are provided here. 4B. 1
80
2
3
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QUIZ FOR CHAPTER EIGHT 1. Complete the incomplete voice so that the suggested embellishing tone results. Identify the embellishing tone.
2.
Add the specified embellishing tone in each of the four-part passages.
3.
Create the requested suspensions.
4. Provide complete Roman-numeral analysis of the following passage. Circle and label all embellishing tones. Then identify the cadence.
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CHAPTER NINE Melodic Form THE PHRASE (pages 140-147) It’s interesting to begin by asking students to explain what a phrase is. Some unusual answers are usually forthcoming. Despite the fact that most students will have used the term many times, they may find it difficult to formulate a succinct and accurate definition. We tell them to take heart in the knowledge that there are many ways of defining a phrase (witness the four definitions at the beginning of this chapter). The last of these is perhaps the most useful, despite its imprecise terminology. What constitutes a complete musical thought? Must a phrase end with a rhythmic pause or can it be terminated solely by a harmonic cadence? These questions highlight some of the problems that complicate phrase definition and identification. Some students may wonder why Example 9-3a on page 142 cannot be regarded as two two-measure phrases. The answer is probably that the four measures provide a more complete musical thought than either of the twomeasure units. And that might be because no harmonic movement takes place in the two-measure units. Still, this exemplifies the problems associated with defining phrases solely in terms of length. We advocate flexibility on this issue. Point out to students that this is only one of many areas of musical analysis where multiple viewpoints may be acceptable. The Musical Sentence (page 146) The prominence of sentence structure in classical melodies has recently drawn interest. This type of phrase construction (1+1+2) occurs frequently because of composers’ natural inclination to state an idea, repeat it, and grow it. It occurs in melodies of all periods, can be seen in structures larger than the phrase, as will be pointed out in the chapters on musical form, and is a natural way to go about composing, as shown in Chapter 33. Phrase Relationships (page 146) The method of symbolizing phrase relationships used here is the standard one, which of course provides no way of distinguishing between contrasting and similar phrases (both are symbolized a b). The matter of similarity versus contrast is another subjective area that can provide fertile soil for debate. Rhythm is arguably the most important criterion in such determinations. Where the distinction is not all that clear-cut, it’s probably not all that important.
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COMBINING AND EXTENDING PHRASES (pages 148-163) The criteria for assessing phrase relationships extend to the discussion of the period, with the exception that exact repetition of a phrase cannot form a period since, by definition, the final phrase of a period ends more conclusively (hence differently) than the first. Because the term parallel period is used only when two phrases begin alike (the second thus a varied repetition of the first), we have the irony that a contrasting period can be composed either of similar or contrasting phrases (both symbolized a b). This is possibly the one case in music theory where yet another term could be useful. Examples 9-14a-f show the various possible phrase relationships reduced to simplest terms. Double Period (page 154) It’s helpful to use the term “phrase pairs” in describing the double period. If two phrases begin alike, the period is parallel (assuming the second ends more conclusively than the first). Similarly, if two phrase pairs begin alike, the double period is parallel (assuming the second pair ends more conclusively). Phrase Extension (page 158) We’ve included a distinction between pre- and post-cadential extensions because we think it’s important for students to know what is being extended. Is it the approach to the cadence or the final cadence chord? The two effects are quite different. The Dave Grusin excerpt (“It Might Be You”) is a wonderful example both because the tune is well-known and because the two types of extension occur back-to-back. Example 9-20, also familiar to most students, is quite unusual in its consistent three-measure phrases. You might review the concept of hypermeter here and ask students to classify this example as duple, triple, or quadruple. The eight measures that follow the given ones divide unusually as well—into a fivebar and three-bar unit. Additional Phrases and Periods for Study: If you don’t mind hopping around the text a bit, you might draw on the following for identification at this point: • Example 7-1b on page 101: A two-phrase group • Example 7-6 on page 107: A two-phrase group and also an example of the musical sentence • Example 11-1 on page 180: An eight-measure phrase group (4+4). Do you recall the “plagal half cadence” on page 88? The first phrase here ends on IV also. • Example 11-4 on page 183: A period (a b). • Example 11-13 on page 190: A musical sentence
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• • •
Example 12-11 on page 201: A phrase group or, if you prefer to introduce the concept, a modulating period Example 13-19 on page 221: A period (a b or a a1) or an eight-measure phrase Example 17-9a on page 287: Another modulating period, if you’re so inclined
Suggested Additional Uses of Drills and Assignments (Workbook): Many of the melodies in the Workbook assignments can be used for R & R (review and reinforcement) of concepts introduced earlier in Part Three. • ASSIGNMENT 1A2 on page 96: Tonic-dominant axis and step progression • ASSIGNMENT 1A3 on page 97: Musical sentence ASSIGNMENT 1B2 on page 98: Tonic-dominant axis and LSA • ASSIGNMENT 2A1 on page 100: Sequence • ASSIGNMENT 2A4 on page 101: Tonic-dominant axis and step progression • ASSIGNMENT 2F on page109: Double APPs, SUS, double RETs, and other assorted NCTs. Aural Drill: Melodic dictation can be used to reinforce the concepts presented in this chapter. Ask students to draw the number of bar lines needed for each melody and to number the beats beneath each measure. Then play the melody and ask the students to do any or all of the following: • Place a T or D above each beat on which a tonic or dominant occurs. • Place a phrase mark at each melodic cadence and identify the cadence as conclusive (C) or inconclusive (I). • Use letters to symbolize the phrase relationships. • Bracket any sequential passages and identify the repetition as real or tonal. • Notate under the numbered beats the rhythm of the passage. • Notate the complete melody on staff paper. Supplementary Examples The following examples of phrases and periods are appropriate for study. All are found in Analytical Anthology of Music, Second Edition, by Ralph Turek. •
•
Repeated phrase: Mozart Piano Sonata K. 332 (I): mm. 94–109 (page 216) Schumann Kinderscenen, op. 15, no. 8 (“By the fireside”): mm. 1-8 (pages 325-326 Parallel period:
84
Haydn Piano Sonata H. XVI: 37 (I): mm. 1–8 (page 187) Mozart Eine Kleine Nachtmusik (I): mm. 28–35 (page 223) Beethoven Piano Sonata op. 10, no. 1 (I): mm. 73–81 (page 261) • Contrasting period: Mahler: “Nun will die Sonn’ so Hell aufgeh’n” from Kindertotenlieder: mm. 4–15 (page 400) • Modulating period: Haydn Piano Sonata H. XVI: 37 (III): mm. 20–28 (page 192) Beethoven Piano Sonata op. 53 (I): mm. 1–8 (page 270) Schumann Kinderscenen, op. 15, no. 2 (“Curious Story”): mm. 1–8 (page 323) Faure Chansons d’Amour, op. 27, no. 1: mm. 3–10 (page 395) • Three-phrase period: Beethoven Symphony No. 7, op. 92 (II): mm. 51–74 (pages 293–294) • Double period: Anonymous Menuet BWV 115: mm. 1–16 (page 81) Schumann “Ich will meine Seele tauchen” from Dichterliebe, op. 48: mm. 1–16 (page 329) ****************************************************************** SOLUTIONS TO ASSIGNMENTS 1. The Phrase 1A. 1 Phrasing: Similar phrases a (mm.1-4) b (mm.5-8) Sequences: mm.5-8 are a loose sequence of mm.1-4.
85
2 Phrasing: Contrasting phrases a (mm.9-12) b (mm.13-16) The eight measures comprise a musical sentence.
3 Phrasing: Contrasting phrases a (mm.1-4) b (mm.5-8) No sequences are present although the sub-phrase units are melodically similar. The eight measures comprise a musical sentence. 4 NOTE: The first measure of the passage is m. 5. Phrasing: Contrasting phrases a (mm.5-8) b (mm.9-15) Mm. 11-12 are a tonal sequence of mm. 9-10. 1B. 1
2
3
1. a: mm.1–4 a1: mm. 5–8 2. The second phrase is identical to the first except for the more conclusive cadence on the tonic. 3. No motives are present. 1. a: mm.1–4 b: mm. 5–8 2. The second phrase contrasts with the first in every respect. Both end inconclusively with a half cadence on beat three. 3. The rhythmic figure of m.4 probably meets the minimal requirements of a motive because of its reappearance in sequence at m.6. 1. a: mm.1–4 b: mm. 5–8 2. The second phrase contrasts with the first. It can be argued that the second phrase—ending with a tonic on the downbeat—has greater finality than the first. 3. No figures recur with the persistence typical of a motive.
86
4
1C.
1. a: mm. 48–51 b: mm. 52–55 2. The second phrase bears little similarity to the first despite prevalence of the dotted-eighth and sixteenth figure. It ends more conclusively on the tonic. 3. The dotted figure is motivic. Solutions will vary. None are given for this assignment.
2. Combining and Extending Phrases 2A.
1 2 3 4 5 2B. 1
Conventional phrase analysis does not afford the option of symbolizing parallel periods as either a a’ or a b. Therefore, any phrase analysis of a b will here be considered a contrasting period. It is entirely possible that we may differ in our views as to what constitutes similar or contrasting phrases. Consistency is more important than complete agreement. Contrasting period a b forming a musical sentence. (Might also be considered a phrase group) Parallel period a a’ Contrasting period a b Repeated phrase a a’ Contrasting period a b
Phrases a and a’ = parallel period; a’ extended precadentially (mm. 15-18) Step progression A – Bb – C in mm. 14-18
87
2 Simplest analysis: Parallel period a (mm.1-12) a’ (mm.13-22) Both 8-m. phrases are extended pre-cadentially. Opinions may vary as to exactly which measures represent the extensions.
2C. 1 1. 2. 3. 4. 5.
Rimsky-Korsakov: Scheherazade (third movement) No motives exist. The second phrase ends more conclusively—metrically on beat one on the tonic pitch over a root-position tonic triad. a b The phrases form a period. NCTs are labeled.
88
2
Chopin: Mazurka, op. posth. 67, no. 4
1. 2. 3. 4. 5.
Motive: mm.1-2 Both eight-measure phrases end conclusively on the tonic on beat one. a a1 The phrases form a phrase group. No phrase extensions are present.
3
Netherlands hymn: Prayer of Thanksgiving
1. 2.
Motive: m.1 Whether viewed as two 8-m. phrases or four 4-m. phrases, only the final phrase ends with the tonic on beat one. As 4-m. phrases: a b c d As 8-m. phrases: a b As 8-m. phrases, the two form a period. Viewed as 4-m. phrases, they form a double period. Where seventh chords exist, the seventh has not been labeled a NCT.
3. 4. 5.
89
2D. 1
Haydn: Piano Sonata, H. XVI:47 (third movement)
90
2
Mozart: “Durch zärtlichkeit und Schmeicheln”
3
Mozart: Piano Sonata, K. 282 (Menuetto I)
2E.
Student solutions will vary. None are given here.
2F. 1
Chopin: Prelude op. 28, no. 7
1. 2. 3. 4. 5. 6. 7.
The two phrases form a parallel period. On music On music. On music. The motive is stated in sequence-like repetition throughout. On music. On music. Two-pitch step progressions exist in m.5-8 (D-C)
91
2 Haydn: “Gennzinger” Sonata (first movement) 1.
2. 3. 4. 5. 6. 7.
Phrase a: mm. 0–4 Phrase b: mm. 4–8 Phrase c: mm. 8–12 The first two phrases are similar, the second almost a sequence of the first. The third phrase contrasts with the first two. Contours: Ascending; Ascending; Descending or Archlike Motive: mm. 0–1 Sequences: On score Tonic-Dominant Axis: On score High point: m. 8, beat 2 Step progressions and large-scale arpeggiations: On score
92
2G. Student solutions will vary. None are provided here.
93
QUIZ FOR CHAPTER NINE 1.
Answer the following questions for the melody below: 1. The first phrase begins in m. ___ and ends in m. ___. 2. The second phrase begins in m. ___ and ends in m. ___. 3. The phrase relationship is best described as: a a; a a1; a b (Circle the best answer.) 4. The phrases form a period. Yes___ No___ 5. A cadential extension is ___ is not ___ present. Give the reason for your answer: _________________________________________ 6. Which of the following are present: (a) a motive (b) sequence (c) step progression (d) none of these 7. Circle the notes most important in forming the tonic-dominant axis. Mozart: Piano Sonata, K. 311 (second movement)
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2.
Answer the following questions concerning the melody below: 1. Identify the phrases and symbolize their relationships. 2. The phrases form a period. Yes___ No___ 3. A cadential extension is ___ is not ___ present. 4. The sequence in mm. 1–2 is ____________ . (real or tonal?) 5. Another sequence appears in mm. _____. It is ________ . (real or tonal?) 6. Circle the notes involved in the large-scale arpeggiation of the tonic in mm. 1–4. 7. Circle the three tones most important in creating the tonic-dominant axis. Beethoven: Sonata for Violin and Piano, Op. 24 (I)
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PART FOUR VOICE LEADING (CHAPTERS 10–14) Four-voice part writing is a topic that may be scaled back in order to make room for others equally vital for today’s musicians. We realize that not everyone will share this opinion, and this has prompted the organization of Part Four. All the important voice-leading considerations—the principles governing the individual lines, chord voicing, and chord connection—are presented in Chapter 11, so that students are equipped in this one chapter to go forth and part write with some degree of success. From here, you can choose your route. Follow the traditional path and proceed directly through the remaining three chapters of Part Four; or skip next to “Part Writing Suspensions” on pages 202-204 of Chapter 12, where the 4-3 and 9-8 are covered in the context of root-position triads, followed by “Suspensions and First Inversion” on pages 213-215 of Chapter 13, where the 7-6 and 2-3 are covered in the context of first inversion. Whichever route you choose, you can allocate more or less time to second inversion (pages 215-222). Students already know the most important principle in this regard, which is to double the bass. Add to that the metric positioning of the chord, stress stepwise motion into and out of it (the arpeggiated six-four chord excepted) and voila! Seventh chords are so much a part of all music that we don’t recommend omitting any part of Chapter 14. Our heavy reliance on the Bach chorales needs no apology. As for the limitation to four-voice texture, mastery of this format enables students to deal with three- or five-voice textures when the need arises. No additional voiceleading problems or considerations attend three-voice textures. While five-voice textures do involve additional doubling and registral considerations, this texture is not commonly encountered and, after all, there’s only so much that can be accomplished in a core theory course. You should continually remind students of the melodic aspects of voice leading. It’s far too easy to lose sight of this when grappling with problems of doubling, spacing, parallelisms, and all the rest. This is partly the reason for Chapter 10, which focuses on melodic principles as they apply to the outer voices. Frequent class singing of student work will help to reinforce the importance of the melodic dimension and its guiding principles, and it will also help to relate theory to performance. The aural benefits are an added bonus.
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CHAPTER TEN Melodic Principles of Part Writing/ The Outer Voice Framework MELODIC PRINCIPLES (pages 167-169) Chapter 10 serves a two-fold purpose. It serves to introduce part writing by addressing the two most prominent, if not most important, musical lines—the melody and the bass. It serves as an early introduction to counterpoint, a topic that is taken up more fully in Chapters 18 and 19. Good counterpoint between the outer voices goes a long way toward facilitating the part writing of the inner voices. The melodic principles cited here apply with equal force to all melodic and contrapuntal writing, whether for two voices or four, and students need to learn them well. CREATING AN OUTER VOICE FRAMEWORK (pages 169-177) As a topic piece, we’ve chosen a song students are likely to have heard in its popular renditions. This is in keeping with our goal of using the familiar to teach the unfamiliar. We feel it makes the learning of 1:1 counterpoint a bit less “academic” in the student mind than the typical “Fuxian” presentation in whole notes. We’ve chosen to present the conversion of first species counterpoint to second species in terms of the standard nonchord tones, providing students with an opportunity to apply a recently learned concept. Added Practice We’ve added ample exercises within the chapter to assure that students have an opportunity to apply the concepts as they are presented. ****************************************************************** SOLUTIONS TO ASSIGNMENTS 1. Melodic Principles 1A. T.T. = tendency tone 1 Key: Ab
97
2
3
4
1B. 1 1. 2. 3. 4.
5.
Each voice is within its range. The lines are moderately disjunct. Chromatic intervals are avoided. The o 4th from m.2 to m.3 is resolved. Leaps larger than a fifth (other than octaves) are avoided in the soprano. The minor sixth in the bass is common and is resolved inward by step. All leaps are followed by motion in the opposite direction (not always by step). Sensitive tones are resolved.
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2 1. 2. 3. 4.
5.
Each voice is within its range. The soprano is primarily conjunct, the bass less so. Chromatic intervals are avoided. Leaps larger than a fifth (other than octaves) are avoided. The successive leaps in the bass in m.1 and m.2 (which outline a triad) are followed stepwise in the opposite direction, as is the leap in m.3. Sensitive tones are resolved.
1C. 1
2
3
4
5
6
7
8
9
10
1D. 1.
Soprano range: G4 to E5 Alto range: E4 to B4 Tenor range: A3 to F4 Bass range: A2 to D4
99
2.
Leaps larger than a third: Soprano: 0 Alto: 2 Tenor: 3 Bass: 12
3. 4.
Voice with the largest leap: Bass Most disjunct voice: Bass
1E.
Parallel: 1 Similar: 8 Oblique: 11 Contrary: 15 2. Creating An Outer-Voice Framework 2A. Possible solutions follow. 1
100
2
3
4
2B. Although students are asked to begin these exercises on different pitches, the actual chorale melodies are added here for your reference. The complete Bach harmonizations appear in the Bach-Reimenschneider 371 Harmonized Chorales, Nos. 370 and 293. 1 J. S. Bach: “Kommt her zu mir, spricht Gottes Sohn”
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2 J. S. Bach: “Was gott tut, das ist wohlgetan”
2C. One of several possible solutions appears below.
2D. One of numerous possible solutions appears below.
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CHAPTER ELEVEN The Melodic Factor in Four-Voice Part Writing/ Voicing and Connecting Chords REVIEW OF MELODIC PRINCIPLES (pages 179-180) Four-part music is most effective when its component voices form interesting melodic lines. Therefore, attention is paid first to the characteristics of the individual lines. Following all of the procedures for doubling, spacing, and chord connection will not compensate for poorly constructed melodies. Range, contour, and interval structure are prime concerns, as is the treatment of sensitive tones, which should almost always be resolved, even in the inner voices. Examination of any number of Bach’s chorale harmonizations will reveal that conjunct motion predominates. Example 11-1 (page 180) In part music, no individual voice is likely to span its entire total range, and in fact, the alto and tenor voices often exhibit quite restricted ranges, as they do here. In Bach’s chorale harmonizations, the bass is the voice most likely to approach its total range. VOICING CHORDS (pages 181-184) Students seem to have a hard time appreciating the subtleties of spacing, especially when chords are played on the piano, where sympathetic vibration of strings tends to “fill in” most voicings. You might place a single harmony, spaced half a dozen different ways, on the chalkboard and have the class sing each. Discussion of the different effects can be revealing. It is worth stressing that structure is determined by the distances between the three upper voices only. Doubling (page 182) Unless one is attempting a precise emulation of the voice leading in the Bach chorale harmonizations, the Short Rule of Doubling (page 183) is all that students need. We prefer not to overly restrict them with negatives (don’t do this, don’t do that) so that part writing becomes more the creative activity it is than an academic chore. The alternative doubling practices on page 184 provide options for those students capable of dealing with them. CONNECTING CHORDS (pages 184-191) These principles apply to triads in all positions and thus pertain also to Chapters 12 and 13. They are presented in what is generally conceded to be their order of importance.
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Part writing is a little like the card game Bridge, where you can play a passable (though not inspired) game by simply following a set of rules without fully understanding why. We want students to know why, and so we’ve provided both a rationale for the procedures discussed in this section and some flexibility. Consecutive Perfect Fifths and Octaves (page 185) The term “consecutive” is perhaps preferable to “parallel” when discussing perfect consonances of the same kind in succession. The reason is that such a succession may actually involve contrary motion, as in Example 11-7b. (Parallel fifths by contrary motion seems paradoxical on the surface and is a bit of a mouthful.) In our experience, students have difficulty accepting (or at least understanding) the historical and acoustic explanations for the prohibition on consecutive fifths, octaves and unisons. How does one then justify the allowance of consecutive perfect fourths? The ban became decidedly less a factor in the nineteenth century, and students regard it as irrelevant to today’s music. Therefore, we present this purely as a stylistic trait, to be observed in the baroque style. We find almost no point in hunting down direct fifths and octaves. Students already have enough to master, and the “problems” do little to detract from otherwise well-written passages. Voice crossing and overlap are even lesser evils, and judiciously used, are not objectionable. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1C on page 123: In the interest of reinforcing earlier material, you might ask students to provide lead-sheet chord symbols in addition to Roman numerals. • ASSIGNMENT 1F on page 125: Before examining this assignment, you might use it for two-voice dictation, aural interval recognition, and/or cadence identification. • ASSIGNMENT 2B on page 127: You can follow up this exercise by asking students to rewrite the alto and tenor voices. The soprano and bass lines are acceptable as they are. Suggested Aural Quiz • •
10 two-chord successions, soprano and bass only: Ask students to identify the soprano-bass motion as contrary, oblique, similar, or parallel. 10 two-chord patterns (root-position to root-position): Give soprano and bass pitches and harmonic function for first chord and ask students to provide this information for the second chord.
104
•
1 two-voice dictation, approximately two measures in length: You might use two-measure fragments from Assignment 1I on Workbook page 137 from the next chapter for this purpose. ****************************************************************** SOLUTIONS TO ASSIGNMENTS 1. Voicing Chords 1A. 6 1 viio 2 v 6 ii
7 V (X)
3 I
6
4 viio (X)
8 vi (X)
9 viio
6
5 i (X) 10 V
1B. 1
2
3
4
5
6
7
8
9
10
1C. 1
2
3
4
5
6
7
8
9
10
105
1D. No. 7 cannot be completed according to the doubling preferences because first inversion would place the leading tone in the bass, thereby doubling it. 1
2
3
4
6
7
8
9
5
10
1E. Depending on their choice of soprano pitch, student solutions will vary. None are given here. 1F. 6
6
Chord:
V | I I | IV I | V V I | IV V IV | I V V | I
Voice Doubled:
B
B B B B
B B S B
B B
B B B
Chord member doubled: R
R R R R
R R 5 R
R 3
R R R R
Scale degree doubled:
1 1
5 5
5 6
1 5 5
5
4
1
5
4
B
1
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2. Connecting Chords 2A. 1 voice overlap
4
8
+2nd
2
3 // 5ths and 8ves
5 // 5ths and 8ves 6 // 5ths and spacing 7
// fifths and octaves
2B. 1 voice crossing 6 spacing
// 5ths
2 // 8ves
7 doubling
9
+2nd
Voice crossing and overlap 10 // fifths
3 // 5ths 8 doubling
4 doubling
5 // 5ths
9 large leap 10 voice crossing
107
2C. 1
2
3
4
5
6
7
8
9
10
108
2D. Part writing will vary depending on the voicing chosen. Possible solutions are given here. 1
2
6
7
2E. 1
2
6
7
11
3
8
3
8
12
13
4
5
9
10
4
5
9
10
14
15
109
2F. 1 Plagal
4 Deceptive
2 Perfect Authentic
5 Phrygian Half
3 Half
6 Imperfect Authentic
110
QUIZ FOR CHAPTER ELEVEN 1. In the following melody, identify the features not in keeping with the melodic principles given in your textbook.
2. Identify the part-writing error in each of the following by placing the letter corresponding to the error committed in the blank provided. a. Spacing b. Voice overlap c. Voice crossing d. Consecutive octaves e. Melodic augmented second f. Consecutive fifths g. Doubling h. Voice not within range i. Unresolved tendency tone 1
2
_____
3
_____
4
_____
5
_____
_____
3. Regarding the given pitch as the soprano, write the requested chords in the inversion and structure indicated.
111
4. Add alto and tenor to the given soprano-bass framework. Identify the motion between the soprano and bass, and provide harmonic analysis.
n n
Motion: __ __ __ __ __ __ __ Key___:
___ ___ ___ ___ ___ ___ ___
n
n
__ __ __ ___ ___ ___ ___
__ ___
113
CHAPTER TWELVE Part Writing with Root-Position Triads/ The Chorale PART WRITING (page 193) The comparison of part writing and golf seems apt. Mastery of either activity practically precludes mastery of the other. Most musicians we’ve known have neither the time nor the inclination for golf. Of the very few golfers we know, none part write. We trust this comes as no surprise. THE CHORALE (page 194) You might ask your students if any have a favorite hymn, and if so, might they make a copy (or bring in the hymnal)? For students who sing in church (choir or congregation), this brings part writing into the orbit of their everyday lives. The four-part arrangements found in hymnals are generally much less complex than Bach’s chorale harmonizations and thus make good points of comparison. Have students compare the quality of the inner voices, the sophistication of the harmonic structure, and the voice leading. PART WRITING WITH ROOT-POSITION TRIADS (pages 194–201) In this section, voice-leading principles are applied to root-position triads in all root relationships (fifth, second, and third). Students should actually be able to part write each of these situations upon completing Chapter 11. The “Short Rule of Chord Connection” given on page 200 is especially helpful to them: retain the common tone(s) if present, in the same voice or voices; and move the outer voices in contrary or oblique motion if possible. You can add this: Move the three upper voices in contrary motion to the bass when no common tones are present. PART WRITING SUSPENSIONS (pages 202–205) Suspensions present a lot for students to grasp at once, and they require ongoing reinforcement. This is one reason for spreading them over several chapters, the other being to tie them to the chord positions under study. You may wish to review their initial presentation as embellishing tones on pages 128–131. Only those that occur over root-position triads—the 9-8 and 4-3—are discussed here. Suspensions and harmonic motion (page 204) As the illustration on this page shows, the 4-3 suspension can decorate a plagal cadence (the 9-8 possible if the harmonic motion is reversed, i.e., I-IV),
114
and the 9-8 suspension can decorate an authentic cadence (the 4-3 possible if the harmonic motion is reversed, i.e., I-V). Both suspensions can decorate a deceptive cadence or (less commonly) the reverse harmonic motion (V-IV or vi-V). Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1A on page 132: Once suspensions have been covered, you can return to this exercise and have students add either a 4-3 or 9-8 suspension (let them figure out which is possible). A suspension is not possible in No. 3 because the Csoprano pitch (and leading tone) is the note that would represent a 4-3 suspension resolution. • ASSIGNMENT 1H on page 136: Students can be asked to identify the motion between the soprano and bass. • ASSIGNMENT 1I on page 137: Students can also be required to add leadsheet symbols and/or Roman numerals. • ASSIGNMENT 2E on page 140: Bach’s harmonization of this chorale appears as No. 116 in the Bach-Riemenschneider 371 Harmonized Chorales. You might have students analyze the additional NCTs present in this harmonization. SOLUTIONS TO ASSIGNMENTS 1. Part Writing with Root-Position Triads 1A. 1
6
2
7
3
4
5
8
9
10
115
1B. The individual lines should be as shown below although the voice in which they appear will vary depending on the voicing of the first chord in each. 1
6
2
7
1C. 1
6
3
5
9
10
3
4
5
8
9
10
8
2
7
4
116
1D. 1
2
3
4
5
1E. 1
6
2
3
7
4
5
8
117
1F. 1
5
1G.
