PROLONGATION OF SEVENTH CHORDS IN TONAL MUSIC Volume II
Examples
Y osef Goldenberg With a Foreword by
L. Poundie Burstein
The Edwin Mellen Press Lewiston •Queenston• Lampeter
Library of Congress Cataloging-in-Publication Data Goldenberg, Yosef. Prolongation of seventh chords in tonal music : volume II : examples I Y osef Goldenberg ; with a foreword by L. Poundie Burstein . p.cm. Includes index. ISBN-13: 978-0-7734-4852-0 ISBN-I 0: 0-7734-4852-7 I. Title. hors serie. A CIP catalog record for this book is available from the British Library. Copyright
©
2008
Y osef Goldenberg
All rights reserved . For information contact The Edwin Mellen Press Box450 Lewiston, New York USA 14092-0450
The Edwin Mellen Press Box67 Queenston, Ontario CANADA LOS ILO
The Edwin Mellen Press, Ltd. Lampeter, Ceredigion, Wales UNITED KINGDOM SA48 8LT Printed in the United States of America
Prolongation of Seventh Chords Vol. 2: Examples
Yosef Goldenberg
To my parents, Gideon and Esther
LIST OF EXAMPLES 1.1: Chord prolongation versus tone prolongation.................................................. 1 1.2: Combining circular and transitive motion ....................................................... 1 1.3: Prolongations that do not compose out............................................................ 1 1.4: Horizontalization of a chord that does not literally appear.............................. 2 1.5: Space-filling motion within the boundaries of a second.................................. 2 1.6: Space-filling motion in connective arpeggiations and linear progressions ..... 2 1.7: Space-filling motion from incomplete neighbors ............................................ 3 1.8: Horizontalization of intervals through subdivision incongruent with the harmony...................................................... 3 1.9: Subordinations ................................................................................................. 3 1.10: Concepts of seventh chords ........................................................................... 4 1.11: Recognition of the tertian relationship between the fifth and the seventh..... 4 1.12: Reverse hierarchy for contextual consonance and dissonance ...................... 4 2.1 :The normative situation: dissonances transformed into consonances ............. 5 2.2: Dissonant support ............................................................................................ 5 2.3: Seeds of PD in strict counterpoint: Decorated suspensions............................. 5 2.4: Schenker’s application of decorated suspensions ............................................ 6 2.5: The cambiata as related to the decorated suspension....................................... 6 2.6: Exceptions in strict counterpoint for diminished triad in root position ........... 6 2.7: Rudimentary prolongation of diminished £− in strict counterpoint.................... 6 2.8: Justification of the diminished £− ....................................................................... 7 2.9: The apparent passing tone................................................................................ 7 2.10: The apparent passing tone with accompaniment ........................................... 7
2.11: Radical potential of the leading tritone’s gravitation..................................... 8 2.12: Violating the distinction between the melodic functions of steps and leaps . 8 2.13: Streching and quasi-streching of seventh chords........................................... 9 2.14: Space-filling motion in seventh chords: connective motion.......................... 9 2.15: Space-filling motion in a third-space above a triad ....................................... 9 2.16: Space-filling motion in a third-space below a triad ..................................... 10 2.17: Dissonant surface harmonization of a conceptually consonant primary tone ................................................... 10 2.18: Delayed resolution ....................................................................................... 10 3.1: Prolongation of seventh chords in pre-Schenkerian literature: Heinichen .... 11 3.2: Prolongation of seventh chords in pre-Schenkerian literature: Rameau........ 11 3.3: Prolongation of seventh chords in pre-Schenkerian literature: Kirnberger ... 11 3.4: Prolongation of seventh chords in pre-Schenkerian literature: Hynais ......... 12 3.5: Prolongation of seventh chords in pre-Schenkerian literature: Louis and Thuille ........................................................................................... 12 3.6: Dissonance treatment in strict counterpoint as merely analogous to free composition in Schenker’s Harmonielehre ........................................ 12 3.7: A seventh chord as a true Stufe in Schenker’s Harmony ............................... 13 3.8: Seventh chords and harmonizability in Schenker’s Harmony....................... 13 3.9: Augmented fourths as harmonic intervals in Schenker’s Counterpoint I...... 14 3.10: Passing motion within seventh chords in Schenker’s annotated copy of Bach’s Prelude BWV 894 ....................................................................... 14 3.11: A seventh chord as a true Stufe in Schenker’s Beethoven’s Ninth Symphony................................................ 15 3.12: Schenker’s argument against understanding the seventh as representing a second in Beethoven’s Ninth Symphony........................... 15 3.13: A composed out seventh chord in Schenker’s Beethoven: Die letzten fünf Sonaten. Op. 109. ............................................. 15 3.14: (True) seventh progression in Schenker’s Beethoven: Die letzten fünf Sonaten. Op. 110. .............................................. 16 3.15: The leading-tone tritone in Schenker’s Counterpoint II .............................. 16 3.16: Passing chords within a seventh chord discussed in Schenker’s response to Schoenberg in The Masterwork in Music II..................................................................... 16
3.17: A vertical dissonance in Schenker’s discussion that prohibits such a phenomenon in The Masterwork in Music II.............. 17 3.18: A prolonged seventh chord in Schenker’s tonal analysis of Stravinsky ...... 17 3.19: A prolonged seventh chord in a stable passage in The Masterwork in Music II.......................................................................... 18 3.20: A textbook representation of a prolonged seventh ...................................... 19 3.21: Structural priority of a seventh chord according to Lehrdahl’s and Jackendoff’s Time-Span Reduction Preference Rule 2 ..... 19 3.22: Types of suspensions: Clark’s argument after Schenker ............................. 20 3.23: Analogy between tonal and post-tonal prolongations.................................. 20 3.24: Motivic parallelism between structural levels in post-tonal music.............. 21 3.25: Prolongation of seventh chords using set theory ......................................... 21 4.1: Unsupported stretch passing from a cover tone............................................. 22 4.2: Background seventh in an inner voice ........................................................... 22 4.3: Unresolved seventh in an Urlinie from ^5 ...................................................... 22 4.4: Unresolved seventh in an Urlinie from ^8 ....................................................... 23 4.5: Background connection between ^7 and ^4....................................................... 23 4.6: Unsupported ^3 in an unprolonged formiations .............................................. 23 4.7: V7 in a fifth-line above two bass arpeggiations ............................................. 24 4.8: Forcing the ^4 to function as a (lower-level) primary tone ............................. 24 4.9: IV7 at the deeper levels .................................................................................. 24 4.10: Schenker’s approach to the complete upper neighbor to ^3 .......................... 25 4.11: The fallacy of ‘consonant preparation’ to V7 ............................................... 25 4.12: V7 as the product of an apparent incomplete neighbor tone ........................ 25 4.13: Dilemma between complete and incomplete neighbor................................ 26 4.14: Incomplete neighbor before interruption ..................................................... 26 4.15: The seventh as a lead-in before interruption................................................ 26 4.16:Another context for the ^4–^2 connection........................................................ 28 4.17: Exploitation of both contexts for the ^4-^2 connection................................... 28 4.18: Reaching-over from the seventh of V7......................................................... 29 4.19: Reaching-over from the seventh of V7 after descent ................................... 29 4.20: Unfolding of the leading-tone tritone .......................................................... 30 4.21: Dissonant unfolding in the bass ................................................................... 31 4.22: The lowered second scale degree in the Urlinie .......................................... 31
4.23: Priority of diatonic dissonances ................................................................... 31 4.24: Secondary dominant seventh chords............................................................ 32 5.1: The two senses of 8–7.................................................................................... 33 5.2: The seventh in lower counterpoint................................................................. 33 5.3: The seventh proceeding in ascent .................................................................. 33 5.4: Comparative investigation of prolongations of the seventh .......................... 34 5.5.: Types of neighbors to seventh chords........................................................... 35 5.6: Seventh progressions (segmented into thirds) versus a sixth plus a second .. 35 5.7: Oster’s criterion of distinguishing true seventh progressions........................ 35 5.8: Derivations of Oster’s rule............................................................................. 35 5.9: Descending major-seventh progression ......................................................... 36 5.10: Illusory descending seventh progressions.................................................... 36 5.11: Problems concerning seventh progressions ................................................. 36 5.12: Further problems concerning seventh progressions..................................... 36 5.13. Descent from the octave of from the seventh?............................................. 37 5.14: Ascending true seventh progressions........................................................... 37 5.15: Alternative illusory seventh progressions.................................................... 37 5.16: The status of the seventh that enters in the middle ...................................... 38 6.1: Independence of V7 after 7–6 series .............................................................. 39 6.2: V7 as analogous to consonances in second species........................................ 40 6.3: V7 as preparation for suspension.................................................................... 40 6.4: V7 as resolution of suspensions...................................................................... 40 6.5: V6–7 appoggiatura ........................................................................................... 41 6.6: V8–7 as a lead-in from interruption ................................................................. 41 6.7: An analytical dilemma in Beethoven, Piano Sonata Op. 53/I........................ 41 6.8: V8–7 appoggiatura to a passing seventh .......................................................... 41 6.9: Appoggiaturas to inverted V7 ........................................................................ 42 6.10: V§°–¶¦ .............................................................................................................. 42 6.11: De-tonicization of V .................................................................................... 43 6.12: Gradual transformation of V into V7 ........................................................... 43 6.13: V5–7 space-filling motion ............................................................................. 44 6.14: V5–7 as a true neighbor ................................................................................. 44 6.15: Other forms of space-filling motion toward V7 ........................................... 45 6.16: Space-filling motion from an initial seventh ............................................... 45
6.17: Rhythmic normalization of subordination to V7 ......................................... 46 6.18: Types of subordinations to V7 ..................................................................... 46 6.19: Other subordinations to V7 .......................................................................... 47 6.20: Subordination of seventh chords to V7 ........................................................ 47 6.21: Subordinations to inverted V7 ...................................................................... 47 6.22: Apparent subordinations to V7 ..................................................................... 48 6.23: Space-filling motion within IV–V7 .............................................................. 49 6.24: Space-filling motion within II–V7 ............................................................... 49 6.25: Space-filling motion within VII–V7 ............................................................ 50 6.26: Space-filling motion within VII7–V7 ........................................................... 51 7.1: Harmonies that emerge in prolongations of V7............................................. 52 7.2: Single third progressions within V7 ............................................................... 52 7.3: Parallel third progressions from the root and the third to the third and the fifth of V7 ........................................................................ 53 7.4: Other parallel third progressions within V7 ................................................... 54 7.5: Voice exchanges of thirds within V7 ............................................................. 54 7.6: Combinations of third progressions within V7 .............................................. 55 7.7: Chromatic filling of a single third progression in V7 ..................................... 55 7.8: Chromatic filling of parallel third progressions in V7 ................................... 56 7.9: Chromatically filled voice exchanges in the upper thirds of V7 .................... 58 7.10: The omnibus progression............................................................................. 58 7.11: Omissions from the omnibus ....................................................................... 60 7.12: Harmonic variants of the omnibus as result of neighbors............................ 60 7.13: Displacements in the omnibus ..................................................................... 61 7.14: Insertions into the omnibus.......................................................................... 61 7.15: Outer expansion of the omnibus .................................................................. 62 7.16: Combination of modifications of the omnibus ............................................ 62 7.17: Apparent omnibus........................................................................................ 63 7.18: Altered third spaces within V7 ..................................................................... 64 7.19: Third progressions that exceed the limits of V7 ........................................... 65 7.20: (Ascending) sixth progressions within V7 ................................................... 66 7.21: A complex sixth progression within V7 ....................................................... 66 7.22: Descending sixth progressions within V7 .................................................... 67 7.23: Diminished fifth progressions within V7 type 1........................................... 67
7.24: Diminished fifth progressions within V7 type 2 via II ................................. 68 7.25: Other harmonizations of diminished fifth progressions within V7 type 2.... 68 7.26: Diminished fifth progressions within V7 type 3........................................... 69 7.27: Ascending diminished fifth progressions within V7 .................................... 69 7.28: Perfect fifth progressions within V7 type 1 ................................................. 70 7.29: Perfect fifth progressions within V7 type 2.................................................. 71 7.30: Perfect fifth progressions within V7 type 3.................................................. 72 7.31: Combinations of perfect and diminished fifth progressions within V7........ 72 7.32: Ascending augmented fourth progressions within V7 ................................. 73 7.33: Descending augmented fourth progressions within V7 ................................ 74 7.34: Perfect fourth progressions and combined fourth progressions within V7 .. 74 7.35: Schematic true seventh progressions within V7 ........................................... 75 7.36: Hybrid segmentation of a seventh progression within V7 ........................... 76 7.37: Accompanying seventh progressions within V7 by parallel motion............ 77 7.38: Accompanying seventh progression within V7 by means of voice exchanges....................................................................... 78 7.39: Filled second motion V8–7 in a single voice................................................. 79 7.40: V8–7 voice exchanges ................................................................................... 80 7.41: Register transfer of the consonant tones of V7............................................. 81 7.42: Register transfer of the tone of the seventh of V7 ........................................ 81 7.43: Accompanied register transfer of the seventh of V7 .................................... 82 7.44: Register transfer of the seventh of V7 without linear connection ................ 82 7.45: Register transfer of the seventh of V7 through multiple octaves ................. 83 7.46: Ascending register transfer of the seventh................................................... 84 7.47: Simultaneous augmented fourth and diminished fifth progressions within V7 without diatonic subdivision........................................................ 84 7.48: Simultaneous augmented fourth and diminished fifth progressions within V7 adjusted by means of delay.......................................................... 85 7.49: Simultaneous augmented fourth and diminished fifth progressions within V7 adjusted by means of chromatic insertion ................................... 86 7.50: Other counterpoints to diminished fifth progressions within V7 ................. 87 7.51: Simultaneous linear progressions within V7 involving an ascending diminished fifth progression .................................. 88 7.52: Upper neighbor to the root (of V7) alone ..................................................... 88
7.53: Inversions of upper neighbor to the root of V7 ............................................ 89 7.54: Upper neighbor to the octave of V7 ............................................................. 89 7.55: Upper neighbors to the root and the fifth of V7 ........................................... 89 7.56: Insertion of secondary neighbors within V7................................................. 90 7.57: Upper neighbors to the root, the third and the fifth of V7 ............................ 90 7.58: Upper neighbor to the fifth of V7 alone ....................................................... 90 7.59: Lower neighbors to the consonant members of V7 ...................................... 91 7.60: Combinations of neighbors within V7 in contrary motion........................... 91 7.61: Upper neighbors to the seventh of V7 without change of harmony ............. 91 7.62: Upper neighbors to the seventh of V7 with chromatic filling in .................. 92 7.63: “I”¢− as a three-voice upper neighbor to V7—schemes ................................. 92 7.64: “I”¢− as a three-voice upper neighbor to V7—example ................................. 93 7.65: Other harmonizations of V7–8–7 .................................................................... 94 7.66: Harmonizations of V7–6–7 ............................................................................. 94 7.67: Analytical dilemmas: V4–I3–V4 ................................................................. 95 7.68: Lower neighbor to the seventh of V7 harmonized as VI .............................. 96 7.69: V7-6-7 employing mixture ............................................................................. 97 7.70: Chromatic inflection of V7-6-7 neighbor motion ........................................... 98 7.71: Special neighbors to V7 (a): enharmonically chordal neighbors.................. 99 7.72: Special neighbors to V7 (b): whole-tone non-diatonic neighbors .............. 100 7.73: Neighbor parallel motion in all four voices within V7 ............................... 100 7.74: Neighbor contrary motion in all four voices within V7 ............................. 102 7.75: Double neighbors to V7.............................................................................. 103 7.76: Selected combinations of third progressions and neighbor motion ........... 104 7.77: Chopin, Ballade No.3, coda (an outstanding case for Ex. 7.76b) .............. 105 7.78: Mixture as means of prolonging V7 ........................................................... 107 7.79: Reaching-over within prolongation of V7: regaining the same pitch ........ 108 7.80: Reaching-over within prolongation of V7: achieving a higher register ..... 108 7.81: Reaching-over within prolongation of V7: aiming at another pitch class .. 109 7.82: Bass divider within V7 harmonized as II ................................................... 109 7.83: Bass divider within V7 harmonized as II7 .................................................. 110 7.84: Bass divider within V7 harmonized as V/V ............................................... 111 7.85: Bass divider within V7 harmonized not as a root....................................... 111 7.86: Bass arpeggiation within V7 ...................................................................... 112
7.87: Equal division of the octave within V7 through transposition ................... 112 7.88: Equal division of the octave within V7 via smooth voice leading ............. 113 7.89: Voice exchanges within equal division of the octave into four within V7. 114 7.90: Voice exchanges within equal division of the octave into three within V7 117 7.91: Prolongation of V# ..................................................................................... 118 7.92: Prolongation of V$ ..................................................................................... 118 7.93: Prolongation of V2 ..................................................................................... 119 7.94: Prolongation of an apparently inverted V7................................................. 119 7.95: Prolongation of V7 with changing inversion (root position excluded)....... 120 7.96: Motion from V2 to V7 ................................................................................ 122 7.97: Enharmonic parentheses within V7 ............................................................ 123 7.98: Apparent enharmonic parentheses within V7 ............................................. 125 7.99: Prolongation of a major-minor seventh chord as ∂VII7 in minor................ 125 7.100: Prolongation of a major-minor seventh chord as mixolydian tonic? ....... 126 7.101: Prolongation of a major-minor seventh chords in chromatic functions... 127 7.102: V7 prolongation throughout a rondo episode ........................................... 128 7.103: Prolongation of V7/VI in the bridge......................................................... 129 7.104: Prolongation of V7 in the recapitulation bridge ....................................... 130 7.105: Prolongation of V7 in the development (i): Beethoven, Symphony No. 3/I.................................................................. 131 7.106: Prolongation of V7 in the development (ii): Beethoven, Piano Sonata Op. 81a/I .......................................................... 133 7.107: Prolongation of V7 in the development: apparent and problematic cases 135 7.108: Prolongation of V7 in codas ..................................................................... 136 7.109: Prolongation of V7 throughout entire sections of an idiosyncratic form.. 138 7.110: Prolongation of V7 in parallel periods—type a)....................................... 139 7.111: Prolongation of V7 in parallel periods—type b)....................................... 140 7.112: Prolongation of V7 in stable sections ....................................................... 141 7.113: Prolongation of V7 across formal sections ............................................... 143 7.114: Prolongation of V7 across movements in a multi-movement cycle ......... 145 7.115: Integrative analysis of Beethoven, String Quartet Op. 18, No. 2/IV ....... 146 8.1: VIIº7 prolongation as neighbor unfolding.................................................... 150 8.2: Harmonies (triads) that emerge in prolongations of VIIº7 ........................... 151 8.3: Appoggiaturas to VIIº7 ................................................................................. 151
8.4: Subordinations to VIIº7 ................................................................................ 153 8.5: Subordinations to VIIº7 in major.................................................................. 154 8.6: Single third progressions within VIIº7 ......................................................... 155 8.7: Parallel third progressions within VIIº7 ....................................................... 156 8.8: Voice exchanges between the fifth and the seventh of VIIº7 ....................... 157 8.9: Voice exchanges between the third and the fifth of VIIº7............................ 158 8.10: Voice exchanges between the root and the third of VIIº7 .......................... 160 8.11: Third progressions within VIIº7 in different third spans ............................ 162 8.12: Chromatic third progressions within VIIº7 ................................................ 162 8.13: Avoiding clashes in voice exchanges of thirds within VIIº7 ...................... 163 8.14: Third progressions in VIIº7: altered spaces................................................ 166 8.15: Third progressions exceeding the limits of VIIº7 ....................................... 166 8.16: Apparent third progressions within VIIº7 .................................................. 167 8.17: Sixth progressions within VIIº7 ................................................................. 167 8.18: The upper fifth of VIIº7: the problem of retaining the seventh.................. 168 8.19: VIIº7-3 fifth progressions type 1 ................................................................. 168 8.20: VIIº7-3 fifth progressions type 2 ................................................................. 170 8.21: VIIº7-3 fifth progressions type 3 ................................................................. 171 8.22: Selected fifth progressions in the lower fifth of VIIº7 ............................... 171 8.23: Parallel fifth progressions within VIIº7 ...................................................... 172 8.24: Fourth progressions in VIIº7 ...................................................................... 173 8.25: Combinations of fourth progressions and fifth progressions within VIIº7. 174 8.26: Illusory diminished seventh progressions.................................................. 175 8.27: Descending diminished seventh progressions in various segmentations... 176 8.28: Ascending diminished seventh progressions ............................................. 178 8.29: Doubly diminished seventh progression.................................................... 179 8.30: Register transfers in VIIº7 .......................................................................... 180 8.31: Avoidance of direct augmented second through filling in......................... 180 8.32: Avoiding augmented second through insertion ......................................... 183 8.33: Ascending register transfers within VIIº7 .................................................. 184 8.34: Non-linear register transfer within VIIº7.................................................... 186 8.35: Counterpointing linear progressions within VIIº7...................................... 187
8.36: Neighbors to VIIº7: difficulty to determine whether the seventh is stationary ............................................................... 188 8.37: Upper neighbors under (or above) a stationary diminished seventh.......... 189 8.38: Lower neighbors under (or above) a stationary diminished seventh ......... 190 8.39: The problem of a lower neighbor to the diminished seventh..................... 192 8.40: Further harmonizations of VIIº7–6–7 ........................................................... 193 8.41: Upper neighbor to the diminished seventh ................................................ 194 8.42: Enharmonic parentheses within VIIº7 by means of a semitone lower neighbor..................................................... 195 8.43: Enharmonic parentheses within VIIº7 by means of upper neighbors......... 197 8.44: Full enharmonic parentheses within VIIº7 by means of linear progressions................................................................. 198 8.45: Open enharmonic parentheses within diminished seventh chords ............ 199 8.46: Back-relating resolution within enharmonic parentheses in VIIº7 ............. 200 8.47: Prolongation of a diminished seventh chord in a special chromatic context.................................................................... 201 8.48: Prolongation of common-tone seventh chords .......................................... 202 8.49: Larger-scale prolongation of VIIº7: Beethoven, Piano Sonata Op. 2, No. 2/I .................................................... 203 8.50: A problematic large-scale prolongation of VIIº7: Wagner, Parsifal, Prelude to act 3 ............................................................. 205 9.1: Half-diminished seventh chords as inversions of dominant seventh chords 206 9.2: Parallelism between minor-minor II7 and half-diminished II7 ..................... 206 9.3: Harmonies that emerge in prolongations of II7 ............................................ 206 9.4: Subordinations to II7 .................................................................................... 207 9.5: Third- voice exchanges within half-diminished II7 ..................................... 207 9.6: Fifth progressions within half-diminished II7 .............................................. 208 9.7: Seventh progressions within half-diminished II7 ......................................... 210 9.8: Filled voice exchange in the 7–8–7 space of a second in half-diminished II7 ................................................................................... 211 9.9: Neighbors to half-diminished II7 ................................................................. 212 9.10: Prolongation of half-diminished II7 as the product of mixture in major .... 212 9.11: Prolongation of half-diminished attenuated II7 in chromatic context ........ 213 9.12: Parallel third progressions in the lower spans of minor-minor II7 ............. 214
9.13: Third- voice exchanges within minor-minor II7 (in major)........................ 215 9.14: Neighbors to minor-minor II7 .................................................................... 216 9.15: Bass divider within minor-minor II7 harmonized as VI............................. 216 9.16: Large-scale prolongation of minor-minor II7 ............................................. 217 9.17: Prolongation of half-diminished VII7 in major .......................................... 218 9.18: Prolongation of half-diminished altered IV7 .............................................. 219 9.19: Prolongation of minor-minor IV7 .............................................................. 220 9.20: Prolongation of minor-minor VI7 in minor ................................................ 221 9.21: Prolongation of non-tonic major-major seventh chords ............................ 223 9.22: Prolongation of major-major I7 (in major) ................................................. 224 10.1: Schenker on diminished third progressions ............................................... 225 10.2: Hierarchical status of diatonic and augmented sixths................................ 225 10.3: Perceptions of diatonic versus augmented sixths....................................... 225 10.4: ßVI as anticipation of the German augmented sixth................................... 226 10.5: Structural priority of the German augmented sixth over a preceeding ßVI 227 10.6: ‘Preparation’ of (subordingation to) the augmented sixth ......................... 228 10.7: Third progressions in augmented sixth chords: the lowest (diminished) span ..................................................................... 229 10.8: Third progressions in augmented sixth chords: the middle (major) span .. 230 10.9: Third progressions in augmented sixth chords: the upper (minor) span.... 230 10.10: Parallel third progressions in augmented sixth chords ............................ 231 10.11: Fifth-progressions in German-type augmented sixth chords ................... 232 10.12: Neighbors to German-type augmented sixth chords................................ 233 10.13: Support for motion that prolongs German-type augmented sixth chords 234 10.14: Wide prolongation of a German augmented sixth chord ......................... 235 10.15: Enharmonic parentheses within augmented sixth chords via ßII¢− ............ 236 10.16: Consonant ßII within prolongation of augmented sixth chords................ 237 10.17: Back-relating resolution within enharmonic parentheses in a diminished-third chord ...................................................................... 239 10.18: Expanded enharmonic parentheses within augmented sixth chords........ 239 10.19: Enharmonic parentheses within the German augmented sixth without reaching ßII.................................................................................. 241 10.20: Apparent enharmonic parentheses within augmented sixth chords ......... 242 10.21: Hybrid combinations of enharmonic parentheses.................................... 243
10.22: Prolongations of French-structured augmented sixth chords................... 243 10.23: Large-scale prolongation of a French-structured chord? ......................... 245 10.24: Prolongation of rare types of augmented-sixth seventh chords ............. 246
LIST OF ABBREVIATIONS USED IN THE EXAMPLES ant.
anticipation
app.
appoggiatura
aug,
augmented
cons.
consonance
CP
Counterpoint = Schenker [1910. 1922] 1987 (see bibliography)
dev.
development
diss.
dissonance
DN
double neighbor
enh.
enharmonic
EP
enharmonic parentheses
exp.
exposition
FC
Free Composition = Schenker [1935/1956] 1979 (see bibliography)
FGA
Five Graphic Analyses = Schenker [1933] 1969 (see bibliography)
IN
incomplete neighbor tone
MG
middleground
MW
Das Meisterwerk in der Musik = Schenker [1925. 1926. 1930] = 1994. 1996. 1997. (see bibliography)
P
passing tone
PD
Prolongation of Dissonance
perf.
perfect
ii p. p.
pedal point
prog.
progression
rcp.
recapitulation
rg.-ov.
reaching-over
SFM
Space-Filling Motion
sup.
support
sus.