2
6
3
7
8
Hope that your students do not turn in part writing that looks like this! Errors to identify: m.1, beat 2-3: // 5ths m.1, beat 3: spacing m.1, beat 4: leap in tenor m.1, beat 4 to m.2, beat1: // 5ths and 8ves m.2, beat 1-2: // 5ths m.2, beat 4 to m.3, beat1: // 8ves m.3, beat 1-2: // 8ves m.3, beat 3: doubling m.3, beat 3-4: // 5ths and 8ves m.3, beat 4 to m.4: // 8ves
1H.
4
118
X: Complete seventh chord (no doubling) O: Soprano doubled in first inversion Common tones are retained in most cases: chords 4-5, 9-10, 10-11, 12-13, 13-14 1I.
Part writing will vary. No solutions are given here.
2. Part Writing Suspensions 2A. 1
2
3
4
5
2B. 1
2
6
7
3
8
4
9
5
10
119
2C. 1
2
3
4
5
6
2D. 1
2
3
4
5
6
7
8
9
10
120
2E. This harmonization is No. 116 from the Bach-Riemenschneider 371 Harmonized Chorales. Bach’s harmonization contains a few more NCTs and a couple other distinctions.
2F. 1
121
2
2G.
Solutions will vary. None are provided here.
122
QUIZ FOR CHAPTER TWELVE 1.
Write the requested triads, using appropriate doubling and spacing.
2. Part write the following for four voices in the major or minor key indicated by the chord symbols.
3.
Complete the following suspensions in four voices.
4.
Add alto and tenor to the soprano-bass framework given.
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CHAPTER THIRTEEN Part Writing with Triads in Inversion FIRST INVERSION (pages 207-215) Inversion and Bass Line (page 207) The guidelines that we give students regarding first inversion grew out of the contrapuntal practices of the Renaissance, when line and interval—not chord and inversion—were the governing forces. It’s true that today’s composers may seek to “melodize” a bass through the use of inversion, but it’s worth pointing out to your students that the bass originated as a melody, not a mere harmonic support. Doubling in First Inversion (page 208) Doubling would be relatively straightforward were it not for first inversion. This is where the melodic and harmonic forces collide head-on, and it involves a degree of judgment not required in root-position and second-inversion triads. Why Not the Other Tone? (page 209) On page 209, we’ve tried to shed light on what seems to students a rather arbitrary and mystifying doubling preference (the outer voices). We’ve tied this preference to the need to keep the voices in their respective “corridors.” Doubling an inner voice can lead to either spacing problems or voice crossing and overlap. Of course, other forces are at work here, too. For example, when the soprano and bass are one-and-the-same chord members, the outer voices are de facto doubled. Chord Connection (page 210) Students should try hard for conjunct motion in the bass. Of the chord connection guidelines given here, No. 4 merits particular attention. Stepwise bass motion to or from a first-inversion triad (unless a repeated chord) is the norm. Guideline No. 5 is new at this point: Leave the doubled tone in contrary or oblique motion where possible. Inversion and Harmonic Weight (page 211) Play the first two measures of “Mary had a Little Lamb,” first harmonized 6 this way: C – G – C – G – C – C -C; then this way C - G 4 - C6 - G 64 - C - C - C. Ask students to describe the effect of each and to state their preference. It’s an easy way to make the point about the harmonic weight of root position vis a vis inversion. Move from this example to the more sophisticated ones in the book.
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Suspensions and First Inversion (page 213) 9-8 and 4-3 suspensions normally require normal doubling upon resolution—a doubled bass (because they resolve into a root-position triad). Likewise, the 7-6 and 2-3 suspensions normally require normal doubling on resolution—the soprano or bass (because they resolve into a first-inversion triad). THERE IS ONE BIG CAVEAT: The suspension resolution should not be doubled. This means, of course, that the soprano should not be doubled if the suspension is in the soprano, and the bass should not be doubled if the suspension is in the bass (as it always is in a 2-3 suspension). SECOND INVERSION (pages 215-223) The six-four chords are presented in their traditional classifications. You may wish to stress that the six-four chord—whether cadential, passing, pedal, or arpeggiated—is subsidiary, either to the chord following it or the chords surrounding it. The cadential six-four chord is revealed upon resolution to be a dominant; the passing and pedal six-four chords are contrapuntal elaborations of the chord that precedes and follows them; and the arpeggiated six-four chord is usually a prolongation of the root-position form of the chord. Other points to stress: • the relative infrequency of second inversion compared with root position and first inversion • the fact that second inversion is associated almost exclusively with the primary triads • the uniform doubling procedures in all four types (i.e., the doubled fifth) Even today, second inversion occurs mostly in the primary triads. However, voice leading is less strictly observed than in earlier music. The folk and popular examples given here can be compared to others in the book. On page 222: Example 13-20b (“Can You Feel the Love Tonight?”) is similar to Example 16-2b (“Hymn to Freedom”) on page 266 (m. 4). They might be called “half-pedal six-four chords” or “plagal-cadence six-four chords” because they resemble both the latter part of the pedal six-four chord and a plagal cadence. Both have a gospel flavor. The chart on page 224 summarizes the essential features of the standard six-four chords.
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Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1B on page 144: Once Chord Connection on page 210 has been covered, you can return to this assignment and have students resolve these chords in various ways. • ASSIGNMENT 1E on page 147: Following is Bach’s part writing. You might make this available to students to compare with their own. J. S. Bach: “Gott lebet noch”
• •
ASSIGNMENT 1I on page 150: You might play these bass lines with an added soprano for two-voice aural dictation exercises. ASSIGNMENT 1J on page 151: You might use this exercise as a review of seventh chords. Ask students to identify the various types present. Following Chapter 14, you can return to this song and ask students to describe the voice leading in these same chords.
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126
Suggested Aural Quiz •
•
10 triads in root position, first inversion, and second inversion: Students are to identify quality, inversion, and chord member in the soprano. 10 three-chord patterns. Use two each of the following (one in major and one in minor), in different keys. Play the tonic triad before each. I
6
6
- V4
-
I
- V
-
I
6
I4
6
I
- IV 4 - I
V
6
IV -
•
6
I4 -
V
6
I 4 - IV
Ask students to identify the type of six-four chord and the mode, as follows: passing V (major or minor) cadential (major or minor) pedal IV (major or minor) pedal I (major or minor) passing I (major or minor) 1 two-measure four-voice passage featuring triads in all inversions (give starting soprano and bass pitch).
******************************************************************
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127
SOLUTIONS TO ASSIGNMENTS 1. First Inversion 1A. 1
2
1B. The bass note is given here. Inner voices will vary with voicing and doubling chosen.
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128
1
6
2
7
3
4
5
8
9
10
1C. Voicings may vary, and this may also result in different voice leading. Remind students that doubling the bass is not an option where the V appears in first inversion. 1
6
2
7
3
4
5
8
9
10
1D. Student solutions will vary depending on the soprano and initial voicing chosen. A solution is given here. For greater uniformity of response, you may wish to give students the initial soprano pitch.
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129
1
2
3
5
6
9
10
4
7
8
11
12
1E. The tenor line could definitely be made more interesting than here. The virtue of this part writing is that the line is easy to sing.
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130
1F.
1G. 1
6
2
3
7
8
4
5
9
10
Chapter 13
1H. 1
131
2 is in error. The 2-3 suspension should appear over the V6. 2
3
5
1I. 1
4
6
Chapter 13
132
2
1J. The lead-sheet symbols given here reflect the chords as originally given (i.e. prior to adding the suspensions, which of course add ninths to the chords they adorn). Also, it’s worth mentioning to students that adding complete lead-sheet symbols is a purely academic exercise intended to enhance their familiarity with the system. Not all of these chord symbols would likely appear on the music since they do not truly reflect the nature of the chords. For example, the chord of m. 7, beat 3 is actually a V with a PT C, and the entire measure is more accurately represented as a V7.
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Chapter 13
134
2. Second inversion 2A. 4 6 6 6 7 6 6 1 A: I I | V V 3 | vi V I ii | I 4 V I || (cadential) 6
2 D: vi | ii | I 4 V | I || (cadential) 6
3 a: i | V 4 | i
6
4
6
6
7
| V 3 | i | iio6 | I 4 V | i || (passing and cadential)
4 Eb | Ab/Eb | Eb | Ab Db/Ab Ab | Eb Ab/Eb | (pedal) 2B.
Solutions will vary depending on soprano chosen.
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135
2C. Students’ answers may vary. Inner voices will probably be similar to those shown here, although they may be exchanged where a different opening structure is chosen. 1
2
3
4
5
6
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136
2D. 1 2
Cadential Cadential. Metric placement incorrect. The cadential six-four should be metrically stronger than its resolution to V. 3 Passing six-four 4 Passing six-four. Incorrect doubling in the six-four chord. 5 Pedal six-four. Bass and one other voice should remain stationary through the six-four chord, and the non-doubling voices should both resemble upper neighbors.
2E. The bass line (given here) is determined by the Roman numerals. Inner voices will vary and are not provided here.
2F. The six-four chord in m.8 is a cadential six-four.
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2G. The six-four chord in m.2 is a cadential six-four (cadential six-fours do not necessarily appear only at cadences.) The six-four chord in m. 4 is a pedal sixfour. 1
2 This one takes a little effort to avoid the consecutive fifths that are almost mandated by the iii-IV in m.1 along with the passing seventh between the two chords. It is possibly why this particular progression is among the least common in Bach’s harmonizations.
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QUIZ FOR CHAPTER THIRTEEN 1.
Add alto and tenor to the soprano-bass framework.
2. Complete the following passages in four voices, approaching and resolving the given six-four chord in an appropriate manner. Then, identify the six-four chord type.
3.
Name the six-four chord type described by each statement:
1,__This six-four chord occurs over a bass line that contains repeated pitches. 2.__This six-four chord is always metrically stronger than its resolution. 3.__This six-four chord is the only one that is not a primary triad. 4.__This six-four chord occurs over a bass line that moves stepwise in a single direction. 5.__This six-four chord occurs over a disjunct bass line.
Chapter 13
a. b. c. d. e. f.
Cadential six-four chord Passing six-four chord Pedal six-four chord Arpeggiated six-four chord All of the above None of the above
139
Chapter 14
140
CHAPTER FOURTEEN Part Writing Seventh Chords Generally, seventh chords are easier to part write than triads. In four voices, doubling is not required, and voice leading’s prime directive given on page 225—neither double nor fail to resolve a tendency tone—applies to every seventh. SEVENTH CHORDS OF DOMINANT FUNCTION (pages 226–232) Similarities in function and resolution suggest that the chords under discussion here be considered together. These seventh chords are different from the rest. They contain the tonicizing tritone (scale degrees 4 and 7). This sensitive tandem is best resolved the same way in all three chords. Example 14-2 (page 226) When the leading tone is in an inner voice, the composer often chooses to resolve it or not depending on whether melodic or harmonic factors are more important at that moment. This is an excellent opportunity to stress once again that part writing, as with all composition, involves a balanced approach to linear (melodic) and vertical (harmonic) forces. Chord Member or Not? (page 227) A “guiding principle” is given only because students feel more comfortable with a guideline rather than with generalizations. We opt for a flexible approach to the question of whether a harmony should be analyzed as a seventh chord or as a triad with an embellishing tone. This normally is not an issue that warrants extensive debate, since even the longest of chord sevenths in the music of, say, Wagner can often be viewed as greatly elongated suspensions or passing sevenths. You may wish to establish your own criterion here. For a short tour of the dominant seventh chord in the hands of some major composers, you might return at this point to the following and discuss the treatment of the sensitive tones in each: Example 3-16 on page 45 (Bach) Example 4-7 on page 58 (Handel) Example 6-2 on page 81 (Mozart) Example 6-9 on page 87 (Beethoven) Example 8-9 on page 127 (Chopin)
Chapter 14
Page 229 The unresolved leading tone, the ascending chord seventh, and the delayed resolution of the chord seventh are exceptional practices that are noted here without extensive elaboration. In most situations where the seventh moves upward rather than downward, this tone is found in the melody (soprano), as in Example 14-5. You might ask students how m. 1 of Example 14-10 differs. Page 230: You can use Example14-5 to demonstrate the functional and voice-leading similarities between the dominant seventh and leading tone seventh chords and also to help students hear the difference in sound among the three chords. Change the tenor pitch in m. 2 (beat 2) to B and then to Bb. The Leading-Tone Seventh Chord (page 230) Abbreviated the coverage of these two chords is possible because voiceleading practices are the same as for the V7. The consecutive-fifth problem noted in Example 14-7a is encountered again when a IV7 resolves to a V, and for the same reason. We prefer not to burden students unduly with this relatively infrequent issue. Here, as elsewhere, we’ve tried to pare coverage in order to save time for new topics and matters we deem more important. NONDOMINANT SEVENTH CHORDS (pages 232-240) Despite the important common feature shared by all seventh chords, i.e., the stepwise downward resolution of the seventh, all seventh chords do not occur with equal frequency, nor do they occur in the various inversions with equal frequency. This aspect of seventh chords accounts in part for differences in harmonic style from period to period. We’ve mixed examples from the Bach chorale harmonizations with examples from the traditional, popular and jazz repertories to show the applicability of these chords from style to style. Three points are worth stressing at the outset: • The treatment of all seventh chords is practically identical. Thus, all essential voice leading principles have already been covered. • Nondominant seventh chords (with the sole exception of the supertonic) appear much more often in root position than in inversion. • The seventh can usually be regarded as a PT or SUS.
141
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Example 14-13 (page 235) A potential point of confusion exists here. The lead-sheet symbols DO NOT reflect the harmonies; they are the harmonies indicated in the original publication. The Roman numerals reflect the actual harmonies used in the arrangement. Example 14-14 (page 235) Nondominant seventh chords, sequences, and chain suspensions form a trio that recurs time and again. The harmonic pattern given here, or portions of it, often undergirds such passages. It appears so frequently that it is very much worth students’ time to learn to play it. Have them transpose and practice it in various keys. The I7 (page 238) Common ways to symbolize the major-major seventh chord on I and IV are IM7 and IVM7 You may require your students to use this notation if you wish to stress the difference between this chord type and the V7 (which is a major-minor seventh). We prefer to keep things as simple as possible. Using the superscript seven alone to indicate a diatonic seventh above the root (whether major or minor) makes it possible to symbolize all diatonic seventh chords in the simplest way. The only additional refinement concerns the need to distinguish between the two types of seventh chord available on the leading tone. Beyond this, the only other chord that requires a special symbol is the comparatively rare tonic mM7 (in minor keys). Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1E on page 161: Where neither the leading tone nor the seventh is in the bass, the chord can resolve to a different inversion. Have students identify these and provide alternative resolutions. In some cases, voice-leading choices must be made (such as opting for an incomplete I to avoid consecutive fifths). You may wish to use these examples for class discussion. • ASSIGNMENT 1F on page 161: Additional practice can be gained by inviting students to the chalkboard to transpose the bass line of No. 1 (mm.1–2 or mm. 3–5) to a new key and then choosing a different beginning soprano pitch. • ASSIGNMENT 1G on page 162: You might ask students to add or remove accidentals necessary to turn the leading-tone seventh chords into dominant seventh chords and vice versa. • ASSIGNMENT 2E on page 168: Although it tends to “eat up class time” quickly, in-class performance is important. These chorales sound fine
142
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whether sung by the class or played by a string, woodwind, or brass quartet. Many major-mode excerpts can be performed in the parallel minor mode, by changing the key and adjusting the leading tone accordingly. Doing so can heighten students’ awareness of the similarities and differences between major and minor keys and pave the road to later topics, such as mode mixture. In No. 1, for example, the doubling in the second chord sounds less acceptable when played in F minor because the chord then becomes a diminished triad and the doubled tone acquires a greater need for resolution. Suggested Aural Quiz An aural quiz on seventh chord identification and resolution is appropriate at this point. A suggested format follows: • 10 four- or five-chord successions, each containing a seventh chord of dominant function: Students are to locate the seventh chord (Chord No. 2, Chord No. 4, etc.) and to identify the type (Mm7, om7, or oo7). • 10 seventh chords (dominant-functioning and nondominant): Students are to identify the type (mm7, Mm7, and so on). • Play a tonic followed by a two-chord succession involving a seventh chord (i.e., ii7-V): Students are to identify the succession by Roman numeral. • 1 four-measure passage for SATB: Students are to indicate by measure number and beat each seventh chord they hear. (Option: You may also ask them to identify the seventh chord by Roman numeral.) ******************************************************************
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SOLUTIONS TO ASSIGNMENTS 1. Seventh Chords of Dominant Function 1A. 1 D (or d) 6 E (or e)
2 X
3 A (or a)
7 Bb (or bb )
4 X 8 X
5 Ab (or ab )
9 Cb
10 F (or f)
1B. Students are instructed to resolve both the leading tone and the seventh. By the time they complete this exercise, they should be comfortable with the incomplete tonic. In these solutions, the tonic is tripled in the absence of the fifth, although a doubled third is equally possible. Linear considerations normally will determine which option is invoked. 1
6
2
7
3
8
4
5
9
10
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1C.
1D.
145
Student solutions may have the inner voices exchanged. 1
2
9
10
3
4
11
5
12
6
7
13
14
8
15
Solutions will vary. However, no matter which voice carries the seventh, it should be resolved. Likewise the leading tone if it appears in the soprano. The voice carrying these sensitive tones is shown. 1
6
2
7
3
4
5
8
9
10
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1E. Both root position and first inversion are options for Nos. 1, 3, 4, 6, 7, 9, and 10. The leading tone in the bass requires a root-position resolution in Nos. 2 and 5. The seventh in the bass requires a first-inversion resolution in No. 8. 1
2
6
7
3
4
8
5
9
10
1F. Solutions will vary. Harmonic analysis follows. 6 6 6 6 1 Eb: I V 3 I I | V5 I V | vi ii V V2 | I ii I4 V | I || 4
6
2. B: I iii | IV V
7
4
4
| vi V V 2 | I
6
4
I | V3 I
6
6
1G. 4 1 a: viio 3
2 bb: viio
1H.
6 5
6
ii | I 4 2
6 b 2 D : viiø 5
6 3 B: V 5
4 Ab: V
7 Db: V 2
4 8 a: V 3
6 9 F: viiø 5
4
6 4
V | I ||
5 d: viio
6 5
4 10 e: viio 3
Things to watch: In No. 1, the alto must rise to double the third because doubling the root would result in consecutive fifths against the soprano. For the same reason, the
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bass must rise to the chord third in No. 3 and the tenor must rise to double the third in No. 6. Nos. 8 and 10 resolve to a six-four chord (doubled bass). 1
2
6
7
3
8
4
5
9
10
1I. 1
4
7
2
5
3
6
8
9
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10 1J. 1
2
148
Chapter 14
149
3
The seventh in m. 93 evaporates in the tonic that follows it.
2. Nondominant Seventh Chords 2A. 1
6
2
7
3
8
4
9
5
10
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150
2B.
2C.
1
2
6
7
3
4
8
9
5
10
Students’ solutions will vary. None are provided here.
2D. Phrases a and b form a contrasting period. Any harmonization should reflect the melodic sequences.
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2E. 1
2
Although the vi7 in m.1 resembles a suspension, this “suspension” would be considered metrically unusual because the dissonance is weaker than the resolution, a reversal of the typical metric placement of a suspension.
2F. 4
m.6: V 2 4 m.8: IV 2 7 m.9: ii 7 m.10: V 4 m.12: viio 3 m.14: viio 34 m.16: IV 24 7 m.17: ii 7 m.18: V 4 3
4 3
(suspended C in bass resolves downward to B in m.7) (suspended B in bass resolves downward to A in m.9) (suspended G in alto resolves downward to F in m. 10) (suspended C in soprano resolves downward to B in m.11) (suspended Bb in tenor resolves downward to A in m.13) (suspended Ab in tenor resolves downward to G in m.15) (suspended E in bass resolves downward to D in m.17) (suspended C in alto resolves downward to B in m.18) (suspended F in soprano resolves downward to E in m.19)
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QUIZ FOR CHAPTER FOURTEEN 1. Place an X beneath each chord that is not a dominant seventh or leadingtone seventh chord. For the remaining chords, indicate the key in which each appears diatonically.
2.
Provide the complete Roman-numeral symbol for each chord.
3. Precede each given tonic with the indicated chord, in an inversion and a voicing that produces the best possible voice leading.
Dominant 7th
Leading-tone 7th Dominant 7th
Leading-tone 7th
Chapter 14
4. Indicate the keys in which each chord appears diatonically and indicate the chord’s function in those keys.
5. Complete the following two-chord resolutions in four voices and provide harmonic analysis:
6. For the following excerpt, provide a Roman numeral analysis of all seventh chords. Then circle the chord seventh and draw an arrow to its note of resolution.
153
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PART FIVE
BASIC CHROMATIC HARMONY (CHAPTERS 15–17) An Anecdote from My Past (by Ralph Turek): I used to tell my students of an enduring memory from the earliest days of my college teaching. A composition student—who happened to be married to a wealthy funeral director—had written an opera (unsupervised). The music department, at the time seeking benefactors, agreed to stage it. The performance was a marathon event in C major—ENTIRELY. Two hours in the key of C with nary a whiff of chromaticism, nor a single modulation underscored. In a particularly painful way, the importance of harmonic and tonal variety in tonal music was demonstrated. Part Five contains two chapters on secondary function followed by a chapter on modulation. Chapter 15 introduces tonicization in a more-or-less traditional way while Chapter 16 pairs jazz and popular styles with voice-leading concerns. Chapter 17 introduces the simplest types of pivot-chord and chromatic modulations. Following a unit on counterpoint (Part Six), Part Seven returns to chromatic issues and builds on the foundation provided here.
Recommended time allocation: 6 weeks
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CHAPTER FIFTEEN Secondary Function I Secondary dominants and leading-tone chords are the simplest forms of tonicization. All the secondary functions—V/, V7, viio/, and viiIo7/ (viiø7/) —are presented here in a single chapter since there really is little difference in their treatment. To generalize: Secondary dominants and leading-tone chords are treated like primary dominants and leading-tone chords in virtually all important respects. SECONDARY DOMINANTS (pages 245-252) Example 15-2 (page 247) Playing the first four measures using exactly the same harmonization in mm. 3-4 as in mm. 1-2 will make it clear to students how important a single secondary dominant can be in adding variety to a repeated phrase member. Example 15-3 (page 247) Singing provides aural and physiological reinforcement of concepts and brings theory closer to practice. Having altos and tenors sing the two top notes of each chord an octave lower makes this exercise singable by the class. The points that follow this illustration should be stressed. Students need to be alert to the possibility that any major triad or major-minor seventh chord not diatonic in the key might be a secondary function. At this point, you might place various triad types and seventh chord types on the board, asking students if the chord can function as a secondary dominant or dominant seventh chord and, if so, which chord it would tonicize. This chapter contains many very brief examples. While this is perhaps necessary for clarity, students also need to see concepts and techniques within a larger context. The following longer excerpts from Chapter 25 contain secondary functions that might be discussed at this time: p. 444 p. 452 p. 458
Chopin: Prelude op. 28, no. 7 Beethoven: Piano Sonata op. 14, no.2 (second movement) Schumann: Kinderszenen, op. 15, no. 6
The Tonicizing Tritone (page 248)
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You might mention that the tonicizing tritone is present in every secondary function except the V/x. SECONDARY LEADING-TONE CHORDS (pages 252-255) These chords are presented in a manner parallel to the secondary dominants but somewhat abbreviated. Stress the points on page 254. For additional examples of these chords, see: p. 401 p. 438 p. 443 p. 452
p. 479
Schubert: “Sehnsucht”, mm.3 and 6 Brahms: Waltz, op. 39, no. 3, m.7 Mozart: Piano Sonata K. 332 (I), m.82 Beethoven: Piano Sonata op.14, no.2 m.11 m. 12 Beethoven: Piano Sonata op. 13 (II), m. 20
viio7/vi viio /V viio7 /vi viio/ii, viio7/V viio7/vi
At this time, you may wish to return to the “tonal planetary system” (Example 5-12 on page 73) and ask students to add all secondary leading-tone triads and seventh chords. The increasingly cluttered “orbits” will graphically illustrate the wide variety of harmonic choices that have suddenly become available. As an additional class activity, you might ask students each to create a path to the tonic, playing these at the piano to demonstrate the many possibilities. VOICE LEADING (page 255) Emphasize this fact: No new voice-leading principles govern secondary functions. Students simply need to remember how to view them. If they view them as being in the key of the tonicized chord, then they will use voice leading practices identical to the chords they’ve already part written–V, V7. viio, viio7, and viiø7. This extends even to the deceptive cadence, as shown in Example 1512d. Secondary Function and Chromatic Lines (page 258) Chromatic lines usually result from either chromatic passing tones or secondary function. Additional examples are Example 17-11 (m.15), Example 201 (m.6), Example 21-12 (m.3), and Example 22-2a (m.37). Harmonic Sequence and Secondary Function (page 260) As Examples 15-17a and b show, harmonic sequences, chromatic lines, and secondary function often run in packs. Because sequences (melodic or harmonic) are perhaps most often stepwise, chromatic lines are the inevitable result.
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Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1D on page 172: You might suggest to students that the “trick” here is to recognize that, for each of the three secondary functions, the same chord is tonicized—i.e., in 1, it’s a G (minor or major) triad. Therefore, the real question is: In what key is the g major (minor) triad VI? ii? V? Thinking of the exercise in this way should greatly decrease students’ response time. You might also turn the question around for a different set of keys. Ask, for example: “What would be this chord’s function in the key of F? (V/ii) In e? (V/III) In d? (V/iv),” and so on. • ASSIGNMENT 1E on page 173: Once voice leading has been covered in Section 3, you can return to this assignment and require students to voice the chords for SATB and resolve them. • ASSIGNMENT 2A on page 179: As with Assignment 1D on page 172, each of these chords tonicizes only one thing. For additional practice, you can augment the number of keys here, or rephrase the question for additional keys. (For 1: “In what key would this chord function as a viio7/ii? Of iv?” And so on.) • ASSIGNMENT 2C on page 180: This can be used for aural identification. Give the first chord as the tonic and have students identify the tonicization. ****************************************************************** SOLUTIONS TO ASSIGNMENTS 1. Secondary Dominants 1A. 1 V/ii
2 V/iv
3 V/V
4 V/III
6 V/iv
7 V/V
8 V/vi
9 V/ii
5 V/ii 10 V/vi
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1B. Voicings will vary. 1
2
3
6
7
1C. 1
6
4
8
2
7
5
3
8
9
10
4
5
9
10
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159
1D. 1
2
3
4
5
6
7
8
9
10
b
a
Gb
f
Eb
g
b
G
D
F
A
Eb
C
C
Bb
Ab
Gb
Db
Db
e
Ab
c
Gb
Eb
c
d
Ab
A
f
E
1E. 1
2
3
4
5
6
7
8
9
10
1F.
Only the empty slots are filled in for No. 1.
1
C: I
viio/IV IV
6
V/V viio /ii viio/V
V
6
V/vi viio/iii viio/vi vi V V 5 /IV
2
6 g: V 5
|
|
7
4
V V3
6
iv |
V5
I
6
| i |V5 /V | V |
4 6 6 6 7 7 Ab: I V 2 | I V 5 | I V vi V3 /V | V | viiø 3 V2 | I V /ii | ii V | I 4
3
i
6 V 5 /iv |
IV ii
6
4
4
1G. 1 A hemiola is produced in mm. 20-21, created by the melodic pattern, the bass, and the harmonic rhythm, all of which suggest a duple meter for the two measures.
Chapter 15
2
160
Chapter 15
161
3 The tonicizing tritone and its resolution occurs in the two uppermost notes in mm.189-190, 191-192, 192-193, 193-194, 194-195, 195-196, and 196-197.
2. Secondary Leading-Tone Chords 2A. 1
2
3
4
5
6
7
8
9
10
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162
2B. 1
2
6
7
3
4
8
9
5
10
2C. 7 7 7 1 Bb: I V /V V 2 G: I V /vi vi 3 D: I V /IV IV 4 Ab: I V 5 /ii ii 5 F:I vø /V V 6 a: I vo /iv iv 6
7
7
4
6
7
7 A: I viio /V V 8 c: I V2 /iv iv6 9 B: I V /IV IV 7
10 E: I V /ii ii
2D. 1 V/vi or viio7/vi
2 V/vi
6 viio7/vi or V/vi
7 V7/IV or viio6/ii
9 viio7/III
2E. 1
3 viio7/vi
4 viio7/vi
8 viiø7/V or viio7/iii
10 V7/IV
4
6
7
7
G: vi V 3 /V | I 4 V viio /vi vi | V /vi vi IV I | 6
7
viio I ii 65 viiø /V | V
5 viio6/iv
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2
163
6
4
6
6
6
6
C: I V 3 I V | I ii V V 4 | I viio 6/ii ii | I 6 V I | 5 2 4 7
7
7
4
4
6
7
V I V /ii ii | V /iii iii V3 /IV | IV IV ii 3 IV |I 4 V I || 2F. 1
Melodic form: a (m. 25) b (m. 29) b1 (m. 33) Varied repetition: • mm. 27–28 repeat mm. 25–26 with a new texture (melody doubled in thirds beneath a trill). • m. 30 is a sequence of m. 29 • m. 31 is a modified sequence of m. 29 • mm. 33–35 are a varied repetition of mm. 29–31, with dynamics reversed The final phrase is extended cadentially (mm. 36–38). Harmonic analysis:
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164
2
3. Voice Leading 3A. 1 2
6
7
3
4
8
9
5
10
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165
3B. Voicings will vary. The bass and harmonic analysis are shown below. 1
2
3
4
6
7
8
9
3C. 1
2
3
4
5
6
7
8
5
10
Chapter 15
3D.
166
Chapter 15
167
QUIZ FOR CHAPTER FIFTEEN
1.
Write the following chords on the single staff below:
2.
Resolve the chords to the root-position chord they tonicize and provide harmonic analysis.
3.
Realize the figured bass line for four voices and provide harmonic analysis.
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CHAPTER SIXTEEN Secondary Function II JAZZ AND POPULAR STYLES (pages 264-273) Example 16-1 (page 264) If you’re fortunate enough to have four male singers (two of whom are tenors!), this is an opportunity to have fun with the barbershop quartet style. We’d recommend assigning the passage to the group a couple classes in advance. Unless you’re truly lucky, the bass in mm.13-16 will need to be sung up an octave. Examples 16-2a and b (pages 265-266) Here’s another opportunity for fun if you have a piano major that can play these in class. It is difficult to overstate the importance of the tonicizing chord group (iiV) in jazz. You might ask students to practice the following exercises at the keyboard. The tonicized chord can be a pure triad. Optionally, the tonicized chords (the whole notes) can be omitted to produce a succession of ii7-V7 harmonies. 1
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169
2
Examples 16-9 a and b (page 272) The popularity of the I-bVII-IV pattern—repeated famously in the outchorus to the Lennon/McCartney song “Hey, Jude”—demands its mention. If II can be analyzed as V/V, might not bVII be analyzed as IV/IV? Whether this truly tonicizes IV (Is plagal tonicization possible?) is a question we’ve left open for discussion. We see no harm in thinking of it this way. MELODY HARMONIZATION (pages 273-276) Look for as many ways as possible to drive home the point that secondary dominants and leading-tone chords are handled in a manner identical to primary dominants and leading-tone chords. You might recap the points on pages 255256–the “do’s and don’ts” of part-writing secondary functions—do resolve, don’t double. Probably the most useful part-writing advice is given in No. 4: Part write as though the music were in the key of the tonicized chord. Following this “rule of thumb” practically assures satisfactory part writing of secondary functions. Suggestions for Additional Practice You can press into service some examples from other points in the text here. Ask students to create tonicizing chord groups in the following: • Hammond and Sager: “When I Need You” (Ex. 4-1) mm. 11–12: Fm - B mm. 15–16: Em - A • “I’ve Been Working on the Railroad” (Workbook Assignment 1E2) m.7: Em - A
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m.8: Am - D m.9: Am - D - B m.12: Fm Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1E on page 192: An easy way to get additional use out of this assignment is to change the Roman numeral beneath the line (i.e., the chord being tonicized). You can also play these chords for aural identification. • ASSIGNMENT 2C2 on page 197: You can ask students to compose sequential statements of the first two measures, up a step each time, and symbolize the tonicizing chord groups appropriately. ****************************************************************** SOLUTIONS TO PRACTICE ASSIGNMENTS 1. Jazz and Popular Styles 1A.
1B. The key for No. 10 was to be A, as shown below–not E. Apologies. 1
2
3
4
5
6
7
8
9
10
Chapter 16
1C. 1
2
171
7
7
7
7
mm. 1-2:
ii - V G
mm. 5-6:
ii - V F
mm. 9-10:
ii -
mm. 13-14
iiø - V g
mm. 15-16:
iiø - V a
m. 2:
iiø - V a
m. 3:
ii - V C
m. 4:
ii - V F
m. 5:
ii - V Bb
m. 6:
ii - V
m. 8:
ii - V C
7
Eb
7
V
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
Ab
7
Chapter 16
172
1D.
1E. 1
2
3
4
5
6
7
8
9
10
11
13
14
15
12
Chapter 16
173
1F. The following solutions are voiced in a pianistic manner. You can require your students to voice the chords or simply to place block chords on the lower staff. This depends on the ability level of your class. Alternatively, you may require jazz majors or students studying jazz to voice the chords while the other students place them in simple position.
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2. Melody Harmonization 2A. Student solutions–harmonization and part writing–will vary. A possible harmonization for each passage is given below. 1 4 6 6 6 7 6 6 4 F: I IV I vi | ii V 2 /V V viio /vi | vi vi ii V 5 /V | V V2 I | 6
6
ii I 4 V | I || 2 4 6 6 6 6 6 c: i| V | V 2 /iv | iv iv | V IV V | i i | V/V | V | 6
6
i i | iio
2B. 2C. 1
6
7
iio | viio /V V | i ||
Student solutions will vary. None are provided here.
Chapter 16
2
175
Chapter 16
176
QUIZ FOR CHAPTER SIXTEEN 1.
Part write the following tonicizing chord pairs:
2. Bracket and symbolize the tonicizing chord groups in the melody that follows. Fain and Hilliard: “Alice in Wonderland”
3. Add the bass line and give the Roman-numeral symbols for each tonicizing chord group.
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CHAPTER SEVENTEEN Modulation I Most students at this point in their studies know what modulation is. Sort of. The true-false “quiz” on page 277 encourages some careful thinking about it. Having been introduced to secondary function in the preceding chapters, students can correctly view modulations as greatly extended tonicizations. Only modulations to closely related keys are considered here. This is in keeping with the generally chronological format of the text, since Baroque music rarely moves beyond the circle of closely related tonalities. It is also pedagogically necessary since modulation in the nineteenth century involves harmonic complexities for which students are unprepared at this point. Two distinct kinds of modulation are treated in this chapter—modulation by common chord and chromatic modulation. MODULATION BY COMMON CHORD (pages 278-285) Two terms that are used widely as synonyms are pivot chord and common chord. I have introduced both terms here. Common chord is perhaps the clearest at this point, but pivot chord is ultimately more useful for three reasons: 1. The term pivot conveys the idea (accurate most of the time) that the tonal change “turns” on a specific chord. 2. In Chapter 23, enharmonic modulation will often be found to involve a pivot chord that is diatonic in the old key but enharmonically respelled in the new key. Although the chord is the pivotal point in the modulation, it is technically not a common chord. 3. Use of the term pivot permits expansion of the concept to include, if you like, a chromatic pivot—a chord that functions diatonically in one key and as a chromatic harmony of one sort or another in a new key. This happens quite regularly in music of the late eighteenth and the nineteenth centuries, and it helps students to understand the nature of such modulations if they are conditioned to look for the pivotal point and assess the chord’s dual harmonic function at that point. The imagery of the pivot chord as the “hinge” on the door that opens into the new tonality is useful, as is the concept of “crossing a tonal border.” Example 17-3 (page 282): The situation where a group of chords can be considered to be pivotal is not at all uncommon. In such cases, the modulation occurs very subtly, almost imperceptibly. You can establish your own criteria here for locating the precise point of modulation, although our preference is to allow some flexibility.
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Example 17-4 (page 283): Other ways of describing closely related keys are: 1) those differing by no more than one sharp or flat from the original key; 2) those having a tonic that is diatonic in the original key. CHROMATIC MODULATION (pages 286-293) All the chromatic modulations considered in this chapter involve closely related keys. Later, it will be shown that the distinction between pivot-chord modulations and chromatic modulations can become blurred. We’ve made a clear distinction between the two at this point in order to keep things simple. Of the two characteristics listed here, the first is the more important—a common chord is not present in a chromatic modulation. The Rule of Chromatics (page 286) This discussion assumes students are familiar with the solmization syllables introduced in Chapter One. “Ti” and “fa” are the stepping stones to the neighboring keys. Students seem to grasp this concept readily. Modulation or Tonicization? (page 291) The question of whether a new tonality has been established admits a certain amount of subjectivity. People tend to hear differently. Our attitude is this: The more difficult it is to decide whether a passage constitutes a modulation or a tonicization, the less critical the decision probably is. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1A on page 198: As an informal variant of this exercise, place a chord on the chalkboard and ask students to name its function in various keys. • ASSIGNMENT 1B on page 199: You can vary this drill by asking students to name the accidentals that would suggest a modulation to one or another closely related keys. • ASSIGNMENT 2C on page 204: Require students to recompose from the point of modulation, moving to a different closely related key in the same number of beats as the original passage. • ASSIGNMENT 2G on page 208: Ask students to add lead-sheet chord symbols above the music. ******************************************************************
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SOLUTIONS TO ASSIGNMENTS 1. Modulation by Common Chord 1A. 1 2 3 4 5 6 7 8 9 10
Chord: F c B g eb Bb d a E Ab
Keys: F: I d: III B: V C: IV c: i Eb: vi Ab: iii g: iv B: I g : III E: V F: IV g: i Bb: vi Eb: iii d: iv b b b b e:i G : vi C : iii b : iv Bb: I g: III Eb: V F: IV b a: iv d: i F: vi B : iii a: i C: vi F: iii e: iv E: I c: III A: V B: IV b b A:I f: III D:V Eb: IV
1B. 1 2 3 4 5 6 7 8 9 10
Key: Db e Bb c d E B Gb b Ab
Closely Related Keys: bb, Gb, eb, Ab, f G, b, D, a, C g, Eb, c, F, d E, g, B, f, A F, a, C, g, Bb c, A, g, B, g g, E, c, F, d eb, Cb, ab, Db, bb D, f, A, e, G f, Db, bb, Eb, c
Key Implied: f a g E Bb A f eb f Db
1C. Student realizations will vary. Roman numerals given here do not include the inversion superscripts, which are those of the figured bass. 1
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1D. 1 2 3
Modulation: m.6 Pivot chord: m.5 (Bb: vi F: ii) Modulation: m.5 Pivot chord: m.5 (bb: i Db: vi) Modulation: m.5 Pivot chord: m.4 (G: I C: V)
1E. 1
Solutions will vary. Likely pivots are shown below. pivot: m.2, beat 1 Bb: vi F: i pivot: m.1, beat 4 f: iv Ab: ii pivot: m.2, beat 1 D: ii b: iv (or D: viio b: iio) pivot: m.3, beats 1, 2 or 3 Ab: vi Eb: ii
2
3 4
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2. Chromatic Modulation 2A. 1 2 3 4 5
Pivot-chord modulation Chromatic modulation Pivot-chord modulation Pivot-chord modulation Chromatic modulation
D: V6
E: IV6
D: viio6 D: I6
b: iio6 b: VI6
2B. Part writing will vary. If you wish to achieve some uniformity in student solutions, you can give the starting pitch or chord shown in the solutions below. 1
2
3
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2C. 1
Chromatic modulation
2
Common Chord Modulation
3
Common Chord Modulation
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Solutions will vary. None are provided here.
2E. A likely harmonization of this melody follows:
2F. 1. 2. 3. 4. 5. 6.
The modulation occurs in m. 6 and is chromatic. An escape tone can be found in m. 1 and m. 5. An anticipation can be found in m. 7. A 4-3 suspension with ornamented resolution appears in m. 8. This is an 8-measure modulating period: a = mm.1-4, b = mm. 5-8. The Sarabande is a triple-meter walking dance (slow) with an accent on or elongation of beat two. Each of these characteristics is present. Harmonic analysis:
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2G. 1 Of course, some students may argue that there is no modulation here–only two tonicizations. And they’d be correct to do so. We’re asking them to consider these as modulations purely for the sake of the practice in identifying keys and common chords. In this regard, it would be just as possible to analyze the first tonicization as a modulation to A.
2
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QUIZ FOR CHAPTER SEVENTEEN 1. Name the principal key to which the following sets of keys would be closely related: a b c d e
c, Bb, g, Ab, f Principal key: ___ b, A, f, G, e Principal key: ___ , E, D, c A, b Principal key: ___ b b b b G , b , f, A , e Principal key: ___ Principal key: ___ a, C, g, F, Bb
2. Name the old and new keys in a modulation containing the given pivot chord. Assume the chord to be functioning as a pre-dominant in the new key. Give its function in both keys.
Old ___:___ New___:___
Old ___:___ New:___:___
Old ___:___ New:___:___
Old___:___ New___:___
Old___:___ New___:___
3. Given the key signature, name the key implied by the consistent appearance of the indicated accidentals. Key signature
Accidental(s):
Key implied:
3 flats 4 sharps 1 flat 2 sharps 1 sharp
Db E, Dn C Cn, D C
__________ __________ __________ __________ __________
4. Circle the pivot chord in the following modulating bass line and indicate by Roman numeral its dual harmonic analysis.
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PART SIX COUNTERPOINT (CHAPTERS 18–19) The history of Western music is the history of setting musical lines one against another, point against point (punctus contra punctum). Early on—in the Middle Ages and Renaissance—the melodic lines determined the harmonic structure. In the Baroque era and beyond, the melodic lines were conditioned by the harmonic structure. Part Six comprises two chapters. The first is an introduction to counterpoint that builds on the foundation laid in Chapter 10 (the outer-voice framework). It couples a greatly abbreviated species approach with a look at various styles and concludes with the Bach Two-Part Inventions. Chapter 19 focuses on the fugue. The goal here is not to create skilled contrapuntists— impossible in two chapters at any rate—but rather to instill an appreciation of the role of counterpoint in music and to provide some experience employing its basics.
Recommended time allocation: 6 weeks
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CHAPTER EIGHTEEN The Art of Countermelody THE BASICS OF TWO-VOICE COUNTERPOINT (pages 297-307) “America” lends itself well to the species counterpoint approach. Moreover, students can see the practical value of counterpoint as a technique for variation and arranging more readily with a familiar tune than they can with a more traditional Gregorian-chant “cantus firmus.” Essentials of Counterpoint (page 299) The eight principles cited here are the basis of tonal counterpoint regardless of the level at which it is written or studied. Example 18-3 (page 369) Two factors make b sound more truly contrapuntal than a. a involves no dissonance; and b distributes activity among the two lines more equally. Counterpoint in Jazz and Popular Styles (page 304) This part of the chapter is intended to sensitize students to the presence of counterpoint in today’s jazz and popular styles. You might have your class identify the eight principles at work in the examples. If your school has a jazz program, or at least a jazz ensemble, you might borrow a score from the director. Almost any such score will contain at least a two-part counterpoint—a countermelody against the melody—such as that shown in Example 18-10. J. S. BACH’S CHORALE HARMONIZATIONS (pages 308-309) Polyphonic or Homophonic? As with so many musical elements, texture is tinted with shades of gray. Musical works may fall anywhere along a continuum from intense polyphony to complete homophony. Once again, you can use Example 18-11 to demonstrate the added musical interest that counterpoint provides. As a review, you might have your class identify the various nonchord tones in Bach’s harmonization (b). BACH’S TWO-PART INVENTIONS (pages 310-315) A complete list of contrapuntal devices on page 312 would include retrograde and invertible counterpoint. Neither of these techniques nor diminution are found in Invention No. 1. However, Example 18-14 contains a perfect example of inverted counterpoint (mm.1-8). Retrograde is, in fact, a more
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artificial device Bach employed only rarely. It is found more commonly in the atonal and twelve-tone repertoire of the twentieth century. Some informal drill requiring students to illustrate the contrapuntal devices is beneficial prior to moving ahead with the analysis of Invention No. 6. ANALYSIS: INVENTION NO. 6 (pages 315-320) This invention, like quite a few in the set of fifteen, is basically a rounded binary structure with the first part coming to a cadence in the dominant and the second part returning to the tonic. In Chapter 25 (Binary and Ternary Forms), the CONCEPT CHECK on page 459 refers students back to this invention. Page 315: I often refer to invertible counterpoint as “mutual imitation”—voices imitating each other at the octave (or some other interval) simultaneously. Bach’s Two-Part Inventions are filled with this. Clear examples are: Invention No. 4, mm. 3–6 Invention No. 5, mm. 12–20 Invention No. 8, mm. 16–18 Invention No. 9, mm. 1–3 and 17–19 Invention No. 14, mm. 1–6 and 11–16 Not surprisingly, every one of the major-key inventions follows the general tonal plan of Invention No. 6: tonic– dominant– related key(s)–tonic. Implied Harmony (page 317) This is the most difficult part of the chapter for many students. The five guidelines given here, together with principles of functional harmony that students should already know, provide tangible techniques for the harmonic analysis of two-voice music. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1A on page 211: Before examining this assignment, you might use it for two-voice dictation or aural interval recognition. • ASSIGNMENT 1D on page 214: You might ask students to part write the resulting 1:1 counterpoint, adding alto and tenor. • ASSIGNMENT 2A on page 218: You can follow up this exercise by having your students provide harmonic analysis or asking them to rewrite the alto and tenor voices. • ASSIGNMENT 3A on page 221: Students might be asked to vary the motive in other ways as well. For example, you might ask students to use
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•
•
only the latter part of the motive—upright or inverted—in sequence, or to state an augmented form of the motive in inversion. ASSIGNMENT 3C on page 222: Invite students to the chalkboard to write the motive of mm. 1-2 in sequence at various intervals, in inversion, augmentation, retrograde and combinations of these prior to answering the given questions. ASSIGNMENT 3G on page 226: Have your students provide harmonic analysis of this invention. Where one voice or the other arpeggiates, the analysis will be fairly easy. At other points, have students focus on the intervals that are metrically accented as these are the most indicative of the implied harmonies. Suggested Aural Quiz
•
•
•
• •
10 two-chord successions, soprano and bass only: Students are to identify the soprano-bass counterpoint (contrary, oblique, similar, or parallel motion). 10 two-chord patterns (root-position to root-position): Give soprano and bass pitches and harmonic function for the first chord; ask students to provide this information for the second chord. Two-voice dictation, two to four measures of 1:1 counterpoint. (You might select from the choral melodies with figured bass contained in the Bach-Reimenschneider 371 Harmonized Chorales) Two-voice dictation, two to four measures of 2:1 counterpoint. A motive followed by several contrapuntal variations (sequence, inversion, inverted sequence, fragmentation, and so on): Students to identify the contrapuntal device employed. SOLUTIONS TO ASSIGNMENTS
1. Two-Voice Counterpoint 1A. Handel: Suites de Pieces pour le Clavecin, second collection (no. 3) 1. 2. 3.
Imperfect consonances: 23 Perfect consonances: 3 Dissonances: 1 On music The PT is the most common embellishing dissonance here as in most of Bach’s music.
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1B. Bach: English Suite no. 3, BWV 808 (Gavotte I) Although P4s are not identified as dissonance here, you may wish to discuss the ambivalent nature of this interval. We feel it is something better reserved for a class in counterpoint.
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1C.
Handel: Sonata for Flute and Continuo, op. 1, no. 5, HWV 363b (Bouree) 1. Oblique motion predominates, as is typically in largely 2:1 counterpoint. 2. 2:1 is the predominant species. 3. Imperfect consonances occur 16 times, perfect consonances occur 8 times, and dissonances occur 4 times. 4. On music. 5. On music. 6. The soprano is the more active voice.
1D. Students’ counterpoint will vary. Only the harmonic analysis is provided here. 6
4
6 6 6 7 6 6 6 b: i | v viio /v v v | iiø 5 - iiø - V - V 2 | V viio /V V V | I || V
1E. Other solutions are possible. 1
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2
1F. Student solutions will vary. A possible solution follows.
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1G. Students can have fun with this one, creating their own arrangements of the famous tune. The 4:1 counterpoint in mm.13-16 is Pachelbel’s own.
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2. J. S. Bach’s Chorale Harmonizations 2A. Bach’s harmonizations of these chorales are given here, with nonchord tones reinserted. 1 is No. 80 from the Bach-Reimenschneider 371 Harmonized Chorales. 1 J. S. Bach: “O Haupt voll Blut und Wunden”
2 J. S. Bach: Wachet auf, ruft uns die Stimme” 2 is No. 179 from the Bach-Reimenschneider 371 Harmonized Chorales.
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2B. Bach’s harmonizations of these chorales are given here, with nonchord tones reinserted. 1 J. S. Bach: “Jesu, deine tiefen Wunden”
2 J. S. Bach: “Befiehl du deine Wege” 2 is No. 367 from the Bach-Reimenschneider 371 Harmonized Chorales.
3. J. S. Bach’s Two-Part Inventions 3A. a: Inversion b: Transposition, Fragmentation, and Sequence c: Transposition d: Transposition and Augmentation e: Fragmentation and Sequence
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3B.
3C. 1. Sequence (tonal) 2. Measures 5-6 are an inverted counterpoint of mm. 3-4. 3. a. m.8 = fragmentation and augmentation b. m. 11 = fragmentation c. m. 15 = inversion, fragmentation and augmentation 4. 6 7 6 d: i | viio | i | viio 5 | i | iv | 7
7
7
7
7
7
F: ii | V | I | ii | viiø | I | vi | V | iii | 6
ii 5 V | I 3D. 1
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2
3
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4
3E. 1.
Imitation a fourth below: m.1 left hand
2.
Imitation a fourth above: m.4 right hand
3.
Imitation a fifth below: m.4 left hand
4.
Imitation an octave below: m.2 left hand
5.
Chain suspension (the resolution of one suspension becomes the preparation for the next): mm.5-6 right hand
6.
Modified sequence a fifth below: m.1 left hand
7.
Tonal sequence a second below: m.4 right hand
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3F.
3G. This invention is filled with sequence, imitation, melodic inversion, and invertible counterpoint. Almost every measure provides an example of one or more of these techniques. 1. Motive: m.1, beats 1-2 2. Inverted counterpoint: mm.6-8 (vs. mm.1-3), mm.9-11 3. Melodic inversion, imitation and sequence together in mm.4-5 Imitation; mm.12-13 Melodic inversion and sequence: mm.14-16 4. The invention remains basically in Bb throughout, with tonicizations of F (m.8), g (m.9), Eb (m. 10, 13, 14, and 17-18), and c (m.11), all closely related keys. 5. Canonic imitation: m.16-18 (right hand imitating left)
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CHAPTER NINETEEN The Fugue Fugal procedure is not as rigorous or consistent as the literature written about it might suggest. To be sure, practices coalesced at the hands of Bach to produce fugues that can serve as textbook models. However, this does not necessarily convey inferior status upon fugues by Bach, Handel, Pachelbel, Frescobaldi, Dave Brubeck, John Williams, and others that do not conform to the “textbook model” in all respects simply because they do not conform in all respects. The definition given at the beginning of this chapter allows for the diversity of fugal procedure. THE BASICS OF FUGUE (pages 322–330) Eight fugue subjects are embedded in this discussion. You might compare their features and then ask students to compile a list of common characteristics. The Workbook provides additional examples for study. Although the threefold model of exposition-development-recapitulation has some merit, it can create the impression that the fugue’s structural divisions reinforce this design—an impression at odds with the fundamental premise of the fugue, which actually shares more with rondo and ritornello forms, e.g., a theme that returns amid digressions. The term “development,” as used here, refers to a technique, not a section per se. We’ve preferred the term “ending” to “recapitulation,” which is perhaps most appropriate when a return of the subject (one statement at the very least) in the original key occurs near the end of a fugue in a very obvious way. Page 329 Of the traditional features described here, the counterexposition is perhaps the least critical and the most problematic. Fugue No. 1 of WTC I, for example, can be said to have a counterexposition because it does contain a second complete set of entries in the tonic-dominant axis and it commences immediately upon completion of the exposition. Yet, Bach neither initiates nor terminates this “counterexposition” with any significant event (e.g., a cadential punctuation) and, in fact, he places one of the fugue’s four cadences right in the middle of it (in m. 10). There is no suggestion that Bach attached any special significance to this passage or considered it a structural division. If you wish to keep things as simple as possible, don’t burden students with the concept of counterexposition. After all, it’s just a group of entries.