suspension
TW
Der Tonwille = Schenker [1921–24] 2004. 2005. (see bibliography)
FOREWORD The contrast between consonance and dissonance is fundamental to most tonal music. Typically, intervals and chords are regarded either as consonant or as dissonant, with a sharp line demarcating these two categories. But attempts at an absolute separation of the functions and capabilities of consonances and dissonances fall apart under certain circumstances. Most notably, seventh chords often are treated differently than other dissonant configurations. Indeed, sometimes seventh chords are treated as ersatz consonances, even within music of the eighteenth and nineteenth centuries. To be sure, it is not easy for music theorists to account for the special status of seventh chords, but it is also not easy for them to ignore it. Heinrich Schenker was among those who grappled with the treatment of sevenths and seventh chords. For Schenker, the tension created by dissonance and the sense of stability and resolution afforded by consonance form a primal source of tonal expression, drama, and structure. This principle, as codified in the concepts of species counterpoint, lies at the core of his theories. Although Schenker identifies many instances in which an apparent consonance can function as a dissonance on a deeper level and vice versa, for the most part he insists that on deeper levels dissonances will be subordinate to consonances. One consequence of this attitude is Schenker’s famous prohibition against the prolongation of sevenths. It should be noted, however, Schenker’s opinions concerning the prolongation of sevenths did waver over the course of his career. Indeed, even in Der freie Satz he shows a more flexible attitude regarding this issue than is commonly
iv acknowledged. As with Schenker himself, his followers likewise have shown ambivalence in their attitudes regarding the prolongation of sevenths. While a few have adhered in their analyses to the Schenker’s admonition against prolonging sevenths, others either have ignored this prohibition or have argued against it. But to allow the prolongation of sevenths in Schenkerian analysis welcomes inevitable risks: how can one allow certain dissonances freer reign without upsetting the distinctive roles of consonance and dissonance that lie at very heart of Schenker’s theoretic system? It is this issue that Yosef Goldenberg addresses in the present study. Although many other theorists have written intelligently regarding the prolongation of dissonance, arguably none have examined this problem with the care and thoroughness as seen here. In this book, Goldenberg examines at length the writings of Schenker and others regarding the prolongation of dissonance, provides a logical and musical justification for such prolongations based on principles of strict counterpoint and related concepts, and offers a variety of compelling analyses to support these views. The ideas presented here are not a mere revision of Schenker’s ideas, but rather stand as a reengagement and elucidation of principles that are central to Schenker’s method. As such, this study should have a profound impact on approaches to Schenkerian theory as well as to tonal music in general. Prof. L. Poundie Burstein, Music Department, Hunter College and the Graduate Center, CUNY
PREFACE Prolongation of seventh chords is a subject that has both a clear focus that enables the meticulous detailed presentation of the entire spectrum of its specific manifestations, and by the same time also rather wide theoretical and analytical implications, including the essence of prolongation and of dissonance. Based on the theories of Heinrich Schenker, this study explores one of the most problematic issues in the theory, an issue that has caused recurring confusion. Theoretically, prolongation of seventh chords ought not to exist, mainly because sevenths are dissonances, whereas normative prolongations apply to consonances only. In fact, the original subject planned for this work was Prolongation of Dissonances in Tonal Music, based in turn on a general idea to work on Prolongation of Dissonances (mainly in post-tonal music). As I realized the sheer amount and variety of material, I have decided to concentrate on prolongation of seventh chords alone. However, the general theoretical problem concerning prolongation of dissonance is crucial to the final narrower topic, and thus remained within the study. My focus in this work is more technical than philosophical. I have attempted to draw the entire range of procedures that prolong seventh chords in tonal music, based on a typology of seventh chord types and of voice leading techniques, mainly passing motion in each of the emerging chordal spaces, and neighbor motion to each tone of the seventh chord (not necessarily the tone of the seventh itself). Although in principle I studied prolongations of all seventh chords, my interest was in those prolongations that are actually used in the tonal literature. Accordingly, the chapters on prolongations of dominant and of diminished seventh chords are detailed, while those on other seventh chords are modest. The
vi repertoire discussed in this study is wide, ranging from Bach to Mahler and Skryabin. Most examples are drawn from the work of the composers Schenker himself admired. While a systematic philosophical exploration of the same topic must remain the task of other scholars, who might find this work as raw material for their purposes, various aesthetic and semiotic remarks do crop up in the present work in passim. The musical examples are separated from the text, but they are of course an essential part of the work. Most of the examples are Schenkerian voice-leading graphs. Others include recompositions, quotations of musical excerpts and compositional experiments. In both text and examples, raised and lowered tones are indicated in relation to the key, and not necessarily in their actual appearance, e.g., c in A major is ß3, not 3. Accidentals to the left of a chord relate to the root, and to the right of the chord relate to the third, e.g., in C major ßVI is Aß major, VIƒ is A major, and ßVIß is Aß minor. Bibliographic references in the body of the work usually indicate author and year. References to Schenker’s main writings are made in abbreviations, which are explained in the list of abbreviations. With some works, especially by Schenker, I have tried to indicate the exact date of the original editions /source language, but with later works I used a later edition. I wish to thank Eytan Agmon, Dalia Cohen, Roger Kamien, Timothy Jackson and Naphtali Wagner for their perceptive comments on various stages of this work.
1
Ex. 1.1: Chord prolongation versus tone prolongation a)
(1)
versus (2)
chord prolongation
!
¥¥
BB B
g
N
b)
tone prolongation prolonged e and g N
BB
¥¥
B BB
B
I I (prolonged harmony)
g
BB
C C
c is not prolonged but only stretched
C C
simple arpeggiation: streching (no prolongation) of C5/3; quasi-stretching (rudimentary prolongation) of the tone c.
Ex. 1.2: Combining circular and transitive motion a) circular prolongation of the tone e
!
¥ BC CB
g
b) circular prolongation (through voice exchange) of the interval of a third (c-e)
CB
CCB
C
¥ C B C
CB
e
C C
BC B B a
Ex. 1.3: Prolongations that do not compose out a)
b)
g
!
N
B
BB
¥¥
BB
neighbor motion
≠
AA A AA
AA
B
YB mixture
XB
≠
YX A A AA
2
Ex. 1.4: Horizontalization of a chord that does not literally appear Free Composition, Fig. 134, 9: Schubert, Piano Sonata D. 958/IV © 1935 by Universal Edition A.G., Wien/UE 6869 Rights for the English edition belong to the estate of Ernst Oster.
A minor
C minor
Eß minor
Ex. 1.5: Space filling motion within the boundaries of a second a)
! C C C C C C C
b)
=
illusory 7th progression represents an inverted 2nd
c)
C C C C C C C C C C C
=
=
C C
CWC C
illusory 9th progression represents an expanded 2nd
C C
chromatic motion within a major 2nd
Ex. 1.6: Space filling motion in connective arpeggiations and linear progressions a)
b)
Song without Words Op. 102,2
#
8
B C ¥ ¥ ¥ h connective bass arpeggiation
9
B C C C C C C WW C C WC C C C C C connective 4th progression
c) 5^
^6
g
^ (5) ^2
B ¥ C C C ( ¥B ) ! B ¥ ¥ h
connective linear progression in an upper voice
3
Ex. 1.7: Space filling motion from incomplete neighbors a) but b)
g
ant.
=
C C C C ! C
^3
^2
C C C C
C CC C CC
C
g
^4
C
≠
C
C CC C CC
exceptional
normative
Ex. 1.8: Horizontalization of intervals through subdivision incongruent with the harmony a)
b) Brahms, Symphony No. 1/I c) 327
!
CC CC
C CY C W W CC XXW CCC XX CCC Y C W W CC C YC
=
329
C C = CC CC YYY C C C C C XC XC C C C C
CC CC
equal division of the octave not arpeggiation
¥ ¥ ( ¥ )¥ ¥ ¥ ¥ ¥WC ¥ h
diatonically equal division of another interval
=
CCC
( )
C
linear progression with emphasis on non-chordal tones
Ex. 1.9: Subordinations a)
!
b)
CC¥ C ¥ C ¥ ¥ h *
c) (after Rothstein) (cf. Ex. 6.18)
g
*
C¥¥ ¥C ¥ ¥ C
C
I (V) IV V64 35 I V back-relating subordination: back-relating dominant
¥ ¥
¥
I
V
I
¥ ¥
¥
¥ ¥ ¥ ¥ C ¥ ¥ h
=
¥ ¥ ¥ ¥ ¥ ¥
d)
¥ ¥
¥
¥ C C C C ¥ ¥ h
I (II) V I I V I I (II) V I forward-relating subordination linear filling of the within the time span subordination process of the resolution forward-relating subordination outside the time span of the resolution
4
Ex. 1.10: Concepts of seventh chords a) Schenker
b) Rameau c) early Schenker d) C. P. E. Bach
[The example applies in principle to any seventh chord] p becomes
!
¥¥ ¥ ¥¥ ¥¥ ¥ ¥
after Harmony , §99
¥¥¥ ¥¥ ¥ ¥ ¥
BBBB
8 7 7 the seventh as a passing tone
CC
CCC
+
C
=
from Versuch , p. 274, Fig. 355
¥ ¥ # ¥C C ¥¥¥ C CCC C
(8 7)
piled-up thirds combining two triads
¥
¥¥ C ¥¥¥ CC C ¥
(5 7 )
Ex. 1.11: Recognition of the tertian relationship between the fifth and the seventh Counterpoint I, Ex. 254, retranscribed and annotated: Schubert, Waltz, Op. 33, No. 11, mm. 5-8 © for the English edition 1987 by Schirmer books h
W C C C C C C ! # W C
[7th]
CC
p
!
CC
C
C
] [7th] C C C C C C B
C #
h
h [
h
C C C C C C
h
h
p
p
!
h = harmonic tone p = passing
C
CC C
CC
#
C !
C
CC
Ex. 1.12: Reverse hierarchy for contextual consonance and dissonance Bach, Three-part Invention in F minor (after Dahlhaus and Rothgeb) 1 Dahlhaus, Rothgeb: absolute consonance; contextual dissonance
Y ! Y YY T C C C T C # YY Y Y C
C XC
C 5
YC
XC
#4
absolute dissonance; contextual [relative] consonance
C
CC #
C !
CC C
5
Ex. 2.1: The normative situation: dissonances transformed into consonances a)
b)
c)
initial ascent
C C ¥ !
C ¥ C C C
¥
¥
passing dissonance
C CC C C ¥ ¥ C passing tone now capable of receiving prolongation
consonant support
Ex. 2.2: Dissonant support a) Bach, St. John Passion. b) Chorale: O grosse Lieb (quoted in FC, Fig. 115,3b) 10
CC
# YY
C CC
WC
leap
CC
YY
C C
WC
C
CC
CC
Ì
(I
VII º7 / VI)
potential prolongation
Ex. 2.3: Seeds of PD in strict counterpoint : decorated suspensions a)
b) (Jeppesen)
c) Bach, Allabreve, BWV 589 29
C C B A ! 7
AC B C W CB C
6
“parasitic” dissonance
d)
!
e)
C C C B A 7
WW B
*
6
AC C C B 2
= not
3
BC
*
BC B C C C C CC 7 6 (quoted by Clark)
but
A C ant.C C C
A C C INC C
2 (3) 3
2
(4!)3
6
Ex. 2.4: Schenker’s application of decorated suspension Haydn, Die Schöpfung. Die Vorstellung des Chaos 3 4^
! |
(IN)
BO WC B B X AA
YYY
C
C
Q
^3
C C
(VII º7 ) V57 6
B
¥A
¥
I (5)
6
( )
Ex. 2.5: The cambiata as related to the decorated suspension diss.
! c CA C
resolution (insertion)
C
A
C A
Ex. 2.6: Exceptions in strict counterpoint for diminished triad in root position a) interpretations of Counterpoint I, Ex. 331 * 6 5 4 3
!
b) (Jeppesen) c) (Salzer d) explanation and Schachter) of c)
6 5
dim. *
3
A C C C C C C C C ¥ A ¥ W ¥ WAA A A A p p
C C C C A
4 2
5 3
Ex. 2.7: Rudimentary prolongation of diminished 63 in strict counterpoint a)
b)
!
*
A
B A B
AB
*
A B
c)
p
AA
A
AC C C C A AA
A
¥ ¥ ¥ ¥ B B B B ¥ ¥ ¥ ¥ BO C B B A A A A
7
Ex. 2.8: Justification of the diminished 63 analogous to but not to b) c) normative Schenkerian explanation of V
a)
ascending leading tone
descending leading tone
AAC ACC
! A
descending leading tone (VII6 ) inverted third between leading tones; diminished fifth completes the chord
A
^ 2 of the Urlinie
AC
ascending leading tone
bass arpeggiation
V V third between fifth between structural outer voices leading tones: third completes the chord root completes the chord
Ex. 2.9: The apparent passing tone a)
b)
c) Bach, Cello Suite No. 5. Prelude 27
30 *
A
AB B !
A
true passing tone
# YY ( C¥ ) C C C C C C C C C X C C C C C C XC Y
BA B AA
apparent passing tone
*
apparent passing tone creates subordination to dissonance
d) after Aldwell & Schachter
B
! B
B C C
AA
=
3rd p
from
B C ( B BB ) B C C
C C CC C C C
apparent passing tone as a product of displacement
Ex. 2.10: The apparent passing tone with accompaniment a) FC , Fig. 111,d1 (first instance)
C C ! CCB C C
=
C
(=IV –
I)
b)
c)
alternative
CCC CC C
(IV I)
CCB CC CC C
VII
C
C CC
not!
C
CC C CC
p I literal retention of 6^ forces a true passing tone
A A AA A A A A
=
*
A AA A A A A
successive major thirds merge into a conceptual dissonance
C
C
C C C
( BB ) B
B
B h
¥
¥B
g
¥B 7th ¥ B¥
g N
N
radical alternative: the leading tritone unfolds a structural neighbor chord
B h
B
b)
BB
B
BB
CCC C C C C C C C B
B
B
BB
set class 3-1
! WX CC
CWCXC
WC XC
CWC C
seventh chord
C
CCC C C
a) adjacent tones in the same harmony a1) (Straus) a2)
C
YY CCC C
=Y ?
leaps necessarily represent vertical harmonies?
YC C C
YCYB P alternative
(Y C ) ( Y C C C Y C Y C Y C)
b2)
=
p
(C) C C C C C C C (C) analogous case employing a seventh chord
C C C C C C C
b3)
b) leaps that do not belong to the same harmony b1) (Larson)
BB
B
B
I VI7 II7 V7 I Schenkerian representation of a Rameauian idea: imposing a seventh on every chord except the tonic
B¥ ( BB ) B
7th
c) (Renwick)
Ex. 2.12: Violating the distinction between the melodic functions of steps and leaps
normative explanation: the leading tritone as substitution
!
C
C
derives from
a) (after Schachter)
Ex. 2.11: Radical potential of the leading tritone’s gravitation
8
9
Ex. 2.13: Stretching and quasi-stretching of seventh chords b) Schubert, Schwanengesang . c) (compare No. 11: Die Stadt (after Morgan) with Ex. 7.7)
a) Schubert, Impromptu, D. 899 (Op. 90), No. 2
1 43 44 50 52 83159 169
7
g
b 6^ 5^
*
g
11
20 23 stable *
^ 3
*
B CC OO CC OO CC OO Y C C C C Y ¥ B B Y Y Y ( BB ) ¥ C C C X C WC C C C g B X ¥ X CB BB W ¥ B C OCWC CYCXC C O # YY B Y B B Y Y¥ B YY Y B h (º7 46 53 ) Y ! YY B
b 6^ ^5
^ 1
V79 8
I
CTCº7
I V7 I conventional passing sonorities
I
Ex. 2.14: Space-filling motion in seventh chords: connective motion a)
b) Bach, Gott, wie groß ist deine Güte c) after Free Composition, Fig. 103, 2a 6
#
^6 ^ ^ dim. 5th2 = 6
6^
5^ and not unfolding
B C C ¥ ¥ Y C C ¥ ! Y C C C C C W CC C C C C C C W CCC C h ( C )
^ [implied] 5 ^ ( # 7)
C C C C C C C C C C C C C dim. 7th C W CC C (
)
[IV V] [IV V] connective bass connective diminished-fifth progression connective seventh-arpeggiation: in the upper voice diminished-seventh not arpeggiation of II7 progression
Ex. 2.15: Space-filling motion in a third-space above a triad a)
b) Bach, English Suite No. 2. Bourrée No. 2 1
C C C CC C C C C C ! B 5
(7)
5
≠
C
CCC
WWW
better than
CCC I5
XC C CA CC C CC CC CC CC (6) b 7 6
5
CCC I5
g
N
C CA CC X CC CC CC CC CC h 6
5
10
Ex. 2.16: Space-filling motion in a third-space below a triad a)
b) Schumann, Album für die Jugend. No. 3: Trällerliedchen(after Schachter) 1 leading
≠
! BBC C C C C
CCC C
C C C C C C C ¥ C C C C C C C following
(“III”)7
(“VI”)7
V
I
Ex. 2.17: Dissonant surface harmonization of a conceptually consonant primary tone a) Beethoven, Piano Sonata b) Beethoven, Piano Sonata Op. 10,3/II (after FC, Fig. 39,2) Op. 26/III (after FC, Fig. 40,6) 1 6 initial ascent
! Y
7 ^3
9
CC W CC C X CCB W CC C CB C WC C C h
1 9
YYYYYY
17 18
^3 2^ arpegg.
B CB CC X CCC CBB h
Ex. 2.18: Delayed resolution (after Aldwell and Schachter)
g
versus extended (prolonged) 7th
delayed resolution
¥
! B # C B
V7
C
¥
B C B
C CB
C C
Ì
B I
C
B ¥ V7
C
B C
C
C C
C
C C B I
11
Ex. 3.1: Prolongation of seventh chords in pre-Schenkerian literature: Heinichen General-Bass (1728), p.596 (quoted in Buelow 1962, 223), shortened, retranscribed and annotated
C C C C B OC C C C C C B O BO C C BO 3 C C C C C " 4C # 3 C BO 4
7 8 7
7 8 7
7
BO
BO
7
BO
Ex. 3.3: Prolongation of seventh chords in pre-Schenkerian literature: Kirnberger The Art of Strict Musical Composition Vol. 1, Ex. 5.15, retranscribed
BC
BC C
#
! B C
7
7 6 3
C
B C
6 5
CC
C
C
7 6 3
7 3
C C
12
Ex. 3.4: Prolongation of seventh chords in pre-Schenkerian literature: Hynais “Die Harmonik R. Wagners in Bezug auf die Fundamentaltheorie Sechters,” p. 52 (from Wason 1985, 101), retranscribed
BO Y BB OO
C OW C Y BB O
BO
BO
WB O
#
! W BBB OOO
C
C
Y BBB OOOO B C
XB O
D
F
Ex. 3.5: Prolongation of seventh chords in pre-Schenkerian literature: Louis and Thuille, Harmonielehre (1920 ed.?), Ex. 69.b-c, retranscribed and annotated
! c BB
CC CC
B
B
C 3 4 W CB O
# c BB
CC
CC
BB
43
b.
C: V
c.
I
CC
a: V
C
BB O O
CC W CC
BB OO I
13
Ex. 3.7: A seventh chord as a true Stufe in Schenker’s Harmony Harmony , Ex. 127 (161): © Copyright 1978 by Universal Edition A.G., Wien/ UE 6866 © for the English edition 1954 by the University of Chicago
14
dim. 7th chords
(!7)
(!7)
15
Ex. 3.11: A seventh chord as a true Stufe in Schenker’s Beethoven’s Ninth Symphony Beethoven, Symphony No. 9/II, mm. 117-126 © for the English edition 1992 by Yale University Press
Ex. 3.12: Schenker’s argument against understanding the seventh as representing a second in Beethoven’s Ninth Symphony Beethoven, Symphony No. 9/I, mm. 142-143 © for the English edition 1992 by Yale University Press
a) Fig. 73, retranscribed: flute part 7th
Y ! Y TU
CYC C C C C C CYC C C C C
b) Fig. 77, retranscribed: oboe part (Wagner suggests also for flute) 2nd
YC C C C C CYC C C C U C C T C T T
16
17
Ex. 3.17: A vertical dissonance in Schenker’s discussion that prohibits such a phenomenon in The Masterwork in Music II.
“Further Consideration of the Urlinie: II,” Fig. 17: Beethoven, Piano Sonata, Op. 10, No. 2/I Vertical bracket
Ex. 3.18: A prolonged seventh chord in Schenker’s tonal analysis of Stravinsky “Further Consideration of the Urlinie: II,” Fig. 31: Stravinsky, Concerto for Piano and Winds/I (rehearsal no. 11)
18
Ex. 3.19: A prolonged seventh chord in a stable passage in The Masterwork in Music II “Further Consideration of the Urlinie: II,” Fig. 2: Chopin, Berceuse , Op.57, mm. 3-7 (levels d-e)
19
Ex. 3.20: A textbook representation of a prolonged seventh a) Beethoven, Bagatelle, Op. 119,1
b) Cadwallader and Gagné
c) alternative
25
YY Y C C C C C ! BB O C BO
C C C 7thC C Y C C C YYY C C C C ( C C ) C CC C Y Y C C C C C¥ C
Ex. 3.21: Structural priority of a seventh chord according to Lerdahl’s and Jackendoff’s Time-Span Reduction Preference Rule 2 A Generative Theory of Tonal Music, Ex. 7.17 (excerpt)
Bach, St. Matthew Passion . No. 44. Befiehl du deine Wege , mm. 1-2 ©1983 by MIT Press
!
5 4
9 8 5
3
A BA B
B B AA
7 5
A 6
BA B
(not)
7 5
6 3
BB B A B
but
but
6 5 4
6 5 5 3
AB B AB B A B B
(not)
1) Clark’s observations a) true suspensions b) false suspensions
6 2
AA B B
(not)
7 3
6 2
6 3
B A B BB
but
7 5
8 7 6 6 3
B B B B AA
AA A 7 4
6
BA ¥
(not)
7 4
A
AB
(not)
3
¥
2) problematic configurations a) b) c)
Ex. 3.22: Types of suspensions: Clark’s argument after Schenker
B
AA 7 4
8 5
(not)
B
20
21
22
Ex. 4.1: Unsupported stretch passing from a cover tone a)
b)
B B B B B B
! B
c)
cover tone
“unsupported stretch”
C C C B B B B B ¥ B B B h
C C B B B B
B
B
normative paradigm
B
^ analogous case from 8
alternative
Ex. 4.2: Background seventh in an inner voice
B ! BB
BBB B
# B I
BBB B
V7
I
Ex. 4.3: Unresolved seventh in an Urlinie from ^ 5 ^ ^ ^ 5 4 3
!
^ ^ 2 1
B B B B B B B B I V7
c)
b)
a)
?
I
^ 3 ?
5^ 4^
5^ 4^
B B C C C BB B B I V7
I
^3
B B C C C B¥ B B B I
I V7 potential context
23
Ex. 4.4: Unresolved seventh in an Urlinie from ^ 8 a)
b) Mozart, Symphony No. 35/I 1 6 ^8 ^7 ^6 5^ 4^ ^ (4
^ 8^ 7 6^ 5^ 4^ ^3 ^2 ^1
13
10 ^3
2^
1^ ^ 3)
WW ¥ C C C C CXC C W C C B C B B B B B B C C ! C C C C C C B 8 8 8 8 C DN C C C B # B W ¥ C B W C C C C ant.
?
V7
I
I better: I
I
V8 7
I ?
V7
I
Ex. 4.5: Background connection between ^ 7 and ^ 4 a)
!
b)
B B B B B B B B B B B I V(7?)
=
B B B ¥ ¥ ¥ B B B
c)
= B B B B B B B B B B B I V(7?)
I
B B B B B B B B B B B ¥ ¥¥ ¥ B B B B B B I V8
I
Ex. 4.6: Unsupported ^3 in an unprolonged form
!
a) (after FC , Fig. 16,5 [ii])
B B B B B ¥ 7th B CB B h Ì
I
IV
V
I
b) (after FC, Fig. 16,6 [i])
B B B B B B 7th CB B ¥ h Ì
I
II
V
I
c) (after FC, Fig. 16,5 [iv])
B B B B B 7th B ¥ CB B h Ì
I
IV V46
5 3
I
7I
24
Ex. 4.7: V7 in a fifth-line above two bass arpeggiations a) (Schenker avoids)
consonant preparation? *
*
B !
b) (after FC , Fig. 19a)
B B B
V7
I
B BB
I
V
B
B B B
B
B
I
¥
7th
h
¥ B
IV 8 V7
I
B
I
h
B
B ¥
¥
II
V
B I
^ Ex. 4.8: Forcing the 4 to function as a (lower-level) primary tone a) ^ ^ 5 4
!
b) ^ ^ ^ 3 2 1
B B 3rd C B B C BB B B B B I V7
I V I
^ 5
or
B
C C C ¥B B B B B B B 4th
B 8va I
^ 3^ 2
V[8?]
^ 1
^ 5
?
I
Ex. 4.9: IV7 at the deep levels a) Free Composition, Fig. 15,2c (first configuration) © 1935 by Universal Edition A.G., Wien/UE 6869 Rights for the English edition belong to the estate of Ernst Oster.
b) Free Composition, Fig. 16,2c (first configuration) © 1935 by Universal Edition A.G., Wien/UE 6869 Rights for the English edition belong to the estate of Ernst Oster.
^ ^ ^ 3 2 1
B C C B C C B B B B B B ¥ B
( )
I V I
^ 4
V7
I V I
25
Ex. 4.10: Schenker’s approach to the complete upper neighbor to ^ 3 Free Composition, Fig. 32,5 © 1935 by Universal Edition A.G., Wien/UE 6869 Rights for the English edition belong to the estate of Ernst Oster.
Ex. 4.11: The fallacy of “consonant preparation” to V7 a) (fourth species)
!
A
B
B B A 8
7
A
6
b)
B B
7
=
A
6
A A
8
A
6
but
g
N
A
B ¥
6
I IV8 V7 I
A
B
B ¥ ¥ B h
g
N
=
B ¥ B B B B I
V7 I
Ex. 4.12: V7 as the product of an apparent incomplete neighbor tone a)
!
3^
b) 4^ IN
g
B ¥ C B ¥ h
I
IV
2^
^1
3^
B ¥
B B B B
V
I
c)
B I
h
4^ N
g
3^
C C C ¥ B 7th ¥ B
IV
V7 I
^3
?