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Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT D on pages 233: This fugue is a virtual study in suspensions. No less than 33 suspensions occur in these 22 measures. All types are represented—2-3 (nine times), 9-8 (three times), 7-6 (twelve times), and the 4-3 (nine times). Ask your students to identify them. The fugue also contains a counterexposition, if you wish to raise this issue. • ASSIGNMENT E on page 235: This fugue contains a tonal answer that could just as well be real. Have your students make the change (C to D), and ask them how they would justify the D within the C-minor harmony (an appoggiatura). Ask them which answer (real or tonal) they prefer. Have students identify the two episodes that are most alike (mm. 9–10 and mm. 22–23). Have them compare the two, especially identifying the invertible counterpoint. Suggested Aural Quiz You might draw upon any two-voice counterpoint from the fugues presented in this chapter for two-voice dictation. The following passages are suggested as a few possible examples, ordered from easiest to most difficult: Example 19-6: mm. 26–28 (Alto and Bass) Example 19-7: mm.12–13 (Alto and Tenor) Assignment D on Workbook page 233: mm.16-19 (Tenor and Bass) SOLUTIONS TO ASSIGNMENTS A. 1 2 3 4 5
Tonal: First note answers the subject’s dominant with the tonic. Real Real Tonal: First note answers the subject’s dominant with the tonic. Tonal: First note answers the subject’s dominant with the tonic; the answer’s tail is a transposition to the subdominant (e.g., a fifth lower) rather than dominant and contains additional modifications at the end.
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B. The answer should be real. Countersubjects will vary. A possible solution follows.
C. 1
Johann Pachelbel: Fugue in C Major
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J. S. Bach: Fugue no. 17 from WTC, Book I
D.
J. S. Bach: Fugue no. 9 from WTC, Book II
1.
The exposition ends in m. 7 (or 9). A clear cadence follows the exposition at m. 9. What type of cadence is this? HC The order of entries is BTAS. The answer is real. A countersubject is not present. After the exposition, the next group entry occurs between m. 9 and m. 12. Stretto occurs at m. 9 and m. 16. The first episode of the fugue begins at m. 12 and ends at m. 16 with a PAC. The primary developmental technique employed in this episode is imitation. The excerpt ends in the key f. A third group entry appears in mm. 16. This group contains entries at: mm. 16, 17, 19, and 20. Compare mm. 16-17 and mm. 19-20, and describe Bach’s use of invertible counterpoint in these measures. The alto of mm.16-17 is transposed and placed in the bass in m. 19-20. The soprano is placed in the tenor. The tenor of mm. 16-17 is placed above these voices (slightly modified in mm. 19-20.
2. 3. 4. 5. 6. 7. 8. 9. 10.
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J. S. Bach: Fugue no. 2 from WTC I
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Tonal plan: c – Eb(m.11) – c (m.15) – g (m.16) c (m.20)
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F.
J. S. Bach: Fugue no. 11 from WTC I
1.
Exposition m. 1: S m. 4: A (tonal) m. 9: S End of exposition: m.13 CS: mm. 4–8 in alto, then following link (m. 9), mm.10–12 in soprano
2.
Subsequent appearances of subject: m. 17 in soprano m. 21 in alto m. 25 in bass m. 27 in alto (stretto) m. 36 in soprano m. 38 in alto (stretto) m. 40 in bass (stretto) m. 46 in bass m. 48 in alto (stretto) m. 50 in soprano (stretto) m. 64 in soprano (modified beginning)
3.
Cadences m. 36: Phrygian HC in D minor; m. 46: PAC in D minor; m. 56: PAC in G minor
4.
Tonal Plan F (m. 1) d (m. 33) g (m. 47) F (m. 56) Brief references to Bb are scattered among mm. 58–65. The exposition and counterexposition feature a vacillation between tonic and dominant.
5.
Contrapuntal techniques: In mm. 30–36, a fragment of the subject is stated and imitated sequentially in the upper voices. The bass contains an inverted fragment (m. 31) repeated sequentially in m. 33.
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QUIZ FOR CHAPTERS EIGHTEEN AND NINETEEN 1. Using Roman numerals, show the harmonic succession implied in the following passages.
2.
Answer the questions concerning the excerpt that follows.
1.
Cite a reason why this invention should not be mistaken for a fugue. _______________________________________________________
2.
Does this invention contain a countermotive? __________
3.
Locate by measure and voice (S, A, or B) all appearances of the motive. _______________________________________________________
4.
What fugue term applies to the motive as it appears in m. 2? __________
5.
To what tonality does this passage modulate? ______
6.
Name three contrapuntal techniques observable in mm. 4–5. _________________ _________________ __________________
7.
To what earlier passage does the one beginning on beat 3 of m. 6 and ending on beat 2 of m. 7 relate? Describe precisely the relationship. _________________________________________________________
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J. S. Bach: Three-Part Invention No. 8
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PART SEVEN ADVANCED CHROMATIC HARMONY (CHAPTERS 20–24)
Part Seven builds on the foundation for harmonic chromaticism laid in Part Five. The approach is roughly chronological, and this is reflected in a general way in the musical examples. Haydn, Mozart, Beethoven, Schubert and Brahms comprise the bulk of the music in Chapter Twenty (Mixing Modes); to these are added Schumann, Chopin, Verdi, and Gounod in Chapter Twenty-One (Altered PreDominants); Tchaikovsky and Mahler make their appearance in Chapter TwentyTwo (Other Chromatic Harmonies), which focuses on altered dominants and embellishing diminished seventh chords; Saint-Saëns and Liszt appear in Chapter Twenty-Three (Modulation II); and Puccini and Wagner weigh in in Chapter Twenty-Four (Harmonic Extensions and Chromatic Techniques), which introduces triadic extensions and linear chromatic harmonies. In keeping with the basic goals of this book, contemporary popular and jazz composers are represented in each of the chapters as well.
Recommended time allocation: 9 weeks
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CHAPTER TWENTY Mixing Modes We’ve combined the techniques associated with mode mixture into a single chapter. This includes change of mode, modal borrowing, and chromatic-third relationships. All were used during the eighteenth century (somewhat more commonly in the Classical half) and throughout the nineteenth century as well. All had the effect of expanding the tonal spectrum beyond closely related keys. In addition, chromatic-third relationships helped to initiate the breakdown of the dominant-tonic polarity so thoroughly engrained in the tonal structure of music in the Classical period. CHANGE OF MODE (pages 338-342) An interesting fact of certain harmonic developments is that devices and techniques initially employed at large structural levels are “compressed,” or employed in more local ways in subsequent historical periods. This is true of change of mode. In the Baroque era, it typically occurred only between movements, as in the dual gavottes (one in major, the other a recasting in the parallel minor) found in some suites. See, for example, Bach’s English Suite no. 6, BWV 811. That practice was continued by Classical composers in minuet-trio movements, where change of mode was often employed as a primary element of sectional contrast. An example is the third movement of Beethoven’s Piano Sonata op. 7. In addition, however, Classical composers often used change of mode between phrases, as Example 20-2 shows. Composers of the nineteenth century commonly employed the technique on a chord-to-chord basis, a technique termed “modal borrowing” to denote its more temporary and short-term character. Page 341: You might point out that enharmonic changes of mode normally occur in movements that are in keys with large numbers of flats or sharps. When anything less than five flats or sharps are involved, enharmonic respelling is seldom encountered. MODAL BORROWING (pages 342-350) Of the common borrowed harmonies shown in Example 20-4, the most common of all—and the earliest to be employed routinely—is the viio7. After this chord, the borrowed subdominants are the most common, practically guaranteed to cast a Romantic shadow on any passage. Students might ask how many borrowed harmonies a passage can contain before it becomes a mode change. As with modulation and tonicization, the answer
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may not be clear-cut, and it may not even be that important. The difference is one of degree, not kind. Establish your own guidelines if you like. CHROMATIC-THIRD RELATIONSHIPS (pages 351-359) This part of the chapter concerns not harmonies themselves but the relationship between harmonies. As with borrowed harmonies, the most common chromatic-third relationships (shown in Example 20-13) occur in major-key settings. Two of the chords (bVI and bIII) might function as borrowed harmonies, while two (VI and III) might function as secondary dominants. Here we are noting two things—the chord’s function and its root relationship with the preceding or following harmony. As with change of mode, the history of chromatic-third relationships appears to be one of continuing compression—from movements (Haydn) to sections within movements (Beethoven) to individual chords (Brahms, Wagner, and others). You might mention that Beethoven favored this relationship in his major-key sonata-form movements, as did Schubert. A particularly well-known example is the second movement of Beethoven’s Symphony no. 5 (see Example 23-16 on page 410). Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1A on page 241: You might invite students to the chalkboard to voice and resolve these chords appropriately for additional practice similar to Assignment B. • ASSIGNMENT 2A on page 249: After completing this exercise, you might have students regard the second triad of each pair as the tonic, adding the appropriate Roman numeral to the first. • ASSIGNMENT 2E on page 251: Ask students to locate an opportunity in No. 1 to substitute a borrowed pre-dominant (m.7). Supplementary Examples The following examples of change of mode are appropriate for study at this time. All are found in Analytical Anthology of Music, Second Edition, by Ralph Turek. C.P.E. Bach: Prussian Sonata no. 1, m. 18 Haydn: Piano Sonata H. XVI:37 I, m. 29 (this passage also contains a Neapolitan sixth chord resolving by way of viio7/V); III, m. 21. Beethoven: Piano Sonata op. 10, no. 1, m. 73 Beethoven: Piano Sonata op. 53, m. 200 Beethoven: Symphony no. 7 in A Major, op. 92, m. 102 Suggested Aural Quiz
Chapter 20
•
•
•
214
Play a major tonic triad, followed by five three-chord successions, such as: I - iv - V VI - iv - I iiø7 - V - I IV - viio7 - I ii6 - iio6 - V Ask students to identify the borrowed harmony. (Optional: Ask students to identify the entire succession.) Ten examples: Have students number their papers from one to ten. Play a major tonic triad followed by one of the following: i; iii; bIII; III; vi; bVI; VI. Students are to identify the second chord. Chromatic-third relationships are present in a number of examples in the ensuing chapters. You might play some of these and ask students to identify the type of relationship. For example, in Haydn’s Piano Trio H. XV:18 (first movement) on page 285: Play mm.165–168, which shift from F to A.
****************************************************************** SOLUTIONS TO ASSIGNMENTS 1. Change of Mode and Modal Borrowing 1A.
1 2 3 4 5 6 7 8
Key: C Key: F B: Key: Bb Eb: Key: Ab Key: Bb: Key: C Key: A D: Key: D
Chord: Chord: Chord: Chord: Chord: Chord: Chord: Chord: Chord: Chord: Chord:
iio iv i iv i iio 7 iiø iio bVI bIII 7 viio
Chapter 20
9 10 11 12 13 14 15
215
Key: Eb Ab: Key: D Key: F Key: G C Key: C Key: A Key: D: G:
Chord: Chord: Chord: Chord: Chord: Chord: Chord: Chord: Chord: Chord:
iv i iio 7 iiø iv i 7 iiø 7 viio bVI bIII
1B. No. 3 in this voicing presents part-writing problems when resolving to V or iv, necessitating the resolution to iiø7. 1
2
3
4
5
6
7
8
Chapter 20
1C. 1
2
3
4
5
6
7
8
9
10
216
Chapter 20
1D. 1
217
Students’ part writing will vary. A sample solution for No. 1 follows.
6
D: 2
I viio 5 I I
6
6
6
7
7
6
| IV I iv iio6 | I4 V viio /vi vi | iiø 5 V I ||
Harmonic analysis for No. 2 follows. Ab:
1E.
1
2
I | iv iiø
4 3
6 4
| I
7
6
viio /vi vi | ii V | I ||
Solutions will vary. Sample solutions follow. In all cases, the major tonic has been preserved in order to maintain the general major-mode feeling. Some borrowed harmonies create voice-leading problems (for example the augmented second between the leading tone and minor sixth degree that necessitates changing the voicing of the chords or even the soprano pitch).
Chapter 20
3
4
218
The final chord must be changed on repetition to avoid an augmented second in the soprano.
Using the bVI in m.3 would create an augmented second in the alto.
1F. 1
2
This is a mistake. No. 1 was inserted here again instead of the correct exercise. No.1 cannot be harmonized with a borrowed submediant without creating parallel fifths and octaves between bVI and V. The correct exercise appears below.
Chapter 20
219
3
1G. 1 4 4 6 6 6 6 6 G: V 2 | I | V 2 | g: i | iv V/III | III VI | iio V5 | I v | X | 7
7
6
4
4
6
V | V | I | I V V3 | I | I V V3 | I 2 Ab: 3 F:
This passage affords the opportunity to revisit the tonicizing chord group introduced on page 267 4
6
6
6
7
4
7
6
6
7
I | V 3 | I V 5 | I | iio 4 | V | iio 4 I 4 V | I ii 4
7
6
I X V /ii | ii ii 2 iio v 2 | iii
2. Chromatic-Third Relationships 2A. 1 VI 2B. 1
2 III
3 bVI 4 III 2
5 bIII 3
6 VI 7 VI 8 bVI 4
9 III 10 VI
5
Chapter 20
220
2C. When part writing a root-position bIII or bVI, doubling the root trumps the normal caution not to double an altered tone. Remind students again that chromaticthird relationships typically occur in a context where traditional part writing rules are somewhat relaxed. 1
2
3
4
5
6
7
8
9
10
2D.
1
2E. 1
Although students are free to choose their beginning soprano pitch, the individual voices should move in the manner shown below. 2
3
4
5
Students’ solutions will vary. Harmonic analysis follows.
Chapter 20
G:
221
I V4 I | bIII i | iv V | I | I V V 2 | III vi | ii V | I ||| (V/vi) 6 6
4
6
6
2
2F.
Schubert: “Der Müller und der Bach”
The chromatic-third relationship is shown in boldface. Bb: V7/ii | ii | V7 | I | VI 6 G: I
6
2G. 1 1. 2.
6
| ii | V7 | I ||
Brahms: Piano Sonata, op. 1 (Fourth Movement) Four tonalities: F (m.172), A (m.177), D (m.182), d (m.184) F returns in m. 186. The third-relationships between the various tonalities in this passage can be expressed relative to the original key or the new key, as follows: Relationship between m. 176 and m. 177 F: I - III A: bVI - I Relationship between m. 176 and m. 182 F: I - VI D: I - bIII Relationship between m. 176 and m. 184
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222
F: I d: i
-
vi III
3.
Mode mixture: m. 184 (Change of mode from D to d)
2
Wagner: “Elsas Traum” from Lohengrin (Act One, Scene II)
Harmonic analysis:
Ab: I bVI | bIII 6 7 D: VI vi | I 4 V
| I
i
6
7
6
F: vi | I 4 V | I iv 5 6 6 7 Ab: ii 5 | I 4 V | I
1.
2.
3. 4.
The phrase begins in Ab and ends in D, passing through the chromatic-third related Cb (enharmonically B) in m. 41. The enharmonic change of mode from Cb (B) to b on beat 4 of this measure creates the vi in D major. The tonalities that begin and end the phrase display the most remote possible tonal relationship (the tritone). Two processes occur: an enharmonic change of mode (b is enharmonically cb), and modulation (b functions as vi D). This is a modulation through change of mode. In m. 43, another modulation by change of mode takes place, though without the enharmonic respelling. In m. 45, Wagner uses the borrowed iv in F as a pivot (ii) to Ab.
2H. Leslie Bricusse and Anthony Newly: “Goldfinger” F: I bVI | I bVI | ii V | IV V | V/iii IV 7
2I.
Rossini: “Domine Deus”
1.
Identify two chords that are in chromatic-third relationship. Indicated in boldface below. Identify a change of mode. Measure 96 Locate a modulation and the common chord if one is present. In red below.
2. 3.
Chapter 20
4.
5.
223
Diagram the melodic phrase/period structure, identifying the phrase relationships in the manner described in Chapter 9. a (mm.88-91) b (mm.92-95) a’ (mm.96-99) b’ (mm. 100-103) No period Compare the music in the first eight measures with that in the last eight measures. Measures 96-103 are practically a repetition of mm. 88-96 in the parallel minor. Both phrases end with half cadences.
6.
Using Roman numerals, symbolize the relationship between the opening key and the key to which the passage modulates. I – bVI
7.
Provide complete harmonic analysis. 7
6
6
D: I V | I | V 5 I | V V 5 | I 4 6 b: III V 3 | I iio6 | I 4 V |
4
D: V 2 | 7
6
6
d: i V | i | V 5 i | V V 5 | i 4 6 6 7 Bb: iii V 3 | I ii | I 4 V | A: viio4/2
Chapter 20
224
QUIZ FOR CHAPTER TWENTY 1.
Illustrate in the simplest position, the five borrowed harmonies employing the lowered sixth scale degree in the requested keys. Provide the Roman-numeral analysis symbol beneath each chord.
2.
Realize the following two-chord figured basses and provide harmonic analysis. Circle the analysis symbol of the chord that functions as a borrowed harmony.
Chapter 20
225
3.
Harmonize the following soprano pitches in such a way that one of the common chromatic-third relationships discussed in this chapter results. Then part write these harmonies for SATB and provide harmonic analysis.
4.
Provide a complete harmonic analysis of the following excerpt, including identification of all modal borrowings and chromatic-third relationships. (Your choice of excerpt here)
Chapter 21
226
CHAPTER TWENTY-ONE Altered Pre-Dominants The Neapolitan sixth and augmented sixth chords are presented together in a single chapter to emphasize their functional similarity as altered pre-dominants. Then too, there is really no need to devote a separate chapter to the Neapolitan sixth chord. In both of these types of altered pre-dominant, no new voice-leading principles are involved. The basic rules of doubling apply and the extra tendency tone (the altered tone) is resolved in the manner of all tendency tones. This point bears repeating often. We’ve chosen to present these harmonies initially in the context of their earliest and most typical use. For this reason, the musical examples are in minor keys. You should feel free to discuss their use in major keys also at this point. However, we have reserved this for a later time. THE NEAPOLITAN SIXTH CHORD (pages 361-367) Early examples—always in first inversion—indicate that composers initially regarded the Neapolitan as a chromatic enhancement of the pre-dominantto-dominant motion rather than as a major triad on a chromatically lowered root. The similarities in function and treatment of the N6 and its diatonic relatives, the iio6 and the iv, shown in Example 21-2 reinforce this idea. Example 21-2 You can turn this into a useful keyboard exercise by playing the examples in this order: b, a, c. Leave off the resolution to V until after the third chord (c) is played. In other words, play iio6 - N6 - iv - V. This effectively demonstrates the difference and kinship in sound among the three pre-dominants while showing clearly their voice-leading similarities. If students understand the ramifications of this, they should be able to use the N6 in a stylistically appropriate way with little difficulty. Example 21-3 makes the same points in a well-known passage. Example 21-4 For some reason, students seem to have trouble remembering the unique melodic interval (the o3) that characterizes the typical resolution of the N6. We’ve had success giving it a colorful name, such as the “DLT” (“double leading tone”). In this edition, we’ve continued to use the sandwich analogy, substituting the trendier burrito for the BLT. Regarding the inward collapse of the o3 to the tonic, the mental image of a slab of Neapolitan ice cream is helpful, the tonic the vanilla middle with the outer stripes the half steps above and below it.
Chapter 21
227
Example 21-5a Perhaps Chopin’s penchant for running circular fifth patterns (cf. Mazurka op. posth. 67, no. 2 on Workbook page 306) led to his employment of the Neapolitan as a full-fledged member of the circle of fifths here and elsewhere: VI - N - V - i. Although the root-position Neapolitan was a somewhat later development, note that the next example (Example 21-5b), composed after Chopin was dead, remained the more traditional usage. Example 21-8 Almost everyone who hears this piece recognizes it. Almost no one knows the name or composer. AUGMENTED SIXTH CHORDS (pages 367-377) Discussion of these chords begins with musical examples. Example 21-12, with the melodic reduction that follows, clearly demonstrates the linear origin of the chord. Once students understand that the double tendency tone to the dominant that forms the augmented sixth interval is present in all three of the chords and that the tonic is also present in each, constructing and identifying them are much easier tasks. We’ve had success with this 4-step procedure: 1. Identify the dominant of the key. 2. Write the minor second above it in the bass and the minor second below it in an upper voice. A bit of double talk here actually seems to help: “Half step above below and half step below above.” It sounds confusing, but students remember it for just that reason. 3. Add the tonic in another voice. 4. The rest is “as easy as 1-2-3.” (For the It+6, double scale degree 1; for the Fr+6, add scale degree 2; for the Gr+6, add scale degree 3.) Again, you can stress that no new part-writing procedures are necessary. Altered tones are not doubled and they resolve in the direction of their inflection—as always. The doubly augmented fourth chord, along with the enharmonic use of the Gr+6 as V7/N, are reserved for later. This has the double advantage of considering these applications in the proper chronological sequence (e.g., they are more typical of nineteenth-century usage) and keeping the initial presentation of the topic as simple and straightforward as possible. Example 21-20 The passages in this example show all three augmented sixth chords and reinforce several points made in the chapter.
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228
Example 21-21 Thelonius Monk’s classic ballad “Round Midnight” succinctly shows the single pitch difference among the three chords. As the melody note drops from 3ˆ to 2ˆ to 1ˆ , the chord changes from German to French to Italian. (Easy as 3-2-1.) It also shows that the augmented sixth interval does not expand to the octave when 7 the chord of resolution is a V . Suggested Additional Use of Drills and Assignments (Workbook): • ASSIGNMENT 1B on page 257: For additional part-writing practice, students can be asked to part write a resolution for each of these N6 chords (either to V, to i - V, or to viio7/V - V). • ASSIGNMENT 2A on page 264: Students need considerable practice in spelling and, especially, part writing augmented sixth chords. You may wish to have students voice each of these chords for SATB and part write their resolutions. • ASSIGNMENT 2C on page 265: You can specify the chord of resolution here—V, V7, i, or perhaps even viio7/V. Suggested Aural Quiz •
10 chords: Play a tonic triad, then play one of the altered pre-dominants followed by a chord of resolution. Students are to identify the type of altered pre-dominant. (Option: Students can be required to identify the chord of resolution as well.) • 10 harmonic successions of five or six chords each: Students are to identify (by number, i.e., “Chord 1,” “Chord 2,” and so on) the altered predominant. 0Possible harmonic successions are i - VI - iio6 - Fr6 - V, or i V6 - i - iv - N6 - viio7/V - V, and so on. ****************************************************************** SOLUTIONS TO ASSIGNMENTS 1. The Neapolitan Sixth Chord 1A. 1
2
3
4
5
6
7
8
9
10
Chapter 21
229
1B. 1 X
2 g
3 a
4 X
6 bb
5 e
7 eb
8 X
9 b 10 f
1C. 1
2
3
4
6
7
8
9
1
2
3
5
10
1D.
6
7
8
4
5
9
10
Chapter 21
230
1E. 1
2
3
1F.
Part writing will vary. Harmonic analysis for Nos. 1 and 2 follows.
1 Measure 1 contains an error: The figured bass should read: “I 6+ 6.” Please see Errata. 6 6
6
6
6
7
6
6
a:
I V i | N V | V /iv V /iv | iv I 4 iv | viio 5/V V
2 f:
i iv V V 2 | i
6
4
6
4
VI V V 2 | III III
6
6
6
6
7
6
| I ||
viio 5 i N | viio /V V | i ||
Chapter 21
1G. 1 f:
231
4
6
6
6
7
i viio 3 /iv | iv | N viio /V | i 4 V |
2 Bb:
V /ii | ii | V
f:
i | VI | iv | N | V | VI | V 5 /V v iiø | V |
4 b:
V i 4 V i 4 | viio 3 i | viio 3 i | N | viio /V i 4 |
7
7
| I | 6 7 g: III | i | N | viio /V | V |
3 Be sure to caution students regarding the transposition of the Bb clarinet part (sounding a major second lower than written). 6
6
6
6
6
7
4
6
4
6
7
6
7
6
Chapter 21
1H.
232
Chapter 21
233
2. Augmented Sixth Chords 2A. 1 Fr+6 6 It+6
2 It+6 7 Gr+6
3 Fr+6 8 Fr+6
4 ++4 9 Fr+6
5 It+6 10 Gr+6
2B. 1
2
3
4
5
6
7
8
9
10
2C. You may wish to give this helpful hint to students: Resolve the bass first– in augmented sixth chords, downward by half step and in Neapolitan sixth chords, upward by step. Next, resolve the altered tone (in the direction of its inflection). 1 2 3 4 5
6
7
8
9
10
Chapter 21
234
2D. 1
2
3
5
6
7
4
8
2E. A goal of this assignment is to sensitize students to the commonalities in these chords and also to the subtle differences in sound and appearance of the augmented sixth chords. 1
3
2
4
Chapter 21
2F. 1
2
3
4
235
Chapter 21
236
2G. 1
This is practically all tonic and dominant, with an It+6 at m. 20.
2
6 6 6 6 a: i iv 4 i | i iv 4 i | C: I IV 4 I | I IV 4 I | a: V
d: V
6 6 VI 5 iiø 5 | (G#7)
6 7 iiø 5 viio | a: iv
Fr+
6
6 7 iiø 5 viio |
(D9) V
The chords of beats 1 and 3 of m. 26 are auxiliary to those of beats 2 and 4. Lead sheet symbols are perhaps more meaningful here than Roman numerals. 3
6
6
E: I I I
6
7
ii
| V V | I I
--- IV | V
V* viio
6
6
7
V /V | V V /V V 6
6
| I vi It +
| Gr+
|
--- V
|
* The lower notes here are double passing tones. 4
F:
V
|
V
|
I
|
|
V
|
I
|
6
I4
I
|
Gr+6 |
Chapter 21
237
QUIZ FOR CHAPTER TWENTY-ONE 1.
Identify each of the following as a Neapolitan sixth chord or an augmented sixth chord (specify Italian, French or German), and indicate the key in which each would function as such.
2.
Write and resolve appropriately the indicated chords:
3.
In the following melody, indicate which of the harmonies listed are possible at the designated points: N6; Fr+6; Gr+6; V7/V; None. Where more than one of the harmonies is possible, list all of them.