4^
^3
B B C C C B¥ ¥ B ¥ 7th B h I
IV V7 I potential context
26
Ex. 4.13: Dilemma between complete and incomplete neighbor Hassler, Lustgarten , No. 24 a) (FC, Fig. 116) 1
11
b)
12
1
g
c) 11
12
g
IN
N
W W BC ¥ BC B B ! B C B ¥ B h
BC ¥ CC B BC C B B ¥ B h
( )
normative reading
1
11
12
g
N
BC ¥ CC C BC C B 7thB B ¥ h alternative
Ex. 4.14: Incomplete neighbor before interruption
rather than b)
a) 3^ 4^ IN
2^
g
3^ 4^ IN
g
!
B ¥ C B B B ¥ h
rather than
!
3^
g
^2 4^
B B C B B I V5 7
3^
2^ ^1
B B B B B B I
V
I
^ ^ 2 1
g
IN
I (IV )8 V7 I IV (but see Ex. 4.17)
Ex. 4.15: The seventh as a lead-in before interruption a)
4^
B ¥ C C B ¥ C B B B B B ¥ 7th B ¥ B h h
V I
I IV
^ 3
g
B ¥ C B B B B ¥ B h
V
I IV
^ ^ 3 4 N
2^ ^1
b) ^3
4^ N
3^ 2^
g
^1
B C ¥B B B B B B B B B I
V5 7
I
V
I
V
I
27
28
29
Ex. 4.18: Reaching-over from the seventh of V7
^ ^ pattern in selection from Free Composition, Fig. 41 a) ^3-4-5
© 1935 by Universal Edition A.G., Wien/UE 6869 Rights for the English edition belong to the estate of Ernst Oster.
b) support by V(7) (1)
g C C C C C C C C C C CC C C C C C C C C C C
! I
V
(2)
I
V7
I
I
V7 I
30
Ex. 4.20: Unfolding of the leading-tone tritone a) Free Composition, Fig. 43d,1-2 © 1935 by Universal Edition A.G., Wien/UE 6869 Rights for the English edition belong to the estate of Ernst Oster.
b) Free Composition , Fig. 43e © 1935 by Universal Edition A.G., Wien/UE 6869 Rights for the English edition belong to the estate of Ernst Oster.
c) invertible counterpoint of Free Composition , Fig. 43,e2
! C C C C C C 6th
aug. 4th
6th
d) Free Composition, Fig. 41, a1 © 1935 by Universal Edition A.G., Wien/UE 6869 Rights for the English edition belong to the estate of Ernst Oster.
e) added bass to Free Composition, Fig. 43, e1 © 1935 by Universal Edition A.G., Wien/UE 6869 Rights for the English edition belong to the estate of Ernst Oster.
!
C C C C C C C C C
I
V7
I
31
Ex. 4.21: Dissonant unfolding in the bass Mendelssohn, Song without Words, Op. 62, No. 1 1 10
W ! B #W
15
C B
I
C
g
18
C
g
22
C
YC
C IV
C
C C C C
1
B
B
C B
¥C
C
24
18
=
B C
V65
I
I
h
g
V65 I
B
B
24
C
I V7 / II
Ì
¥ C C
C C C
Ì
I V 7/ b II
# YY ¥ Y C Y C
Ì
g
N
Ì
I V7/ III
¥ C C
C C C
¥ C C C CC CC
(2)
I V7 / III
¥ C C
C WC C
Ng ¥C C C C C
(2)
C
CC
Ì
I V7 / IV
¥
C
P
¥ C C X C CC
(3)
Ì
(I 8 7 ) I V7 / IV
b
P
¥ Y C CC C C C C C ¥
(3) sus.
C
Ì
Ì
I V7 / V
h
C C C C W CC C C ¥
¥ C (X ) C
sus.
(4)
I V7 / V
h
C W CC C C ¥
C
¥ C C C
(4)
I
C
P
¥
Ì
C V7/ VI
C C C
¥ YC C C CCC C
C C C
V7 / VI
(5)
I
¥
C
P
C C W C CCC
¥
(5)
or
or
Ì
Ì
C I V7 / VI
¥
C C C C CC C
¥ YC C
g
N
I V7 / VI
C
C W CC C ¥
C C C
¥ C C
g
N
C
C
Ì
I V7/ n VII
¥ sus.C CC C X CC C C C C ¥ C
(6)
# I V7 / VII 5
¥
C WC C WC
¥ sus.C C C WC WC
(6)
Ì
C C YC
P ¥ Y YY C CC Y CC C ! Y
in (1) minor:
#
!
¥C W sus. CC C C
in (1) major:
Ex. 4.24: Secondary dominant seventh chords
YC Ì
I V7 / bVII
¥
C C YC C
¥ Y PCC Y CC C C C
32
Ì
33
Ex. 5.1: The two senses of 8-7 a)
b)
!
B B A
V8
B
B B B
B B B
I
IV8 V7
I
II10 V7
I
B B B
7
c) (equivalent to b)
B B B
Ex. 5.2: The seventh in lower counterpoint a)
B !
A
6
A B
7
b)
A
A B
10
8
B
AA
7
5
Ex. 5.3: The seventh proceeding in ascent b)
a) 4th *
C C C C C ! C C
V5
8
I
g INg 3rd CC C C C C C
V5
7
I
B
+ + +
melodic seventh interval
melodic dissonant interval
active tone of the seventh
prolonged seventh chord
5 3
4 4
7th
3 5
2 6
1 7
+
+
+
[V] 71 -
# #7 n 8 7 7
C WC XC 5 5
4 6
3 7
+
+ [in some seventh chords] +
[V] 73 64 -
CC C C C C
C
C C C C C C C C
C C C C C
C WC C
C C C C C C C C
[V] 71 26 +
#
!
c)
7th
b)
a)
Ex. 5.4: Comparative investigation of prolongations of the seventh
+
+
-
[V] 75 -
6 6
5 7
+
-
-
7
[V] 31 22 -
1 3
C C C
C
C C C C
C C C
C
C C C C
d)
34
35
Ex. 5.5: Types of neighbors to seventh chords a)
b)
neighbor to the tone of the seventh
neighbor under a stationary seventh
¥A ¥ ¥ A
AA
A¥ ¥ ¥
A !
(V)7 6
(V)71 2 1
7
Ex. 5.6: Seventh progressions (segmented into thirds) versus a sixth plus a second
versus b) Mozart, Symphony No. 40/I
a) Mozart, Die Zauberflöte. No. 3: Dies Bildniss 1
4
6
5^
4^
^3
2 3 5^
5 ^ 4
7
9 ^3
illusory 7th illusory 7th 6th 6th C C C C C C C C W C C C C C C C C C YY C C C C C Y C C C C C Y Y C C ! C CC C not! C CCWC C C V7
I
I
(II 2 )
I
V(7)
I
Ex. 5.7: Oster’s criterion for distinguishing true seventh progressions
but b)
a)
g
illusory seventh progression
!
C C C C C C C C C C
=
C C C
V8 7
I
B
g seventh true progression= C C C C C C C C C C C C C C
C
V7 I
Ex. 5.8: Derivations of Oster’s rule a) unfilled arpeggiations but 2) 1)
= g = C C C C C C C C C C C C C C C C C C C C C ( C C )C C C C C C C C C B C C C C C C C ¥ C C C C =
!
b) shorter linear progressions 1) but 2)
V7 I
=
V8 7
I
V7 I
V(8)7 I
36
Ex. 5.9: Descending major-seventh progression 7th
C
WC WC C C C ! C C ! C (
= )
WC C B
[I 7 8 ]
Ex. 5.10: Illusory descending seventh progressions a)
b) Beethoven, Symphony No. 7/III 3
initial ascent (vertical 7th)
initial ascent 7th = 2nd B C C C C C C C C C C C C C (B ) Y B C C
7th = 2nd 7th = 2nd C C C C C C C C C C C B C C CC B C
!
V7
I
10
6
7th = 2nd
I
I
V
I
Ex. 5.11: Problems concerning seventh progressions a) ?
!
c)
b)
d) (analogous)
normative
8va 7th! 5th (not 6th!) B B C C 7th B ( BB ) B B C C C B B B C C B C C C C C C A C C C C C C B C C C C B A B B B B B B B V8 7
I
V
I V7
I
I
I V
I
Ex. 5.12: Further problems concerning seventh progressions a)
b)
!
or
7th B C C C 8va ( BB ) B B C C C C C C C B C C C A C C B B A
B C C 7th C C C C B B B A
V8 7
or
?
( )
I
V
I
V8 7
7 I
?
B C C C 8va ( B B ) C C C CC C B A
( )
V8
7
I
37
Ex. 5.14: Ascending true seventh progressions a)
C C C C C C ! C CC CC
c)
4^
4^
C
C C C C C C C C C C
7th
V7
b)
C
7th
h
N
7
V7
7
C C C C C C C C C 7th
II V7
7
Ex. 5.15: Alternative illusory seventh progressions unlikely
absolutely illusory
b)
a)
c) Beethoven, Symphony No. 4/I 203
212
217
XCWC C C X C C C (C ) C C C C C ( C ) C C C C C C YY C C C C C C ! C C C W CC C C C C W C X CC flute
7th
5
7th
7th
4 3
10
9 8 in D: V8
7
I
1
C
5
(7) 8
10
C C C C C C
C
C
CC
!
8
(7)
5
=
C
C
CC 10
C 8
7
(7)
C C C C C (C ) C
(7)
C
( )
C
(1a and 2a may be regarded identical; both work in both melodic directions)
10
C
C C C C C C
(8) 7
C
C
C ( C )
C
(7)
C
C (C ) ?
(7)
C
( )
?
C
C C C
C
C
C C
C
C
!
C
C
C
C C C C C C 10 7
C h C
C
10 7
7th h C
b) the seventh c) the seventh is shifted back retains conceptually
2. inverted arpeggiations within sixth-span
!
C C C C C
=
1. open position/scattered contour
a) the 7th is merely passing
Ex. 5.16: The status of the seventh that enters in the middle
38
#
!
A
A
I
7 6
5 6
A
7 6
V7
A
7
BA B AB B BA B A A
a) (after Salzer)
6 7
6 7 6
14
15 sus.
g
sus.
g
sus.
6
g
17 not sus! ant. =
c) Brahms, Ballade, Op. 118, No. 3 aug. 4th ant.
I
In V: I b
A WWW A
5
A XA V7 in V: V7
A YY C
7
C
7
YC
6
C C
7
C C
6 7
B
7
6
I
B
V7
B
5th
g W W W X AB X B AB B AB W A Y Y C C C O C C O C C O B C C C B A YC B B AA B Y C CB O C BB Y CC CC CC Y CCC CCC
11
b) Haydn, Piano Sonata Hob. XVI: 26/I
Ex. 6.1: Independence of V 7 after 7-6 series
39
40
Ex. 6.2: V7 as analogous to consonances in second species a)
b)
!
AA
V57
A
A A
V87
I
A
B WB Y AA A
I
V75
AA 9
266 P
N
A A
#
A
B B A
A
265
A
P
AB W B A
c) Beethoven, Symphony No. 5/IV
BA A
#
A
I
Ex. 6.3: V 7 as preparation for suspension a)
b) analogous to:
! A
AA
BA B A
V7
I4
AA B B A
6 4
3
5 4
B B A
V8
3
BA B 7
I4
3
c) Free Composition , Fig. 63,1 © 1935 by Universal Edition A.G., Wien/UE 6869 Rights for the English edition belong to the estate of Ernst Oster.
Ex. 6.4: V7 as resolution of suspensions a) Beethoven, Bagatelle b) (after C.P.E. Bach) c) Mozart, Adagio, K. 540 Op. 33, No. 7
!
5
YYYY
6
C C CB O C C C CC B BB OO I
V47 3
30
(lower 2-3 in relation to the 7th)
BC C B I
7 6
5
BC C C B C 7 6 4
C C BB B
5 3
13 12 7
Y C C # WW Y Y C C C X C C W C YCYC C XC h h! ! 6
7
6
7
[II] 43 [V]53 [II]43 [V]53 of a b of g
41
Ex. 6.5: V 6-7 appoggiatura a)
!
B AA A
B
V6
7
b)
B W W BBB A BB # V # 42 6
7 5 3
Ex. 6.6: V8-7as a lead-in from an interruption
B CB C B B B B
!
I V8 7
I
Ex. 6.7: An analytical dilemma in Beethoven, Piano Sonata Op. 53/I a) (Schenker) 1
!
23
35
1
g
g
23
g
N
BB
C
I
V7 /
C
34
b) (Kamien, Krebs, Aldwell and Schachter)
C W CC
C BB
Ì
#
III
C
34
35
C W CC III # Ì
I
V/
Ex. 6.8: V8-7appoggiatura to a passing seventh Beethoven, Piano Sonata Op. 10, No. 3/III (after Sadai)
!
1
5 6 not a neighbor
g
WW I
7
g
g C BB C C C CC C CC C C C CC CC C C h
8
V8 7
I
[6 5 in relation to momentary bass]
V
V(7) 6
(6) b5
in relation to root: V8 7
T
g C # YWCO C
jh
C h
C
C
I
31
g
Ci
C
[in V:] I 6
(I 64 )4 3
in relation to root: V8 7
C O WW C C C
C C C
WW C C C C
C
C C C C !Y CC
29
34
(IV)
CC C C
CC
V8 7 6 4 V 22 1
I4 3 6 I 23 1
C C C C C C C C C C C C
C
in relation to root:
CC
V IV 2 1
C XC C
C C C C W C W CC
32
b) Mozart, Piano Sonata K. 284/I c)
18
a) Handel, Suite No. 3 in series 1. Allemande (after Oster)
Ex. 6.9: Appoggiaturas to inverted V7
7
V 52
Y C
Y BBB B
10
B
6 4
CC
CC
d) Fauré, Mirages . No. 1: Cygne sur l‘eau
42
!
V8 7
( b VII)
BC CC CC C (X ) C CYC C
Ì
a) (after FC , Fig. 113,3a)
WWWW V8
7
(II)
C ¥
13
C B C
B
6
I
CC ¥
¥
21
V8
(IV) 7
g
151 282
Y B C C CC ¥ B C C CC
69
V8 7
([II] 6 4)
X CC YXX CCC XY CCC W X # WW W X C C XCXC
6
!
V8
C
W W CCC
7
7
( n VII b 7 )
XC h
Y CCC
g
17
CCC C C
C
YC WC
Ì
24
b) Bach, c) Beethoven, d) Chopin, e) Brahms, French Suite No. 6. Symphony No. 6/I Prelude Op. 28, No. 9 Symphony No. 2/IV Sarabande
Ex. 6.12: Gradual transformation of V into V7
43
44
Ex. 6.13: V5-7space-filling motion a)
b) Schubert, c) Mozart, Piano Sonata K. 333/I Piano Sonata D. 575 (Op. 147)/III 28 29 45 47 49 51
g
g
23 80 81 87
g
BC CC ¥C W B Y C Y CC C WW CC X CC XX ¥C C YY CB W Y CC C CC ¥C B ! C C C W CC X CC C WCXC WC YC YC XCWC # W Y B YC C C C B C C Y B C B
94
( b III) V5 b6
(“I”) V5 6 7
( n III 6)
n
7
Ex. 6.14: V5-7 as a true neighbor
g
!
N
BB C C ¥ BB B 7th I V5
6 7
I
V5
(III# ) 6 7
23 80 81 87 94
alternative ant.
g
CCB W Y C C C W CCC X CCC CCB B YC C C B V
(III #)
I
ant.
47 49
V3
4
5
5
5
6
# WW C C WC C WC C B h
5
ant.
dim. 5th
ant.
7
XCWC
b5
I
B
C C CB W W X C ant. C C C C ( C ) C C W( CC ) C C ( C ) C W C C C C C C ! C
25 33 36 37 40 41 44
a) Beethoven, Piano Sonata Op. 28/III (after Forte and Gilbert)
YYYY V8
B
54
# 7 n7
YYYY CCB CCC C Y CCC
50
V8
C
C
#7 n 7
C
CCB CCC Y CCC
(potential)
b) Haydn, Piano Sonata Hob. XVI:43/III
Ex. 6.15: Other forms of space-filling motion toward V7
6th
V 8(12 11 10
6th
9
8)
7
¥¥ CC C C C C C C C¥ 6th 6 3 6 6 6 6 3 3 3 3 h6 C C C C C C3 ¥
c)
45
46
47
Ex. 6.19: Other subordinations to V7 a)
b)
c) Schubert, Moment Musical No. 2
(after Cadwallader and Gagné)
g
C ¥ B
! CC 7th C B # (VII) V 7
h
Ng C B B
or
C B B
C C B
V7 I
VI (V 7) I
(VI)
1
?
18 32 N
YYYY B
¥
36
g
B
7th
YY YY B ZY CC CC Y C X CB B I ( bVII b )
V7 I
Ex. 6.20: Subordination of seventh chords to V7 a-b) Beethoven, Piano Sonata Op. 57/I (b) 54 (a) 238
Y XC C C CO ! Y Y CC CC CC CC OO # YY Y
Y Y CC Y CC h
C C C CO
VII 2 7 V52
h
CC
7th
CC
II 4 3
V7
c)
h 3 1
2
CC
7th
5
5
IV 6 5 7 V 64 2
V7
7 [in 5 1 III b :] V 4
CC
C
V7 5 3 1
Ex. 6.21: Subordinations to inverted V 7 a) Beethoven, Symphony No. 7/I 142
WWW C X C ! XC h # WWW WC VII b7
146
C
g
152
C WC C
75
76 x3
C C
Y CCC
C C
V65
b) Chopin, Mazurka Op. 24, No. 2
I
87 88
89
* (enh.!)
Y C Y Y CCC W CC
g
X X CC
Y C Y C Y C C X CC X C X CC YC VIIº2/
b III Ì
[in VI: VII65 V43
I]
48
Ex. 6.21 - continued c) Beethoven, String Quartet Op. 127/I 7
YY B O Y !
9
10
d) Mendelssohn, String Quartet Op. 13/I 234
C C O C C C O C BC B B WCO C B B WB B
BO BO BO B C
# YY B O Y BO
BO B C ¥O BO BO BO
236
C C
C h
II7 V43 I6
C
C C
II 43
V2
Ex. 6.22: Apparent subordinations to V7 a) Mozart, Die Zauberflöte. No. 15: In diesen heil’gen Hallen
WWWW g C ! p # WWWW T
1
=
h
CC OO CC C O CC C O
CC T
h
f
C T C
C C C C C
CC C C
plagal
C
C C
C
I II6
C C (V7 )
I
b) Scarlatti, Keyboard Sonata K. 471 (after Rothgeb) 51
W C B !
54
C C C C C C BB OO C C C C C C #W C C BO C
=
B
C C C B B C V7 Ì
II
“I” V
C
I6
150
prolonged 7th
=
C C
C C
CC W CC
V7 IV
h
C
7th
B C C C
b)
C 6 3
g
dim. 5th
h
in V: II
# YY
Y !Y
not
(c #)
9
(VIIº 7/VI?) ( b VII) (VIIº 2) V7
ant. CC C C C C C CC C CC C X C X C C C 5th C C YC C YC C
7
6 6 6 3 3 3
6 6 6 6 3 3 3 3
IV6
C C C
2
7th
7th
C
I
II 6
V7
4
V7
WW C C B C C C C C C C C C C C C aux. h
WW ¥ C C
1
90 91
C CC C C (C ) C C W C C C C CC CC C C C C 7th
4th
86
WW C C C C C C C C C W C C h
WW
84
c) Mozart, Rondo K. 485
a) Beethoven, Bagatelle b)Beethoven, Piano Sonata Op. 14, No. 1/III Op. 119, No. 11 (afterFC, Fig. 100,3h)
V7
C C B
7th prog.
Ex. 6.24: Space-filling motion within II-V7
IV
progression # W W illusory C C C seventh CWCWC C h
[ ]
C C W W CCC W C C C ! []
147
a) Haydn, Piano Sonata Hob. XVI: 32/III
Ex. 6.23: Space-filling motion within IV-V7 subordination
IV
h
C
3rd
V7
B
7th
B C C
d)
h
h
IV
V7
CWC ¥
7th
CYC C
B
e)
49
h
C
I
[in III: II
YY B
C
g
12
C
7th
C
C
C XC
C
V3
C
C
15
C
C
7
16
C
III
I]
C
C
17
7th 3rd
(VII)
V7
# C C B
! CB
a)
6th
7th
(VII)
V7
C B C C C C
BC
b)
b
VII 6
V7
CC C CC CC CC C 5th WW C C C C C h
WW
62
c) Haydn, String Quartet Op. 33, No. 3/IV 59
6 dim. 5th
7
Ì
8 ]
4 ( b II 6) (II b2 1)
V(7)
g
rg-ov.
g
rg-ov.
C X CC
56
bVII
(V 6)
5th
CC
C WC C
C
CC
C V7
WC
CC
Free Composition , Fig. 98,1b)
e) (after
V 7 [in D:] VII 6
YY YY Y C Z C C X C Y C C Y C C Y
7th
C YY YY Y C CC C CC C CC Y C
54
d) Chopin, Polonaise Op. 26, No. 1 (after FC, Fig. 99,2)
(aug.)
in E (III) minor:II7
[
5
C Y C C Y C Y C [ XCC ] YC C YC YCY C C hg YYY Y CC Y CC X CC YY CC XX CC CC perf. 4th
YYY
Ex. 6.25: Space-filling motion within VII-V7
#
!
YY B
1
c) Beethoven, Piano Sonata Op. 49, No. 1/I d) Schoenberg, Gurrelieder. No. 1: Nun dämpft die Dämmrung jeden Ton
Ex. 6.24 - continued
50
51
Ex. 6.26: Space-filling motion within VII7-V7 a) Wagner, Tristan und Isolde. Prelude 3
b) Brahms, Symphony No. 4/I 4
27
c) Mozart, String Quintet K. 593/I 31
113 117 (latter time transposed)
64 102
(b # ) *
g W C W CC W W BC Y CC X C C C W C C C C C C C C W C ! W CC W CB W W CC X C C C C C C C C CC CC W C C C * # C C C W CC C W CC WW C X C W C X C C W W B h h h h *b becomes
becomes
dev.
(d
(VIIº 2) 7 V 53 2 1
106
V7
VII 7
in b III:
X CC X CC
Y CC
*
XC XC c)
(VII 64 ) m 2 VIIº V2 7
e) Schumann, Novelette No. 3
d) Mozart, String Quintet K. 593/IV 131
b
d)
(e
YC W ! W C # WW C
VIIº 65
C XC YC
132
YC C C C XC C CC C C C C g C C
C
42
45
(b b
a)
g
W W Y C C X CC W CC (X )W CCC CC W CC WX CC X C (notated f n)
C C
V7
I
(b III)
V8 7
128
Ì
I
VII 7
V2
A
IV6 I 64 2 2 1 1
VI
3 0
AC CC C A
CCC
1 2
1 2
1 2
II 64 III6 harmony
quartal
A A CA CAA CA V7
V71
2
6 (II 4)
3
V7
C
CC
C
C C ! C
C
b)
a)
C
(III 6) 6 5
C
as in
YYYY V7
CC C CC C
1
C
C C CC
C
6
C C
CC C (III 6 ) 6 5
C
CC
8
Chopin, Mazurka Op. 50, No. 2
V35 42 31
7
(IV6 )
(IV 6)
P
BCC PC B C CC
BC NC C C C C N
b)
Ex. 7.2: Single third progressions within V7
Number of foreign tones 0 Number of 4 chordal tones
!
AAA
(white noteheads: chordal tones [including the seventh]; black noteheads: non-chordal tones)
a)
Ex. 7.1: Harmonies that emerge in prolongations of V 7
C C 4
3
(non-tertian sonority)
V75
C
CC
c)
(IV 6) 7 V51 42 31
N
BC PC C C CC 7
V73
C
CCC
d)
CC 2
cons. sup. (II)
V31 42 31
7 6
C
C 1
V7
C
CC
e)
1
7
V3 4 3
7 6 5 1 2
(VI)
N
(non-tertian sonority)
N
CC C NC C CC CC C CC
C NCC C CC C CC
c)
6
(III)
cons. sup.
C
C
5
CC
(apparent “I” 43 ) 7 6 7 5 4 5 V3 1
CC NC C CC CC C C CC
52
53
Ex. 7.3: Parallel third progressions from the root and the third to the third and the fifth of V7 a)
b)
c) Brahms, Violin Sonata Op. 78/I 1 16
B C C C C ! C 10 10 10 10 10
# C C C C C
(IV6 ) (IV 6) 7 V31 42 53 42 31
18
* B C C C W B C C C C C C C C C C C 10 10 10 10 10 B C C C 10 10 10 C C W B C C CC C C C 7 V 53 1
4 (II 4 3 ) (II 3 ) 4 2
5 4 3 3 2 1
g
23
YYY Y C C C Y ! Y ¥C C
28
CCC
32
33 37
C C C Y C C C Y CC C C C X C sus. 10
sus.
C
10
dim. 7th = aug. 2nd
7 5 3
V 65 of V
10
3rd
C CC C C C C CC C
(II 43 ) (II7) (II 43) (I43) (IV6) 7 I V 53 4 5 4 3 4 (7 6) 5 1 2 (5 4) 3 2 1 12 3
# YY Y Y X CC C X C C X C C C X C C Z C YY 10
* C *CC C CC CC CC CC CC Y CC C C C B C C C 3rd C
10 10
d) Chopin, Etude Op. 10, No. 5 (after The Masterwork in Music I)
4 (II b 13 )
b 42
3 1 7
21
4th
C C C B I
54
Ex. 7.4: Other parallel third progressions within V7 a)
b) Mozart, Piano Sonata K. 280/I 13
15
c)
d)
17
g
involving parallel fifths
N
! CC CC C CC CC Y C C C C C CC CC CC CC CC C C [plagal root relations] # B Y C C C C C C C C C (I 64 ) (I 64 )
I
CC CC C CC CC C C CC C C
V 73 62 51 62 73
(VI) (VI) 7 6 5 6 7 5 4 3 4 5 V3 2 1 2 3
B
B
(I53)
(V)
V75 64 53 64 75
C C C C C C C C C C
V75 64 53 64 75 I [+ root supports]
Ex. 7.5: Voice exchanges of thirds within V7 a)
Schubert, b) Wandrers Nachtlied, Op. 4, No. 3
as in
as c) Schubert, inverted Piano Sonata in D. 784 (Op. 143)/I
2
158
C B C C WW C C ¥ C C C CC ! C C C CC C C C C C B B C (III6 ) 765 V53 6 7
(III6 ) 7 65 V53 6 7
(set 027 as quartal harmony) 7 V53 44 35
B
W¥ C¥ C
159
160
(full harmonic rhythm!)
C
C
C WC
BB C
C
C C C C
(set 027 in the form 057)
V43
6 5
(II64 ) 7
V 35 1
2 2
1 3
55
Ex. 7.6: Combinations of third progressions within V7
!
a)
b)
C C C C C B
CC CC C CC CC C CCB CC CC CC C C
BC C C C C #
Beethoven, Piano Sonata Op. 90/II as (inverted) in 41 43
(I 6 4) 7 V 55 3
V71 62 53 62 71
6 4 6 4
(I6 4) 6 7 4 5 6 5 4 3
5 3 7 5
c) Handel, The Messiah . No. 3: Every Valley Shall Be Exalted
!
WWWW
W ! WW W B C C C W CC C C C CC (“I” )
B
W CC
CC W CC
CC W CC (IV 6 )
7 5 V 33 1
4 2 4 2
d)
CC
CC CC
CC
CC
CC
CC W CC
CC
CC
CC
CC CC
CC
(IV6 ) 3 1 5 3
(“I” )
[V 56 ]
39
# W W W W W CC [in V:]
C C W W W W C CC W CC CC C
4 2 4 2
(VI) 5 3 3 1
7
V 53 1
6 4 4 2
(VI) 5 3 5 3
6 4 4 2
7 5 3 1
#
!
V8
B
163
7 3 1
4
2
5 3
I
C C C WC CWC C C CYC XCYC XC B
g
161
a) Mozart, Symphony No. 36/I (after CP I, Exx. 200-1) 7
hypermeter according to design
4 5
7 5 3 1
I
in relation to the root:
V65
#1 4 2
5 3 4 3
CC X CC C
(VIIº/VI) (IV 6 4)
g ! YY CC CC CC C C ¥ C C h
g
*
I
CCC
C C C g W C ¥ C C C C YY C C W C
1
1) theme 8
IV
b) Schubert, Piano Sonata D. 960/III
Ex. 7.8: Chromatic filling of parallel third progressions in V7
81
in relation to IV:
C
C
82
VII º7 /
II
VI
Ì
II
Ì
XC C VIIº7 /
C C C C XC h
*
CC C C Y C C Y CC C C
77
2) end of scherzo
C
C
#
V7
¥
X ¥CC
83
C
I
C ¥ C
C¥
84
56
8
V
# YY Y Y C
Y ! Y YY C
7
C
C XC
3 1
4 2
C < C WC
e n omitted
10
C
5 3
C
C 10
C
CC
C
4
6
C YC XC
C XC
7
C
g
17
7 5
C
10
I
B
B
YYYYY
V71
b2
YYYYY C Z C h
C
g
19
h C
ant. ant.
ZC YC
C
C
C
25
5 3 1
C Y C ZY CC Y C ant. C C
C
ZC
octatonic tetrachord = 3rd
CC Y C
CZC
C
24
4 (VIIº7 ) (II43 /II) (V 3 / b VI) b 8 9 8 7 6 b 5 bb64 5 b 1 3 3 2
C
22
18
5
1
3
d) Chopin, Nocturne Op. 27, No. 2
c) Chopin, Waltz Op. 34, No. 1
Ex. 7.8 - continued
57
Ì
7 V53
4 4 #4
#4 n
3 5
CWCXC C B
*
7 V53
B b 66 5 6 7
bn6
C C YC C
*
harsh
B YC XC C C
b)
!
2
4
Y CC W CC
CC Y C C X C C CC Y CC CC
4
5
3
#1
2
7
1
V 53
b# 3 1
of II)
2 2
b b 23 n 13 # b 13
b III?)
C
1
7 V53
B
2 2 1
(6 5)
2
b b3 n 3
b III?)
4
4
CWC C
3 5
4 # 4 n n44 # (3) 5 3
[in IV:] V65
in relation 7 to root: 5 3
(V 7
( b III)
I)
CC C Y CCC Y CC C Y C YY CC
5 3
I )
4
(II)
C CCC W X CCC CCC C C C #6 6 (IV 5 V4
CC C W CC C YC
4
3
V2
( b III 6)
I6
Y CC Y C C Y CC (XY) CC
5 4 3
YC C CC CC XC YC XC B CC
6
CC C W CC C CCC C YC C
#4
CC CC CO YC YY X C C h
YY B C O C
5
d) Skryabin, Prelude Op. 11, No. 22
b) potential tonicizations
# #4 n 4
WCXC C
B X C W C ant. C C W C X C ant.C C C
c)
CCC YY CCCC X C CC XC XC
3
#6 6 7 6 (6 5)(IV 5 (II4 ) (V2/ (7) (IVb 3 ) (II 4) (V7/
C CC W C CC C YC
(Yellin) 1
a)
Ex. 7.10: The omnibus progression
#
!
harsh
B *C W *C C C
a)
Ex. 7.9: Chromatically filled voice exchanges in the upper thirds of V7
58
59
Ex. 7.10 - continued c) Brahms, Scherzo Op. 4, 2nd trio
60
Ex. 7.11: Omissions from the omnibus a) Omissions in both voices (1) Schubert, (2) Piano Sonata D. 959/I
(3)
197 (retransition) octatonic tetrachord
half-diatonic
!
CC W CC
CC W CC X CC CC
2 2
b b2 n1 3 3
(II 64)
in relation to the root:
C CC C
W CC W CC
7 3 1
V 56
Y CC Y CC
Y CCC YC
(V 7 of b III) 7 3 bb3 1 2 6 V5
7
half-diatonic
X CC CC
C CC
Y CC Y CC C
X CC CC
X CC CC (II 64)
2)
b b2 n1 3 3
bb 32 n 22
7 3 1 V 65
7
1 3 7
b) Omissions in one voice (1) only used form (2) not on other tones (3) not in the (not in reverse) not as anticipation upper voice
Y CC Y CC
! C CC W CC C X CCC C C C sus.
(VIIº 6 5 of VI) 7 3 1
#1
2 2
X CC C
bb 2 n 1 3 3
V65
Y CC X CC C C C C
C CC Y CCC X CCC C YC C C
7 3 1 V65
7
sus.
X CC CC X CC Y CC C C C C CC Y CC X CC CWC
ant.
(V b 7?)
(VIIº7 of VI)
b b 3 n 2 b(1) n 1 2 2 3 3
7 3 1 7
#1
2 2
bb 2 n 1 3 3
V7
Ex. 7.12: Harmonic variants of the omnibus as result of neighbors a) b) Schubert, Piano Sonata D. 894 (Op. 78)/I
#
!
C CWC CC Y CC 1 V 57 3 6 5
C CC Y CC NC C Y CC
W
X CC CC
W
# 1 (IV2 6) b 3 n 3 b 3 42 b 52 1 7
52
54 half-diatonic
C CC W CC C CCC
W CC
WC XC C
C
N
1 V 57 3 6 5
# 1 (IV2 ) b 3 42 6
C
3 5 1 7
6 5
61
Ex. 7.12 - continued c) Verdi, Otello, Act 4 (after Yellin) 23
W
d)
26
! W CC X CC W CC X CC
CC Y CC CC Y CC C C
C C CC
(b#)
N 5
N
(f‹)
(IV 6 )
[in B?:] 7
V 53
1
b b#531
5
CC W CC CC Y CC X CC
WC XC C WC C # W C C W CC C Y C C N
C NC C NC C C WC XC YC XC
(VI)
# 4 n5 bb 2 n1 3 3
4 2 2
XC YC XC YC C C C C C C
7 (never 5 resolved) V 3 1
6 4 2 2
b# 3 1
7
bb52 n 1 3 3
(“French”) enh. “French” 6 4 3 [in II: II 53 ] #1 7 6 7 6 7 V53 b 3 2 b 2 1 1 #1 2 b3 n 3
Ex. 7.13: Displacements in the omnibus a)
b) Puccini, Tosca, Act 1, scene 1 (after Yellin)
problematic doubling
*
Ì
Ì
Ì
bb 33
7
V13
1 3
7
V31
6 (II b41 ) b b 22
38
39
WC C C C C X C C YCXC [ C ]W C C YY X CC YC C YC C
! CC C W C C Y CCC X CCC CC C Y C X C Y C X C YC CYC C XCYCXCYC C # C ( bVII)
37
YY
Ì
5
V 13
1 3
7
3
1
Ex. 7.14: Insertions into the omnibus a)
b) Brahms, Symphony No. 2/I 78
CC Y CC Y C C C C WC #
!
sus.
bb 4 - b 3 V7
sus.
sus.
9- 8
7 -# 6
sus.
Y CC C CC W C Y C C X C CC Y CC X CC 7- 6
B
82
C C B
B
WW C V C W C C W CCC W CC W CC W CC pC C C C W W W W CC W X CC WW CC W X CC [in local III: # [in f : V7
“V2
C C B
W CCC WW CCC CCC N NC C W CC pCC C C C ant.
I6”]
I]
62
Ex. 7.14 - continued c) Schubert, Piano Sonata D. 664/III 67 74
69 76
71 [ 72 ] 78 79
* not yet
W W W W CCCC W CCC CC CC CC CC CC CC CC CC CC C C ! f fz fz fz(X )fzC p 3rd X C W C # WWW WC C WC XC CC B C V17
#1
(II
b3
2
V7)
“I”
(5
n3
4)
I
Ex. 7.15: Outer expansion of the omnibus Mendelssohn, Reiselied , Op. 34, No. 6
W
45
47
CC C W CC C #WWC XC
3rd
!
aug. 4th
48
ant. W C X C C CCC X CC CC C C C C C C C C
[In III:] V65
BCC C B
Ì
2/
V7
I
Ex. 7.16: Combination of modifications of the omnibus Beethoven, Symphony No.9/II. Trio 466
468
WW C !
C
471 nested prolongation
C
C
XC
octatonic tetrachord=3rd
CC
YC
# WW C
octatonic tetrachord = 3rd
1
YC p
sub.
CC
in b III: VIIº7/VI
b
2
475
X NC Y CC C
omission N
X CC
C
X CC W CC
WB
C fp B
(not a 4th a 2 - d 1 )
omission
7
V 35
X CC
473
V8
bb 3 3
(“I 64 ”) 6
7
b 52
n 13
I
*
C
C C C C
34
*
C
C
*
36 C
C
37 C
C
C
g
*N
38
*
40
in III:
#
V 65
# b
7 5 3 ( 2 3) 1 ( 2 1)
in relation to root: 2 2
(II 6 4)
7
8 6 1 (4)
C YC XC YC XC YC C YC C WC C N N
(inner attacks remain ) (a # ) (a #)
p
7 5 3
9
8
I
B
W C X CCC C CCB C N N C C C ! C CC Y CCC C CC Y CCC C CC W C CC X CCC Y CCC X CCC Y CC X CC fz fz fz fz fz
*=
Schubert, Piano Sonata D.845 (Op. 42)/I a) exposition bridge
Ex. 7.17: Apparent omnibus
C
*
C
6
(V 5 of III )
n VII 56
*
196
C
(transitive)
(II 46 )
C
197
C
C
*
4 3
9
V 68 75
C * (notated n c )
198
200
8
I#
WX CCC C W BC N N W C Y C X C W C Y C Y C X C C C C C CC CC C CC CC C CC W C CC CC CC CC W C X C fz fz fz fz fz (inner attacks remain p ) (a #) (a #) C WC XC YC XC YC XC YC C YC C WC XB C N N
*
194
b) recapitulation bridge
63
(1)
(a #?)
b3
1
(a b?)
(enh. VIIº2 ) 7 V3 #1 3
V73
#5
I
#W C
! C
W C
160
C
V 71
C
C
Ì
g CC
CC
b3
( bVII)
C
C
185
C
189
quasi-aux. cadence (I) I 1
CWC C XC CWC XC
CC
N
161 167
[174: rondo theme] 177 184
3
CC W C W C C C
C
CCC C C C WC C (W C ) ( X C )
(3)
(2)
b) Beethoven, Piano Sonata Op. 14, No. 2/III
V71
# C C YC C C
CCC ) Y C ( X C ) ( !
a)
Ex. 7.18: Altered third spaces within V7
V75
C b3 5
CC C Y C C C
(4)
V73
CC b1
C YC YC C !
(5)
C
3
V75
# 57
n 75
C C WC C C XC C C C XC CC
(6)
64
(“III 9”)
b)
c)
g
alternative N
avoiding the alternative
d)
V7
9
7
V7
8
63
67
V7
(V7/V) 9 7
C CCC CC X CCC W CCC X C CC X C ! XC XC C h C # WWWW C C C C X C C WC
WWWW
60
or
7
65 67
V57
V7
(V 6 5) 8
7
g C Ng CCC CC X CCC W CCC X C CC X C XC XC C h C WWWW C C C C X C C WC h WWWW
60
f) Haydn, Piano Sonata Hob. XVI:22/I (recapitulation bridge)
V7
BBB
9 7
V 7 9 b9
B
g
(II) 9
octatonic 4th = major 3rd
V7
b8
7
C C YC YC C
g)
7 5
V7
(IV) 9
7
*
b8
7
X CC
W CC
550
of A * = non-functional half-diminished seventh chords
(VII 43 ) * 7 9 b9 V
C C W C C C Y Y CC W C W C X CC Y C C C YC XC C h
g
546 547
h) Wagner, Tristan und Isolde Act 2, scene 2
7
N
C CCCC C CC C CCCC C
e) other harmonizations of the ninth
CB C C C C CC C C C C CC CC CC CC CC CC C CCC C CC CC CC CC ! C C C C C BB C C
a)
Ex. 7.19: Third progressions that exceed the limits of V7
65
66
Ex. 7.20: (Ascending) sixth progressions within V7
!
a)
b)
c)
C
C C C C C C
CC C C C C C
C C CC C C C
C
C
V73
5
C
V 75
(7)8
(7) 8
C
V7 8
3
3
5
Ex. 7.21: A complex sixth progression within V7
a) Brahms, Symphony No. 1/I (retransition)
g g YY ¥ Y CC X CCC W C Y !
263 321 333 335 (e # )
337
339
343
Y C X Y CC C C Y W X C CC X CC X( CC ) W C ( C )X C
6th
C X W C CC X C
ant.
# YY Y ¥
[in b:] # (IV 65 I 64
6
5
[in d:] # 5 I 3 ) (IV 65 I 64
* V8
7
6
[in f:] # 5 I 3 ) (IV 56 I46
*
*
7
5
C W X CC C X C
6
5
6
5
WC C X C Y C X C (X ) C C C YC WC
# YY Y B
[in b:]
# (IV 6 7
[in d:]
6 5 I4 *
#6 6 I5 3)(IV 5 I4 *
[in f:]
# I 5)(IV 6
* = in retrospect, not cadential 6 4
3
I
YC XC
Y C XW CCC Y C
Y C X Y CC C C
octave divided equally into four
YY B Y C X CCC W C Y !
¥
# I 53 ) IV 65 V V 7 of V of V
* = in retrospect, not cadential 46
b) mightg have been
g
5
XC ¥
elided
#6
WC C adjustment X C Y C X C C (X ) C C Y C C YC C h Y C C WC C h h 5
V8
341
6
5
6
C YC XC YC YC YC C C h
6 5 I4 *
[in a b :]
#6 6 I5 3) (IV 5 I4 *
I5 3) 7
C
=
V8 7
C C
B
V7
h
C C C C C C C C
unless
V8
C
P
? 8 7
C C C5th?C C C
b)
dim. 5th
C
V7 (6 5 4 3 ) I
# C
C C C C C C !
a)
g
C C
I V(7 6) 5 (4 3) I
C
C C C C C C C
(no 5th-progression) IN
b)
I
B
C
BC
1 ant.
C C
CC CC C C
5 7
V8
g
11 aug. 4th
13
16
6th
11
g 12
7 V5 1
C
7
I
¥
18
6 5 # 12 73 I
C WC C C 8 n7 4 3 2 2
#7
3rd
CC C CC C C W CC C X CC W CCC CC C C
9
d) Schumann, Dichterliebe. No. 7: Ich grolle nicht
dim. 5th dim. 5th C ant. C C CC C C W C X C C C C CC CC C CC CC CC C C C C CC Y CC CCC CC C ¥ C C C C C X CC CC W C YW C C X CC X CCC WC CWC XC C C C C
7 9 gradual transformation to V7
CC W CC C C C CC B
6th CC CC C C C C C C C C C
c)
c) Bach, 12 short preludes No. 1, BWV 924 (after Jonas)
Ex. 7.23: Diminished fifth progressions within V7 type 1
!
C C C 6thC C C
a)
Ex. 7.22: Descending sixth progression within V7
67
C
C I
60 X2
61
dim. 5th
62
63
V7 (6
C 5 4 3) I
(“I”) (II6 )
7th
¥ C C C C C C h
10 10 10
B
CC CC CC C C CC C C C C B C C C C C C C ant.
59
c) Gluck, Orfeo ed Euridice. Che faró
XC C CC
V7 (6 5 4
(III7 )
3)
V7 (6 5 4
( bVII) 3)
C C C C (X ) C CC Y C C
C C CC C C CC C
! C
b)
a)
C
C
V7 (6 5 4
# (VII 5 )
3)
CC C C C C W CC
c)
V 7 (6 5 4
(V b) 3)
CC C Y CC C X C C C C
d)
C C C
C C CC C
dim. 5th
31
IV
V8 7
V/
C
# 2^
C
(6 5
V7 (6
# 5 #4
3
# (VII # 5)
3)
C C WC WC C W CC (X ) C
e)
Ì
4
b 2^
7 3) I
C
V 7( b 6 b5 4
(bII63)
N
3)
C YC YC C C Y C XC C C C
f)
II (tonicized)
C
33
( C C CC W CC C C
C CC C C
CC
32
ant.! C VC C WWWW W C C V C C C W C C C C CWC C
g
30
W W W W W C ( CCC ) ( C ) CCC C W C C
29
(reaching-over?)
28
d) Chopin, Barcarolle
Ì
Ex. 7.25: Other harmonizations of diminished fifth progressions within V7 type 2
V7 (6 5 4 3)
C
V7 (6 5 4 3)
C (II 6 )
C
N
C CC C CC C CC
b)
(II)
# C
C C C C ! CC CC C CC
a)
Ex. 7.24: Diminished fifth progressions within V7 type 2 - via II
68
V7 (6
(I 6 4)
4) 3
C C C C ! B
a)
as in
7
V53
(I 6 4) 3 7 5
(I 6 4) 7 5 3
32
type 3 type 1 C C C C YYY C C C C CCC CCC CC C CC C
28
Haydn, Piano Sonata Hob. XVI:43/I
V7
(I)
C C C C C C C
b)
Ex. 7.26: Diminished fifth progressions within V7 type 3
V7
(VI)
C C C C C NC C
c)
N
(
)
V7
(VII 7/V)
C C C CC X C BWC C
d)
69
g
!Y C C C
I(V)
V7
C
C C C C C
C( C )
C C
ant.
3
I
C
C C C C C
4
or
g
C
#
!
5th
V71 2
3
4
5
B C C C C
B
a)
5th
V75 4 3
2 1
CB C C C C
B
b)
3
I
V7 I
C
4
C
C
5th
11 13 14 15 16
(not 6th!)
17
V71
Y C
CC
[accompaniment left off to avoid clash]
2
3
4
5
I
B
Ng YC CWC CWC B C Y C X C Y C Y C X C Y C Y C C C C C C W C XC Y XC XC
10
c) Chopin, Waltz Op. 34, No. 3
1 9
2
C C C C C C C C C C
1
Ex. 7.28: Perfect fifth progressions within V7 type 1
#Y
2
(after Cadwallader and Gagné)
1
d) Bach, The Well-tempered Clavier, Vol. 1. Fugue in F Major
Ex. 7.27 - continued
70
C N
C
(VII 7 ) 7 V11 2 23 4 1 5
C C C C C
C
22
7 V15
(V7 V 71
I
Ì
30
34
38
41
42
V7/ II) ( bVII) b(53 2 6) 4
perfect 5th
7 5
I
X C BC C X C C X C C C C XC W C C WC WC W CC C X C W C C C C C C C C WC C WC C X C WX CC W CC WX CC X CC C C C C XC XC C C C B
26
CC
(I 7) 6 7 3 4 2 3 4 5 (+root)
P
CC
N
C C C C CC C
CC
BB C
c)
b)
d) Chopin, Etude Op. 10, No. 3 1) (after Free Composition, Fig. 153,3)
V71 2 63 4 75
(III)
B C CC C CC
C
N
WWWW C C ! C C # W W W W W C CC C
#
! B
B
a)
Ex. 7.29: Perfect fifth progressions within V7 type 2
V7 I
(II
25
30
V7)
34 41 42
g Ng C C C C C C C C C C W CC CC WC C C C X C C CC C h
23
C B C C WC C C B h
g
22
2) alternative (no full PD)
71
Ì
dim. 5th
(I 6 4)
V75 64 53 42 31
# C
perf. 5th
CC CC C C C C CC !
a)
dim. 5th
Ì
dim. 5th
118
d) Beethoven, Ah, Perfido!
7
1 6 5 4 3 V(7) 2 3 4 5
1 2 3 4
5
V 53 44 53 62 17
7
V31 42 53 64 75
7
YYY C C C C C 6 (IV 6 4 ) (IV5 )
C C C C C perf. 5th
perfect 5th
7
6 7
6 7 6
7
6 7
125
(not 6th!)
6 4 4
5 3 5
(V b )
CC X CC
dim. 5th dim. 5th
C C
4 2 6
3 1 7
C
C
perfect 5th (Phrygian) sus. sus. sus. sus.
6
g C XC C C C C C Y XX CC C C X C C C X CC X C YYYYY X C X CC
YYYY
[in relation to alto:]
122
e) Chopin, Piano Sonata No. 2/I
(7 [in V/c 8 7 5 (never 3 resolves!)]: 1
121
dim. 5th C C C C C C C C C C Y Y Y C C C CC C CC CC CC C
c)
(IV6 )
perf. 5th
C C C C C
C C C C C
B
b)
Ì
Ex. 7.31: Combinations of perfect and diminished fifth progressions within V7
72
73
Ex. 7.31 - continued f) Beethoven, Violin Sonata Op. 47/III
g) Schubert, Piano Sonata D. 959/I
317
1
5th W W W CC dim. C C C C CC CC ! perf. 5th dim. 5th C W # W W CC CC CC CC C perf. 5th
7
V35 1
(VI) 6 4 4 2
WWW
7
12 dim. 5th
13
C C C C C C C C ( CCC ) C X CC X CC X CC C W CC C g (ambiguous segmentation)? ant. ? C ? X XC WC C WC C YC XC C C C C
WWW C ¥
perf. 5th
(“V 6 5 I”) (VII°7) 6 ( bVII) (IVm 46) (IVm )
(VI 6 ) 4 3 2 1 6 7 4 5
5 3 5 3
6
7
V 14
I
b
3
2
b
3
4
5
Ex. 7.32: Ascending augmented fourth progressions within V7 a)
b) Beethoven, String Quartet Op. 59, No. 3/I (after FC, Fig. 148,2)
!
30
C B V7
C 1
C 2
h
CC
3
B
BC
BCC
I
V7
B
35 40 aug. 4th
CC
41
C Y CCC X CCC XC C P
CC W CCC C C C *
* not resolution
1
42
not resolution? 2
3
g
43
B
CB I
?
?
7
V8
B
C C C C
b)
7
dim. 5th aug. 4th
YY X CC CC CC CC CC T U Y CC CC Y CC CC Y CC C C C YY
aug. 4th
7
7
Ì
C
C
Ì
C
C Y C CC C C YC C
Ì
8
V 8 7 /V 8 7 /V 8 7 /IV
g = X CC C CC C C
8
c) Brahms, Fugue on a theme by Handel from Op. 24 (after Free Composition , Fig. 87,2)
!
perf. 4th
C C C C
V 87
B
B
Ì
a)
5
Ì
V10 7
CC C C C C C C B B aug. 4th
aug. 4th
b)
7 10
perf. 4th
8
perf. 4th
V75
B 5 8
CC C C C C C C
B
B
c)
B 10
V 87
perf. 4th
7 5
C CC CC CC
BC aug. 4th
d) aug. 4th
V75
(“III 6”)
B perf. 4th
CC CC CC CC
B
e)
10 8
aug. 4th
V78
5 10
(succession of dissonances)
B perf. 4th
C C C C C C C C
f)
Ex. 7.34: Perfect fourth progressions and combined fourth progressions within V7
V10 7
# B
! C C C C
a)
Ex. 7.33: Descending augmented fourth progressions within V7
V7
B
B
aug. 4th
(succession of dissonances) 10 7 V 75 8
B
perf. 4th
CC CC CC C C C
g)
I
B
C C
C C C ¥g ¥ C
d)
74
75
ant.
3 true 7th-prog. fifth: third: type 2 type 1
4
5
I
V7
(“I”
II6 VII/V
V)
I
C C C C C C C C Y C ¥ C Y C XC XC XC C C ! Y B C C C C C WC C # YY C C C C Y C XC XC C h h
1
Bach, French Suite No. 2. Sarabande.
or
?
I
g
C C C h
4th
4
V
(IV 6
V)
IV 7 V 56 /V
5
I
C XC XC C
C WC
ant. C C ¥ C C C C C C C C XC XC XC C C
3
B C C CC C C h
C C C
1
Ex. 7.36: Hybrid segmentation of a seventh progression within V7
76
7 V5 64 35 42 31 2 1
5th V
7 6
B
# C C C C C
)
C
C
C C
g
(retransition)
g
199
g 7th
b) Schumann, Piano Quintet/I
I V
5
7
(9
4
b 8) 6
7 5 3
b6 b42
5 3 7
4 2 b 67
5
4
°7) 4 3 3 2 1
bb32 b27 b71 7 6 5
(°7 º7 °7
C Y C CC CC Y C C C C C C C C C Y Y Y B B CC Y C C Y C C Y CC X C Y C YX CC CC C C CYC XCYC 4th or 6th C Y C C 7th C C C C B C C C C Y ( C ) Y Y B 7th
8 7 6 5 (4 3) 6 5 (4 3) 7 5 4 3 2 1 V 6 5 4 3 2 1
7th
C C CC CC CC ( C C C C
7th
C C C C C C C !
3rd or 5th
a) shorter linear progressions
Ex. 7.37: Accompanying seventh progressions within V 7 by parallel motion
B
I
B
207
77
7
V 1
(5 3
7th
WWW C C CC C CC CCC !
!