Chapter 22
238
CHAPTER TWENTY-TWO Other Chromatic Harmonies ALTERED DOMINANTS (pages 378-384) Just as all the most common borrowed harmonies share a common altered tone (the minor sixth scale degree), all the altered dominants involve the same altered scale degree—2, the chord fifth—which is either raised or lowered chromatically. Very occasionally, other alterations of the dominant appear, such as the vø7, which has modal implications, but these are too infrequent to warrant “muddying the waters.” Once again, the “DO-DON’T rule” applies: don’t double the altered tone, but do resolve it. Example 22-1 illustrates it concisely. As Examples 22-2 a and b show, the chord usually emerges from an unaltered dominant that is already present. Example 22-3 (page 381): The second-inversion altered dominant seventh is one key signature away from a French sixth. You can point out that the bass in the altered dominant seventh is an altered tone (the chord fifth) where it is a diatonic tone in the French sixth chord. Important point: The voice leading is identical in both. If you prefer, you can require your students to indicate inversion in the altered dominant chord symbol. The problem is that the symbol then becomes cumbersome; what’s more, the defining feature of these chords, i.e., the altered chord fifth, gets lost in the symbol. EMBELLISHING DIMINISHED SEVENTH CHORDS (pages 384-391) After all the time spent stressing the leading-tone function of the diminished seventh chord, students may be distressed to learn that, in certain cases, it does not function in this way (as viio7). Like the functional diminished seventh chord, stepwise motion prevails in most of the voices. There the similarity ends. In one case, however, an embellishing diminished seventh chord might also be viewed in a functional way—where it resolves to a tonic six-four chord. For example:
Chapter 22
239
a
b
6 4 is better analyzed: iio7 C:
I
6 4 V
viio7/V
I
V
In a, the symbol iio7 exists only to reflect the resolution of D upward to E in the I 64 . If the cadential six-four chord is removed, the resolution will be directly to V. The D should now be spelled Eb to reflect its downward resolution to D. The spelling in b—F-A-C-Eb— now reflects the chord’s harmonic function, where the spelling in a reflects the chord’s voice-leading. The key to recognizing an embellishing diminished seventh chord is its resolution. You can tell your students that a quick way to identify one is to look for a common tone between the diminished seventh chord and the resolution chord. If a common tone is present, then the chord is probably embellishing. You might also stress that an embellishing diminished seventh chord in root position will always resolve to a first-inversion tonic or dominant because the raised root in the bass must resolve upward. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1B on page 271: Students can be asked to voice these chords and part write their likely resolutions. • ASSIGNMENT 1C on page 272: Play these chords (in random order, with or without their resolutions) and ask students to determine whether the chord contains a raised or lowered fifth. • ASSIGNMENT 2A on page 276: Ask students which of the embellishing diminished seventh chords might also be a functional diminished seventh chord (viio7/x) in the given key. Have them assign its Roman-numeral symbol. (Nos. 1, 3, 5, 7, 9, and 10—all iio7 chords—can so function, as viio7/iii. The other chords—all embellishing the dominant—can only tonicize the leading tone because the chord root is the raised sixth degree of the scale.) ******************************************************************
Chapter 22
240
SOLUTIONS TO WORKBOOK ASSIGNMENTS 1. Altered Dominants 1A. 7 1 Ab: V + 6 F: V+
2 Eb: V-5 7
7 Gb: V + 7
5 G: Vb5
7
3 D: V+
4 E: V -5
7
8 D: V-5
9 Bb: V-5
10 Db: V +
7
Note: Inversions are not shown in these chord symbols. (See comment on page 379.) 1B. 1
2
6
7
1C. 1
5
3
4
8
2
6
5
9
10
3
4
7
8
Chapter 22
241
1D. 1
2
6
3
4
7
8
5
9
10
1E. 2
1
5
3
6
4
7
8
1F. For No. 3, both lead-sheet and Roman numeral symbols are given. 1
6
6
6
7
6
7
e: iv | iio | i | iv | V /V | i | V-5 | I |
Chapter 22
242
2
A: I V+ I | iii 4 | I V+ I | iii | I V+ I | c: VI i iiø 5 |V | I |
3
Db Fm7 Bbm7/F | Ebm7 Ab7/Gb | Db/F Db+/F | Gb Eo7/G | DbMaj7/Ab
6
I
iii
7
4
vi 3
6
7
| ii
4
V2
6
6
| I
6
7
7
6
V+/IV | IV viio /V | I 4
1G.
Chopin: Grand Valse Brillante, op. 34, no. 2
1.
Measures 53–68 can be described either as a double period (a + a ) or a 1 parallel double period (a + b a + c) depending on whether you regard the phrases as four-measure or eight-measure units. The melodic flourish in mm. 66–67, through its contour, suggests a hemiola grouping of three 2-beat patterns (four eighth-notes each). The left hand, silent in m. 66, resumes the meter’s normal three-beat grouping in m. 67. A change of mode takes place at m. 69. Measure 64 contains a bVI. A Neapolitan sixth chord appears in m. 70 and m. 75. A viio7/vi appears in m. 55. A V7/vi appears in m. 58. A V 7 appears in m. 60.
1
2.
3. 4. 5.
+
2. Embellishing Diminished Seventh Chords 2A. 1
6
Solutions might vary depending on the voice in which students choose to place the common tone. 2 3 4 5
7
8
9
10
Chapter 22
243
2B. 1
2
3
*
4
5
*Soprano and bass can be exchanged here, producing a vio 2 . 4
2C.
1
4
Part writing may vary. The best process is perhaps to write the bass of the embellished chord first since that is given, then to follow the method described on p. 387 for constructing the chord preceding it (the embo7). Depending on the identity and inversion of the embellished chord, one of the voices might not be able to move into it by step. However, in each case, the altered tones should do so (resolving in the direction of their inflection). 2 3
5
6
Chapter 22
2D. 1
244
Probable solutions follow.
2
3
2E.
This assignment places selected members of the I or V in the soprano and bass to provide an opportunity to resolve the diminished seventh chords in a variety of voicings. Stress that the given chord is either the tonic or dominant. You can require that students retain the same voicing for both given chords or permit them to change the voicing.
Chapter 22
245
1
2
3
4
5
6
7
8
9
10
2F.
Analysis will vary depending on what are viewed as NCTs. No solutions are provided here.
Chapter 22
246
QUIZ FOR CHAPTER TWENTY-TWO 1.
Place the symbol that correctly identifies each altered dominant in the top blank. In the bottom blank, identify the key in which the chord so functions.
2.
Add the key signature. Then part write in four voices and resolve the indicated altered dominants in the most appropriate manner.
Chapter 22
3.
Place Roman-numeral symbols in the blanks provided. Brahms: Violin Sonata op. 100 (first movement)
247
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CHAPTER TWENTY-THREE Modulation II Modulation is a topic too big to be covered adequately in a single chapter. That’s why the introduction in Chapter Seventeen is followed here by a more complete discussion. Students might take comfort in knowing at the outset that this chapter merely delves further into the two types of modulation they already know—common-chord and chromatic modulations. THE THREE Cs: RECOGNIZING THE SIGNALS (pages 393–396) We’ve extended the analogy of the tonal border introduced in Chapter Seventeen to include the signposts that announce a new tonal region—chromatics, clue chords, and cadences. “The three Cs,” as they’re called in this text, provide students with three tangibles for identifying tonalities. It’s a musical fact that most pieces move initially to the sharp (or less flat) side of the tonic. Hence the particular importance of determining which chromatically raised pitch is acting as the new leading tone (“ti”). You may wish to reinforce the points on page 393 with immediate drill. If so, go at this time to Assignment 1A on Workbook page 281. It’s worth pointing out that, where several different accidentals appear, some may represent only tonicizations or chromatic nonchord tones within the new tonality. Again, the more consistent the accidental, the more likely it is part of a new key. In the event that accidentals don’t give a clear picture, students should look for clue chords, the most important being the Mm7, which has the singular function of dominant in tonal music. Students should be adept by now at recognizing dominant seventh chords. However, you might do some reinforcing drill asking students to spell or recognize these chords and the keys they imply. Consistent accidentals and clue chords are often sufficient to identify a key. If not, have students look for cadences. In most cases, these will reinforce the evidence provided by accidentals and clue chords. You might spend time teaching students how to recognize cadences, which are often more obvious aurally than visually. In multi-part music, cadences are often overlapped by new phrase beginnings. Students should examine the individual musical lines for signs of a cadence. As with accidentals, final cadence chords are good clues to the key, usually being either the tonic or the dominant. BACK TO THE TONAL BORDER (pages 396–403) We’ve given the three most common situations at “the tonal border,” ordered from simple to complex. Although simplistic, the diagrams give students a handhold in this murky region of harmonic analysis. The bulk of this section
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guides students step-by-step through examples containing chromatic modulations, again ordered from simple to complex. In the process the concepts of chromatic pivots (page 398) and enharmonic pivots (page 403) are introduced. THE SECRET LIVES OF CHORDS (pages 404–413) This section treats the two most common agents of enharmonic modulation—the German sixth chord and the diminished seventh chord. Example 23-8 on page 404: This demonstrates the enharmonic potential of the German sixth as succinctly as possible. We recommend pausing right here for some drill respelling dominant sevenths as German sixths and vice versa. You can give students the chord and ask them to respell it, or you can give a key and have students spell both versions of the chord. You can then ask students to resolve both versions. You might lead into the discussion of Example 23-9 by asking students about the dual spelling of the note—D to Eb—in the voice part in mm. 30–31. The doubly augmented fourth chord in this measure (spelled enharmonically as a V7 in E minor) resolves in typical fashion to a cadential six-four chord in Eb (m. 31). D (=Eb) is the enharmonic common tone. Example 23-10 on page 406: Rapid changes in tonal orientation produce a particularly jarring effect in this passage from Chopin’s Fantasy in F minor. The cadential six-four chord in Ab (m. 19) is followed directly with a modulation to F minor on beat 2. Example 23-11 on page 407: You might follow this example with some immediate drill, asking students to respell (and resolve) a variety of diminished seventh chords enharmonically in various keys. You might voice these chords for students or require them to do so. ******************************************************************
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SOLUTIONS TO ASSIGNMENTS 1. Recognizing Signals 1A. 1 Eb 2 a 3 c 4 c 5 C b 10 c 7 G 8 D 9 f
1B. 1
2
3
6 D (The flat sign should be b.)
Beginning tonality: Eb Ending tonality: f Conflicting accidentals signal a minor key, the chromatically raised pitch the new leading tone. Beginning tonality: b Ending tonality: D Cancellation of the A leading tone and the chromatically lowered C (the new “fa”), along with the half cadence on the dominant D, suggest G. Beginning tonality: Db Ending tonality: Bb Of the 3 cancelled accidentals, the A is most remote from the original key and thus the new leading tone.
1C. You may wish to apply voice-leading principles in a more general way at this point. More distant modulations, more nonharmonicism in the melodic lines, and wider melodic leaps make this increasingly necessary. 1
2
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2. Back to the Tonal Border 2A. 1
Solutions will vary depending on the initial voicing selected. Analysis follows. Modulation: Chromatic pivot 7
6
d: i iiø viio | i
6
6
V5 /iv IV | e:
2
6
7
III | viø V 5 i | V | i ||
Modulation: Enharmonic pivot
Eb: I I 2 vi viio /vi | vi viiø /V V viio /vi | vi V2 /IV IV iv | 6 B: vi | IV V I || 4
3
7
7
6
6
Modulation: Modulation through change of mode 6
6
A: I vi ii V | I iv C: 2B.
4
7
7
6
ii V I | IV viiø /V I 4 V | I ||
Haydn: Piano Trio, H. XV:18 (first movement) 1. This passage begins in A minor. It modulates first to F major at m. 164. The new accidentals—Gn and Bb—represent chromatically lowered tones, and the more remote of these from the previous key of A minor is Bb, the new “fa.” In m. 168, all pitches diatonic in the original key of A return. 2. The only cadence in this passage is at the end. In m. 168, a cadential six-four chord precedes a dominant, which resolves to the tonic in m. 169. 7 7 3. The “clue chords” in this passage are the V of m. 164, the viio in m. 167, and the cadential six-four chord in m. 168.
2C.
Haydn: String Quartet, op.74, no. 3 (second movement) 1. The excerpt begins in E minor. 2. At m. 26, a pivot chord modulation to C major occurs (e: i = C: iii).
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3. Gr +6 This chord resolves to a major tonic six-four. The upward resolution of the Eb would be better reflected by respelling the pitch as D transforming the chord into a ++4 chord. 4. Measures 34-35 involve a modulation back to E minor, as follows: C: I vi
viio /vi | vi e: iv i
| 5. Gr+6 6. At m. 38, the music changes mode from E minor to E major. 3. The Secret Lives of Chords 3A. 1
3B.
2
3
4
5
In these solutions, the leading tone, in an inner voice, has been unresolved in favor of a complete tonic chord of resolution. It is equally possible to resolve the leading tone, leaving an incomplete tonic. 1
2
3
4
5
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3C. 1
2
3
4
1
2
3
4
3D.
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254
4
2
1
3
2
3F. 1
Beethoven: Sonata for Horn and Piano, op. 17
C:
I | I | e: Gr+ | Gr+ | i 4 V | i | C:
6
6
6
7
6
7
6
6
7
6
6
I | I | e: Gr+ |
7
Gr+ | i 4 V | i | V /IV | IV ii | I 4 V | I
2
Eb: Eb: E:
Brahms: “An eine Äolsharfe,” op. 19, no. 5 6
6
I vi | I vi | V | IV | iv | Gr+ | E: V7 | viio7/V | viio7/V | V7 | N | I |
6
V7 | I 4 | viio7/V | viio7/V | V |
Answers to Questions: 1. 2. 3. 4. 5. 3G.
The chord of m. 43 functions as a Gr+6 in Eb and as a V7 in E (the enharmonic Neapolitan). The modulation is chromatic. All four diminished seventh chords are functional, tonicizing V. The return to Eb is accomplished through an enharmonic pivot in m. 47, which functions as I in E and as the Neapolitan in Eb. The passage ends with a half cadence: vii7/V - V. See answer to Question 1.
Following are the key elements of harmonic interest in Schubert’s “Die Liebe hat Gelogen”: 6
6
m.1-2: N resolving to V via Fr+ 6 m. 4: Fr+ m. 5: Change of mode to C major with V/ii on beat 3 7 m.6: Borrowed iv on beat 1, V /IV on beat 4 m. 8: Modulation to Bb via borrowed i in C (acting as ii in Bb) m. 8-9: Chromatic- third relationship (bb to Db), Db acting as IV in Ab
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m. 10: The chord on beat 1 acts as a borrowed iv (enharmonically spelled) in the preceding key of Ab and as the ii in the new key of B m. 10-11: Melodic/harmonic sequence of mm. 9-10, moving through B and A, in the same way that mm. 8-9 passed through Bb and Ab. m. 11: Change of mode on beat 4 m. 13: Chromatic modulation back to C minor 6 7 m. 16: Gr+ in A minor (spelled as V in Bb), with chord of resolution (A minor six-four acting as pivot to C major.
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QUIZ FOR CHAPTER TWENTY-THREE 1.
Name the beginning and ending tonalities for the following passages:
1
2
3
2. Name the key most likely implied by the appearance of the given “clue chord,” and indicate the chord’s probably function: 1 Key:
2
3
4
5
___
___
___
___
___
Function: ___
___
___
___
___
3. Provide harmonic analysis of the following figured bass line and identify the type of modulation. Show key change where needed.
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CHAPTER TWENTY-FOUR Harmonic Extensions and Chromatic Techniques TRIADIC EXTENSIONS: CLIMBING THE OVERTONE SERIES (pages 414-428) The idea that Western music’s evolution is reflected in the harmonic series can be extended through the sixteenth partial and beyond, where we encounter the half step so important in the atonal repertoire and microtones that characterize some more recent music. The Dominant Ninth Chord (page 414) Ninth chords tend to lose their identity when voiced so that the ninth is compressed to a second. The identity crisis becomes worse when any member but the root is on the bottom. Example 24-2 would sound more like a viiø7 with an added tone if the root G were transposed up an octave, for instance. Although voicings such as those in Example 24-3 are the most typical, ninth chords do appear in inversion (see Example 24-5) and in a variety of voicings, especially in jazz styles. Added Practice (page 420) The ninth in this V9/V resolves, in both the voice and accompaniment, to Bb in m. 54. The secondary dominant ninth chords in Example 24-7 are: m. 186: V-9/iii m. 188: V-9/ii m. 190: V-9 In all, the ninth resolves downward by step and might alternatively be analyzed as a suspension. Other Ninth Chords (page 420) The minor ninth and major ninth chords will be revisited in Chapter 31 (Harmonic Principles in Jazz). Eleventh Chords (page 422) The further the triad is extended, the greater the number of possible voicings. Example 24-12 is typical Wagner, in that the root of the V11 forms a pedal point, over which the upper voices weave a counterpoint. The eleventh appears almost incidentally in these passages. The eleventh chords in Example 24-15, on the other hand, are more vertical and more purely harmonic.
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Added Practice (page 424) Lead-sheet symbols for Example 24-14 are: Db9 Bbm11 | Ebm Ab9 | Db /F Bbm | Ebm11 Example 24-18 on page 427 Chopin’s music teems with dominant thirteenth chords. The thirteenth is almost invariably in the melodic line, the rest of the chord providing the harmonic support. Ravel’s music also teems with thirteenth chords, in addition to elevenths and ninths, often using all seven scale degrees rather freely, in ways that approach pandiatonicism, as the following example shows: Ravel: Pavane (Pour Une Infante Défunte)
Added Practice (page 428) In Example 24-4, a dominant thirteenth chord appears in m.2. This thirteenth steps back down to F, the chord fifth. LINEAR CHROMATICISM (pages 428-429) Although the term “chord mutation” is often linked in contemporary usage with something “wrong” or unnatural, it is fairly descriptive. The gradual nature of the chord change is what should be stressed when addressing this topic. In most instances of chord mutation, the component voices form chromatically descending or ascending lines. While it is possible to find examples of the technique by Liszt and others, Chopin employed it often enough to be regarded as a defining style trait. At times, the harmonies that result are functional, and at times they are not. Example 24-20 is an iconic example of the technique.
259
HARMONIC SEQUENCE (pages 430-433) Harmonic sequence is a technique broadly applied in many styles and periods. In this part of the chapter, it occurs in conjunction with harmonic innovations recently discussed—with chord mutation in Example 24-21, with dominant thirteenth chords in Example 24-22, with triadic extensions in Example 24-23, and with expanded tonicizations in Example 24-24. Added Practice (page 431) In both dominant thirteenth chords, the root, third, seventh and thirteenth are present. These are the essential chord members in a four-voice thirteenth chord. In both cases, the thirteenth resolves downward to the tonic (Ab in m. 82 and Gb in m. 84). Added Practice (page 433) Example 24-22 and Example 24-24 both involve a ii-V pattern that is restated sequentially a step lower. Both melodic patterns involve motion downward from 4ˆ to 1ˆ . The descent in Example 24-22 is larger-scale—a step progression—while that of Example 24-24 is more immediate. In Example 24-24, the harmonic progression in mm.16–19 is identical to the first eight measures, but a fifth lower (i.e., beginning in the key of Gb). The final two measures are in the key of Ab. The largest-level sequence is four measures long. Within this pattern lies the one-measure ii-V pattern that is repeated a second lower. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1A on page 297: You can follow up on this drill by having students voice (and resolve) the chords. • ASSIGNMENT 1B on page 297: You can also ask students to name the chord’s secondary function in a given key, or alternatively, you can ask students to identify the key in which the chord would be analyzed as a particular secondary function. For example, “In what key would chord no.1 be a V-9/vi?”). • ASSIGNMENT 1E on page 299: This piece can be analyzed for its harmonic and melodic sequences. Suggested Aural Quiz •
10 ninth chords (voiced or unvoiced, harmonic and/or arpeggiated). Students are to identify the type of ninth chord (i.e., MmM, Mmm, mmm, and so on). Note: You may decide how many types to include
260
in this quiz. Alternatively, you might play 10 chords—a mix of triads, sevenths and ninths—and have students identify them as such. • Harmonic dictation: A 4-measure pattern such as the Chopin Mazurka op. 7, no. 2 on page 304 (mm. 21–24). Give the beginning harmony in the left-hand part and ask students to illustrate the voice leading in a manner similar to that shown in Example 24-21 on page 430. ****************************************************************** SOLUTIONS TO ASSIGNMENTS 1. Triadic Extensions 1A. 1
2
3
4
5
6
7
8
9
10
1B. 1
2
3
4
5
6
7
8
9
10
261
1C. 1
2
3
4
5
6
7
8
9
10
1D.
1E. 1
1
2
3
5
6
7
8
c: i | V /v | V | i | VI 4 | viio 3 | V /VI | VI | V 7
6
7
4
9
-9
|
V /iv | V /nVII | V /III | V /VI viio /iv | iiø 5 | I 4 V | i 4 9 7 9 7 11 13 Eb: vi I 3 | V /V V /V | V V | V /IV V /IV | 7
2
4
13
7
7
7
11
IV+ viiø | V V
13
7
| V
7
6
6
7
262
1F.
1. 2. 3. 4. 5. 6.
Dominant-minor ninth with thirteenth: m.4 Minor seventh chord: m.10 Major seventh chord: m.5 and m.15 Major ninth chord: m.9 Minor eleventh chord: m.11 Dominant thirteenth chord: mm.2 and 6
263
2. Linear Chromaticism 2A. To avoid becoming mired in too many secondary dominants, we’ve analyzed a modulation every measure or so. Other ways of analyzing this passage are equally valid.
2B.
264
2C.
265
3. Harmonic Sequence 3A. These are challenging harmonic passages that admit several possible analyses. Feel free to disagree or to propose alternatives. 1
2
3
266
3B.
The pattern of m. 21 is repeated in sequence in mm. 22, 23, and 24.
3C. 1
Mozart: Minuet, K. 355
Harmonic sequence: mm. 5–6, mm. 7–8 (a second lower), mm. 9–10 (a fourth higher) Melodic form: a (mm. 1–4) b (mm. 5–16); mm. 12–16 are a cadential extension (mm. 12–16); a and b form a contrasting period. 2
Chopin: Ballade No. 2, op. 38
Key: F 13
vii /ii | ii vii
i
V
| I
The V is missing the fifth (G), ninth (D) and eleventh (F). This is typical. Both the seventh and the thirteenth resolve downward.
267
3
Liszt: “Valle d’Obermann”
1. The two keys in the “piu lento” are Eb minor and A minor. 2. Both chords are German augmented sixth chords, and both resolve to a tonic six-four chord. 3. Both diminished seventh chords are spelled according to their function as leading-tone seventh chords. 4. At m. 34, a harmonic sequence begins that progresses from E minor to G minor, and then from G minor to Bb minor.
268
QUIZ FOR CHAPTER TWENTY-FOUR 1
The following questions refer to Chopin’s Prelude op. 28, no. 9.
1. Two examples of linear harmonies appear in m. 4. Symbolize them by Roman numeral. _____ _____ 2. In mm. 5–8, as many as four brief tonicizations can be identified. List the tonalities. 1) _____ 2) _____ 3) _____ 4) _____ Describe the chromatic relationships that exist among these tonalities. __________________________________________________________________ 3. Within the final tonicization of mm. 5–8, a modal borrowing occurs. Identify it. ________________ 4. Describe the type of modulation that occurs from m. 8 to m. 9 and describe the relationship between the two tonalities. __________________________________________________________________ 5.
Tonicizations occur in mm. 10–11. Name the tonicized keys. ___ ___
2 Identify the following harmonies and provide an appropriate resolution for any three.
3
Add the key signature and illustrate the indicated harmonies.
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CHAPTER TWENTY-FIVE Binary and Ternary Forms THREE WAYS OF LOOKING AT FORM (pages 437–444) Regarding symmetry: Short works are often perfectly symmetric. The longer the work, the less symmetric it’s likely to be. Regarding motivic analysis: This is the crux of most musical analyses. How do the parts relate to each other and to the whole? This is where the three composer choices, introduced back in Chapter 7 (page 105), make their reprise. Regarding musical process: Motivic analysis alone does not account for the way a work affects the listener. Identifying the musical processes sheds some light on this admittedly subjective topic. In general, works that are primarily thematic are more immediately accessible than those that are heavily developmental. Could this be what made much of Beethoven’s music such an earful in his day (and still does)? Why so many thematic examples? Most of the musical examples in the book are thematic. This is partly because thematic passages make more sense in isolation than transitional, developmental, or cadential passages, which most clearly reveal their role in a larger context. Then, too, most popular music is entirely thematic. Examples of a thematic process that relies almost entirely on a motive can be found on Workbook page 94 (Ponchielli’s “Dance of the Hours”) and text page 135 (Bricusse and Newley’s “Pure Imagination”). You may wish to ask students to search back and find examples in earlier chapters that demonstrate the other processes. Some are cited below. Thematic: Schubert: Impromptu op. 142, no. 2 (Workbook page 248) Chopin: Prelude op. 28, no. 7 (Workbook page 109) Rossini: “Domine Deus” (Workbook page 256) Developmental: Bach: Invention no. 14 (Workbook page 227) Haydn: Piano Trio, H. XV:18 (Workbook page 285) Haydn: Piano Sonata, H. XVI:27 (Workbook page 247) Transitional: Mozart: Piano Sonata K. 332 (Workbook page 209) Transitional leading to thematic: Chopin: Mazurka op. 7, no. 2 (Workbook page 304) Transitional leading to cadential:
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Mozart: Minuet, K. 355 (Workbook page 307) Cadential: Bach: Fugue no. 2 (WTC I) (page 236) Kuhlau: Sonatina op. 59, no. 1 (Workbook page 86) Mozart: Piano Sonata, K. 309 (page 159) Brahms: Symphony no. 3, op. 90 (page 354) STATEMENT-RESTATEMENT (pages 444-447) Exact restatement adds nothing new to a composition and thus does not constitute a formal element. Varied restatement, on the other hand, does. AA1 represents this simplest of two part forms. Example 25-7 is as simple as simple binary gets. Here, the phrase structure and sectional structure are one and the same—a parallel period. Furthermore, only one process is present—the thematic. Example 25-8 is the same basic form, but longer, and it contains more processes—thematic, cadential, and transitional. The Coda (page 447) We like to reserve the term “coda” only for post-cadential extensions that follow what might otherwise be the final tonic chord. These extensions can range from a few beats (hardly worth calling a “coda” but still the same animal) to dozens of measures. Students seem able to recognize the cadential process more easily than they can the transitional and developmental. Repeated harmonic formulas, with or without pedal points, provide the clearest signals. The term “coda” is often used in jazz and popular music in a looser way, mainly as a shorthand way of condensing a lead sheet to eliminate writing out repetitions. (See page 457.) STATEMENT-CONTRAST (pages 449-451) The choice of whether to symbolize a form as A A1 or A B can sometimes be as difficult as deciding whether to characterize two phrases as a a1 or a b. You might revisit the two patriotic songs in Chapter Seven to make this point. Both “The Star-Spangled Banner” and “America” are simple binary. Ask students which one is more likely to be symbolized A B. (The former might be symbolized A B while the latter is closer to A A1.) In truth, strong contrast in binary forms is fairly uncommon. Strong contrast usually necessitates an element of return (restatement) in order to give the impression of a complete, unified whole.
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STATEMENT-CONTRAST-RESTATEMENT (pages 452-459) Restatement complements contrast. Restatement occurs in both the rounded binary and ternary forms. The difference between the two resides largely in the length of the return, the strength of the cadence preceding it, and the tonal stability or lack of it in the B section. Other factors, such as the musical process present in B (usually thematic in ternary and developmental in rounded binary) and the tonal character of A (progressive in rounded binary) also play a role. Example 25-13 (page 454) The rounded binary form is found in hundreds of popular songs and the majority of the “Tin-Pan Alley” standards. The B section, called a “bridge” separates the initial A from its return and works its way back to the return, often sequentially, ending with a half cadence. Also called the thirty-two bar form (A = 8 mm. + 8 mm., B = 8 mm., A1 = 8 mm.), it is frequently notated as shown on page 457, with first and second endings for A and its repeat and a D.C. al coda instruction at the end of B directing the musician to return to A and continue until the coda sign, at which point in the A the musician is to proceed to the separately written ending measures. Regarding the Drills and Assignments The four works of Part 2 (starting on Workbook page 315) are: 1) simple binary; 2) rounded binary; 3) ternary; and 4) simple binary with coda. The last— and Liszt (couldn’t resist the pun)—presents an opportunity for classroom debate. Does the coda begin with the strikingly different musical passage beginning at m. 32? Some students will think so. We'd argue against that. This passage is a precadential interruption extending the dominant—not a post-cadential extension of the tonic. The would-be final chord does not appear until the end of this interruption, in m. 38. From that point on, the music is post-cadential. Note the pedal point and its unusual placement in the inner voices of the Neapolitan sixth chord (that resolves in a plagal manner directly to the tonic). You might have students diagram the form of each work in the same way. Following is a suggested format for 1—the J. S. Bach French Suite no. 6 (Sarabande): Section: A Phrase:
B c AC
f
a (mm. 1–4) b (mm. 5–8) c (mm. 9–12) d (mm. 13–16) d (mm. 17–20) e (mm. 21–24)
Tonality: E Cadence:
B
E AC
AC
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SOLUTIONS TO ASSIGNMENTS 1. Three Ways of Looking at Form 1A.
Mozart: Piano Sonata K. 280 (first movement) This excerpt may look harmless, but the ensuing questions require some rather careful attention to the music. Be prepared for some differences of opinion. Here’s a view. Feel free to take issue.
1.
2. 3. 4.
5.
6.
7.
The opening measures are thematic. They contain a melodic idea with clearly profiled contour and rhythms, a mix of conjunct and disjunct motion, and a stable tonal environment. A pre-cadential extension in mm. 10–12 delays the arrival of the authentic cadence until m. 13 by repeating the three measures leading to it. A post-cadential extension follows the cadence in m. 13 and lasts until m. 17. These measures repeat the V-I motion under pure arpeggiation. The first cadence is expected at m. 8. This would resolve the dominant of m. 7 and complete an eight-measure phrase. The cadence occurs at m. 13, after which a pronounced rhythmic change occurs. 7 6 The harmonic pattern of m. 18—viio /V - V — is repeated in sequence a step lower, tonicizing IV in m. 19, III in m. 20, II in m. 21 and returning to the tonic in m. 22. In mm. 17–22, a two-measure pattern is repeated a third lower beginning at m. 20. The sequence is almost a real one. Only the last beat (m. 21, beat 3) does not conform. Even though no modulation occurs, the harmonically unstable chords of mm.17–22 give the feeling of tonal motion. The passage is non-melodic, consisting of sequential statements of arpeggiations, giving it a transitional character. Actually, the passage simply interrupts the cadential process on either side of it. 6 The music beginning at m. 23 is pre-cadential, prolonging the ii leading to the half cadence at m. 26.
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1B.
273
Beethoven: Piano Sonata op.2, no.3 (third movement) Developmental: mm.17–28 Fragmentary; short motive development through sequence and voice exchange; harmonically unstable with tonal allusions to C minor, Bbminor, Abmajor, and C minor again; lack of cadences Cadential: mm. 28–36 Dominant prolonged under repeated cadence pattern
1C. 1
Beethoven: Piano Sonata op.14, no.2 (first movement) Thematic process: mm. 1–13 Transitional process: mm. 14–20 Cadential process: mm. 20–25 C
R
C
V
V
V
C
C
V
C
V
V
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C
V
V
C
2
Tchaikovsky: 18 Pieces, op.72, no.5 Entirely thematic C
V
R
C
C
V
V
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R
2. Statement and Contrast: Binary and Ternary Forms 2A. 1 J. S. Bach: French Suite no. 6, BWV 817 (Sarabande) 1. Simple Binary (asymmetric) A B a b c d mm.1-4
E 2.
3.
mm.5-8
c
mm.9-12
B
f
mm.13-16
e mm.17-20
E
Phrases a and b = modulating period. Phrases c and d = period Phrases e and f = period The dotted eighth and sixteenth note figure of m. 1 is motivic.
f mm.21-24
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4.
m.5: AC in B (or HC in E) m.16: AC in f m.24: AC in E
5.
m.1 m.3 m.18 m.21
7
E: V /vi 7 E: viiø /V 7 E: viiø /V 7 E: V /IV
2 Beethoven: Piano Sonata op. 26 1. Rounded Binary A B a b a b1 c Ab
mm.1-4 mm.5-8 mm.9-12 mm.13-16 mm.17-20
2.
3. 4. 5.
A1 a
d Eb
b1
Ab
mm.21-26 mm.27-30 mm.31-34
Phrases a, b, a, and b1 = double period. Phrases c and d = phrase group Phrases e and f = period mm.24-26 = post-cadential extension of HC in m.24 mm.19-20 = tonal sequence of mm. 17-18. m.6 V7/V m.17 V/ii m.21 viio7/vi m.22 V/vi m.23 viio7/iii
3 Chopin: Mazurka op. 17, no. 2 1. Ternary Although this work does not demonstrate all the distinguishing features listed on page 459, it is better analyzed as ternary than rounded binary. The A section ends harmonically closed in the original key of e minor. The B section contrasts strongly in its own key and, while it does lead back to e minor, it does so only after a lengthy cadential extension of the HC at m. 39 that morphs into a transition. These measures add substantially to the length of B and helps to separate it from the ensuing A1. A1 restates the original three phrases and adds a cadential extension that gives it the strength of a full return.
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A a
277
b1
b
a
b2
b
mm.1-4 mm.5-8 mm.9-12 mm.13-16 mm.17-20
mm.21-26
e
B c
c1
ext.
mm.25-32
m.33
m.39
A1 a
b
mm.53-56 mm.57-60
C
b1
ext.
mm.61-63
m.64
e
2. The final phrase might cadence at m. 64 but for the elision and extension that takes its place. The extension precedes the cadence and can be termed precadential. 3. Principal elements of contrast in B are the key, the texture (change in left-hand accompaniment), the presence of pedal point, the melody, and the harmonic rhythm. 4. The music becomes transitional at m. 49. 5. The dynamic accents help to emphasize the syncopation that gives the middle section its vitality, perhaps in compensation for the slower harmonic rhythm and extension melodic repetition. 6. Measures 39-49 are a prolonged dominant in C. 4 Liszt: “Il Pensieroso” 1. Simple Binary The use of a single letter to represent each phrase indicates the degree of unity that characterizes this piece. A A1 Coda 1 2 3 4 a a ext. a a ext. * A a c
m.1
m.5
m.9
m.14
a-E
e
g
m.19
c
m.21
m.27
m.33
m.39
Measures 33-38 extend the V7 of m.37, delaying its resolution until m.39, the would-be final cadence. The ensuing measures are a post-cadential extension of sufficient length to justify the term “coda.”
2. The three tonalities of the first section, c#, e, and g, display an unusual chromatic-third relationship (minor keys a minor third apart).
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3. Measures 33-39 twice run the circle of fifths via secondary dominants: 7 9 7 9 7 7 7 C – F – B – E – Ao – each time ending with a iv – V in the key of c. 4. The Neapolitan occurs, in root position and embellished, in mm. 19-20. It appears again in the coda at mm. 40-42, amidst a tonic pedal point and resolving directly to the tonic. 5. Answered above. 2B. 1 Corelli: Trio Sonata op. 4, no. 3 Simple Binary 1. A B A b c m.1
m.5
m.9
A
d f A
m.14
2. The rhythmic motive heard first in the violins and the lower neighbor-note motive first heard in the cello, both in m.1, are unifying features in this short piece. 3. The principal tonality, A, is not reflected in this modal key signature. Typical of music in this period, the key signature often lacks one flat or one sharp, reflecting the role played by musica ficta in the transformation of the Dorian and Mixolydian modes to our present-day minor and major systems. 4. The isolated B of m.3 is the first hint of a possible modulation to the dominant. It is immediately counteracted by Bn in m.4 and thus not indicative of a tonal change. 5. Each cadence contains the “Corelli Clash,” a mannerism peculiar to the composer involving the simultaneous resolution of a 4-3 suspension in one voice and an anticipation of the leading tone in another voice. 6. The second section begins and ends in A. Within this tonality, a tonicization of f occurs mm.12-13). 2 Schubert: impromptu op. 142, no. 3 Form: Rounded Binary Phrases a + b = period Phrases c +a1 = period A B A1 ext. A b c a1 m.1
m.5
m.9
m.13
m.17
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Harmonic Analysis: m.1 4 7 6 6 4 7 6 6 7 7 Bb: I I | V 3V | I ii 5 | V 5/V V | I I | V 3V | I viio /V | V I || m.9 6 V/vi vi | vi 6 6 F: ii V | I ii 5 | V m.13 6 6 7 7 b B : V/V V | I V 5/IV | IV viio /V | V I 4 | V I | 7
7
V I | V I ||
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QUIZ FOR CHAPTER TWENTY-FIVE Mozart: Piano Sonata, K. 332 (first movement) 1. Which musical process in underway at m.102? __________________ List three reasons for your choice. 1.___________________________________________________ 2.___________________________________________________ 3.___________________________________________________ 2. Locate an example of a cadential process that becomes transitional. Measures: _____________ 3. Identify the musical process underway at m. 116. _________________ Where does this process begin? ______ Where does this process end? ______ Explain why you identified the process as you did. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ 4. The cadence at m. 123 is: _____________. The chord preceding the cadence chord is: ________ (Give RN) 5.
The five keys in the excerpt are: ___ (key) beginning at ___ (measure number) ___ (key) beginning at ___ (measure number) ___ (key) beginning at ___ (measure number) ___ (key) beginning at ___ (measure number) ___ (key) beginning at ___ (measure number)
6.
What pattern do you observe in the succession of tonalities? ________________________________
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Mozart: Piano Sonata, K. 332 (first movement)
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Schumann: “Valse noble” from Carnaval, op. 91. Identify the form. Complete a diagram showing sections, phrases, and tonalities. Sections: Phrases: Tonalities: Cadences: 2.
Cite ways in which the music beginning at m. 9 contrasts with mm. 1–8. 1)__________________________________________________________ 2)__________________________________________________________ 3)__________________________________________________________
3.
Show (rhythm only) the unifying motive: ______________
4.
Identify the chromatic harmonies at: m. 33: ___ m. 37: ___ m. 38: ___
5.
Locate an 8-measure step progression. __________
6.
Locate an example of a melodic and harmonic sequence, and describe it. ____________________________________________________________ ____________________________________________________________
Schumann: “Valse noble” from Carnaval, op. 91.
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CHAPTER TWENTY-SIX Introduction to Sonata Form A BRIEF HISTORY (page 462) Sonata form, the most important musical structure of the classical period, evolved gradually, and the features that it comprises coalesced only toward the end of the eighteenth century. Key elements include the establishment of opposing tonal areas (usually with attendant thematic material), subsequent melodic and harmonic development of the thematic material, and the restatement of opening ideas with a reconciliation of the initial tonal opposition. These features underlie the vast majority of sonata-form movements. MOZART: EINE KLEINE NACHTMUSIK (page 463) We’ve selected the first movement of this work as the chapter’s topic piece because we feel hard pressed to find an example that so closely approaches the “textbook model” while being so readily recognizable and concise. Feel free to bring your own favorite examples to the classroom. Closing Section (page 467) You may wish not to make a distinction between a closing theme and a codetta. However, it seems consistent with the attention we’ve paid to musical process to distinguish between music that is primarily thematic (the former) and music that is primarily cadential (the latter). This is especially true because the two processes are capable of producing quite different musical affects. Development (page 468) Development sections quite often break down into distinct subsections based on one or more of the following: 1) material being developed; 2) tonality; 3) texture; 4) rhythmic character. You may wish to have your students identify and label subsections based on these factors. Eine Kleine Nachtmusik contains a more-or-less uni-sectional development. Recapitulation (page 469) It is usually fascinating to examine how the transition in the recapitulation differs from its initial appearance in the exposition. On page 470 we’ve identified
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four distinct composer choices, although these choices may be combined in many ways. ****************************************************************** SOLUTIONS TO ASSIGNMENTS A.
Beethoven: Piano Sonata op. 10, no. 1 (third movement)
Form 1. The exposition ends in m. 45. Although mm. 12-15 might be viewed as a transition to the secondary key, the process here is actually more cadential than transitional, amounting to nothing more than an extension of the cadence that occurs at m.12. (A typical feature of a transition is modulation, which does not take place here.) 2. The key of the second thematic/tonal area is Eb. This key is, with respect to the home key, the relative major. 3. The exposition ends with a cadential passage called a codetta. This passage begins at m. 37, although the music turns cadential in nature as early as m. 24. (Measures 24-37 can be viewed as a long cadential extension of the short secondary theme.) 4. The development begins in m. 46. It focuses on material from the first thematic/tonal area. The “fate” motive beginning at m. 54 might be considered a retransition, preparing for the return of C minor by way of a prolonged viio7. 5. The recapitulation begins in m. 57 in the key of c. 6. In the recapitulation, the second thematic/tonal area begins in m. 74 in the key of C. This key is, with respect to the home key, the parallel major. 7. A coda begins in m. 106 in the key of Db. The move to a new key, especially one as distant as the Neapolitan, is a departure from the customary function of the coda, which is to prolong the tonic. Other Questions 1. The phrase/period structure of mm.1-8 is: a a’ (period) 2. Fermatas occur at three points. What two musical processes does each fermata separate (thematic, transitional, developmental, cadential)? m.16: cadential and thematic m.73: cadential and thematic m.106: transitional and thematic m.113: thematic and cadential
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3. 4.
B.
A passage based entirely upon the sequential treatment of a motive occurs between m. 49 and m. 54. The process is developmental. Identify by Roman numeral the following harmonies: m.3, beat 1: It+6 m.37, beat 2: viio/ii m.38, beat 4: viio7/vi m.41, beat 4: Gr+6 Mozart: Piano Sonata K. 330 (second movement)
Form 1. The exposition ends in m. 31. There is no transition to the secondary key, which begins abruptly at m. 14. 2. The key of the second thematic/tonal area is Bb. This key is, with respect to the home key, the dominant. 3. The exposition ends with a closing theme at m. 21. 4. The development begins at m.32 and consists of two subsections. The first begins in f. The musical material is best described as new, as it is only tenuously related to the melodic material found in mm. 3-4. The second subsection begins at m. 43 in the key of Ab and develops material heard in mm. 8-9. 5. A very brief retransition occurs in mm. 48-50. 6. The recapitulation begins in m. 51 in the key of Eb. 7. In the recapitulation, the second thematic/tonal area begins in m. 64 in the home key of Eb. 8. A coda is not present. Other Questions: 1. The music at mm. 58-63 is cadential, a prolongation of the tonic of m. 58 through tonic-dominant harmony. 2. The most remote tonal region of the movement occurs in mm. 46-47. The key suggested at this point is ab. 3. The developmental process is most evident in mm. 43-49, where the fivenote motive first heard in mm. 8-9 is heard in partial sequences that tonicize f and Db. Prior to these measures, the development section is mostly thematic.
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CHAPTER TWENTY-SEVEN Introduction to the Rondo PERSPECTIVE (page 477) The classical rondo (pronounced RON-do) evolved from the Baroque rondeau (pronounced ron-DO) through a gradual process in which the episodes and refrains grew in length and shrank in number. Of the many variations on the rondo principle, only the five-part rondo is covered in this brief chapter. Still, all the elements present in longer and more involved rondo movements are found in the topic piece. BEETHOVEN: PIANO SONATA OP. 13, SECOND MOVEMENT (page 478) We’ve selected the first movement of this work as the chapter’s topic piece for its familiarity, for its straightforward, transparent application of the rondo principle, and for the opportunity it affords to revisit some chromatic harmonic techniques covered earlier. The Refrain (page 478) If you prefer, you can refer to the refrain as the “rondo theme.” It might also be called the “first refrain,” since its initial reappearance is termed “second refrain.” Refrains generally tend to involve the thematic process, whereas episodes may be thematic, developmental, or even transitional. Even if thematic or developmental, episodes will often become transitional (more precisely, retransitional) at their conclusion. The Coda (page 483) It’s worth making the point that codas have the same formal function, whether in a fugue, a sonata form movement, a rondo, or a song. In all cases, they follow and prolong the would-be final cadence. Along the same lines, it’s worth stressing the similar function of the episode (a digression, tonal and/or thematic) in both the fugue and the rondo. ******************************************************************
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SOLUTIONS TO ASSIGNMENTS A.
Haydn: Piano Sonata H XVI:37 (third movement)
Form 1. The form of the refrain is rounded binary. 2. The first episode begins in m. 23 in the key of d. This key, with respect to the home tonality, is the relative minor. The episode then modulates to F. NOTE: The last sentence in Question 2 as posed in the Workbook incorrectly refers to the refrain. Please see errata. 3. The form of the first episode is binary. 4. The second refrain begins at m. 45. It is an exact repetition of the original. 5. The second episode begins at m. 67 in the key of G. This key, with respect to the home key, is the subdominant. 6. The final refrain begins in m. 98. Unlike the first two refrains, the repetition of the first 8 measures is written out. This is because the melody is given a different accompaniment. The same is true of the b section, which receives an accompaniment different from the original both times. 7. The transitional process is evident in mm. 84-97. 8. This movement is primarily thematic. The transitional process occurs but once (mm. 84-97), and the cadential and developmental processes do not occur at all. Other Locate an example of each: • • • • • •
Viio/V: mm. 89-90 V/ii: m. 114 Deceptive cadence: mm. 23-24, and mm. 27-28 V7/IV: m. 18 V7/V: m. 112 viio/vi: m. 5
B.
Mozart: Piano Sonata K. 333 (third movement)
1. 2.
The refrain begins at m. 1 and ends in m. 16. The first episode begins at m. 24 in the key F. A transition to this episode occurs in mm. 16-24. While the episode may be viewed to encompass mm. 16-40, we prefer to break things down further based on the compositional processes present. Measures 16-23 begin thematically but acquire transitional features at m. 21. Measures 24-36 are more thematic,
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3. 4.
5.
6. 7. 8. 9. 10.
both melodically and in their harmonic stability, and mm. 36-40 bear the hallmarks of a retransition. The refrain appears three more times: at m. 41, m. 112, and m. 205. A retransition precedes these reappearances of the refrain. These retransitions begin at m. 36, m. 105, and m. 179. Note: Other viewpoints may be entertained here. The long retransition that emerges from the intempo cadenza becomes mildly developmental (mm.186-199) before resuming its dominant prolongation. Indeed, the in-tempo cadenza might be viewed as extending all the way to the refrain at m. 205. The longest and most complex episode (the “C section”) of the movement begins at m. 65 in the key of g. This episode contains three subsections that differ in tonality, musical material, and texture. The first subsection, at m. 65, is followed by a second at m. 76, in the key of Eb, and a third at m. 91 that begins in the key of c. The third subsection of C develops material from the refrain, stating the music of mm. 1-4 sequentially and then compressing it. The final refrain is followed by a coda, which begins at m. 221. This is a seven-part rondo. Cadential extensions occur at m. 32, 89, 103, 144, 156, 179, 213, 216 and 228. The key at m. 95 is Bb. In this key, how would you symbolize the tonicization in m.99? Actually, the passage begins in Bb and quickly changes mode to bb. In Bb minor, the tonicizations are V7/VI and V7/iv. The chord of m. 102 begins as an It+6 and changes nationality during the measure (Fr+6 and Gr+6). A diagram of the movement follows:
Section: Measure: Key:
Subsection: Measure: Key:
A tr. B ret. A tr. C ret. A tr. B ret. A Coda 1 16 24 36 Bb mod. F
41 56 65 105 112 127 148 179 205 221 Bb mod. g Bb Bb
a 65 g
C b 76 Eb
c 91 c - bb
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PART NINE MUSIC IN THE TWENTIETH CENTURY AND BEYOND (CHAPTERS 28–33) This part of the book comprises of six chapters that deal with the music of the recently completed century. The composers singled out for extended coverage are Debussy, Stravinsky, Bartók, Schoenberg, and Webern. Many others are represented in the musical examples. We’ve tried to vary the presentation in these chapters in such a way that longer, in-context excerpts balance shorter examples that isolate specific techniques. Students generally have an easier time with this material than with nineteenth-century music because, in certain respects, it’s a new beginning—new harmonic syntax, new melodic and rhythmic techniques, and so on. Even though this is true to an extent, it’s important to emphasize the continuity that characterizes musical style as it evolves. Music’s evolutionary flow might be likened to the flow of a river, with its various branches that may either break off to seek their own destination or spill back into the main channel. By the same analogy, it’s possible to think of the various composers as tributaries feeding the main stream. The final three chapters are devoted to jazz, blues, and popular song. In scope and depth of coverage, these chapters represent the book’s unique contribution to the pedagogy of music theory. We, the authors, feel that it’s irresponsible to send music graduates out into today’s musical milieu without adequate preparation in the area of vernacular music. All of the parceling and paring in the book to this point has been for the purpose of creating the space necessary for an adequate treatment of these topics.
Recommended time allocation: 6 weeks
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CHAPTER TWENTY-EIGHT Syntax and Vocabulary SYNTAX (pages 487-496) Debussy’s great harmonic contribution was not so much an expansion of the vocabulary as it was a retooling of the syntax—using familiar chords in unfamiliar ways. The resulting sound is profoundly different. You might ask students to rearrange the five chords in Example 28-1 to form a functional harmonic progression. The likely result would be: Gm - Fm7 - Dø7 - B7 - E (iii-ii7-viiø7-V7-I). Play it both ways for them. Planing (page 488) Debussy looked to the distant past for inspiration. Perhaps he discovered planing in the fauxbourdon of the thirteenth century or the parallel organum of the tenth. His prelude, “The Sunken Cathedral,” would suggest as much. Stepwise parallelism invariably produces non-functional chord successions such as those on the next page. Concept Check (page 490) The three passages of Example 28-6 have these features in common: 1) They are triadic; 2) the triads move in parallel motion; 3) the triads do not progress in the traditional functional way. Of the three, the Rodgers is the most conservative, employing a mixture of functional and non-functional motion. Example 28-7 (page 492) Ask students to sing the tonic after playing this passage. This will drive home two facts: the augmented triad is rootless, and a succession of them creates tonal ambiguity. Modality (page 492) The Church modes were introduced along with scales in Chapter One to provide perspective on our major and minor tonality. Now—finally—students can see them at work. Debussy’s music is filled with what might be called “fleeting modality.” The Sarabande from the suite Pour le piano on Workbook page 369 contains references to Dorian, Phrygian, Mixolydian, and Aeolian modes. Jazz Studies majors will have their own way of thinking about the modes, owing perhaps to George Russell’s seminal The Lydian Chromatic Concept of Tonal Organization, and the work of David Baker, Jamey Aebersold, and others. However, we feel it still beneficial to relate the modes to our familiar major-minor tonality.
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NEW MELODIC AND HARMONIC STRUCTURES (pages 496-506) The scales introduced here—major and minor pentatonic, whole tone, and octatonic—are by far the most common of the “new” scales employed in the twentieth century. All have features at odds with major-minor functional tonality, although they can be used in ways that are still tonal. The connection between melodic pentatonicism and quartal/quintal harmonies should not be overlooked. Concept Check (page 497) Example 28-15 employs the minor pentatonic scale. The emphasis on Eb in mm. 62–64 and the Bb pedal point on the bottom provide a strong tonic-dominant axis, and it’s difficult not to hear Eb as a tonal center. Students should know by now that almost every pedal point is either a tonic or a dominant, a quick clue to tonality. Debussy uses the tonic-dominant axis as a way of defining a tonal center in Example 28-17. The bass through most of this passage is the dominant G. Added Practice (page 500) The difference between a quartal and quintal harmony is purely vertical. G-C-F can be voiced downward by fifth or upward by fourth, but the sounds are intrinsically related, although fifths generally imply roots more forcefully than do fourths. Distinguishing between them seems to us not that important. However, the ability to spot them in a melodic line or counterpoint is. Here, the left hand outlines 4-note quartal harmonies through beat 1 of m. 20. Of the remaining two scales—whole tone, and octatonic—the octatonic has received wider attention, probably because it is less severely limited than the whole tone. As a matter of fact, the octatonic scale possesses considerable potential for intervallic and chordal variety despite its symmetry. Three of the four basic triads can be formed on every other pitch, and a diminished seventh chord can be formed on every pitch of the scale. In addition, a dominant seventh chord can be formed on every other pitch, making the chord extremely useful in jazz improvisation. Two V7 chords a tritone apart form a partial octatonic scale. Add the 9 to each of these chords (i.e., G79 and Db79) and you have the full octatonic scale. Time and space precluded a discussion of this in the text, but you may wish to have a jazz studies student or a jazz faculty member talk about this. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1C2 on page 365: You might ask students to speculate about the formal process in this passage and its location in the piece. The process is cadential (tonic prolongation with pedal point and such), and it appears as the coda.