7th
W C CC C C WWW W C C C
79
3 5 1) 7
CC CC C C C CC
W CC CC CC
80
a) Beethoven, Piano Sonata Op. 101/III
[in V:]
Y
Y
7
V1
C
C XC
C C C C C
282
(4 4
(“I”)
7th
C C C
C XC C
7th
b) Beethoven, String Quartet Op. 18, No. 1/I
C
C
1) 7
284
Ex. 7.38: Seventh progressions within V7 by means of voice exchanges
V8
C
7th
7
C C C C C C
C C C C C C C C
8th
c) apparent seventhvoice exchange
78
79
d)
e)
g) Schumann, Frauenliebe f) Brahms, und Leben . No. 2: Violin Sonata No. 1, Op. 78/I Er, der herrlichste von Allen 10
Ì
! CC C CC CC # C C W CC C X C C C C 8
V 73
8
#7 n 7 2 2
3 1
Ì
Ì
(X ) C CC W CC C C C C
g
28
31
Ì
W C C C CWCXC W C C C
(V/V)
(VII# 63)
# V73 75 n 87
# n V 78 7 7
g YYY C C C C C C C C X CC Y C C ant. C YYY C Y C C C Y C ant.
C CXC Ch C
(V56 ) (V2/IV) II56 V43(II43 ) b of V) 1 8
V 57 64
3 b3
#7
2
(5)
(n 7) n 7 5 b2 1
3
B
[ ]
C C C C WC XC
V78
n ## 77 87
cadential in # VII # 5: IV 56 46
#
!
C WC C C C C
a)
as in
!
CC X C C
10
in relation 8 to the root: V7 V7
in # # VII 5 : IV 56 6 4 ## 7 7
cadential
8 V2
n7
YYYY C W C W C C X C C C X CC Y C
YY Y X CC W C X CC Y
9
Brahms, Piano Sonata Op. 5/V
Ex. 7.40: V8-7voice exchanges
g
105 3^
I
V 78
(“V
I”) (“V
#7 #7
8
I”)
n7
n7
I
C YY B ¥ = W CC X X CC Y C CC Y C C X C C B C C WC XC YC C C # Y B B XW CC W CC X CC B Y C
g
©2004 by the Music Theory Society of New York State. Reproduced with permission. 85 97 101 ^3 4^
b) Schumann, Faschingsschwank aus Wien . III: Scherzino
80
V7
# C 7
I
V7
8 (7)
I
C
C
g
IN
C
illusory 7th-prog.
C C C C C C C C C
g
g
b) alternative
C C C C C C C C C !
g
a)
=
C C
C C C
g
Ex. 7.42: Register transfer of the tone of the seventh of V7 76
g
[in V:]
III (I 6 ) V7
g
80
8 7 I (ambiguous hierarchy)
complete register transfer?
78
WWWW C C C C C C W C C X C C C C W (X ) C C h hIN? C C C WWWW C C XC C CWC C C C W
74
c) Haydn, String Quartet Op. 76, No. 6/II
81
4
7
6
g
cons. I 64
7
I
V7 6 5 4
3
2
1
C C C C C ant. C Y C X C Y C C ! B C C C C C (X ) CC CC C C 7th C CYC CYC C #Y CC C CC CC B C
1
Beethoven, Piano Sonata Op. 101/II
6
Ex. 7.44: Register transfer of the seventh of V7 without linear connection
82
6 363-4
7
8
b) Beethoven, Piano Concerto No. 5/I 9
Ì
V7
(V 7
I) (I
(V7 I) (V 7 I) (V7 I) VI IV II
V)
C C C CYC C C C C C C C C C C C C ant. * C C C C C Y C C X C C C C C C Y C C C C Y C C C C C ! C C C C C C C C C C X C ( CC ) Y C C YX CC CC Y C CCC CCC C middle octave: not harmonic C C C C C C Y C C C CYC XC C # YY B B
a)
Ex. 7.45: Register transfer of the seventh of V7 through multiple octaves
83
84
V7
6 3
6 3
6 3
6 3
7 3
ant.
! C C CC C C C C C C dim. 5th 5th C C perf. C C C # C
aug. 4th
( cf. Ex. 6.1cBrahms Op. 118,3)
a)
aug. 4th
V7
7 3
C
C
6 3
6 3
6 3
6 3
C C C
perf. 4th
dim. 5th
CC C C C C C C C
b)
as in aug. 4th
57
7 3
C
6 7 3
C
dim. 5th perf. 4th
6
7 3
C 6
C CC C CC C CC W C
7 6 3 3 V8 7
C
W CC
WW C C
WW C
48 56
Mozart, Symphony No. 35/I
[in V:] V 4 3
7 5 3
6 4
3
# 7 n7
*
7 3
6
(a #?)
7 3
6
7 4 3
6
8 3
7
7
ant. C W C C X C C W g C X C WW CC (W ) C W CC C W CC C CC C C CC C W C C WC dim. 5th perf. 5th WC C Y C C C C W
g
6 aug. 4th (determined by location in the scale) (not a dim. 5th [!])
1
c) Wolf, Spanische Liederbuch . Herr, was trägt der Boden hier (after Williamson)
Ex. 7.48: Simultaneous augmented fourth and diminished fifth progressions within V7 adjusted by means of delay
85
inserted
V5
aug. 4th perf. 4th
(V/) Ì (V7 I7 IV7 VII7 III7 VI 7 II # 7 V7 )
perf. 5th (diatonic 5ths-cycle)
7
g
138
I
C
C C C C C C C C XC YC
dim. 5th
135
C C C C C C C C C # YY C
Y C C Y ! C
g
132 133
Haydn, String Quartet Op. 64, No. 3/I a)
=
V7
?
CC CC C C C C C C C ?
CC C C C C C C XC YC
(problematic verticalization)
?
bass relations: (I V7
CC C C C
synchronized
V
I)
C
CC C C C C C C C C C CC X CC ( C ) Y C not
g
b) perhaps from:
Ex. 7.49: Simultaneous augmented fourth and diminished fifth progressions within V7 adjusted by means of chromatic insertion
g
86
dim. 5th sus. sus.
47
I V 7/V
h
[ b III of V] 9 8 5 6 [7 6]
YY B X CC C CC Y CC CC Y CC ! XC YC C C C pp perf. 4th # YY C C Y C C B
1 35 36 ^ 8
53
g
59 ^7
3
V
CC C CC X CC C C C B fz f XC C B 4
a) exposition bridge
V8 7
7
*7 6 7 6? 6 5
dim. 7th-chords: *
3rd
dim. 5th (not a 6th!)
182 196
2 aug. 4th contradicts the pedal point
1
c) main theme
* I
(
( )
V7 I above I pedal point
( )
C Y C C C X C Y C C sus.C sus. sus. sus. C C C ) C C CC B Y B C C C Y C C X B C C C Y Y C C C C C C C C X C Y C C Y CCC CCC 7th pp fz f = C C C Y C C (Y) C X C C C Y C Y C X C CC C C XC B B Y B YY Y B
162 163167 174
b) recapitulation bridge
©2004 by the Music Theory Society of New York State. Reproduced with permission.
Haydn, String Quartet, Op. 64, No. 3/IV
Ex. 7.50: Other counterpoints to diminished fifth progressions within V7
87
88
Ex. 7.51: Simultaneous linear progressions within V7 involving an ascending diminished fifth progression Schumann, Kinderscenen. No. 8: Am Kamin 1 5
x2
4 8
C
!Y
9
11 3rd
¥ C CC C C C C gh ¥C W C (B )
C
V37
C X CC C
CC
C (W C )
C
C (Y) C C
20
B B
C B
I 6]
I] [in III: V above a pedal point
#4
17
C C C C (X () C ) C C
WC
C
[in II: V
I
C h
dim. 5th
Ì
#Y B
CC
15 16
5
6
7
I
Ex. 7.52: Upper neighbor to the root (of V7 ) alone a)
b)
B
B
YYY X B B
! B #
c)
C C
C
V7
B
XXX B B
YYY C
(VII2 )
d)
C
B B
XXX C Y C C
(VII2)
V7
V7
B
C (Y C C
(VII 2b )
V7
)
6 (II ( 4b))
C
e) Mozart, String Quartet K. 464/I, retransition
g
157
!
WWW ¥ B
165
B[ ]C C C
# WWW B
C XB fp
V7
162
(VII2b )
C XB fp
(VII2 b )
C
B
C C C
C S CC f 7th S C C XC
B¥ p ¥ B
(in exposition: simple ant.) 6 (IV b 31 )
89
Ex. 7.53: Inversions of upper neighbor to the root of V7 a)
CB (Y) C C !
c)
b)
BB
(VII (b)7) V65
C (Y) C C
CB (Y) C C BB
BB B
(VII(b)6 5) 4 V3
(VII(b)43 ) V2
Ex. 7.54: Upper neighbor to the octave of V7 a)
b) Mendelssohn, c) Chopin, Scherzo No. 2 Morgengruß, Op. 47, No. 2 30
#
C B (Y) C C ! B BB
WWW WWW
b V8 ( ) 9 7
8
C CC C C
YYYY
C
YYYY
C C C 8 9 V 73 4
( )
g
B
XC C h
53
8 3
CZC C C C C CC YC C
Y Y
V8
b9 7 1
56
C X C Y C C Y C ( CC ) C ZC C h (VIIº2) 8 b2 1
90
Ex. 7.56: Insertion of secondary neighbors within V7 Mozart, Piano Sonata K. 332/III 96 97
98
99
101
100
C YC C C ! Y CC Y C C Y C C Y C CC X C C C C h h # YWC C C C YC C C C YC C YC C YC C h h 6
V51 of G
7
6
2
1
7
V13 of C
4 2
3 1
Ex. 7.57: Upper neighbors to the root, the third and the fifth of V7 b)
a)
Wolf, Mörike-Lieder. c) No. 18: Citronenfalter in April 1
BCC
! C
5
CCC
5
7 V53 1
5 3 1
6 4 2
B CCC
(IV 6 5)
as in
CC CC CC C C C
(IV4 3) 6 7 6 V53 4 3 1 2 1
4 X3
CW CC C T T U X C CC CC h 6 V53 1
(IV 4 3 ) 7 4 2
g CC C C C CC CWC C h 7 4 2
(6) 6 3 (1) 1
Ex. 7.58: Upper neighbor to the fifth of V7 alone a)
b)
B C C ! BB C V 75 6
5
C C C BB B
13 V 12 7
12
d)
BC C C CC CC CC (IV2) 6 7 6 V43 5 4 1 2 1
CC CC CC CB C C (IV 7) 6 7 6 V 42 53 42
91
Ex. 7.59: Lower neighbors to the consonant members of V7 a)
b)
BC
BBC
(II 6) 7 V
CCC
5
CC
! C CC CC
c) (not usable)
B CCC
5
B
CC CC CC C C C
CC CC CC C C C
(IV 6 4) 4 V3
(IV6) V56
(IV)
V7
C C CBC CCC CC BB
(IV) V2
(“VII”46) V7
BC C C
Ex. 7.60: Combinations of neighbors within V7 in contrary motion a)
b)
BC C C ! C C CC C C
BCCB C C CC
d)
e)
BC C C C C C
C C C CC CC CC
C CC C CC C CC
(II 64 )
(IV) 7 V31 42 1 7
c)
7 V13
3 1 1
(IV6) 7 V51
3 1
2 2
B
4 2
5 1
8 V73 1
(IV) 9 8 4 3 7 1
Ex. 7.61: Upper neighbors to the seventh of V7 without change of harmony a)
g
b) N
¥BB C C BB ! B BB V7
(8) 7
I
or
g INg ¥BB C C B
V7
8
(7)
BB BB I
B
(IV 6) 8 7 8 V73 4 3 1 2 1
92
Ex. 7.62: Upper neighbors to the seventh of V 7 with chromatic filling in a)
b)
g
g
g
CB W C C W C X C
CB C W C X C
CB W C C X C
B
B
B
! #
c)
B
(consonant V) 8 #7 V7 # 7
B
(consonant V) V7 8 # 7
n7
B n7
(consonant V) n7 8
#7
V7
d) Beethoven, Piano Sonata Op. 57/I 23
24
C h
g
32
33
N
C YC YC
Y ! Y YY C # YY Y Y
27-31
CC
C
ant. C X C Y X C Y C CC CC
C YC (consonant V º7 8 5 3
V 71
#
b43
(notated e n)
C YC YC º7
#7
4 2
º7 ) [VIIº2] (n 7) n 7 3 b(3) 2 1
Ex. 7.63: “I” 64 as a three-voice upper neighbor to V 7- schemes a)
dim. 5th
CCC
! B 7
V53
b)
perf. 5th
CC C
8 6 4
c)
CCC
(parallel fifths avoided) dim. 5th
7 5 3
CC
CC
CC
C CB 7
V53
C 8 6 4
7 5 3
g
CCC W W CC C CCC WW CC C X X CCC B (ant. avoids parallel fifths)
7
V53
# # 57 4
8 6
##7
5
nn 75
3
26
g
N
g
32
¥CC B
35
5 6
V73 46
7 5
3
#7 #5
(“I”6 4) 8 n7 6 5 4 3
(I?)
I
! B C C WC C XC C C C C C CC CC C C C ( C C ) Y C CCC h h g # C C C YC XC C C C XC C B ¥ B B
24
V7
B
C
B
24
B I
C C
g
26 32
C B
35
V7
B
C
¥ C C
g
24 26
C
ant.
I
¥
C
C ¥
35
I
V7
B ¥¥ I
?
24 26 32 34 35
^ (2) I I
¥ C B
p.p.
g g B B ¥ B C B
1
Bach, The Well-tempered Clavier , Vol.1. Prelude in C Major (after Five Graphic Analyses) a) b) c) d) alternative BG contexts
Ex. 7.64: “I” 64 as a three-voice upper neighbor to V 7 - example
93
V57 86 75
(I6) 7 8 7 V 53 64 53 (I) 7 8 7 V 53 64 53
CB C C
(III6 )
C C C C C C
C C C C C C
C C C
V57 86 75
(III)
CC C CC C
B
C C C
d)
(III6) 7 6 7 V 53
(III6 5)
V37 6 7
C C C BB
b)
CB C C ! BB
a)
(I43) 7 6 7 V 53 4 5
CC CC CC BB
c)
10
B CC C
(I 6 4)
CC CC CC B V 73 46 37
(I6 4)
7 V 55 3 1
CC
CC (I6 4) 6 7 6 5 4 5 4 3
C C YYY CC CC CC C
6
(VI 2) 7 6 7 V 53 42 53
CC C CC CB CC C
g) f) Mozart, Symphony No. 39/III
C CB CC CC
e)
aux.
17
20
tonicized ( b III)(IVm6) 7 8 7 3 I V31 b42 n 2 b 53 (not n 3!) b42 1 V/
1 11 12 13 15 23
24
cons. support
V 75 46 57
(I)
CC CC CC C C C
h)
6) (IVm
7 V 53 1
(VI) 6 4 4 2
7 5 3 1
CC C C C CC CC C CC
i)
I
g g g X2 Ng X2 ¥ C C YYY CCC Y( CC )Y CC C C X C CC Y C C C C C X B YC C h Yh C 10 (implication: g n 10 C 3rd-progression avoided) C Y C YCXC C CYCYC CYC C C B h h
g
Mendelssohn, Song without Words, Op. 53, No. 1
CC Y C CC Y C YY Y B C Y B (bIII) 7 8 7 b V 53 b63 n 53
d)
as in
C C C YY C YCXC YY
e)
V 75 46 57
Ex. 7.66: Harmonizations of V 7-6-7
#
!
C C C C C C
C C C C C C
B
c)
b)
a)
Ex. 7.65: Other harmonizations of V7-8-7motion
94
^^ ^
IN
5 ^2
6
f
CC CC CC C C CC
4^
^5
tutti
3
1
4
p
winds
5 ^ (3)
7
f
tutti
4^
9
(I
C
N
II6)
C C
V8 7 V (structural I only at 75 or 83! seventh vanishes without resolution)
WW WC I
¥ II6
h V
I
B Y C V7
(I) 6
C
g C
7
I
C
C C C
6 5 4 3
(final resolution ambiguous)
12 ^ ^ ^ 3 2 1
11
C C C C C C Y C X C C C C C C
C
^3
4
C
or
1 2 3
# WW B WC
6
ant.
ant.
5
g B CXC C CC C C g C C C C C C ¥ C C C C C C C C C C( ) C C C C C C C C CC Y
g
4
b) Beethoven, Symphony No. 8/I
g C C ! ( C ) C C C C C C C C CC
1 2 3
a) Mendelssohn, Song without Words, Op. 30, No. 4
Ex. 7.67: Analytical dilemmas: V-I-V
434
95
#
!
7
6
1 2
V53 44
7 5 3 1
V3
7 (6) 6 5 4 2 2 1
(V7/ VI)
Ì
(VI) 7 5 3 1
C C W CC CC X C h
C
CC C C CC C
CC CC CC
C CC C C C
b)
a) 81
8 7
I V/51 of VI
[in VI:]
83
#1
6 4 2
(v/vi) (vi) 7 5 1
C C
C
II7
6
C C YC C C YC h
Y CCC C Y CC Y CCC C Y C Y CC C Y C (X C ) X C C C Y CC C
reaching-over
(enh.) B( ) C Y CC C C Y *C C Y CC C X C W *CC CC C C C C C C C C C C C B h
57 71 79
c) Brahms, Concerto for Violin and Cello/I
Ex. 7.68: Lower neighbor to the seventh of V7 harmonized as VI
6 4
C VI
(expected cadential avoided)
C
CC ant. C
89
96
97
Ex. 7.68 - continued d)
e) Chopin, Nocturne Op. 9, No. 2 1
2
g
3
4
N
C
C C CC C
! C C
C C W C CC X C h
# C
VI)
#1
6 2
V 17
C C C C YY Y B C C C C C C C C C Y C ( CC ) ant. YYY B C C X C C X C C
B
7 1
I
Ì
(V 65 /
VI)
V17 # 1
6 2
b6
7 (5) 1
I
Ex. 7.69: V7-6-7employing mixture a) ^3
^4
g
n ^3
^ (b3)
g
N
C CC Y CC CC X C C C C !
b b6
b)
(or
V57
4 major 64
c)
CC W CC CC C C C #
6 (I 4 )
I
7
I
in minor)
V31
# 46
2
d)
CC Y CC C C CYC C b b 7 6 V31 b42
CC Y Y CC CC C YC C
tonal paradox: enharmonic identity
( VI)
(VI ) 7 5
¥B C
N (P?)
7th
Ì
(V 65 /
g
5
7 3 1
b b b6 7 b b4 3 2 1
( VI ) 7 3 1
7
V 31
7 6 7
# 5 #4 5 V(3 V53 # 42 53 ) (all cases: in minor employing # 6)
7 6 7
C XC C Y C WC C
1 7
6
V53 # # 42 5 3 1
7 6 7
# V53 (n4)2 53
CWC C B
C C C C (X ) C C
?
(potential)
(V2/ II6 )
Ì
CWC C C C C C
C C C C C (X ) C C
d)
Ì
in relation 57# 64 7 to root: V 3 # 2 53
CWC C B
CWC C B
X2
Y CC C C
as in
129
128
Haydn, c) String Quartet Op. 76, No. 4/I
Ì
#
C C C C WC C
b)
C C C ( ! ¥)
a)
Ex. 7.70: Chromatic inflection of V7-6-7 neighbor motion
N
2
8
V 73
YY B
C
7
CC
4
CC ( C C ) C
ant.
3
6 6 2
(V2 /
N
? Ì
B II) over a pedal point (5) 5 7 I 2 3
ant. C C C C C C C C C C C
4th C C C X CC YY C ( C )
1
e) Schumann, Albumblatt Op. 124, No. 9 (Impromptu)
98
#
!
25 33
g
39
WWWW W W XC BXC
(enh: V 2/b III) 7 V 53 # 2 3 b2 1 1
B YC
B
as in
C
33
39
C XC
B C
C ( V C =) X C W C
B
from
25
Chopin, Nocturne Op. 15, No. 2 (after MW II, 20-21)
XC C C C W B C ( W C =) Y C X C W W W W W B X CC W CC
a)
)
(
C
(enh.: V 34 /bV) 7 # 5 V 53 4 1 1 b2
CWC XC C (Y C =) W C X C
B (W C B
b)
)
Ex. 7.71: Special neighbors to V7(a): enharmonically chordal neighbors
C
YY CB C
or
12
C
13
Schumann, Waldscenen. No. 4: Verrufene Stelle
(enh.: V6 5 /VI) 7 6 7 V 35 1 1 b2
(enh.: V 6 /VI) 7 6 7 V 3 (no fifth) 1 1 b2
Y C (Y C =) W C X C Y C (Y C =) W C X C
B
C C B
c)
99
100
Ex. 7.72: Special neighbors to V 7(b): whole-tone non-diatonic neighbors Humperdinck, Hänsel und Gretel . Introduction to act 2: Hexenfahrt 47 48
49 50
x2
x2
Y C Y NC Y C (enharmonic notation)Y C C W C X C (cX C b?) C W C C Y C C WC C WC XCWC XCWC CWCWC XCWCXC W CWC C Ì
Ì
!
N
N (enharmonic notation) N
?
?
Y CC X X CC Y CC CC YY CC CC X C CC YY CC CC X C Y C C C X C CC Y CC Y W C CX CWC CW C # YB N
Ì
Ì
(never resolves: finally, a passing 43 resolves into a stable section in F major)
(parallel 4/3s above a pedal point)
8 # 8 b# 9 n b b n n [in Ab :] V 75 # 75 86 # # 75 nn 75 b 75 46 ##64 n 75 # # 3 3 b3 2 2 n3 3 3 4
##b64 ?
7 5 3
2
1
Ex. 7.73: Neighbor parallel motion in all four voices within V7 a)
c) Richard Strauss, Till Eulenspiegel (after Counterpoint I, 192)
N
C
C
C
C
N
C
C
C C
C C
C
!
C
C
N 7
V53 1
68
67
C C #
b)
(VI 7 ) 8 6 4 2
C
C
C C
C 7 5 3 1
C
C C
N 7
V53 1
(IV7 ) 6 4 2 7
Y CCC WNCC (Y) CCC C W X CC C C
N
7 5 3 1
7
V53 1
# ##42 6
7
7 5 3 1
WW
C
C
C
C
6 V42 1
b7 5 b 32
# WW C X C C YC
!
223
C (W ) C C C WC XC C
C (a b
226
?)
C
C C
C C
C
(a b?)
228
C
C
6 4 2 1
6 4 2 1
7 5 3 b2
(V2 /III) 6 4 2 1 4 3 1
3 4 2
4 3 1
n7 # 7 n 7
(dim.6 ) 3 (VII 2? VII 7/VI?)
7 b8 /#7 5 4 3 4 1 b2
n 7 #6 5 3 b2 1
(Italian)
C W CC X CC W CC X C WX CC X C X C YW CC X C YW CC WC WC XC C C
C WW CC C
(including inner repetitions) (soprano: (all neighbors are whole-tone neighbor) semitones)
222
d) Schumann, Novelette No. 5
Ex. 7.73 - continued
7 1
C
C
C
C =
V7 (3rd inv.)
C WX CC YX CC C C
C
C
# 7 nn 7 #5 5 2 b2
(V2/III)
C WC XC C X C YC h
C WC XC
C
7 V53 (root) 1
ant. ant.
C W CC X C C
from
C
C C
C
1
1
7
V53
2
b8 b6
7 5 b2
C YC C C C XC YC h
or
?
1
C
101
102
Ex. 7.74: Neighbor contrary motion in all four voices within V7 a)
b) Mozart, Symphony No. 40/I
(for diatonic version see Exx. 7.68)
! #
C
C WC C C
C
7 1
C
XC X W CC YC CC CC
(ant.)
W CC C
C C
C
(ant.)
# V# 42
7 5 3 1
4 2
6 5 3 1
7
n2
# #n 64 4 2
(possible without enharmonic transformation?)
CC
C
# #n 64
c)
152
(Y) C CC WC YY X X CC W CC
C X CC C
V53
150
7 5 3 1
C YC XC C YC XC C YC XC C YC XC
( b V) (enharmonically incorrect?) 7 bb 8 n 7 V 53 b53 n 53 n1 1 b1
(cf. diatonic model in Ex. 7.61)
d) Liszt, Piano Sonata (before the espressivo that precedes the fugue) 415
418
419
g
422
431
N g 6th X C W W W W W g X C X C X C C W C X CC C YX CC X X CC YY CC W C W C C W C W C X X CC W C X C ! X C W C X C X C C X C X C W CC W CC W CC C C
C
h
N
# WWWW W C W C
C
N
C b
( bV)
n
C ( bV)
b
8 V 79 8 b 88 b 88 7 (cf. enharmonic model in Ex. 7.97a)
n
8 7
103
Ex. 7.75: Double neighbors to V7 a) double neighbor in a single voice (1) (2)
CC C C C CC
C C C C
! C
6
7
7
V 51 2 7
(1)
(2)
(3)
CC CC CC CC C
CC C C C CC CC
CCC C C C CC CC
(I 6 4)
(II [6])
(III 6 )
V73 8
b) double neighbors in parallel motion
V57 86 64
1
(II43 6 )
(IV) 7
7 5
7
3 1
V31 42 27
V 53 4
2 7
1 2
3 1
c) double neighbors d) double neighbors combined with other motion: combined with other moton: a single neighboring harmony two neighbor harmonies (1) Mozart, (2) (1) (2) (3) Horn Concerto K.412/I 89
?
W W CC CC C CC ! N C (I6 4)
V37 46
8
(IV 7 or VII 7 /V)? 7 6 2 V 31 42 7
7 3
d) - continued (4) Haydn, Symphony No. 104/I
(VI 7 6 V53 44 1 2
of V
7 6
V 31 42
(5) Beethoven, Piano Sonata Op. 2, No. 2/I
98
221
CC
Ì
C C W W C C CC W CC CC CC DN
(VI V8) 7 3 1
CC
II6) 5 7 2 3 7 1
7 1
7 2 7
7 6
CC
(VI II6)
(VI IV)
V 31 42
7th
7 3 V5 1 3 1
6 4 4 2
7 5 2 7
3 1
e) alternatives to double neighbors (1) (2)
224
WWW C C C C C C CC C CCC CCC CC CC DN V35
8 7 3 1
CC C C C CC CC C CC
C CC ant. C C CC C CC CC
(VI) (II 56) 6 5 7 4 3 4 (2) 3 2 7 1
g
IN
CC C C C CC C C
V7
I
C
C C CC C CC Ì
!