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•
•
•
•
ASSIGNMENT 1D on page 368: All these cadences except 4 form another cadence if the chord order is reversed. Ask students what mode would then be suggested. ASSIGNMENT 2A on page 372: Once students have constructed the requested scale, you might have them stack the notes to form either a quartal or quintal harmony. ASSIGNMENT 2C on page 374: For each of the quartal or quintal harmonies, you might ask students to stretch them out into a major or minor pentatonic scale. ASSIGNMENT 2D on page 375: You can ask students to transform each of these melodies into a different mode, either by changing the key signature or by adding the necessary accidentals. Suggested Aural Quiz
An aural quiz on modes, cadences, and chord types is advisable. A suggested format follows: • 5 chords (Mmm9, mmM9, quartal, quintal, whole tone): Students to identify. • 5 modal cadences: Students to identify. • 5 modal melodic fragments: Students to identify. SOLUTIONS TO ASSIGNMENTS 1. Syntax 1A. 1
2
3
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1B. These melodies can be transformed by changing key signatures or individual pitches as follows: Mixolydian: Add one flat Lydian: Subtract one flat n b Aeolian: Change A to A Dorian: Change An to Ab Change Gb to Gn Phrygian: Remove two sharps for key signature and cancel A Mixolydian: Change key signature to four sharps (and cancel A)
1 2 3
1C. 1 2 3 4
Chromatic planing involving Mm7 chords over F pedal and left-hand part that implies I – IV – V in F Chromatic planing involving major triads inside an A major triad, implying A Lydian Chromatic planing of major triads underneath a predominantly F-major melodic line In mm. 21-22, planing of seventh chords diatonic to A Dorian above Dorian scale degrees 1 and 4. In mm.23-24, diatonic planing of triads in C major (exception: m.23, beat 2) beneath a melodic line also diatonic in C major
1D. Assuming the final chord to be the “tonic”: 1 Mixolydian (v – I) 2 Aeolian (v – i) 3 Dorian (IV – i) 4 Phrygian (vø7 – i) 5 Lydian (II – I) 1E. Answers may vary, but each must involve chords that contain the modal inflection. Likely solutions follow: 1 2 3 4 5
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1F. Debussy: Pour le Piano (Sarabande) Form 1. “Compound” ternary A a b a1 m.1 m. 9 m. 15
B c d m. 23 m. 35
A1 Coda a2 d b2 m.42 m.50 m.56 m.63
The form is defined primarily by the cadences and melodic material. Texture remains chordal and fairly dense throughout. 2. Aside from the coda at m.63, the music is primarily thematic. Debussy shows a penchant for repeating motives in pairs, thus the prominence of the two-measure “phrase,” but there is little traditional development here. 3. mm.1-2: C mm.3-4: R mm.4-5: C mm.6-7: V mm.9-10: C mm.11-12: V mm.13-14: C mm.15-16: R (of mm. 1-2) mm.17-18: R (of mm.. 3-4) mm.19: R (of m. 5) mm.20: R (of m. 19) mm.21-22: C Syntax 1. Functional tonal roots lie just beneath the surface here. Here’s one way to hear the passage: C:
m. 50
9
V B:
51 | i ii
V
9
i
52 53 54 55 9 | V | i | E: vi I v | I v I v I | g: VI | V ||
Change the first and third chords in m. 51 to major triads and hear how much more conventional things sound. Measures 53-54 sound distinctly Mixolydian, while the cadence in mm. 54-55 sounds Phrygian–Debussy’s “fleeting modality” on parade.
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2. Planing: mm. 1-4, 11-12, 23-28, 35-41, 56-62 Mode use: Really, a case can be made for finding the entire piece to be modal (although highly variable). Clear modal implications appear at: mm. 35-41: F Dorian; mm. 42-44: E Mixolydian; mm. 66-72: c Aeolian 2. New Melodic and Harmonic Structures 2A. 1
Minor pentatonic on D
2
Minor pentatonic on F
3
Major pentatonic on Ab
4
Minor pentatonic on C
5
Major pentatonic on Bb
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2B. Circled tones are extraneous to scale 1
Whole tone
2
Pentatonic
3
Octatonic
4
Dorian
5
Pentatonic
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2C. 1
2D. 1 2 3 4 5 2E. 1
2
2
Scale: Scale: Scale: Scale: Scale:
3
F G A B C D E F Bb C D E F G A Bb Bb C D E F Ab Bb F G Ab Bb C D Eb F C D E F G Ab Bb BN C
4
Identity: Identity: Identity: Identity: Identity:
5
Phrygian Lydian Whole tone Dorian Octatonic
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3
2F. No solutions are provided for this assignment. 2G.
Debussy: “Des pas sur la neige”
1.
Form: A (m. 1) B (m. 16) C (m. 26) The chief unifying device is the motive heard in m.1.
2.
Falling-third motive: mm. 4, 17, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33
3.
A tonal center of D is created through pedal points as in mm. 1–4, cadence pitches in the bass as in m. 6 and m. 36, and the melodic motive of m.1 on D that is present also in mm. 2–6, 8–11, 16–21, 26–28, and 32–33.
4.
Parallelism (planing) occurs in mm. 5–6, 20–24, and 29–31.
5.
The mode suggested in mm. 1–4 is D Aeolian.
6.
Non-dominant Mm7 chords appear in mm. 8, 9, 10, 23, and 24.
7.
The harmony in m. 14 can be analyzed either as a whole-tone chord or an altered dominant (V7-5).
8.
The harmonies of mm. 23–24 are: Db7 - D7 - Eb7 - E7.
9.
The mode suggested in mm. 28–31 is Db Mixolydian.
10.
The piece ends with a Plagal cadence.
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CHAPTER TWENTY-NINE New tonal Methods PERSPECTIVE The music in this chapter is neither tonal in the same way Debussy’s was nor atonal in the manner of Schoenberg and Webern. It lies on a plateau that separates those two ridges and contains a vast amount of music—most of the music, in fact, written during the twentieth century. It’s on this plateau that we find Ives, Hindemith, Bartók, Stravinsky, Copland, Menotti, and Crumb, to name but a few. The styles are varied, with different harmonic vocabularies, different approaches to rhythm and form, and so on—so much so that music by only a few of these composers can be included here. However, most of them utilized the techniques discussed in this chapter to one extent or another. NEW TONAL VENTURES (pages 507-515) The “quartal cushion” evident in Example 29-1a appears to be more deliberate than in much of Hindemith’s music, where quartal harmonies percolate to the surface as a by-product of his intervallic preferences. These preferences, in turn, relate to the theories of tonality set forth in his book, The Craft of Musical Composition, an interesting read if you‘ve not taken the time. Although quartal harmonies sound much alike, especially when you begin to extend them, there would seem to be some value in finding their “root” in a manner similar to triads—by stacking fourths. The symbols we suggest are by no means standard, perhaps not even common, but we find them useful. Example 29-4 (page 510) a is probably everybody’s favorite example of polychords because it’s so clear. b is more subtle, but it’s probably more typical of the way composers have used these structures. As with quartal harmonies, the symbols used to represent these chords are by no means standard. Example 29-6 (page 512) The same observations hold true for polytonality. a is an utterly clear, notvery-subtle use of polytonality along with some blues inflections. It’s an ideal first example. Even more ideal, perhaps, are some of Milhaud's Saudades da Brazil, which are great fun to play, hear, and discuss. Stravinsky’s polytonality tends to be of a more complex and subtle nature. In b, melody and harmony of a D-minor cast are set against parallel moving eighth-note triads that imply D Phrygian.
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Example 29-7 (page 514) Bimodality can take two forms: different modes on a common “tonic” as here, or the same mode on two different “tonics.” Bartók appeared to favor the former. Example 29-8 (page 514) Like polychords and polytonality, undiluted examples of pandiatonicism tend to be few and short-lived. They also tend to be polyphonic, because the pandiatonicism often is the harmonic result of diatonic counterpoint among several voices. The Rorem example is pure pandiatonicism. The scalar basis for the passage occurs, as a complete two-octave scale, in the left-hand piano part in mm. 2–6. Everything above and around this scalar line is diatonic D major, but hints of traditional harmonic function are few. STRAVINSKY AND BARTÓK (pages 516-523) Stravinsky and Bartók are two composers of the past century likely to retain their place in the standard concert repertoire. A representative look at their work would require a chapter on each composer, something not possible here. Added Practice (page 518) Example 29-9b is Dorian on Eb. Both the ostinato and the horn melody above it involve planing. The horn melody involves open-fifth sonorities with a added third added beneath the highest voice. This chordal structure is maintained throughout the passage. Stravinsky “grows” his melody in typical fashion. The initial three notes are repeated once, then repeated again with an added gesture (mm. 17–18). Measures 17–18 are then repeated with a condensed version of both gestures tacked on (mm. 19–21). Measures 19–21 are then repeated with an additional extension (mm. 22–25). Above the horn melody, the flutes play a fourpitch figure that lies somewhere between an ostinato and a countermelody. Example 29-10 (page 519) This piece from the Mikrokosmos is short enough to be given in its entirety. Consequently, it’s given a more comprehensive analysis that includes form. The first cadence (at m. 23) is more divisive than the second (at m. 34), partly justifying its label as a rounded binary form rather than ternary. Concept Check (page 521) Bartók and Stravinsky employed the technique of “growing” their melodies through the accretion of fragments that are variations of one another.
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For example, the idea in mm. 3–5 is repeated in part with minor pitch/rhythm changes in m. 6. The elements of the original idea are pieced together in a different way in the next gesture (mm. 7–10). Measures 11–14 are yet another variant of mm. 3–5. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 2B2 on page 391: Unfortunately, the incorrect musical example found its way into the Workbook at this point. The correct music is printed here on page 306. If you wish, you can make copies and hand out to students. If you have a capable classical guitar major in class, you might ask that person to play this passage and explain how/why it is idiomatic for the guitar, i.e., how it utilizes the lower open strings and how the harmonic structure of the upper part relates to the guitar tuning. • ASSIGNMENT 2B3 on page 392: If you have two violinists (ideal) or two soprano melody instrumentalists in class, you might arrange an in-class performance of this attractive duet. Suggested Aural Quiz An aural quiz might include identification of harmonic and melodic structures, and perhaps the identification of the overall tonal basis of selected excerpts (i.e., pandiatonic, bimodal, polychordal, polytonal, octatonic, and so on). Some of this should carry over from Chapter 28. A suggested format follows: • 5 chords (quartal, quintal, and polychords of various types) • 5 modal melodic fragments: Students to identify. • 3 short passages that demonstrate pandiatonicism (i.e., the first four measures of Ravel’s String Quartet op. 10), octatonicism (i.e., the first four measures of Bartók’s Mikrokosmos no. 101 “Diminished Fifth”), and polytonality (i.e., mm. 3–9 of Milhaud’s “Botafogo” from Saudades da Brazil) SOLUTIONS TO WORKBOOK ASSIGNMENTS 1. New Tonal Ventures 1A. Some of these harmonies can be viewed in other ways. Much depends on musical context. 1 d 2 g 3 j 4 b 5 e 6 i 7 h 8 a 9 c 10
303
1B. 1 EbQ
2 Bb+ Ab
6 GQ EQ
7 W.T.
1C. +11 1 C9 2
Q
C
3 Bb+11 8 eb d
4 G FQ
5 Abm9
9 EQ
10 A13
Eb E +11 11 Q 9 Q 3 F 4 Am 5 E 6 Eb 7 Am 8 C 9 9 C 10 13
F Q G
1D. 1 is in error. The given pitch should be F, although it is possible to place a second-inversion F triad on the bottom. The constructions shown here are basic. Other ways of distributing the chord members are possible.
1
2
3
4
5
6
7
8
9
10
1E. Student solutions will vary. None are given here. 1F. Student solutions will vary. None are given here.
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2. Stravinsky and Bartók 2A. 1 1.
2.
3.
Hindemith: Sonata for Flute and Piano (first movement)
The tonal center Bb is created by a strong tonic-dominant axis. Bb is the beginning and ending point of the scalar left hand as well as the most frequently heard tone. F is the most prominent tone in the right hand until it moves upward in a step progression in mm. 8–9 to the melodic high point Bb. Quartal and quintal structures appear throughout, some more obvious than others. The right hand of mm. 1 and 2 implies quartal harmonies. The same is true of the flute in mm. 5–6. The triplets of mm. 7–8 are partly quartal. Harmonically, quartal harmonies appear at m. 3 beat 1, m. 10, and m. 12 (an open fifth). The bass line descends through the Aeolian mode (Bb - Ab - Gb - F - Eb Db - C - Bb). The flute melody (in mm. 7–10) contains an ascending step progression through almost the same pitch gamut: Db - Eb - F - G - Ab - Bb
2
Stravinsky: Le Sacre du Printemps (Part Two: “The Sacrifice”)
1.
In m. 13 (and in the measures prior to it), a tonal center of D is defined by both the sustained harmonies and the evolving high-register melodic line. The ensuing measures become less stable harmonically until the music settles on an F minor triad at m. 19. This, then, might be considered the next tonality, although it lasts for only a few measures. The solo violin melody at mm.19–23 is pentatonic, built on the quartad G - C - F - B. Lead-sheet chord symbols may provide the most meaningful analysis of the sustained harmonies in mm. 13–19: A E Fm Dm E F G The chromatic planing in mm. 13-22 involves only minor triads, moving in a continual eighth-note motion. The harmonies are often disguised by the enharmonic spellings. They seem not to define a single scale or mode.
2. 3.
4.
3
Bartók: Sixth Quartet (first movement)
1.
If a tonal center can be said to exist at all, it’s probably one of the notes in the ostinato that is shared by the cello and first violin. The likely candidate
305
2.
3.
4. 5.
would be the lowest pitch in the pattern, B, which is also the metrically accented pitch. Strung together as they are heard, the first violin and cello lines form this repeated succession of pitches: B - A - G - F - G - A. They constitute two-thirds of a whole tone scale. The second violin and viola are imitative, the violin initially imitating the viola by inversion. Beginning in m. 186, the viola imitates the second violin, the figure growing shorter over time. By m. 189, the two upper strings are paired in imitation against the two lower strings. The harmonies formed by the four voices are random and linear, composed of mixed intervals that are by-products of the two ostinatos and the imitative inner voices. It seems likely that Bartók was more concerned with line and process here than with beat-for-beat harmonies.
2B. 1 Stravinsky: Symphony of Psalms (first movement) 1. 2.
E probably has the best claim to tonic in this passage, owing to its prominence in the chant-like melody. The passage is entirely octatonic, with E Phrygian suggested by the melody.
2 Mario Castelnuevo-Tedesco: Platero y Yo, op. 190 (vol. I, no. 2 “Angelus”) This piece has been inadvertently omitted from the Workbook. A twelvetone row appears (incorrectly!) in its place. The piece is included below (and in the errata). Feel free to print it out for your students. 1. The music begins in G and ends in A. 2. The excerpt consists mostly of second-inversion major triads, strung together in parallel fashion, with frequent chromatic-third relationships. Beneath this chromatic planing, an alternating tonic and dominant keep the music firmly anchored in A. 3. V7-I harmonic motion occurs at mm. 50-51, 52-53, and 55-60. 4. Answered above. 5. Answered above. Measure 49 is repeated in sequence in m. 51. Likewise, m. 51 (beasts 2-3) are repeated immediately in sequence in the remainder of m. 51 and m. 52. Measures 53-54 are a repetition of mm. 51-52.
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Mario Castelnuevo-Tedesco: Platero y Yo, op. 190 (vol. I, no. 2 “Angelus”)
3
Bartók: “Song of the Harvest”
1.
In each section, both violins are limited to heavily repetitive melodies comprising the lower tetrachord of the Aeolian (or Dorian) mode. In each section, the tetrachords of the two violin parts combine to form a complete or partial octatonic scale. Measures 16-20 are a transposed and inverted counterpoint of mm. 1-5 in which the individual lines are also melodically inverted. The canon by one measure in mm. 6-14 is transposed and tightened in mm. 21-29 to a canon by one beat, with the leading voice (the dux) and the following voice (the comes) exchanging roles. Measures 30-33 contain a shortened version of the melodic material of the opening measures, but with both violin parts agreeing on the key, so that together, they suggest Eb Aeolian. Answered above. This is a very brief rondo: 1 1 2 A B A B A m. 1 m. 6 m. 16 m. 21 m. 30
2.
3.
4. 5.
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QUIZ FOR CHAPTERS TWENTY-EIGHT AND TWENTY-NINE 1. Illustrate above the given bass notes the following sonorities. The superscripts following Q indicate how many members the chord is to comprise.
2.
Identify the mode suggested by the cadences.
3. Identify each of the following melodies as: a) pentatonic; b) whole tone; c) modal; d) octatonic
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4.
Answer the questions that follow the excerpt. Bartók: Fourteen Bagatelles for piano, no. 1
1
Which term best describes the tonal character of this excerpt? a pandiatonic b pentatonic c octatonic d bimodal e whole tone f planing
2
Name the scale formed by the right-hand part in mm. 10–11.___________
3
Name the mode implied by the left-hand part in m. 11. ___________
4
Name the harmonic structures implied melodically in mm. 12–14. _____________________________________
5
Viewing the right-hand part in its totality, what mode is suggested? ______________
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CHAPTER THIRTY Atonality and Serialism Arguably, atonal music remains a musical anomaly to most students. It likely occupies a miniscule portion of a student’s listening repertoire and is encountered by most music majors only in music history surveys and the final semester of their music theory study. Interestingly, it still may be perceived as “new music” by many students. What has changed since the time most of us were undergraduates is that this repertoire really is “older” music, and we are now charged with covering twentieth-century music in a more inclusive way. Furthermore, the music theory community espouses variable analytic practices regarding this music. The goal here is to present the student with the most common tools of analysis and a fundamental understanding to prepare them for further study at the undergraduate and graduate level. ATONALITY (pages 525- 539) These first exercises familiarize students with the concepts of pitch and interval in atonal music. They are fundamental to the understanding that there is no longer a hierarchy of pitches indicating key feeling. Diatonicism and chromaticism and their relative degrees of behavior no longer exists. We are concerned only with the employment of the twelve chromatic pitches and the intervallic relationships they produce melodically and harmonically on a free and equal basis. The beginning of this chapter involves the replacement of traditional interval names with semi-tone analysis. Students may have difficulty remembering the eleven interval numerals. A simple remedy is to have them memorize the semitone measurement for the minor and major third (I3 and I4), and the perfect fifth (I7) and their various enharmonic spellings. These can then be used as “measuring sticks” for the intervals that surround them. At this point, students will be ready to apply the notion that, in atonal music, we look for ways to demonstrate common relationships among harmonic and melodic intervals. To do this, we are concerned with the shortest distance between two pitches. The I7 (as in the perfect fifth ascending from C to G) and I5 (descending from C to G) are related. The smaller, more direct expression of this interval relationship is preferred, and hence the term “Interval Class.” In this stage of pedagogy, students’ knowledge of traditional interval inversion and “MOD 12” become useful: An interval and its inversion will always span an octave and thus comprise 12 semi-tones. By using simple arithmetic, they’ll be able to determine interval class easily and understand that there are only six (6) interval classes.
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Normal order, best normal order, and prime form are the concepts likely to produce the most student confusion. We’ve attempted to make the distinctions clear on page 531, with a review of all terminology on page 538. The goal in this greatly distilled presentation of atonal set theory is to make learning the system less difficult rather than using it to analyze the music. SERIALISM: THE TWELVE-TONE METHOD (pages 539-553) After grappling with freely atonal music, students should find this part of the chapter easier refreshingly transparent. Example 30-27 (page 540) We’ve tried to convey here a bit of the process by which Schoenberg’s twelve-tone method evolved. Ordering gradually becomes a factor before becoming the essence of his method. The Matrix (page 545) The matrix is a tool that can be especially helpful in analyzing certain pieces and of little use in analyzing others. It really depends on the number of row forms present in a composition. At any rate, you may choose to introduce this tool or not. The assignments reinforce concepts of order, transformation, and transposition. Others reinforce the interconnection of set concepts such as derived set, sub-set (segmentation), series interval structure, and applications for analysis. Completion of all the analysis assignments is possible without constructing a matrix, and while we’ve not included matrix construction as part of these assignments, you are free to do so if you wish. SOLUTIONS TO ASSIGNMENTS 1. Atonality 1A.
311
1B. Two solutions, one ascending and another descending, are given for each example.
1C.
Student solutions may be in differing octaves.
312
1D.
Enharmonic equivalents may be used in various notations.
1
2
(025) 6
3
(036) 7
(0246) 11
(047)
12
9
(0467) 13
(026)
5
(0124)
8
(014)
(015)
4
(0235) 14
(0234)
(0347) 10
(016) 15
(0134)
(0256)
1E. Enharmonic equivalents may be used in various notations for sets and inversions may begin on any note. In these solutions, the first note of the set is used for the first note of the inversion.
1 Set (02356)
2 Set (0134)
3 Set (034)
4 Set (0247)
5 Set (0146)
6 Set (025)
7 Set (0267)
8 Set (03467)
9 Set (0136)
10 Set (0347)
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1F.
1G. Create an interval vector for the following sets.
314
1H. 1. The opening set is (014). Additional appearances in mm. 17-27 are: m. 17, beat 3 in the right hand; mm. 19, 21 and 23, beat 3, between left and right hands; m. 24, second half of beat 1 between dotted half G3 in right hand and left hand parts. 2. (026) appears in m.17, beat one, left hand and again in m.18, beat 2, left hand. 3. As a two-phrase group: Mm. 17-20 consists of music with a trichord orientation. A new pentachord motive begins a linear line in the anacrusis to m. 21, with an extension in m. 24 creating a two-phrase division. As a single phrase: Despite the motivic division described above, the three-note accompaniment in the left hand (trichord or dyad) unifies the music from mm. 17-24 into a single unit. As a four-phrase group: It is also possible to view this passage (mm.1724) in four units (or “phrases”) of approximately two measures each. The first phrase begins in m.17 coming to a cadence in the next measure. A second phrase begins in the right hand (m.19) with a linear motive of a quarter-note/half note followed by a five-note pentachord. A third phrase is a modified repetition of the former phrase. The fourth phrase maintains the essential rhythm of the last two phrases with some pitch modification.
Schoenberg: Klavierstücke, op.11, no. 1
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1I. This excerpt is saturated with the trichord (014). The set occurs harmonically in the upper three strings in mm. 1-3, m. 5, beats 1-2, and m. 6, beats 2-3. Other trichords are a contraction of this set–to (013) in violin 1, m. 4, and in a canonic treatment of its expansion to (015) in the upper strings in m. 5, beat 3 through m. 6, beat 1. Webern: Fünf Sätze für Streichquartett (third movement)
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1J. 1. The predominant set is (027). This set is also a quartal “cluster.” 2. There are four “phrases” in this excerpt. Each phrase consists of two rhythmic segments of eighth- and sixteenth-notes respectively. The sixteenthnote unit acts as the “consequent” segment of each phrase. The phrases are harmonically related by the trichord (027) (with a few exceptions) and the dyad (05) and (07)–IC5. • Phrase One: mm. 111-113 • Phrase Two: mm. 114-116 • Phrase Three: mm. 117-120 (both segments are doubled in length.) • Phrase Four: mm. 123-125 (truncated without second segment) Phrase developments include changes in beat groupings (mm. 111 3+2+2 to 2+2+3 in m.115), changes in right hand and left hand alternations, phrase expansion (third phrase mm.117-122), and the contraction of the rhythmic pattern in m. 116 and the phrase length in mm. 123-125). 3. The right-hand left-hand alternation in m. 113 is reversed in m. 116. The rhythm in m. 116 is truncated by eliminating the 8th-note value on beat 2 and replacing it with a 16th rest. Measure 121 has the same music as m. 113 transposed up by I5 (a perfect fourth). 4. Measures 111 and 114 both have a 3+2+2 beat grouping, but the left-hand right-hand juxtaposition on beat 1 in m. 111 has been reversed on the same beat in m. 114. Measure 114 beat 2 is a transposed fragment of the figure from m. 111 beat 1. The outer right-hand trichords have also been transposed in m. 114. Measure 115 reverses the beat grouping of mm. 111 and 114 to 2+2+3. The trichord (027) has been inverted, placing the I2 on top of the cluster. Measure 120 has the same pitch material as m. 115, but the beat grouping is changed to 3+3+2 expanding this measure by an 8th–note. Measure 122 is a repetition of ms. 121 transposed by an ascending I2.
317
Daniel McCarthy: “The Drums of Moria” from Time Out of Mind: Six Tales of Middle Earth
318
2. Serialism 2A.
2B.
319
2C. 1
& 2
&
Webern: Row from String Quartet op. 28
w #w
w #w
w bw bw nw
bw
w nw nw
Dallapiccola: Row from Goethe Songs (No. 1)
#w
w nw
w #w
w
w bw
w bw
w
bw
The first row consists of three tetrachords, the second an inverted transposition of the first and the third a simple transposition of the first. The first row reveals an intervallic consistency of I1 in every dyad. It also demonstrates an ascending and descending arch from the first to the second. The predominance of IC1 and IC3 gives the row a high degree of harmonic consistency. Although there are 3 occurrences of I1 (hexachords begin with I1), the second row does not have the dyad consistency of the first. The contour of this row is variable. Each hexachord has a static beginning with wide intervals at the end. This row contains two IC6 where the former row contains none.
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2D. 1. 2.
Schoenberg’s Klavierstücke, op. 33a. There are 12 pitch classes present in each measure. Chords 1 and 6 are set type (0127) and intervallic mirrors of one another. Chords 2 and 5 are set type (0258) and intervallic mirrors of one another. Chords 3 and 4 are set type (0146) and intervallic mirrors of one another. 3. The chordal relationships of mm.1-2 suggests that m.2 contains a transposed retrograde inversion of the row form presented in m.1 4. RH m.3: Chord 4, LH m.3: Chord 3, RH m. 4: Chord 5 LH m. 4: Chord 2, RH m. 5: D-C-G with D (LH) = Chord 6 LH m. 5: C-B with Bb – F (RH) = Chord 1 Schoenberg: Klavierstücke, op. 33a
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5. The information gleaned by answering questions 1-4 allows identification of RI5, which is stated melodically in the right hand of mm.3-5. From this, P0 can be constructed. P0: Bb, F, C, B, A, F, C, D, G, Ab, D, E RI5: A, B, F, F, Bb, C, G, E, D, C, G, D 6.
m.6: P0 (last note belongs to next row) m.7: RI5 LH mm.8-9: I5 RH mm.8-9: P0 RH m. 10: P0 LH m.10: I5 RH m. 11: RI5 LH m. 11: R0 7. The right hand states the same pitch material of the three P0 tetrachords from m. 1 and the three RI5 tetrachords from m. 2. The left hand rhythmically alternates the above with the three tetrachords of I5 followed by the three tetrachords of RI5. 8. P0 and RI5 are hexachordally combinatorial, meaning that the first hexachord of each combine to contain the 12-note aggregate, as do their second hexachords.
2E.
Student solutions will vary. None are provided here.
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QUIZ FOR CHAPTER THIRTY The following questions, along with an excerpt for musical analysis, can form a satisfactory testing instrument for Chapter Thirty. 1.
Name the interval class for each of the following:
2. Place the following pitch collections in normal order and then give the set type for each.
3.