97
C C CC C C CC CC C CC
C NCC CC C (W ) CC
Ì
86
Ì
P
V7
I6
104
Ex. 7.76: Selected combinations of third progressions and neighbor motion within V7 a) synchronized motion (1) (2) Chopin, (3) Waltz Op. 69, No. 1 manuscript version 55
CC CC CC ! # B
(5)
56
(6) Clara Schumann, Romance Op. 11, No. 2 5 6
7
YY Y CC W C C CC CC CC CC CC ¥C C C CC CC CC YY C C CC X C C CC Y W CC CC C C YYYY C
(I 64 )
V 73 64 75
(4)
C C C C C C C C C C C Y[C ] C Y C C C C Y C
(“I”)
V73
* * (notated g b)
cons. support
(VI) 7 6 7 6 7 V5 4 3 45 1 2 1
(IV6 ) (VI 7 ) 7 7 8 7 V51 42 31 V51 42 53
cadential enh. # b [in VI : IV 56“I”46 ] 8 7 b7 6 5 6 7 I V 53 1 1 2
g
219
x
220
g
x
g
IN
221 ( ^4 )
I
# YY Y Y B
y
g
(V7
C XC C YC C
N
)
B
C
V71
y
(VII2
B XC YC ZC
x
C B C C C C C XC CXC C C C ¥ YC C CYCZC YYY Y !
218 ^3
a) voice leading graph
2
bb 6
( b VI
V 7 I)
YC Y YC ¥ h Nh
230
231 ^2 ^1
¥
XC
g
7 5 3
C
12
g
y
I
CB Y C C
X CC X C CC C C Y BC B C CCC X C X C W C YYC C X C C C
227
# ) IV 6 5 13 doubling n 8 6 4 1
Y CC C X C C X C
226
Ex. 7.77: Chopin, Ballade No. 3, coda (an outstanding case for Ex. 7.76b)
105
106
107
108
Ex. 7.79: Reaching-over within prolongation of V7 : regaining the same pitch a)
b)
c) Beethoven, Piano Sonata Op. 81a/I 47
!
C C C C # B
V7 6
8
CC CC C CC CC CC CC CC XCXC C C CXC YYY
C C C C C
(= double neighbor)
7
B
! YYY C
V7
5
8
49
7
C C YC C C h
(VII 43
[in V:]V7
5 9 (V9 already at m. 40)
I6 displaced) 7
Ex. 7.80: Reaching-over within prolongation of V7: achieving a higher register a) arpeggiation (for a filled register transfer see Ex. 7.46)
b) direct superposition Beethoven, Symphony No. 6/I 468
470
C
C ! C C CC C CC C C Y CCC XC CCC CCC # B Y C V7
3
5
7
V7
7 8
109
Ex. 7.81: Reaching-over within prolongation of V 7: aiming at another pitch class a)
b)
c) Bach, Violin Sonata No.1/II 47
g
(cf. Ex. 7.68)
!
52 *
d)
55 further prolonged (...)
g
C X CC g C C C C C C C C Y C C C XC C C C C AC C C C C C C C C C C C Y X C C CC Y ¥ C C C C W CC C C C C CC Y C X C C C C C 2 3 2 3 2 3 2 3 h
V754 7
V7
9
(“I”46 )
8
V57 46
(IV6)
(IV)
8 7
V71
I
2
3
4
5
Ex. 7.82: Bass divider within V 7 harmonized as II a)
as in Haydn, Symphony No. 94/I
b)
16 18 Adagio Vivace
! BB
(II)
V7
WW C
C C C
WW C C
Ì
3rd
(V/ II) 7 V
3rd
bass divider
C
(V/ II)
V7
I (for a combination with a fifth progression, see Ex. 7.24d)
12
Y C !Y
C C (X ) C C W CC C C C Y C X CC # YY C h aux. [in II: IV6 V 7 I
V7
CC
W CCC CC CCC X CC CC C C C C C C h C
c) Schumann, Waldscenen, Op. 82. No. 1: Eintritt 8b
g
Ì
# C C C C C C
CC C CC CC C W CC C C
g
21
16
C C CC C C CC C C C C CC C YC C C C YC XC C C C ]
7
V 35 42 31
(II7)
V 53 42 31
7
Ì
(II 7) 7
V 35 24
(II7 ) 3 1
C C C C C I
V7
B C C
bass divider
C
(II7 [VII 56 /III]
)
WCXC C XC C 7
I
B
CC X CC Y CCC C CC
g
609 610 614
disalteration
C C C
# C C C
g
CCC C C C C !
10th = 3rd
606
eva g Y C X C C ant. C W C X C W C Y C X C C CCC CC C C C CCC CC C C C CC C CC C C C C W W CC CC W CC X CC X C W C C W C X X CC X CC W XC CC
g
570 589 590
Beethoven, Leonore Overture No. 3 (in four layers)
Ex. 7.83: Bass divider within V7 harmonized as II 7
110
C
# n V 73 72 81 7
(V/V)
g
N
g
293 304 (1)
Ì
7 V31
C
#7 # 8 n7 4 #4 5 2 2 3
(V7/V)
C C 7 I V31
bassoon
YY B CB X C only Y C (I6 )
C
x
V7
(bVII 6 )
BCC Y C X C ! C C C
a)
C
(VII #63) [inversion of VII # 5] V7
CB W C X C BC C
b)
V7
BB CC
c)
(III 2 )
C
C
N
C
C
eva
3rd
309
g
310
g
(V/V)
bass divider
C C C C C 4 2
#7
C XC
2
# # 84
C 5 3
n7
x C C C C C C C C C C C XC C CC C X C C X C YC C W C XC
306
I
B
B
311
d) Brahms, Variations on a Theme by Haydn. No. 7 (middle section)
B ¥ CC W CC W CC X CC C Y C Y CC Y CC Y CC C CW C
c)
Ex. 7.85: Bass divider within V7 harmonized not as a root
7 #7 n 8 V 3 2 71
(V/V)
C
C C
# C CXC
g
N
CWC C XC C C C
b)
C W C CC C C C !
a)
Ex. 7.84: Bass divider within V7 harmonized as V/V
111
72 75
74 77
79
80
in F: V7
surface motif
(II6)
C ! Y Y ¥C CC X CC CC W C C C C Y CC C X CC Y CC C X CC CC C CC Y CC h C W CC CC X CC C CC W C # Y WC C C C (X ) C B bass arpeggiation
65
g 81
82
4th
84
(
)
(I)
g 85g C C C X CC C Y C C CC CC CC C C YX C B C C C C C C C X CC Y C X C (elision) (elision) CC CC C C C¥ C C C C C C C C
Wagner, Die Meistersinger von Nürnberg. Act 2, scene 3 (Sachs)
Ex. 7.86: Bass arpeggiation within V 7
112
113
C
C YB
C
B
C C YB YB (X ) B C WC WC XB
B C Y CC Y C X B X YC YC XC WC C B
C YB
C Y CC YC WC WC XB C Y C (X ) B B
YB
C YB X B X CC C YC YC XC WC C
G6 5
B
B
WC WC XB YB YC XC WC XB C YC C Y C (X ) B C (X ) C Y B (X ) B
B
C YB C YC
immediate four cycles of inversion and contour rotation: root relations create descending equal division of the octave root relations: ascending G6 Bb 2 D b4 E6 G2 B b 43 E2 G4 B b56 Db 2 D b 65 E 43 5 3 5 equal 3 division V65 into four three cycles of the “Devil’s Mill” required to return to the original inversion (root position avoided)
#
!
B C YC
B
b) inversion of the “Devil’s Mill” (some chromaticism eliminated)
114
115
Ex. 7.89 - continued c) the extended omnibus as a series of truncated classical omnibuses (Wason 1985, Example 2-4, retranscribed)
Y AAC Y C C Y C Y C C YY AAC Y C C Y C YYY CCC W W AC X C W C X C W WC CC W CAA X C C Y C XA
! #
C WC XC WC C C C W C Y C X C W C C Y C X C Y C X C Y C X C C d) exchanging the third and fifth into the root and third
C C (X ) B Y B Y C W C B C CC Y C Y B X B C C X B C X BB C Y B C C C Y B C C C ! CYC C WCW C C C C YC XC WCWC C YC XC WCW C #
C C Y B Y B X C C (X ) B Y B Y C W C X B B X BC C C Y C YY B B X B B YB X C X C (X ) BB Y B Y C B WC B XB CYC YB XB
G7
Bb 2
Db43
E7
V7
G2
B b 34
D b7
E2
G 43
B b7
Db2
E 43
G7
skipping over 65
e) exchanging the fifth and seventh into the third and fifth (respectively)
CB C Y BB YY B C Y C X C W C B Y B Y C Y C ! W B X B Y C C B W BB
X B C C Y CB C Y BB X B C W C (X ) BB
C C Y CC C YY CC Y C X C W C C C C Y C Y C X C W C C C C Y C Y C X C W C B C B # B B C C CB C Y B X C W C X B Y CB C Y C Y C WB XB G7
V7
Bb 2
Db65
E7
G2
B b56
D b7
skipping over 34
E2
G 65
Bb 7
Db 2
G7
V7
G7
B b43
C# 6 5 E7
G43
skipping over 42
Bb65
Db7
E43
G6 5
B b7
Db 34
E 56
G7
YC YC Y C X C Y C X C (X ) C W C X C W C YC YC XB X C W C X C (X ) C C Y C X C Y C X C (X ) C Y C Y C X C C Y B ! CB W C B WB XC WC XB B (X ) C Y C B WC XC B B YC B C YC B B Y C C (X ) B B Y C B C Y C C W B W B X C # WC XB W B C X C W C X B W C X BB Y BC C B B YC C YB WB XB
f) exchanging the seventh and octave into the fifth and seventh (respectively)
Ex. 7.89 - continued
116
#
!
B
WB
C YBWC XX BB
B7
E b7 G7
G6 5 B2
E b 43
W CB X C Y Y B¥ G6 5
X X BB
(skipping over root position)
BC Y C
tethrachords
CWC XB W BC Y C X C YC C CYC XCWC B X C octatonic
B
b) (inversion of a)
B2
Eb4 3 6 (skipping over 5 ) V7
G7
G7
CB W C B B YY BC C X BB
whole-tone scale
BC W C W W CC X C Y B BB WC C C C
c)
V7 V7 Root relations (in all cases) divide the octave into three equal parts, and create a horizontal augmented triad
G7
octatonic tethrachords
WCXC YB X BB W C YC XC C YCYC XC C C
B
BC Y C
a)
B2
E b6 5 (skipping over 43 ) V7 G7
G7
YC CB C W CC WW CC YX CB C BB
YY B C C BB whole-tone scale
CB C W BB
d)
Ex. 7.90: Voice exchanges within equal division of the octave into three (within V7)
117
118
Ex. 7.91: Prolongation of V 65 a) Beethoven, Fantasy Op. 77 142 147 151
g
(notated in B minor until 157)
153
156
Adagio
¥C W X C W C ! W WW h
horizontal º7
g
157 Allegretto
g N W WW W C W C X C C CC
C XX C CC X WWC CC X CCC X CC C C B h B XC C WC N
X W C CC
# WWWW W C
XC
horizontal fits º7
V(b7)
b) contrapuntal source
6 5
WWWW
C C
W C (VIIº7 )
V 65
I
I
Ex. 7.92: Prolongation of V43
a) Schubert, String Quartet, D.887 (Op. 161)/I
W
1 ^8
63 65 ^ N (7)
67
g
C C C W C CC CC X C C C W CC C W CC C C W CC X CC C C C C
! CB C WC # WC WC B C
[in III:IV (*)
I
69
[in VI:I
VII# V43/V
C
WC X CC
72
74
75 ^7
CC BC C C X C C W C X CC W CC X C C CCC CC CC C W C C X C C X C C C C C W C C W C C X C B C C C
4th
V] (*) V I] (VII )
#
#
(*) (II) (IV) (VII )
V
b) Liszt, Années de Pèlerinage. 2nd year: Italie. Sonetto 104 del Petrarca. 1
2
ant.
! WC C C WC YC C WC CWC
# WC C WCWC [in E:]
f # 34 V43 /V
WC WC
3
4
ant. ant. C C W C C Y C Y C C Y C C Y C (XW) CC CC W C C C W C WC octatonic scale octatonic scale YCXC C YC X C Y C C C WC WC C C YC C
ant.
5
C W C ant. CW C C Want.C W W W W C W C X C WC n
(notated c )
W CC W CC W W CC W CC WW W
octatonic scale
a 43
c43
e b 43
f # 43
(equal division)
119
Ex. 7.93: Prolongation of V2 a) Grieg, Berceuse , Lyric piece Op. 38, No. 1 51
55
C
Y XC ! Y W X CCC B # YY
CCC
C
X C W CCC X CC h X C W CC
59
(X ) C CW CC X C Y CC C h Y CCC W X CCC
g
CC C
the seventh as a pedal point
CC
C
XC
C C
(Y) X W CCC
C
(VI 6 )
V 2 /V
b) Liszt,
C WC
61
(diaslteration to) II2
Unstern 117 121
119 123
WWWW W C WC ! C C # WWWW C C W CWC C 6 (VII 4 )
x2
X CC
W CC C
7 #7 5 3 # 1 7 6 V42 # 1 1 #1
127 131-8 x2
129 139
CC
CC
W CC C
N
CC
CC
146, end
C
XC C CWC XC WC C C C C C C C C C C C C
#
in relation to root:
121 125 129
(V 7)
n7 1 2
whole tones
(III)
# 7 n7 #7 1
8
n
N
6 (VII4#)
# #1 n2 1 1
6 6
7 5
5
4 1
7
Ex. 7.94: Prolongation of an apparently inverted V7 Schumann, Piano Trio No.3/I, bridge 25
28 ^8
32 ^7
34
35
YY C B X C C g ! C Cg X C Y C C C C # YY C C B C YC C
[in III:]
I
( 43 V7/III
6 5
37
YC h C
39 b ^7
C C C C C CC Y X C C C YC C
N
Ì (to ^ 5) at m. 55)
C C C C XC C C 7
4) 3
(V 7/VI)
V43
[in relation 7 5 to root:] 3
6 4 4
(“I”)
6 5
7 3 5
I
YYYY ( ¥
# WWWW C C WC
C
C
YYYY
49
WWWW W C C C C C CC C C !
48
)
1
V43
7 5 3
C S C C S XC C CC C C C CC CC C
g
g
3
CC X CC BB
6 4 4
(“I”)
6 5
I
148
g
6
6
6
V65 of V
7 3 1
4 2
4 3
5 3
(diatonic (IV 6 4 ) VII 6 )
6
4
C C C YY C C C X C
147
V
Y ! Y X CC C C Y C C
5 (no literal return 3 to the seventh) 5
C C C C CC C
g
4
3
3) Mozart, 4) Piano Sonata K. 333/I
N
V43
7 5 3 1
6 4 4 2
(VI 6)
C # CC CC C
C NC C C C C
Ì
a) V 56 — 43 or vice versa 1) Beethoven, 2) Beethoven, Piano Sonata Op. 2, No. 1/III Piano Sonata Op. 27, No. 2/I
Ex. 7.95: Prolongation of V7 with changing inversion (root position excluded)
7 3 5 1 6 5
Ì
120
CC C
V2
7 5 3 1
6 6
(III)
# YY Y C C C Y
!
YYYY C
5 7 4 3 2 1 4 3
CC CC
CC C
27 3rd (not 4th!) ant. ant. ant.
4
Y
V2
7 5 3
CC 6 6 4
(IV 6 )
CC
V2
I
4 3
6 6 4 2
5 7 3 1 4 3
(VI 64 )
C C C C C C
N
N
C CC C C C
7 5 3 1
CC
)
5 7 3
CC
(
Y C C CC C C C C CC C N C
3 Ì
26 Ì
C C
(“I” 6) (“I”)
dim. 5th
Ì
6 5
C CC CC C C C
CC C
V2
Ì
V2
6 5
aug. 4th
CC C C C C
C
CC
c) larger motion 1) 2)
Ì
3)
Ì
3)
6th
C
V2
4 3
CC C C C C C
C
CC
Ì
b) V2 - V 43 or vice versa 1) Fauré, 2) Bach, Chanson, English Suite Op. 57, No. 1 No. 4. Sarabande Ì
Ì
Ex. 7.95 - continued
Ì
V 43
6th
6 5
C C C C C CC C
C
C
4)
121
(VII 7/V)
Ì
g
(V 34/V) (6) I
^3
83 ^2
1^
1 77 85 81 trio (horns and bassoons)
II
V7/
89
b) Mendelssohn, Symphony No. 4/III
Ì
92
V2
7
I
V2 of V
[in V:]
IV
7
V
x2 g W C C NC W C C C C W C C ¥ ant. W W B ! C S C C X C W C C C CC C ¥ ¥ W W CC CC CC CC CC W CC W CC CC X CCC C C C C CC C C X C C C C C C h (X ) CC C C C C ¥ C C C C C C C C C C C # C S WC ¥ WCWC XC C WWW C ¥ ¥ B C h ¯ h (or: aux.?)
?
80
a) Bach, Well-tempered Clavier, Vol. 1. Fugue in A minor.
Ex. 7.96: Motion from V2 to V 7
122
V17
7
# #7
1
n7
C
IV
WC
enharmonically # “I 6” # in VII 5 : IV 6 5 4
C
#
W C ) W CC ( W C C C
(=
C
!
C
CC
a)
5
#6
=)
I
C
C
X C X CC
g
7
b#b 65 1
(= (=
98
g
or: # 6 # (II 43 ) “I 64” (subordination b1 with inversion) n7 # ##75 n n 5 7 1 7
N
99 100
101
I
W C ?) XX CC YY CC Y C C Y CC Y C WC) h XC N C Y CC C C C XC h
I V 51 (Cf. Ex. 7.74d [Liszt])
enharmonically # IV in VII #53 :
YY YY C C C C
Y Y Y Y CC C C
97
b) Chopin, Mazurka Op. 59, No. 2
Ex. 7.97: Enharmonic parentheses within V7
C
C XC C h aux. C
backrelating
(alternative in the spirit of Laufer)
123
124
125
Ex. 7.98: Apparent enharmonic parentheses within V7 Beethoven, Rondo a capriccio, Op. 129 149 156 157 158 160
162
CC Y CC YYX CCC
W B WC !
# W B Y CC Y C # ) (IV 6 5
CC Y CC h
(V 7 / b II)
(backrelating V)
I
Y CC b II
Ex. 7.99: Prolongation of a major-minor seventh chord as n VII 7 in minor a)
b) Handel, Keyboard collection No. 1, Suite No. 3. Prelude.
1)
2)
g
g
BC ¥C NCC CC BC ! N
# [in III:
B ¥ h
B
V7 “I 64 ” V 7 ]
I n VII 73 46 73
1 11 12
I
14 15 16
g
IN
BCC ¥CC CC C BCC C h
BC CC CCC CC CC CC C Y C C C C C C CC h (ambiguous
B ¥ C C B h
Y B C C
(VI6) 7 I n VII 53 24 31 1 2 3
I
ant.
[in III:
I (IV)
hierarchy) P?
C WC C h
V 7 “I 64” V7 ]
n VII 7
V65
I
126
Ex. 7.99 - continued c) Chopin, Polonaise Op. 26, No. 1 34 25 36 38
41
42
g
CCB
X3
g
N
W W W W W CBC C C C C C X C CC C C ! C C C # WWWW B
(X ) C
CC C C
B
WC
( n VII 7
# VII 7) 7
V #53
V8
6
I
Ex. 7.100: Prolongation of a major-minor seventh chord as mixolydian tonic? Tchaikovsky, Album for the Young. No. 12: The Peasant Plays the Accordion 1
13 x4
! #
YY CCC CC CCC C CC C C C C YY C (“I”)
in B b major: V 5
7
(“IV”)
I5 in F mixolydian:
7
after the piece ends x2
5th
C CCC C
CC CC CCC CC C C C C
CC NCC CC NCC CC NCC CC CC CC CC CC C C C C C C C
(“I”)
(VI 6)
(“I”)
(“I”)
(“I”)
(“I”)
(“IV”)
(II 6 )
(“IV”)
(“IV”)
(“IV”)
(“IV”)
CCC C [I]
X2
333
[in I # :]
[in implied VI:]
I
V 8 #53 III 1
(II 43) (7) 4 2 3 1
# W W W W CB CC CC CC CC W N
N
W W W W B C C ant.? ! W C VC VC C VC
309 332
(VIIº 43) V
(VII°2)
(=
I
B
X CC ) W C BC h CC CC C
337 340 341
a) Chopin, Scherzo No. 1 ^7
9 X2
V
(II 43) 7 # 53 4 (Vm) (I) 1 2
backrelating
B C C Y NC [in implied IV:]
I
3 7
C 3 1
4th
C CCC CC CCC C C W C C WC N WC CC
1 5 ^8
14
IN
P
16
(
^5
17
passing
“VI b6 1”
[in implied III:]
( bVII ) 7 3 5 4 nVII 1 b 3 b 2 V
1 ) V6
n3
I
C C C XC C CC X CC C C CC C IN IN P Y PC YINC Y C C Y C Y C C W P?CC )X C
^ 6
13
b) Schumann, Liederkreis, Op. 39. No. 8: In der Fremde
Ex. 7.101: Prolongation of major-minor seventh chords in chromatic functions
127
128
C C
(“I”)
YC
ant.
40 gavotte in canon N
I]
43
44 march
(IV)
48 aria
of VI
I V b72 1
[in VI:] (VIIº2 )
(“I”)
[in VI: V (6)
C C
6 2
(8?) 1
7
VI
CC ) C C C C g Y C C ( C ant. C (X ) CC C C C CB Y ¥ Y C C X C C C C C C CC C C ! CC C C C WC h hg 7th g C C C X(?C ) Y C C C W C Y C Y C C C C ( C ) Y C CC C C C C YC B C C C C # C C C YC XC C B B YC C N h h
1 31 32 march
Beethoven, String Quartet Op. 132/I (after Agawu)
Ex. 7.103: Prolongation of V 7/VI in the bridge
129
130
Ex. 7.104: Prolongation of V7 in the recapitulation bridge Haydn, Symphony No. 104/II a) prototype (exposition bridge) 17 ^3
19 4^
g
29
24
21
33 ^3
g
38 b ^3
Ì
C C C YC W B C X C C W C C C C CC W C C C WC C C C C ! CC C C C ¥ C ¥¥ C C B C #W C¥ C C C C XC C h N N as in the theme
(V 4 3 /V)
(“I”6) (IV) 9 7
8
I V 71
10 1
I
b) expansion (recapitulation bridge) 98 100 ^3
101 102 4^
g
109 114
118 120
N
C C C W B C C C ¥ ! C # W B C C C C ¥ I
! 7 V(8) 1
C YC
C YC
C
X C X C C WC X C W C YC X C
C C C (“I” 6)(IV 5 6 ) m 7
C XC
W C W C W W CC W C
W C W°7C X°7C W C X C W C YC XC ( bVn
b 10 b1
b)
(VII6#
#7
n)
(8 -)n 7 n1
122 ^3
C B B I
© 1935 by Universal Edition A.G., Wien/UE 6869 Rights for the English edition belong to the estate of Ernst Oster.
a) Schenker’s reading (Free Composition , Fig. 62,3)
Ex. 7.105: Prolongation of V7 in the development (i): Beethoven, Symphony No. 3/I
131
132
© 1935 by Universal Edition A.G., Wien/UE 6869 Rights for the English edition belong to the estate of Ernst Oster.
a) Schenker’s reading (Free Composition , Fig. 62,4)
Ex. 7.106: Prolongation of V7 in the development (ii): Beethoven, Piano Sonata Op. 81a/I
133
5 7
(not literal 8-7!)
V
YY Y ¥ C C ! B C C C 7th C C C C # YY B Y
g
g ? ( )
* *
86
g
87
N
91
g ant. YC Y C CC Y C
93
g
3rd
96
g
g
dim. 5th dim. 5th
rcp.
103 110
g
g
IN
114
6 54 2
(VI)
b3 2
b2
3rd (according to Schenker)
1 3
6
( b III 6) (b6)
(VI) (IV6) (n6) 7 2
1
I
C XC C C C C C C C C C C C B C CC C Y C Y C C XWXC CCC X YY CC C C Y C C YX CC C CCC X CCCC C X C Y C C =X C C (X ) C C C Y C X C CC h CC 7th not 6th! f p ? f 6 66 66 6 10 10 1010 CC C C XC C C ( C )Y C Y C C C X CC CC C C X C C CC CC C Y C C B Y( CC ) C X C C (X ) C C C C C CC h Y C C C C C P h not yet h N?
ant.
72 74 77 78 82 70 73 (* = unaccompanied tones) ** * * seventh progression
50 66
b) larger context
Ex. 7.106 - continued
134
135
Ex. 7.106 - continued c) precedent: transition from the slow introduction 12
16 exposition
15
g
C (X ) C CC CC YC
Y C ! Y Y ¥ C CC Y CCC
# YY B Y C C C
7 V53 44 35
g
C C CC CC YCXC
C C
n) n2
b2 7
21
g g sus. C CC C C C C C B IN
C
C CC C C 6 6 6 Y C X C X X CC Y Y CC X CC Y Y CC
(IV b61
3 6
g
19
6
5
C
7-6 3
6
CC XW C C Y X CC 4
CC (X ) CC (X ) CC C ¥ 3 4 5
B
6 7 1
I
Ex. 7.107: Prolongation of V7 in the development: apparent and problematic cases a) Haydn, String Quartet, Op. 55, No. 1/I 1 30 63
78 93
*
dev.
C
gradual 7th transformation N
# WWW B X C C B
false rcp.
CXC CWC :
98 111
CX
W CC XX CC
C¥ W C X CC WW CC X CC WW CC
113 rcp.
*
WC
X C¥
XC Ì
( C ) ¥ W W W BC C ! C C
95
10 10 10 XC C C C whole-tone progression C XC : XC C C C C CWCWCWC
BC B
major third = minor sixth, divided equally into two major thirds
I V8 7
( b III:
IV
V7 I) 6
5
7
I
136
Ex. 7.107 - continued b) Haydn, String Quartet Op. 55, No. 2/IV
Y ¥ C¥ #
B
C
!
Y ¥
56 59
54
g
64
71
dev.
C
?
: X C C W CCC
C
:
C
?
Ì
C C
72 74
C
XC C
76
C
WC
C
C
I
V8 7
#8
[--- ?---]
V7 ] = V7/ V 7/
I
V
#8 n8
?
Ex. 7.108: Prolongation of V 7 in codas a) Beethoven, Piano Sonata Op. 2, No. 3/IV 282
298
304
theme *
#
!
B W C W CC X C C C C C C X CC B
h
C
C
(VI # ) 6 6 2
CB B
C
N
7 V51
g
308
5 7 1
I
CC
CC C
C C
g
rcp.