Perform the requested operations on the given twelve-tone row. a. Provide an I6 form.
b. Provide an R4 form.
c. Discuss the intervallic symmetry in this row.
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CHAPTER THIRTY-ONE Harmonic Principles in Jazz WHAT’S THE DIFFERENCE? (page 555) Harmony resides at the core of any competent jazz artist’s improvisations. Because an ongoing cross fertilization occurred between jazz and art music throughout the twentieth century, many harmonies and techniques discussed in this chapter may be familiar from Part Seven: Advanced Chromatic Harmony. The context is, of course, much different. Furthermore, the topic of jazz harmony is so deep that much has been left unplumbed. Time and space limitations preclude discussion of, for example, upper-extension triads, modal harmonies, dominant-seventh octatonicism, and some of the more advanced chord substitution techniques. Tightly packed though it is, the chapter is nevertheless a rather basic look at a vast and fascinating topic. EXTENDING THE TRIAD (pages 556-564) A difference between popular music and jazz lies in how far and how often the triad is extended. Generally, the lexicon of popular music is limited to the triad and seventh chord (those shown on page 556). Jazz is more relentless in its pursuit of the triadic extension, and while almost any traditional jazz tune can be harmonized by the six basic seventh chord types, most jazz artists today will substitute the more complex extensions and alterations shown in Example 31-2. Jazz musicians differ widely in the way they use and symbolize these higher extensions, and students need not memorize them. The six basic seventh chord types are sufficient. If you wish, you can require your class to recognize and/or spell the basic ninth chords, which are obtained by adding a diatonic ninth to each of these. Concept Check (page 561): The basic chord symbols are: FMaj7 | Eb7 | FMaj7 | Eb7 | Bm7-5 Bbm | Am7 Go7 | Gm7 C7 | FMaj7 The E in m. 6 can be labeled a SUS. Example 31-5 (page 563) Voicing is highly varied in jazz. However, voicing with either the fifth or seventh directly above the root is perhaps the most common. When a keyboardist or guitarist is “comping” behind a soloist, the chords are voiced for their overall sound or for the way they fit beneath the highest pitch. Individual voice leading is a lesser concern in this context.
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Added Practice (page 563): Complete chord symbols for Example 31-5b follow. Several of these might be expressed in a different way. Template 1 was used for each chord. Cm7
Cm7
Cm9
Cm7
Add4
11
13
Cm 9 Cm 9
11
Cm 9
CHORD SUBSTITUTION (pages 564-575) Chord substitution involves primarily three techniques: tonicization, tritone chord substitution, and addition of auxiliary chords. The first two are discussed in this part of the chapter. Tonicization was introduced in Chapter 15. Example 31-7b shows its most basic form—the creation of a dominant seventh chord to each succeeding chord. The diminished seventh chord is used to tonicize much less often than the dominant seventh in jazz and popular styles. The Turnaround (page 565) Turnarounds, most commonly variants of the I-vi-ii-V pattern discussed in Chapter Five, are used at the ends of phrases in place of a simple V as a leadback—a turnaround—to the beginning of a tune or the repetition of a phrase. Jazz performers spend much time working through a variety of turnarounds in all keys. More is said about this later in the chapter. Added Practice (page 567) Complete chord symbols for a are: 7 7 13 13 9 D | D | G | G | C
| C
13
| F
7
13
| F
7
F +5
Example 31-11a (page 568) An excellent drill is to have students write out (and/or practice playing) these turnarounds in various keys. The more familiarity with them, the better. Concept Check (page 572) The melody note in each case constitutes the flatted fifth in the substitute chord (see the addition of “-5” to the chord symbols in Example 31-15). Any of these might be symbolized alternatively as an augmented eleventh (-5 = +11). Expanded Tritone Substitution (page 573) This is a more advanced concept that you may wish to forgo in the interest of time. If so, skip directly to Implied Lines on page 575.
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IMPLIED LINES (pages 575-580) Reading Between the Chords (page 575) It sometimes requires a rather convoluted series of chord symbols to suggest what is actually a very simple arranging technique—creating a scalar line in a secondary voice. Jazz musicians learn to recognize the linear potential in certain successions of symbols through repeated encounters. Example 31-20 shows a very common situation. However, with all but a few notes of the chromatic octave usable as an extension or alteration of each basic seventh chord, lines can be sculpted from most chord successions. You might have students arrange Example 31-24a (page 579) for a jazz ensemble using Example 31-18c as a model. Give the melody to trumpets and/or horns, chordal punctuations to the trombones, and the implied line to the saxophones. Or do it a different way. Review and Reinforcement (page 579) The chords of mm. 3–4 are obtained through a two-step process. 1) Preceding each chord with its own dominant seventh chord yields B7 - E7 - A7 D7. 2). Tritone substitution for the B7 and A7 yields the chromatic progression F7 - E7 - Eb7 - D7. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1A on page 408: Alternatively, you can ask students to provide the complete chord symbol, using Example 31-2 as a reference. You might have them voice the second set of ten using Template 1 or Template 2 given on text page 562. • ASSIGNMENT 1C on page 409: Students can be asked to write the basic seventh chord (referring to the basic seventh chords shown on p. 556) that underlies each of these extended harmonies. • ASSIGNMENT 1G on pages 411-412: Students can be asked to provide a Roman-numeral analysis of these excerpts and then identify the extended tonicizations (ii-V patterns) present in each. (Example 2 is more complex than 1.) • ASSIGNMENT 3A on page 419: Students might be asked to arrange the second of these tunes for a jazz ensemble, using Example 31-18c (page 576) as a model. The implied counterlines in mm. 1–4 and mm. 5–8 might be embellished slightly. One could be given to the trombones and the other to the saxophones. ******************************************************************
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SOLUTIONS TO ASSIGNMENTS 1. Extending the Triad 1A. 7
1 F
7
6 C
Maj7
1 F 6 B
m7
+7
2 Abm
3 Em
7 B
8 Go
7
2 Eb
Maj7
7
3 D
m7
7
7
4 E
Maj7
9 G
4 C
m7-5
7
7
5 D
7
10 C
5 C
m7 Maj7
7 E
8 A
9 D
10 G
-11 2 Cm -5
+9 3 F+5
13 4 Bb M9
5 E9
1B. -13 1 G -9 Mm7 Maj9 b 6 6 E MM7 1C.
om7 -9 7 D -5 Mm7
Mm7
8 Gm13 mm7
MM7 +11 9 C -9 Mm7
Mm7 9 10 Fm +7 mM7
327
1D.
1E.
Roland Hanna: Prelude No. 2
Measure:
1
Extended symbol:
Fm
Basic Seventh Chord:
X
Measure:
2
3
4
C /Bb
A
B
X
X
5
6
7
8
Extended symbol:
13 D sus4
13 D 11
Basic Seventh Chord:
D
D
Measure:
9
10
7
13
7
7
7
Extended symbol:
C m
Basic Seventh Chord:
X
F
Measure:
13
14
Extended symbol: Basic Seventh Chord:
7
B -9
7-5
Gm -5
11
Gm
7-5
F
+9
7
C -9
13
C
7
7
D
C m
X
X
F
11
12
7-5
F
7
X
9
Bm
7
F-9 7
9
Bm /A 7
Bm
Bm
15
16
Fm 9 Fm 11
Fm
7
Fm
328
1F.
1
2
6
7
3
4
8
5
9
10
1G. 1 Thielemans: “Bluesette”
2 Evans: “Turn out the Stars” The b13th in m.27 and m. 29 is symbolized here as a 5. Either symbology is acceptable.
329
2. Chord Substitution 2A.
330
2B. 1
2
3
2C. 1
Tritone-related dominant seventh chords: 2 3 4
5
331
2D. 1
2
3
4
5
2E. 1
2 1 2
B7 F7
Bb7 E7
A7 Eb7
Ab7 D7
G G
332
2F.
2G. 1 1.
Bill Evans: Orbit E+7 - Am9 = ii-V D9 = V G+7 - Cm7 = ii-V F+7 = V
2. The passage consists of two statements of a 4-measure melodic-harmonic sequence. Both 4-measure statements also comprise a 2-measure sequence. The pitch level rises a minor third every two measures. 3.
13
m. 2, beat 3 ½ = D 9 m. 3, beat 1 = GMaj9 m. 4, beat 1 = Cm9
333
2
Heyward, Gershwin and Gershwin: “I Loves You, Porgy” If a thirteenth chord includes the eleventh, then this is shown in the symbol. A thirteenth chord lacking the eleventh (usually a dominant thirteenth) is simply shown as, for example, G13.
1.
2.
The question contains an error (see Errata). The tonicized Bb Maj7 in question appears in m. 2. It is preceded by a tonicizing ii-V (Cm9-F9). The Cm9 is, in turn, preceded by the tritone substitute for its tonicizing dominant.
334
3.
The chord at the end of m. 4 is a tritone substitute for A7 (V7/vi). The chord at the end of m. 5 is a tritone substitute for D7 (V7/ii). 3. Implied Lines 3A. The various linear implications of the chord symbols are shown in the following solutions. Students might be encouraged to build more elaborate “arrangements” around them. 1
Comden, Green, and Styne: “Make Someone Happy”
2
Harbach and Kern: “Yesterdays”
335
3B.
DeSylva, Brown, and Henderson: “The Birth of the Blues”
3C.
Andre Previn: “In Our Little Boat”
336
Line implied in mm. 38–43:
337
QUIZ FOR CHAPTER THIRTY-ONE 1. Name the extension or alteration to the basic chord that each pitch represents. Chord:
Pitch:
Dm7 EbMaj7 Bb7 Gm7-5 E7 F7 AMaj7 C7 Am7 D7
G C E
G
C B
D Db B Ab
Extension or Alteration: _______ _______ _______ _______ _______ _______ _______ _______ _______ _______
2. Upon the repeat of the two-measure pattern, make the substitutions that create a chromatic descending bass line of chord roots. (The chromatic line does not need to be unbroken.)
3. Notate the two melodic lines implied by the lead-sheet symbols. The first pitch of each implied line is provided. Dudley Moore: French Waltz
338
CHAPTER THIRTY-TWO The Blues BLUES FORM AND HARMONIC PRACTICE (pages 583–592) Blues form is its harmonic pattern, shown in its pristine state in Example 31-2. This pattern can be spread over twelve measures (the most common form), twenty-four measures (with every chord duration doubled), or with minor accommodations, over sixteen or thirty-two measures. To make an unlikely comparison, the plagal bias toward the subdominant that lends an air of resignation to the music of Brahms seems a fitting setting for the often melancholy lyrics of the early blues. Page 583 The earliest blues recordings such as those by Robert Johnson show the favored key to be E. Guitarists will know why this is so. I (or i), IV (or iv), and V7 are easily playable open-string chords in these keys. Example 32-4 (page 586) The basic blues as played today exists with many minor variations. This one is quite common. It is interesting that the dominant seventh chord, which in art music evokes such a strong need for resolution, has acquired an air of finality in this style. It appears to be more evidence that, in our musical system, conditioning trumps all. Example 32-6 (page 590) The harmonic substitutions here are the same ones introduced in Chapter 31. If students were unclear about extended tonicization and tritone substitution, then they have another chance to understand these techniques now. Example 32-7 (page 591) Although the minor blues differs little from the major form, it seems not to have been worked over as thoroughly as far as harmonic substitution goes. You might challenge some of your jazz students to elaborate this version with additional harmonies. BLUES MELODIC PRACTICE (pages 593–597) The true origin of the blue notes is shrouded in unwritten and unrecorded history. Explanations are really just theories. This one seems to be supported by early blues recordings.
339
Examples 32-9 and 32-11 (pages 594–595) The more basic a blues tune, the more closely it hovers around the bluenotes. These examples are basic blues melodies. The first is the more sophisticated, the second the more elemental. BLUES VARIANTS (pages 595–597) Example 32-12 is a yet more basic blues tune. You can ask students how this one could be transformed from a sixteen-bar blues to the twelve-bar variety. It could be done by eliminating the last four measures and changing the harmony of mm. 9–10 to an altered dominant (which would support the melody notes), then following this with tonic harmony in mm.11–12. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1B on page 424: You can decide how basic or how sophisticated you want these basic blues patterns to be. Add other keys at your pleasure. • ASSIGNMENT 1D on page 426: You can require students to complete the exercise by adding lead-sheet symbols. • ASSIGNMENT 2A on page 427: You might bring performance into the classroom by having students show up with their instruments on a given day and play these scales in unison, ascending and descending, several times. This will add interest and “personalize” the material in a way that merely writing it will not. • ASSIGNMENT 2B on page 428: Although this is contained on the Workbook CD, in-class performance by students would add interest. ****************************************************************** SOLUTIONS TO ASSIGNMENTS Blues Form and Harmonic Practice 1A. Blank measures indicate repetition of preceding chord. 1
340
2
3
4
341
1B. Students adept at music notation software might find a shortcut to completing these and other exercises by doing the first one and letting the computer transpose the rest. This is an unfortunate side effect of technology. Requiring that students do the exercises “by hand” will at least make that option less appealing. 1
2
342
3
1C. 1
2
3
4
1. The basic chord of m. 4 is a G13. It has been preceded by its ii (Dm7). 2. The G13 has then been replaced by a its tritone substitute Db9. 1. The B13 is the tritone substitute for V7 (F7). 2. The Bb-9 is a tonicization (V7) of the iv that normally follows in m. 5.
1. The Bb-13 of m. 4 has been preceded by its ii (Fm9). 2. The Fm7 is an auxiliary chord to the Fm9. 1. 2. 3. 4.
The D13 is an auxiliary chord to the Db13of m.2. The D9 of m. 4 is a tritone substitute for the tonic Ab7. The Eb9 is a tritone substitute for A7, which tonicizes the D9. The E9 is an auxiliary chord to the Eb9.
1D. The raw, unvoiced chords that students are asked to provide are a far cry from the voiced versions and, played as notated, will not sound particularly charming or jazzy. If you have a pianist majoring in jazz studies in your class, you might ask him or her to play the solutions as they would likely do if they encountered the chord symbols in an actual lead sheet. For your reference, No.2 has been voiced in a manner more typical of a minor blues performance.
343
1
2
344
2. Blues Melodic Practice and Blues Variants 2A.
B. Monk’s melody is constructed largely around four pillars of the blue note scale given on text page 594-in F, F-Ab, Bb, and C–with the added An. Monk employs the plagal form (dominant-to-dominant) of the scale. Monk uses a technique of melodic development similar to that used by Stravinsky and Bartok–repetition of melodic fragments with metric shifts and subtle changes in pitch or rhythm–to obtain a highly unified and yet constantly varied result.
345
C.
1
2C. Students’ solutions will vary. None is given here. 2D. Solutions will vary. Possible solutions follow. The left hand is optional. 1
346
2
3
347
2E.
Solutions will vary. None are given here.
2F. 1
2 This pattern has a Dorian sound due to the C#s. If you like, you can have students write the entire pattern using only the pitch material of E Dorian. Alternatively, you can encourage them to experiment with various combinations of minor and modal inflections, as is done here.
348
2G. The 12-bar blues structure is maintained with some harmonic alterations. 1. The first four measures are basically tonic harmony (F9), like the traditional blues. The next two measures (mm. 5-6) are basically subdominant harmony (Bb9), like the traditional blues. However, tonic harmony dos not return in the following two measures (mm. 7-8) as in the traditional blues. Measure 9 turns toward the dominant (C79), as in the traditional blues, but these last four measures feature a less traditional turn-around that approaches the tonic from either side (Eb79 and Gb13). Chords serving as lower neighbors to the pillar chords are prominent in the composition. 2. Solutions are on the music. 3. While it is possible to hear two-measure phrases here (all contrasting), the 4-bar phrase is so engrained in the 12-bar blues that the tendency is to hear units of this length. The phrasing in “Huz Bluz” represents a departure from the traditional a a b structure, and is best analyzed thus: a (mm. 1-4)
b (mm. 5-8)
c (mm. 9-12)
349
QUIZ FOR CHAPTER THIRTY-TWO 1.
In the basic C-major blues as performed today: 1 2 3
An F7 would usually appear in m. ____. A Dm7 could appear in m. ____. An A7 would most likely appear in m. ____.
In the basic g-minor blues as performed today: 1 2 3
D7 would most likely appear in m. ____. Gm6 would be most likely to appear in m. ____ and m. ____. A7 would be most likely to appear in m____.
In what 12-bar major-key blues . . . 1 2 3
would Eb7 appear in m.5? ____(Give key) would C7 appear in m. 10? ____(Give key) would Do7 appear in m. 6? ____(Give key)
2. Name the key and the measure numbers of the 12-bar blues in which the following harmonic successions would appear: 1 2 3
3.
G7 | C7 | G7 | Db7 |
Eb7 | Eo7 | Bb7 | G7 | Ab7 | F7 | Bbm7 | Eb7
Key____ Measures________ Key____ Measures________ Key____ Measures________
4
Fm7 | Bb7 | Eb7 Gb7 | F7 E7 |
1
Bb and C are blue notes in the scale built on ____
Key____ Measures________
2
D and G are blue notes in the scale built on ____
3
G and D are blue notes in the scale built on ____
350
CHAPTER THIRTY-THREE Shaping a Song TEXT (pages 598-605) Some things change and some things don’t. With song, the lyrics have and always will be the driving force. Sensitivity to them means according them proper accentuation and punctuation. Interpret “proper” to mean “adhering to the inflections and cadence of natural speech.” Any treatment of song should begin with these considerations. Words and Rhythm (page 599) You can create additional interest by inviting students to bring to class songs of their choosing and then performing the sort of text analysis done here. Syllabic versus Melismatic Text Setting (page 600) The singing contests that have proliferated on television in recent years encourage contestants to “make the music their own,” which generally translates into liberal melodic embellishment. Thus the melisma is more a performance phenomenon than a feature of vernacular music as notated and published. MELODY (pages 600-605) Most melodies in the popular style contain much repetition. Again, you might ask students to bring to class examples of popular songs with strong motivic relationships. Doing so will make this study more immediately relevant for them. The Harmonic Factor (page 601) It is important that students do not construct their melodies without regard to their harmonic underpinning. They may create their melodies simultaneously with the attendant harmonies, they may begin with a harmonic plan as suggested here, or they may add harmony after they’ve created their melody. Regardless, the harmonic factor must be addressed. If harmonies are added after the fact, then the melody may need to retro-fitted to accommodate them. Song Writing Then and Now (page 604) It’s probably safe to say that song composition was more the province of the formally schooled composer in times past than in the present day. This is likely due to a combination of advanced technology and today’s increased interest amateur music making. At any rate, the differences in songs written “then and
351
now” are partly due to the different ways in which they are created, as discussed here. COMPOSING A SONG STEP-B-STEP (pages 606-612) Often, lyrics that appear to be ametric can still be poured into four- and eight-measure phrases. “The Days of Wine and Roses” is a case in point. However, this must be accomplished with careful regard to the natural accentuation of the words. The four-step process described here may seem academic to students, but much of it becomes almost automatic over time. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1A on page 434: Sample songs for both of these texts are available to hear on the web site. After your students have wrestled with this assignment, you may wish to play these renditions for them. • ASSIGNMENT 2B on page 434: The songs for Text a and Text c are on contained on the Workbook CD (Tracks 200 and 201). The song for Text b (“Because of Love”) can be heard on the web site. ****************************************************************** SOLUTIONS TO ASSIGNMENTS These assignments are composition-based and the results will vary widely. No solutions are provided here.
Appendix A
A-1
APPENDIX A Pitch THE STAFF AND ITS CLEFS (page 613) You’re free to decide how much emphasis to place on the reading of the C clefs. In our experience, the ability to read both alto and tenor clefs has proven more beneficial than using transpositional tricks because the note recognition is more direct and immediate. Of the two clefs, alto is the more important for one reason only—the viola part in a score. Some of your students–trombonists, cellists, and bassoonists–may already have been introduced to tenor clef. Our drills include all four clefs. If you wish to change the C clefs to treble or bass, feel free. THE HALF STEP AND WHOLE STEP (page 616) The half step and whole step are presented again in Chapter Two (Intervals). They are introduced here because they are necessary for building scales. This is also the rationale for discussing enharmonics at this point. SCALES AND KEYS (pages 619-628) Although it’s more historically accurate to speak of a lower pentachord and upper tetrachord, viewing the major scale as two identical tetrachords separated by a whole step provides an easier way for students to construct and identify the major scale. The Melodic Minor Principle (page 627) This principle is referred to at various times. It addresses the reasons for the variable sixth and seventh degrees in the most complete way possible and helps students understand how all three minor scale forms–mere abstractions, after all–are in fact members of a single scale. To this end, you might ask your students to explain how the melodic minor principle produces the harmonic minor scale of Example A1-21b. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 1A: For in-class drill on clef reading, assign a clef and have the class read the letter names in tempo. • ASSIGNMENT 1B: For additional practice, change the clef at the beginning of each line and have students redo the exercise. • ASSIGNMENT 1G: Alternatively, students might be asked to write the interval in the other direction.
Appendix A
•
A-2
ASSIGNMENT 2E: You might ask students to alter the pitches so as to create a different minor scale form. ASSIGNMENT 2F: Students can be asked to renotate or transpose these passages in a different clef. ASSIGNMENT 2H: Ask students what key change would be necessary to place each of these passages in the parallel major mode.
• •
Suggested Aural Quiz •
Play 10 intervals–either half steps or whole steps-and ask students to identify. Play 10 scales and ask students to identify the form-major, natural minor, harmonic minor, or melodic minor.
•
SOLUTIONS TO ASSIGNMENTS 1. Pitch and Its Notation 1A. 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1B. 1 G3 2 E4 3 B3 4 D3 5 A4 6 F4 7 C4 8 A3 9 G4 10 E3 11 G3 12 E3 13 E4 14 A3 15 C4 16 F3 17 B2 18 D4 19 b3 20 G4 21 F4 22 D5 23 A4 24 C4 25 B5 26 G5 27 B4 28 C5 29 G4 30 E4 31 C3 32 E4 33 F2 34 D3 35 B2 36 A3 37 E3 38 G2 39 F3 40 B3
Appendix A
A-3
1C. 1
1D.
1E. 1
2
3
4
5
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Appendix A
1F. 1 w
2 h
A-4
3 w
4 h
5 h
6 w
7 h
8 w
9 h
10 h
1G. Make sure students understand tat they are to write the diatonic interval. No.7 is especially prone to error in this regard. 1
2
3
4
5
6
7
8
9
10
IH. 1
2
3
4
5
6
7
8
9
10
1I. Enharmonic pitches are: 1 and 12; 2 and 5; 3 and 14; 4 and 19; 6 and 15; 7 and 10; 8 and 9; 11 and 16; 13 and 17; 18 and 20 1J. Enharmonically equivalent intervals are: 1, 2, 5, 6, 9, and 10
Appendix A
A-5
2. Scales and Keys 2A. 1
2
3
4
5
6
7
8
9
10
2B. 1
6
2
7
3
8
4
9
5
10
Appendix A
A-6
2C. 1
2
3
4
5
6
7
8
9
10
2D.
Appendix A
2E.
2F. 1
A-7
Appendix A
2
2G.
2H. 1
2
1 C harmonic minor: C D Eb F G Ab B C 2 E harmonic minor: E F# G A B C D# E 3 A major: A B C# D E F# G# A 4 C harmonic minor: C# D# E F# G#A B# C#
A-8
Appendix A
3
4
A-9
B-1 Appendix B
APPENDIX B Rhythm ELEMENTS OF THE PROPORTIONAL SYSTEM (page 629) This textbook assumes that entering music majors are able to read music in at least one clef, including the rhythmic aspect. If they cannot do this, their proper starting point in music theory is a fundamentals course, where the topics discussed here are presented in greater detail and in a more graded fashion. This short primer on rhythm can be fleshed out in class at your discretion. Most students will understand note and rest values. Accent is another matter. Most students think of accent only in dynamic terms. The tonal and agogic accents may be new to them, yet they play important roles in the creation or identification of meter, as discussed in the next section. METER AND MEASURE (page 631) Students at this point may read simple and compound meters well enough without truly understanding the differences. As an experiment, ask your class to explain how 3/2 and 6/4 are performed. If you like, you can combine this section with the further discussion of meter in Chapter 1 (“Metric Matters” on page 11). We’ve found that students have difficulty notating rhythmic passages in the less familiar meters, due in part to less exposure to them in general and in part to a less-than-perfect understanding of the meter’s character (simple duple, compound triple, and so on). Rhythmic transcription exercises provide the cure for this condition. NOTATING RHYTHM (page 636) While students may read rhythms well enough, they may do so without fully understanding the notational conventions that pertain, particularly regarding ties, dots, and beaming. Although music notation can itself comprise an entire course, this brief section provides the minimum they need to notate music according to customary protocol. In point of fact, freshman/sophomore music theory typically deals very little with rhythmic notation once introduced, the thrust of the course being melodic, harmonic, and formal. Suggested Additional Uses of Drills and Assignments (Workbook): • ASSIGNMENT 2A: A further step in this assignment might be to ask students to identify the meter based on the accentuation and draw the bar lines. Another step might be to ask them to transcribe the passage to a different meter that would lead to an identical performance.
B-2 Appendix B
•
ASSIGNMENT 2D: Once students have added the bar lines, have the class clap the rhythms. • ASSIGNMENT 2G: Once students have completed the measure, you might ask them to transcribe the rhythmic pattern to an equivalent meter. • ASSIGNMENT 3C: Once again, you can use these patterns for rhythmic reading practice. This helps to reinforce students’ understanding of the meters. ****************************************************************** SOLUTIONS TO ASSIGNMENTS 1. Elements of the Proportional System 1A. 1
w=4 q
2
w. = 4 q.
3
h. = 4 e.
4
6
e. = 3 x
7
q..= 7 x
8
w. = 3 h
9 q. = 2 e.
1B. 1
2
3
4
5
6
7
h.. = 14 x
5
e=2x
10
q. = 6 x
B-3 Appendix B
8
9
10 1C. 1
2
3
4
5
1D.
B-4 Appendix B
2. Meter and Measure 2A. 1
2
2B. 1
2
3
4
5
6
7
8
2C. 1 3 beats
2 1 ¾ beats
3 1 ⅔ beats
4 4 ½ beats
5 4 ½ beats
6 1 ½ beats
7 4 ½ beats
8 7 beats
9 3 ¾ beats
10 1 ⅚ beats
2D.
B-5 Appendix B
2E. 1
2
3
4
5
2F.
B-6 Appendix B
2G.
3. Notating Rhythm 3A. 1
2
3
4
5
6
7
8
B-7 Appendix B
9
10 3B. 1
3C. 1 2 3 4 5 6 7 8 9 10
2
3
4
5
6
7
8
9
10
B-8 Appendix B
3D. 1
2
3E. 1
2
B-9 Appendix B
3
4