CXC Ì
¥ X¥
Ì
Ì
[in VI:
77
W C C WX CC XX CC Y C C Ì
1 46
V7/ V 7 7
n7
I
137
#Y
I
CBB
1
29
33
37
42
46
g
C
91
99
C
Ì
V7 / III
C
g
V
(VII # 5) (# IV#
)
[in VI: I (VI n
b)
V7 ] III b7
*
IV)
(
)
103 132 165 166 167 170
g ant. ant. C ¥ C ant. ¥ (X ) C C CC CC C W C¥ W X CC W W CC W WW CCC C VW CC WWW CCC YYY CC C X X CC YX CC Y C X YX C CCC W C Y X X CCC W C WX CCB C WC
79 83
*
56 59
55
21
b) middleground context
I (III) V 7 of III
#Y ¥
C¥ C !Y
25
50
Ì
g
[
I
B
B
176
C
V
BB
I
B
B
]
191 207
III (II65) V
B
W ¥C
53 55 56 59
g Y C C C C C (X ) C C Y C C CC X C X C ( C ) Y CC Y C C C C C C C C C XC CC C C C Y C Y C CC X CC X C C C C C WC C WC C CC C C XC C C CC C C 10 (after 21-25) 10 10 10 10 10 YC C CWC CWC C CWC C WCXC C C X C C X C X C C (X ) C h (ambiguous synchronization)
1 19 21
g
Brahms, Capriccio Op. 116, No. 1 a) foreground
Ex. 7.109: V7 prolongation throughout entire sections of an idiosyncratic form
138
g
g
b) alternative
g
g
V7
C ¥
1
g
3
c) Beethoven, Symphony No. 2/IV
g
7 9
(6)
(“I”6
6 or: 6
5) 3 5
5
(V) 7 (I)
?
C C ¥ h
Ì
V
I
12
¥ C C ¥ C C C C
(ambiguous hierarchy)
C C C B B C B B B ¥ C C C ¥ ¥ ¥ WW C C C C C C C C C C C C ¥ C C ! C C CC ? ? [paradox: 7th C see Ex. 4.3] C C C C C C C C CCC # W C C C B B C B B B B C C C C ¥ W ¥ h g g ? ossia: V7 6 5 (I) V I (V7 ) I V (V7 ) I V I WW ¥ C C C C C C C ! C C C C C ¥ C
a) normative reading
Ex. 7.110: V7 prolongation in parallel periods - type a)
139
I V
(II)
I
C ¥
C
# B B
!
C C ¥
1^
B ¥
^3 ^2 ( )
a) basic model (no 7th)
I V7
B B (II)
I
C ¥
^3
^5 4^
C
C C ¥ C C B
B B
^1
B ¥
^3 ^2 ( )
b)
I V
B B
B B
^3 2^(
aux.
B
^1
C C B [------] I
(II V)
)
c) alternative
I
YY B V7
¥
CC C C B YY C C ¥
g
^5 4^
210
( )
216 ^3
^2 ^1
218
(II)
C
C
(bVII)
(VI) 6
YCYC CXC C
DN
5
C I
¥
C ¥ C C ¥ ¥ C CC C C Y C X C C C C C
212
d) Schubert, Piano Trio D. 898 (Op. 99)/I 207
Ex. 7.111: V 7 prolongation in parallel periods - type b)
140
3rd
5
C
g
augmented 4th 3rd
x2
9
g
11
g
* theme
12
13
=3-8
15 x2
21
g
N
23
24
ant.
25
V7
(II7 )
6
5
(VII º 43 ) of V 6
5
8
(“V 65”) 9
(“V 6 5 ”) of II 10
#7
(“V 6 5”) of # VII)
n7
(“V 6 5 ”) of n VII) 7
g g C W CC C CC [ *] X C W C C X C Y C YY C C ¥ (W CC ) C C C C C C C Y C C C X CC C C C CC C C W C C Y C X C X C X C Y C Y Y C X C C C C C W C Y C X ! W C W C X C W C W X CC C W X CC C C XC YC C C W C # YY W C (X C ) C C Y C C C WC XC C B C C C C C 3rd
g
^4
g
A
1
Brahms, Capriccio Op. 116, No. 3
Ex. 7.112: Prolongation of V 7 in stable sections
141
Ì
142
143
g
13
? *
20
3rd
(not by Schenker)
V7
(VI)
# YY C¥ C Y C Y C X C Y C Y C C
dim. 5th
32
Y CC CC X CC
21 30 31
Y ¥ C ! Y C C C C YY C C
1
b) variant (after Schenker)
Ex. 7.113 - continued 20
N
21 ant.
31
32
V7
P
(VI) (“IVb 6”)
N
¥ XC YC N
42
C
BC
45 3^
I
YC YC C C C C B
N
¥C CC CC Y CC Y CC CC CC h N
N
1 13 4^
c) alternative (after Salzer and Schachter) 20
V7
32
IN
YC YC C
IN
ant.
21 31
(VI) (“IVb 6”)
N
P
B XC YC
N
13
BC CC CC Y CC Y CC CC X CC h N
1
d) variant of c
144
h
C
C
in D:
x2
( )
5 7 x2 3rd
C C C
9 11 x2 x2
13 15 17
¥ [in V: [8] ) II V I] 3 6 5
not yet!
b (“I” 7
C
C C ¥ C C C CC X C (C) W C (C) C C C C C CWC C C
I VI V7 (IV of the whole cycle)
# WW B
!
WW B
g
1 3
Schumann, Kinderscenen, Op. 15 2 3 4
(tonicization avoided) *
5 6 13 14 x2
C (“I”46)
ant.
N (a-bb-a)
17
(“I”) 6
(perhaps even)
g
22 23 24
7
(in b III: (V7 “I” 6 4 ( nVII7
V7) # VIIº7) I
C W C ¥ hC
V I
¥ ¥
CXC CC W ¥ Y C Y C C C C C B CC C C B
8 16
C CYC C CXC not yet!
N
C C C C C W X C C C X C C CC C C Ì
1 9
5
Ex. 7.114: V7 prolongation across movements in a multi-movement cycle
145
not yet? 3rd?
?
g
!
I
V7
(“I” 6
VI
V6 4 of V 5
5) 3
I
VI
C
C W C C CC W C C C
C C C C C ant.C ( C ) C C C WC C (X ) C C C C C # W C C ¥ C CC C C C C C C C ( ¥ )
W
g *
g
27
28
I
¥
V7
C
aux.
2 (I 6
V) I
C C C C C C
(less preferable) ?
¥ C C C C C C C C C C C C C C C
g N
25
a2) first theme stabilized 12
21
9
1
5
a1) seeds in the first theme
Ex. 7.115: Integrative analysis of Beethoven, String Quartet Op. 18, No. 2/IV
146
g
72
76
80 84 86
92 96
103
[in V:]
(
I
)
V7 6 4
5 3
[in b III of V:
V7 3
(“I”) 6 7 4 3
b6
I]
(5)
ant.
108
5
C C W C X C CC W C C C (X ) C W CC W CC X CC (W ) C DN CWC C C C C
106
(VIIº 6 5 of V)
C X C (e #3rd C ) NY C W C Y C CC C X CC C W C C W C C X C W C C C C W C W C W C ! BC C C C W CC C C N X CC 10 7 10 10 10 ant. 3rd C CC CC C C W C W C ( C )( W C ) C C C C C XC WC # W ¥ C C C C (X ) C C h h
64 (registers reduced)
b) second group
Ex. 7.115 - continued
I
B
C
CC
112
147
# W
!
W W C¥
C
V 8 7 ( bVI) (IV) V51
7
8 ant. 7 gradual transformation
C Y CC X C C
3rd
g
[ in V:
]
theme
235
239 hybrid octatonic scale
241
243
[in b II: V7 “I” 4 3
Ì
n 2(in retrospect)
VII º2 ]
VII º 6 5]
5
1
n7
g
245
C C C C C XC W C X C Y C Y C X C XCXCXC C C CC W CC (= Y C ) YY CCC C C Y C Y C C (= W CC YC g g Y Y CC (= X C ) CC C Y CC XC C CXC C C h Y C YC
chromatic passing tone
#6 # I VII b61 I VIIb51 b 8 (= #7) 8 b 62
C Y CC C
CC W CC
g
227 231 [retransition] x2 N
C Y C C C[ C
202 211
B Y C C X CC C WC C 7th h 2nd=
BC
?
associative *
Dev.
112 138 140 163 179
c) development and retransition
Ex. 7.115 - continued
148
6 (“I” 4 )
250
253
256
258
CN
261
g
265 267
ant.
264
V
7 1
6
[no root position] 7
[in VI:
#1
VII° 2 V (6)
I] 6 2
V7 /
Ì
IV 7 7
7 1
I
C B ant. C CC C CC CC X C ! C CWC C C C C C WC W C C C N 8 7 C C C C C C C C C #W B C C C C C C C B h
W ¥
g
245 247
d) recapitulation (first group) [tentative]
Ex. 7.115 - continued
=
¥WC
N
C
N ant. CC¥ CCC CC CCC
g
C
CC
C
ant.
C ¥
C C ¥C C C
g
245 256 258 261 264 265 267
149
150
Ex. 7.115 - continued e) coda 358 386 388
390
392
g
394
396
398
8va N
N
W B !
# W
CXC B h
(“I”)
I 8 b7
g
CC C C CC N
CC W NCC #
CC
N I
VII º7
x6
g
(“I”) I) in I: V8
7 (begins inverted) 5 4
I6
V I
6
3
2
Ex. 8.1 VIIº7 prolongation as neighbor unfolding
!
402 408
C C W C C C C C CC CC C C X C C C C C C C C C C C C ( C )C C aux.? C C C C C C C C WC
[in IV:] (V8 7
N
400
I
1
AC CC CXA
AA CA CA CXAXA
A Y AC
I
b 6)
VII 74 3
(enh. VI
! Y Y Y CC C h # YY Y XC
a)
6
A
XXX Y A AA
I
[in III b :] VII63 2
(IV6)
Y CCC Y YYYY CC X C h C YYYYYY C
= (enh.)
6 5
V4 3 I
4
7
b31
VII 54 3
(enh. IV
Y CC X CC C Y Y CC C C h C C C C YYY X C
b)
I
)
I
(II 34 ) in 6 III b: VII 43 2
Y C Y Y Y Y Y CC X C C h CC YYYY Y CC Y
= (enh.)
V7 I
C C C
C
X CC C
Y CCCC W C CCC h
2
T
non-enh.! (enh. in III b : II 7 VII 6 5 ) (II7) 7 6 7 6 VII 43 VII 53 of II 7 (inversion of VII 5 4 3)
g C C C ! Y W C CC C CC T Y CCC W CCC C T h
W C CCC C CCC Y h T
1
c) Schubert, Daß sie hier gewesen, D. 775
1 2
#5 b V 64 VII 3
(= enh.:) (= enh.:) Y Y W CA Y Y W AAC Y AAC Y Y Y CA W CA A XAX A
(= enh.:)
c) special chromatic enharmonicisms
6 quartal #6 b VI b6III 64 IV 64 V6 harmony III 4 IV#41 bII (aug.) [inversion of III #] 3 2 2 1 1 1 1 0 1 1 2 2 2 2
CCC Y ACC CC Y AAC CA Y CA A A A
b) in major
VI 6 III 64 IV64 V 6 quartal VI b 13 harmony (aug.) [inversion of VI b] 3 2 2 1 1 1 0 0 1 1 2 2 2 4
CCC
Ex. 8.3: Appoggiaturas to VIIº7
number of foreign tones 0 number of 4 chordal tones
Y ! Y Y AAA XA
(white noteheads: chordal tones [including the seventh]; black noteheads: non-chordal tones) (=enh.:)
a) in minor
Ex. 8.2: Harmonies (triads) that emerge in prolongations of VIIº7
151
152
b)
c)
d)
e) 107 109
113
Ì
f) Halévy, La Juive. Overture
(IV 6 4) 7 VIIº 52 1
(II2) 7 VIIº 35 2 1
6 (VI 3 ) 7 VIIº 42 13 (IV 4 3) 7 VIIº 54 3 2 1
(VI 6 5 ) 7 VIIº 64 53 2 1
(II2 ) 7 I (VII 53 ) [sequence on the 2 1 appoggiatura]
g
(only enh. local II 2!) 6 (VII 53 ) V64 53 of V 2 1 (inversion of 74 3 )
5 whole-tone steps
C
117 127 129
I
ant. C W C X C W C W C W X C W C YY Y C YY Y YY Y C YY Y C YY Y C W C X C CCC X CC W CC C ! CC CCC W CCC WW CCC X C CC CC C CC C C C C enh. h h h (enh. enh. h º7 spelling) º7 º7 º7 C W C º7 C * C C W C X C W C # YY C W C CWCWCWC VC XC Y Y Y Y h h h Y h X C Y Y hC X C Y Y hC X C Y Y hC X C Y Y hC X C h h h major 2nd = minor 7th =
a)
Ex. 8.4: Subordinations to VIIº7
153
b ) (IV 6 4 b7 VIIº 25 1
h
C XC h
C XC
b7
b7
b6 (VI b53 )
2 1
2
1
6
7
V b42 13 (VII b 31 2 )
(IV b63)
(IV b 6 3)
YY Y Y C ¥ Y NC h I
B
C
C C C g
Y CC C
21
C (no V!)
b) 6 (IVb 6 (II 6 3 ) (IV b 3 ) 2 7 6* b7 Vb42 13 (VII b 31[2] 1 2 1 ) avoided
Y C ¥B Y C X C Y C X C C C h N
h
¥C
becomes g
18 19
f) Mendelssohn, Song without Words Op. 67, No. 1
YY Y ¥ g BC CC C C C C h N (no V!)
YY C CC h C XC h
e)
VIIºb54 3 VIIºb46 53
(IVb43 )
h
C XC
d)
YY CC C Y Y CC C C h h
c)
b b (II 62 ) (VI b 6 3) b7 b7 VIIº 53 VIIº b24 31 2 1
h
C XC
Y CCC
! Y CC
#
b)
a)
Ex. 8.5: Subordinations to VIIº7 in major
CB
B
C
I
23
154
Ì
]
WW
C [V9 ]
CCC W WW C
not enh.! (b II) (IV 6 4) 7 VIIº 3 1
omitted
#Y
VIIº7
≠ 3rd
Ì
3rd
YYY
YYY
VIIº 7
(V6) 5
CC C ( W C ) X C
XC
c)
YYY
YYY
VIIº 5
XC
(V6)
CC ( W C ) C C
d)
7
g
VII º7 /VI
C C C XC
* aug. 2nd
C C YYYYYY C C C
YYYYYY C
40 44
C C
C
VI
CXC C
C XC C C C
42 46
f) Schubert, Impromptu D. 899 (Op. 90), No. 3
6 (enh. VI b 3 1) VIIº 73 5
CC C X C ) C (
YY X C Y
YYY
3rd C C C C (Y) C Y C C C C C C W C Y ! C C CWC C C C C 3rd 3rd aug. 2nd
31
X2
123 127
C XC CWC
C
C
120 124
e) Bach, Chromatische Fantasie
(enh. (IV 6 4 ) b II) VIIº71 3
C # YY X C C (W C ) Y
Y ! Y Y CC
Ì
[
112
b)
Ì
Ex. 8.6: Single third progressions within VIIº7 a) as in Chopin, Scherzo No. 1
155
Ì
CC
YYY
*
*
CC CC W C C X(W CC )X C CC ( ) XC
f)
7
1
I VIIº 53
(º7) (º7) 6 # 5 ##n42 nn#42 1 7
n5 3 n 17
CC
CC
I
Ì
Ì
XC
g
152 f (e #
65
I#
W W W W CB
n n8 b 8) 3 3
?
g
f# )
153 e
# VIIº75 ( # 75
6
n8
) 8 7
79
80
circular 3rd-prog. 3rd
g
81
VIIº 73
83
N
7
1
# I (VII 5#) (passing º7) (VIIº 35
lower-level passing (º7) (6 5) [# # 7] 8 # #46 75 2 3
2
2
1
)
(V6 5) 3
C V7
# 62 # n 52 n 51
C W CC XW CC XX CC
7th
X C ZY CC X C ZY CC YY CC WX CC W C X C W C W C YC YC h (enh. spelling) X X CC YX CC X X CC YX CC X X CC WW CC W C W C lower-level passing (º7)
WB XC XC YC C XC XC YC h X Y C C X X CC B XC
transitive 3rd
65 73 78
becomes
83
8 V[9] 7
#5 (“VII #”)(VIIº7)
ant.
V PC W C WC WC ¥
V PC XW C¥ C h
73 79
V46 53
octatonic fragment
VIIº 7 ( # 7 of V 1 2
YYY C
d) Mozart, Piano Sonata K. 576/I e)
2nd W CC W CC YYY CC WX CC CC X C C W W X C aug. WC C WC C X C 3rd aug. dim. W C C Y C X C C 2nd h 6th 6th 6th
(no enharmonic solution) aug. 2nd
c)
g) Chopin, Nocturne Op. 27, No. 1
WWWW W B
(aug.) (III 6 ) 7 VIIº 5 64 53
Y Y Y CC XC
# YYY CC C ( X C )Y C C C X C ( Y C )(X C ) Y C C C
!
CC
Ì
b)
Ì
Ì
(VI 6) 3 VIIº 1 42 53
YY Y CC ! XC
a)
Ì
Ex. 8.7: Parallel third progressions within VIIº7 156
157
158
159
Ex. 8.9 - continued
c) Schumann, DavidsbündlertänzeNo. 6 41
42 44
43
43 45
46
d) Brahms, Intermezzo Op. 116, No. 6
47
48
X2
WW
WWWW
! CC X CC (WX) CC X CC C W C C C C C X CC X CC C # W W CC W CC (WW) CC W CC C C C W C C Y C C C C h
[in relation to V:
(enh. III #)
(IV b)
6
I VIIº 35 2 of V 1 2
1 3 4 3
(inversions: 65
e)
(IV b )
7 8 7 6
7 7
14
W W W W V C CC
]
6 1
b1
V I b 46
F ܼ 43
5 3
f) Chopin, Mazurka Op. 17, No. 3 17 23
g
V WC CC V C CC
VW C C C V C C WC
(enh. C 53) (III# in relation to V/VI) 6 5
(VII° 43 of V in VI # ?)
6) 5
1
V WC CC
g)
25
N
Y ! Y Y CC
C C
# YY C YXC
CC CC
N
YYYY ¥C CC Y CC Y C Y CC Y C Y CC X CCC h N Y NCC CC Y CC CC X CC C C YYYY ¥ C DN?
(IV 6) 7
VIIº 53 1
4 4 2
3 5 1
*
I
N
N
(bVI6) (=VI/I b) b7 b 6 II VII 53 b44 1 2
N
(bVI6 ) (=VI/I b) b7 b 5 4 3 3 b 4 5 1 2 1
YYY C CC CC C N
YYY X CC CC X CC N
(“I”) 7
I
VIIº 53 1
6 7 4 3 4 5 2 1
(6
10
*
25
6
6)
9th =
(IV2 ) 7 5 1 3 2 5 4 I (nVII) (VI) VIIº 43
(VI 2)
4th
N
2nd
1 2 3 2 6 5
(IV6 4) 3 1
)
27
7 V 9I
C C
C C CC CC CC CC C X C CCC CC X CC C X C C ( C ) ant.
23
# YY C XC Y C C C C C C C (X C
10 10
Ì
10
CC CC C # YYY C C CC
21
Ì
1 15 19
a) Bach, Cello Suite No. 4. Prelude
g
VIIº 7 of V
7 5 3 1 2 2
(I46 )
g
8 7 8
5 VIIº V64 3 of V 1 2 1
(VIIº 6 5)
70 71 76
[in VI: I
C
C C WC
VIIº of V
6 5
7 5 3 1
7 V
2 1 2 3
6 (I4 )
I]
CWC C C h
inner voices figuration
68
ant. BCC W CC W W CC X XW CC C C W C CC CCC WC
64
c) Haydn, String Quartet, Op. 20, No. 2/I
X CC CC W C CC h N or g ? X CC W CC CC X C X CC h N CC
6 V 5
1 3
Y C ! YYXC CWC h g C YY Y W C C X C h
b)
Ex. 8.10: Voice exchanges between the root and third of VIIº7
160
161
Ex. 8.10 - continued
d) Beethoven, String Quartet Op. 131/I 20
19
CC
WWWW C ! XC WC # W W W W X CC
C
( )
C
C W CC
CC X CC W C
284
C X CC C C C
6 3
sus.
C WC
C
p N C C W CC ( X C) V C W C X C
C
N
289
292
298
296
g
YC
YY C Y C C Y C C C C Y C C C C Y CC C ! 10 (6) 6 (10) 10 (6) C CYC C C CYC C C # YY C Y b7
5 3 1
V65 VIIº 7
2
4 3
b24
1 b4 3 2
(IV 4 3 of I b
b4
2
3 3
(II)
8
#7
1
2
V64
I6
294
#6 (IV b5 1)
( # IV7) (=VIIº 7 of V)
e) Haydn, String Quartet Op. 71, No. 3/I 284
g
8 5 3 1
f) Chopin, Scherzo No. 1, Op. 20 37 39 41 43 (first time x2 an octave lower)
300
CC
X CC
WW
WC
W W CC
2) 3 2 1 b4 7
CC
C VC
sus.
(II6)
n VII
289
C X CC CC
10
10 10
CWC (VI 6 )
1 3 6 5
I
VIIº 65
7
162
Ex 8.11: Third progressions within VIIº7 in different third spans a)
b)
Y !YY C C C C # YY X C C Y
c) Schumann, Kinderscenen. Der Dichter spricht
YYY CC C C C X CC YYY X CC CC CC
Y Y Y CC
7
5 3
VIIº 53 3 1
4 4 2 2
CC CC
YYY X CCC
W C
CC CC
7
6 6 4 4
VIIº 55
3 5 1 3
3 1
C
W C C
(passing g b would create enh. VII #) (III 64 aug.)
(VI6 )
VIIº 71 62
10
5 7 3 5
12
C W C C ( CC ) C CC CC
1 3 7 5 4 VIIº 3
Ex. 8.12: Chromatic third progressions within VIIº7 Brahms, Symphony No. 2/I (after Schachter) 14
37
33
41
Ng * aug. 2nd C W C C # W C C X C C X CC W X C C C X C C W C C X C C C C C C motivic g#
b
# WW C WC
6
C
6
C YC
N
e 6
a
6
C WC C
(motivic)
n [in relation to V:] (IV b 6 4 ) ( VII b I IV [in I:] b7 b V VIIº 31 22 13 b13 of V
6 6 ) 1 IV4 I 7 2
b7 1
V4
3
(I 6) 2 4 6 4
(3) 5 5 3 6 5
163
VIIº 2
[in relation 7 to root:] 5 3 1
[in II 5 : [minor]
#
# YY C Y C
7
#7 b8 n8 # 7 n7
enh. enh. # ] IV# 17 I 64 IV 6 5
b8
Ì
XCYCXC
Y ! Y Y X CC Y C X C Y C
Ì
(1)
d) (2) Ì
ø 2 nVII ø7 (II 7 (II 2 of #VI ?) of # VIm?) m 7 #7 b8 n 8 5 3 1 b 8 # 7 n7 7 VIIº 2
b 3 2 21 3 7 VIIº56
7 5 1 3
CXC
C C
133
of I b # (IV 65 I46)
of V
Y
XC Y CCC Y C
130
5
9 *
13
15
7 (VIIº 35 2 1 2 I (VI 5
b13 n 3
6 5 (IV 6 4 VII b 1 n )
)
h
C
CCC W W CC
17
6 # 6) V 6 4
=IV
W ¥ C C C C C W C CC X X CCC C W C CC W C W ¥ C C W CC C X C W C C W C C C C h
1
f) Brahms, Symphony No. 4/I e) Beethoven, Piano Sonata Op. 54/II
YCXCYC Y
C YYY C X C (Y) C X C
YYY X C C
Ì
Ex. 8.13 - continued
5 3
164
[7-8 voice exchange, cf. d)(1)]
VIIº 43 of V? never resolved
C XC
main motive
40
XCYC XC C
Y X CC Y C X C Y C
# Y Y Y CC YY
!
YYYY
38-39
XC CYC XC
42
6 5
[5-7 voice exchange, cf. c)(1)]
C CC
C CXCYC
41
g) Wagner, Parsifal . Prelude to act 3
Ex. 8.13 - continued
C C XC C XC C
CZC C C
7
[3-5 voice exchange, cf. b)(1)]
C C
43
61 62
in relation to root:
of V
7 5 1b 3 3 b3 VIIº 65
2 2
1
n3
(IV 6 I64 ) problematic doubling
7 V(7)
X C Y C C X C CC YYYY (enh. 8 spelling) 8
YYYY Y CCC YY CC X CC X CC YX CC
58
h) C.P.E. Bach, Keyboard Sonata Wq. 57, No. 6/I
165
#3
b3 VIIº 71
enh. (VI b 6)
1
XC
1
#5
(VII #5 )
VIIº 17
XC
CC C W C C C
c)
7
VII º7
(“V9 ”)
Y ! Y Y BBB X C (Y) C C (Y) C C
a)
(“VIIº7”)
X C (Y) C C (Y) C C
BBB
(“VII°7”) V9
or
diminished 9th = enh. 8va
VIIº7
9
7
YYY CB C Y C C C X BB
b)
1
b5
enh. (V 43 of #VI) 7 VIIº(5)
XC
VIIº7
9
too harsh
7
VIIº 53
7
5
b3
(VII b 73 )
C
7
VIIº 53
5
#3
enh. (G# ø6 5)
VII º7
Y Y Y Y CC Y C X CC
(IV) 9
N
7
X CC C CC CC X CC
5 3
C (X ) C XC XC C XC
CC X C W C X C
f)
c) another harmonization of the ninth
n 53
C C XC CYC C
CC C C C (X ) C
e)
Y CBB Y C (X ) C C C (X ) B
7 (n5)
X CCC Y C Y C Y C X CC
d)
Ex. 8.15: Third progressions exceeding the limits of VII º7
VIIº 71
YC
XCWCWCWC XC
CC XC
b)
( b II)
# YY YXC CYC C XC
Y ! Y Y CC
a) [all set in C minor]
Ex. 8.14: Third progressions in VII º7: altered spaces
166
Ì
6th
Ì
c) (enh. 6th
Ì
d) octatonic scale
VIIº 73 1
2nd
6th (enh. (enh. a 7th) c b )
VIIº 75
2nd
3
VIIº 7
5
I
VIIº 57
3
I
in context: a 6th (enh. c b?) C inner prol.: 7th progression b c )? C C C C C YY Y C Y Y Y C C C C C C C XC YY C C C XC YY C XC Y Y C CC C X C X C Y C Y C C C C C ! C C C C X C (enh. g# f# e#) C X CC XC X CC aug. 2nd X C aug. aug.
Ì
b) Ì
a) Ì
Ex. 8.17: Sixth progressions within VIIº7
167
168
Ex. 8.18: The upper fifth of VII º7 : the problem of retaining the seventh a) genuine diminished 5th
g
YY C C C C ( CC ) CC ! Y C X C dim. 5th CC
1
descending
g
VIIº7
7 3 I
YY Y CC C C C C CC ! C X C dim. 5th CC
2
( )
ascending
VII º 73
7 I
b) connective diminished 5th
g
c) step + 4th
g
YY C C C C CC CC YY C C C C C CC Y C Y C C C C X C dim. 5th X C X C 4th CC ant. ( )
VIIº7
V65 I N
g
VIIº 7 V65
ant.
g
I
N
4th dim. 5th C C C C C C YY Y C C YY Y C C C C C CC C C C C CC XC XC X C CC ( )
V65
VII º7
I
V65
VIIº7 I
g
34 35
36 N
g
37
38
(
39 30
or
I
(I VI II6 V7) (I VI II 6 V7 ) 7 6 5 4 3 7 7 6 5 4 3 V7 I VIIº (V )VIIº
)
I
ant. YY Y CC X CC BC CC C C C C CC X[ CC ] CC C C C C CC X CC CC CC X CC ! C C C C C CXC C C C C # YY ¥ X C C ¥ Y h
30
c) Schubert, Symphony No. 4/I (1) theme 36
Ì
g
37
38
(
38
VIIº 7
(I)
quasi-aux.
I
C C C C C h
)
37
C C C CC C C XC C
g
36
C C XC h
( )
C C X CC C Ì
ant.
39
(I VI II6 V7) (I VI II6 V) 7 6 5 4 3 7 7 6 ) V (VIIº (VIIº 5 4 3 ) V 7 I
BC CC C C C C C [ C ] C C C C C C C X CC C h h C C C CXC C C C XC h
g
34 35
or (alternative ending)
169
not
[7 6 5 [in VII:] I VIIº 65
!
C
(“I”) 4
(V)
3]
I VIIº65 !
[not c!]
etc.
N
b)
c)
4
(IV)6 4 VIIº 7 6 5 4
3
( b II) VIIº 7 6 5 4
3
( n VII 7 ) VIIº 7 6 5 4
3
Y Y Y ! Y Y C C C C C Y Y C C C C (X ) C Y Y C C C C C C Y C # YY C CC C YY C Y CC XC YXC XC YYXC YC XC YXC
a)
19
(V7 )
C
C VIIº 7 6 5
Y Y Y X CC
YYY C C C
d)
4
C
C 3
XC
C
b3
n3
(II 7) V7 I
YC WC C C C C C C C C C C C C C C CC C C C YC XC C WC C Y C C C C C C W CC C
VIIº 7 6 5
YC C YC Y W C
? ant. ( ) [ ]
g
Ex. 8.20: VII º7-3 fifth progressions type 2
b
g
C Y C C C Y C C CC XC C C C # YYY C h h
YYY
XC
18
156 157
159 160
d) Bach, Violin Sonata No.1. Adagio
c2) in the development
Ex. 8.19 - continued
170
171
Ex. 8.20 - continued e)
f)
g) Brahms, Concerto for Violin and Cello/I
g
180 184
g
possibly aug. 2nd
Y Y ! Y Y C C W C (X ) C C Y Y C (Y) C Y C C (X ) C C C X C Y C Y CC # YY X C C X C X C C Y Y Y possibly aug. 2nd
(VII#5)
VIIº 7
6 #5 #4
¥ C Y CC CC W C C C X C (Y) CC CC C C C (X ) C C ant.C C C C ant. C XCWCXCXC YC ¥ WCWC WC XCYCXC WC C h
(bII b)
VIIº 7 b 6 b5
3
4
188 193
6 6 [in III] º7 º7 4 º7 4 # 4 V9 VIIº7 6 5 of V
3
º7
3
V
Ex. 8.21: VIIº7-3 fifth progressions type 3 a)
b)
g
c)
g
g
C C C C C Y C C C C C C C YY Y C C C C C C C YYY C C YY ! C C Y C CXC C XC C C X C ( Y C )Y C X C X C C X C X CC (X ) C C h h h (“I”
)
I VIIº71 62 5 4 13 I
(=enh. VIIº2 (III ) of III) 6 5 4 I VIIº 71 1 natural
(VI 7
3 1
I
)
I VIIº71 67 5 4
3 I 1
Ex. 8.22: Selected fifth progressions in the lower fifth of VIIº7 a) type 1
b) type 2
c) type 3
C C Y CC C C CC YY Y C YY Y CC X CC C CC YYY CC CC YY ! C C C C C C C C C C C C XC XC XC XC C C C C (all set in minor) VIIº 71 2 3 4 5
(V 4 3)
VIIº 71 2 36 4 75
(“I”) 7 6 VIIº 31 42 3
7 3 4 5
(VI6 ) 7 VIIº 31 42 3 4 35
172
173
¥
C
(º7 7 1 (V) VIIº 53 # # 64 1 2
º7 2 7 5 3
4
º7) (complete cycle) 3 ## 3 1 1 6 I # 46 75 V
dim. 5th
W X CB
C
aug. 4th aug. 4th
C W CC W CC CC C WC
ant.
C X ¥C
g
3
C
CC W CC X CC X CC W CC
dim. 5th
# W W W W CC V C
!
WWW
1
Schumann, Novelette Op. 21, No. 8
number of 2 semitones 1
W W W (in key) C C C 2
C WC 1
C XC 2
1
C XC
precise “mechanical” sequence (non-functional)
diminution:
2
1
2
1
C WC
adjusted to the key *
C WC XC WC
Ex. 8.25: Combinations of fourth progressions and fifth progressions within VIIº7
174
illusory dim. 7th
d)
g
VIIº 7
C C C XC C C C
XC C
e)
=
aug. 2nd
Ì
illusory dim. 7th
VIIº 7
VIIº 7 V 6
V6
VIIº 7
g
)
Ì
IV
(
)
V18 7
V
g)
2
I
(II6 )
1
6th expressed as dim. 7th
transitive dim. 7th
25 26 [true 7th-prog.: subordination]
C C X CC C CC CC CC C C W C W C C C C CC C C C C C C C h W CC W CC CC [following, illusory 7th-prog.] g W C C C C C [C ] CWC C C
W
21
c) Mendelssohn, Song without Words, Op. 62, No. 3
6th YY Y C C C C C C C X( CC ) W W W W CC X C X C Y C X C X C C C (W ) CC C C h
f)
V6
YY Y g C C C C C (C CXC
b)
6th YY Y C C C C 6thC C X( C C ) YYY X C C C C C C X CC X CC ! XC
#
!
Ì
YYY
Ì Ì
a)
Ì
Ex. 8.26: Illusory diminished seventh progressions
175
176
177
2) (8)-10 11 12
17 18 20
22
3)
4)
8 12 17 18 22
1
! Y CCC Y C YY CC Y C X C C Y CC X C C Y CCC (X ) CCC YY CCC X C Y CC Y CCC C C ant. C C YC C # XC YC C CXCYC C CXC 1 7
VIIº 2
b1 6
6 II b7 5) 2 4
3
enh. (VIIº 43 / bIII5 6 II b 7 5) b 1 2 3 1 3 6 4 3 1 7 1 7 7 VIIº 2
8 29
Y CC C (X ) CC X CC hC g W C Y C C CC XC
Ì
Ì
enh. 4 (VIIº 3 / bIII 5
6
(VIIº7 ) of V
(VIIº 7 )
V57 6 V75 6 of V
I
dim. 7th 7
dim. 7th VIIº 71 62 53 44 35 26 17
dim. 7th
C C C C C CXC YYY C C C C C C XC
b)
Ì
VIIº 17
YY X CC C C C C C C Y !
a)
Ì
YYY
dim. 7th
CCC ( C ) C C C C CXC C C XC h (II 2) VIIº7
c)
Ex. 8.28: Ascending diminished seventh progressions
(II2) V6
VIIº7 ?
CCC ( C ) 6th C C C C YY CXC C C XC h
or Y
N
178
g
C XC
W CC
60
62
64 ^2
65
(IV 64 ) (“I 46”)
enh. bVI b enh. b I b 6 VIIº 7/V “I4 ”VIIº 7/V “I 64” [in I:] enh.b V b enh. b III b6 5 7 4 3 = V7 V65 I VIIº 53 2 1 b n b b 4 5 6 7 of V of V 1 2 3 3
[in V:]
^1
67
(I-true?) 5 3
I
ant. C C YX CC ( CC )(X C W C (X W) CCC X C X C X C X C WC ) B C YC C C C (or: quasi-aux.) C (Y) (X ) C ( C ) Z C (X ) ¥ C W C C X C C? C Y C =X C W C C C C ¥ B
doubly dim. 7th
Y ! Y B X CC C W C C C C # Y Y W CC CC Y CC B
^3
41 57
a) Schubert, Die Winterreise. No. 20: Der Wegweiser
Ex. 8.29: Doubly diminished seventh progression
b bVb 6) (#VIb6) (III 64 ) ( # IV 4 4 enh. enh. enh. # 7 n7 b6 5 4 3 2 1 7 #7 8 2 3 4 5 b6
equal division of the octave
^2
^1
1
I VIIº 75 of V 3
8
(I64 )
V I
C Y C W CC X C Y C X B B YY B X C C C X C C CWC C B C W C W C C C C X C Y C C B C YY B W C C X C of the octave h equal division into four
^3
b) potential for systematic continuation
179
b)
5
3
1
7
VIIº 75 3
1 7
5
VIIº37 1
7
C
CC
C C
4 3
C
C WC
C
(II 6 4 )
95
[in I:] V8b 7# VIIº (2)
C
C
93
C WC C
# [in II 5 :]
#
!
C
85
pivot
C
C
VIIº 2 of IV
[bass:
C (X ) C
7
7 5
becomes
C 5 3
CC
YC YC
CC
deviating* from octatonic
C XC
CC Y CC CX C almost octatonic
b b VIIº 71
YC
C
C W CC
g
96
a) Mendelssohn, String Quartet Op. 13/I
3 1
# 1 7]
a
C WC C W C (X ) C W C
C
g CC Y C C C WC C
V2
C
3
I6
C
d)
3
V
VIIº 7 VIIº7 V65 I of I of II # 5
CW CC C W CCCC W W CCCC WWW CCC C W CCC
5
1
C C C C C C XC
aug. 2nd
VIIº17 7
YY Y X CC
from
99
WC XC WW C C W C
98
5
aug. 2nd YY Y CC C X C C C C C C XC
c)
Ex. 8.31: Avoidance of direct augmented second through filling in
VIIº 7
aug. 2nd YY Y C C C C C C X C YY Y CC C C C X C C C C C ! XC XC aug. 2nd
a)
Ex. 8.30: Register transfers in VIIº7
180
3rd
3rd
VIIº7
2
3rd
4 3
3rd
6 5
3rd
7
2nd CX C YX CC 3rd 3rd YX CC Y CC Y C 3rd C X C aug. Y C X C Y C C # YY W C X C X C Y C (X ) C Y CC W CC X C XC Y aug. 2nd
3rd 3rd C 2nd Y C YY Y C Y C CC X CC YX CC YX CC YX CC Y 3rd C C X C Yaug. C ! (X ) C W C X C X C YX CC (XY) CC 3rd aug. 2nd
Ì
b) Ì
6
10
4 3
6 5
7
Ì
2
XC YC XC
2
WC XC XC YC XC YC
7
Y C X C C W C C (Y) C
C C WC XC XC YC C
VIIº 2
YYY
2
XC CWC C
c)
YYY
Ì
Ex. 8.31 - continued
181
223
[in III b:] I
# Y Y BC Y
VIIº 43 of V
7 1 3 5
C
XC
YC C
YC YC
ZC XC
YC XC
(º7 º7 5 7 1 3 6 5
º7
º7
X2
230 232 235
239 240
3
#1 2
in 8va ( b III: I 6
b1 #7
º7
3 1 n 75
º7
over chromatic step
I6 )
2 (skipping over root of prolonged VIIº43 )
V2
º7
º7) 1 7 3 5 4 3
V6
5 3
W CWC WC W C X C W C W C X C W C X? C X C Y C (X ) C N B * ? single skip
N tonicized N
C W C WW CC W C W C WW CC XX CC X Y C C Y C X C B W C W C W C X C Y C X C X Y CC XY C C X C C
dim. 7th
228
4
Y C (C ) X C Z( Y CC ) C Y C Y C C C X C Y C (X ) C YC WC Y C YC Y Y !
220
d) Mozart, Piano Concerto K. 491/I
Ex. 8.31 - continued
182
183
Ex. 8.31 - continued e) C. P. E. Bach, Rondo Wq. 56, No. 5 (after Aldwell and Schachter) 140
141
?
articulation hemiola
CC
!
BCC
145
?
# B WC XC WC XC
I
153 154
?
C WC XC WC XC
Ì
C YC
# IV 56 “I”6 4 II # 5 * (V 7/III)
B
# 6 # # IV 65 “I” 46 IV 65 “I”46 IV 6 5 “I”4 # b 5 IV (PR Riemannian VI VII relations) * * * (V 7 ) (V7/ # IV) (V 7/ # VI) 8va
# # 7 bn 1 n 1 # 7 7 6 5
VIIº 71 b 1
CC
(to G)
C WC
segmentation according to horizontalized º7 avoided
h
B
( )
should have been
7 truncated
equal division within V
key implications
151
? ? ? CC W CC WW CC W CC WW CC YX CC YX CCC Y CCC X CCC (X ) CCC C C C C C C ?
aug. 4th
CC W CC C C
C
148
# 4 (=n b 42)
n5
3
n2
b3
3 1
2
I
Ex. 8.32: Avoiding augmented second through insertion b) Ì
Ì
Ì
a) Ì
3rd CC 3rdC C 3rd C CC 3rdC X C aug. 2ndC YY Y CC CC X CC 3rdCC CC 3rdC X C aug.C 2nd Y C Y X C C Y ! C C C C C C C CC C 3rd aug. 2nd 3rd aug. 2nd 3rd 3rd 3rd
CC 3rdCC C 3rdC X C aug.C 2nd 3rd X C C C C C C C # YY Y aug.2nd 3rd 3rd C C X C 3rd
6 4 4 2 2 6
(“I” 7
VIIº 53 1
6 4 2 2
5 3 1 7
c)
Y ! Y Y CC XC Ì
VIIº 7
C X CCC C (V6)
Ì
6 5
6 3 3 2 1 2 7 6 5 4
1 7 5 3
5) 3 2 6 4 2
7 5 3 1
3rd
CC 3rdC C 3rdC X C aug. 2nd 3rd X YY Y C C C C CC CC CC X CC aug. 2nd 3rd 3rd 3rd
(“I” 64 7 6 VIIº 53 42 1 6
6 4 5 3 1 7
4 2 6 6
3 1 7 5
6 3 2 6 6 4
1 7 5 3
5) 3 6 6 4 2
7 5 3 1
10 VIIº 71
WWC
6 2
(“I”) 7
(VI)
5
C C XC XC
insertion avoids direct aug. 2nd
aug. 4th
5
9 4
8 3
b
(V 7/IV) 8
[in VI: enh. VIIº 2 VIIº 7
# YY X C Y
of IV
V56
I][in b II:VIIº 7
C
6 I] 5
8
8va
42
44
10 10 10
(alternative: quasi-aux) ?
C CC CC CC C C C CC W C ¥ X C CC W C
g
(IV) 7 (6) 5 4 3
11
IV 6 # 6
V
(II) 2
1
(“I”)
V
I#
C C (X ) C CC C C C C ¥ CWC C ¥
8
41
Y CCC Y CC Y CC Y CC Y CC C C Y C Y C Y C C C C X C X C Y C Y CC X CC (X ) CC CC C C W C X CC XC C C XC ? (alternative) Y C X C C Y C X C C Y C C X C C X C Y C C XC YC XC C C C (after Schenker’s reduction)
CC
(after Schenker’s reduction) no g n no e n
CC C C C YY Y C Y CC Y(Y)C C YY C C Y !
Y CC
5
a) Beethoven, Piano Sonata Op. 111/I
9 6
WC C C
Ex. 8.33: Ascending register transfers within VIIº7
#
!
39
g W ( ¥ C ) C C C C C CC CC CC CC C C W C X C C C C C W C C C C W C C CC
37
d) Bach, Sinfonia (three-part Invention) in E minor
Ex. 8.32 - continued 184
I
(II)
CC W C (X ) CC W C W CC C C WC C XC WC
Vb
[(“I” VIIº 7
(V b) II
Ì
75
76
77
Ì
g
78 79
82
Ì
Ì
g
IV]
V
V
I
B
¥CC
83
I
(X ) C Y C X C Y CC X C (Y)X CC X C CC ¥CC W C X C W C C W C W C Y C WC XC W C (W ) CC W C W C X C W C X C W C V C W C W C (X ) C Y C XC WC XC W C X C WC WC X C VC WC XC B XC (IV)] minor triads in complete ascending circle of fifths through all 12 tones g V I (X ) C Y C X C Y C X C (Y) CC X C W CCC ¥CC W C C W C W C Y C XC WC XC WC C XC W C W C W C W C V C W C V C W C (X ) C (Y) C X C X C X C W C X C W C XC B
minor triads in complete ascending circle of fifths through all 12 tones
C ! Y BC CC C X C C W C C W C # Y B C W CC C C WC C WC WC XC h (ascending diminished seventh chords on every chromatic tone I VIIº 7
tempting but erroneous:
I
74
8va in alto and bass: central portion based on whole tones progression
[(“I”) 7 VIIº
! Y CB CC CC X C # Y B C W CC C WC
or:
# Y BC
! Y CB
73
(X ) C Y C X C Y CC X C X CC X C CC W C C W C (X CC ) Y C W C W C WC C W C W C ) X C X X CC C ( CC ) X C C W C (X CC ) W C W C ( C ) W C W C ( C W C X C C C XC WC XC WC WC VC WC WC C YC XC C CW C C C W C WC XC VC XC WC WC WC WC
65 66 67 68 69 70 71 72 8va in soprano and tenor: whole tone progression
b) Fugue BWV 948, attributed to Bach
Ex. 8.33 - continued
185
186
Ex. 8.33 - continued c) Beethoven, Symphony No. 2/I (alternative to Free Composition , Fig. 100, 2b) 322 326
329
331
333
335
336
C
C
dim. 7th arpeggiation
g
C
rgov.
passing but prolonged *
X CCC ant.X CC Y CC ant.C Y X CC C (WY) CC C CC X C CC = WW B X C C Y C Y C W C W C X C C CCB X CCC X CCC CC C CC ! WCXCWC # WW B W C C X C W C C Y C X C Y C X C W C W C (X ) C C B C W C W C rgov. ant.
rgov.
7 VIIº 5 3 of II 1 8 b7 I 53 #1 1
5
3 5
1 3
CCC C
7 V 65 of II 6 ant.
7
II
I
II
Ex. 8.34: Non-linear register transfer within VIIº7 a)
b)
c) Chopin, Etude Op. 10, No. 3 38
Ì
# YY X C C C C XC Y
Ì
Ì
YY C C C X C Y C !
Ì
C XC C C
X C C (Y) C XC
39 equal division into three
X C W C W C X C C W CC X C W C W C X C C X C C XC
WWWW C
W W W W W CC XW CC YX CC X W CC YX CC X W CC X C X C C W C dim. 5th (whole-tone progression)
VIIº 7
VIIº 7
VIIº 43 of V
º7
º7
7
187
86 87
90 91
[in V:] VIIº 56
5 7 1 3
#4 #2
5 #4 3 #2
3
5
V 34 I
C WC # WW W C CWC CWC C CWC CWC CXC
h
W ! W X CC C C C C CC C C C C CC
83
not 1)
g C
90 91
disalteration
XC
87
5 #4 5
#4
6 7
7
6
[in V:] # III # V 43
[in III:] (VIIº 43)
7 1 3 5
n4
I
C WC CWC CWC C CWC CWC CXC
W W W CC W C
WCWC
86
WW C C C C C C C C C C C C
77 83
a) Beethoven, Piano Sonata Op. 28/I but 2) 95
CC
97
99
(“I”46 ) º7 4 3 inversion of: 5 3 4 5 1 2 1 4 [or: 65 3] 7 7 7 [in IV #:] I VII°35 2 1 of V 1 2 3
V7 IV V 7 I of IV
C C C CYC C X C C (d b?) W C X CC W CC X Y CC C X C C C C C YYYY C C X C C C h h C
C C Y Y Y Y X C C C C X CC
92
b) Chopin, Ballade No. 4
Ex. 8.36: Neighbors to VII º7: difficulty to determine whether the seventh is stationary
188
N
(IV43 ) 7 VIIº 53 4 3 1 2 1 (VI 6 ) 7 VIIº 13 24 31
N
122
versus
*
p
126
125
WWW
VIIº71 of V
(backrelating V 6)
C ( C )W C
2
1
(“I 46 ”)(V7)
C WC h
W W W C CC C W C CC CC C C W C WC
120
C V46 53 I
(“I46”)
C
CC W CC C C C CC
* sus.
129 130
f) Mendelssohn, String Quintet Op. 18/I (end of exposition)
[in VI:] I
dim. perf. dim 5th 5th 5th
(VI56 ) 7 VIIº 53 46 53 1 2 1
Y CC C C N
(IV64 ) 7 VIIº 51 2 1
Y CC C C
YY
e)
(II 2 ) 7 VIIº 53 1 2 1
N
N
Y CC C C
YY
d)
C YYY X CC C C YYY X C C C YYY X C C C CC N N
Y C
YY
c)
YYY X CC C C
YY
b)
# YY X CC C C Y N
! Y CC
YY
a)
Ex. 8.37: Upper neighbors under (or above) a stationary diminished seventh
189
CC
N
n
VIIº 71 ‹ 7 (enh. VIIº 2 of III)
(enh. V7/III)
1
# YY C YXC WC C
!
YYY
a)
(enh. V7/b III)
C
CC
71
b VII 71 # 7 1
I
CWC C C
YY Y C
YYY C YC
(in major)
70
String Quartet Op. 76, No. 4/II
as in Haydn,
#4
# VI
VIIº 75
enh. VIIº65 of
5
#4
5
with lower neighbor to the seventh
7
(enh. V 46 / # VI)
(enh. # V4 3 / VI)
VIIº 53
YY Y X CC X NC C
YYY C
c)
YY Y X CC X NC C
YYY C C
b)
1
7
(enh.
N
1
WC C nVIIø 7= II/VI) 7 # VIIº 3 ‹2 3
YYY X CC
N
YYY C CWC C
d)
Ex. 8.38: Lower neighbors under (or above) a stationary diminished seventh
N
(enh. b II b ) 7 # VIIº 53 #42 53 1 #2 1
N
YY Y X CC WX NCC X CC
YYY C CWC C
e)
190
1
‹7
1
III VII 73
6 (13)
WNC W C
CC
(enh. V 13 7 of III) 5(12) 6(13) 7(14)
# YY C W C [ C ]
C
I6 5
C
C C CC C C
g
g
YY C C C X C C *C CC ! (Y) CC
28
27
f) Chopin, Ballade No. 1, Op. 23
Ex. 8.38 - continued
V 13 7/
C
BB OO
68
C
BB O
C
YC C C C
*
VI
Ì
C
BO C C C C C
C
COC
g
BB O
C
V 13 7/
C C C C C C
BB O O
C C
V/VI
Ì
C
B OO
enharmonically identical with passing chord at m. 27 *
71
191
N
or
V(57 6 7 )I
CC
C C NC C C C
g
CC X( CC )
VIIº 57( 6 7 )I
# YY X( CC ) Y
Y ! Y Y CC C C C C
a)
?
144
147 x2 ?
153 x2
159
g
(“I”)
g
164
167
169
Ì
V18
x3
g
(V 7) (V7) (“I”?II 6VI64) 7 6 7 6 7 7 5 3 5 4 3 2 1 2 (VIIº 7 6 7 3 2
(VIIº7)
g
x3
4 2
b6
5 3 1
7 5 b6 3 4 1 2
5 3 1
) 1
I
C C N C C X C X C C C C C C N CY C X C (X ) C C X C C C C X C YYY C C C C X C X C C C C CC C C C X C C X CC N reversal of g N hierarchy g Y CC CC Y CC CC C C C NC C CC C C C C C C C C C C C C C C C C C C YYY C h h
141
b) Beethoven, Allegretto WoO 53
Ex. 8.39: The problem of a lower neighbor to the diminished seventh
192
VIIº 71 62 71
I
VIIº 7 I
(VII°7)
g
N
(“I”)
N
N
CC C C C C C CC X C C C
or
Y ! Y Y CCC CCCC CCC CCCC CCC XC XC XC
a)
?
N? mixture
(enh. of VIIº 2 (III6 4) of III) 7 6 7 VIIº 53 44 53 1 b1 n 1
(c b ? )
N YY Y CC CC CC C C X C Y CC X C
b)
g
Ex. 8.40: Further harmonizations of VIIº7-6-7
N? mixture
g
d)
N
I
7
VIIº51
6 b61
(V6) 7 n51
I
1
7
VIIº 53
# # 64 ‹27
7 5 3 1
N N YY Y CC CC CC CC YYY CC W CC CC C C C C C CC X C Y C X C CC X C X W CC X C
CC
c)
g
I
[in VI:] 76 7 VII 51 4 5 V of V
#6 (VII 41 )
54
I
g CX C N CWC C Y C C C C W CC C Y CC C( ) WC h * [minor triad]
53
e) C.P.E. Bach, Sonata Wq. 48,1/I
193
b)
7
1
VIIº 53
n8 6 b41
(III 6 4)
mixture
N
7 5 n 31
N
1
7
VIIº 53
(VIIº7 /II # 5 ) 8 # # 64 2
N
7 5 3 1
C YY Y CC X C CC C X C C W C X CC
whole tone above the dim. 7th
C YY Y CC C CC ! C X CC Y C X CC
a)
N
(VIIº 7 of b II) 7 b8 VIIº 53 b 64 1 2
N
7 5 3 1
ZC YY Y CC Y C CC YC X C C C X CC
c)
Ex. 8.41: Upper neighbor to the diminished seventh d)
e)
VIIº 7
b8
(enh. VII ø )
ZC YY Y CC X CC
N? mixture? (a n ? )
7
C
mixture
VIIº
7 1
3
1
#7 n 7
(II # )
YY Y CC X CC Y CC X CC W CC X CC
semitone above the diminished seventh
194
195
Ex. 8.42: Enharmonic parentheses within VIIº7 by means of a semitone lower neighbor a)
b)
Y ! Y YYYY X CCCC
W W W CC W CC C
C
(V 6 5) [in III :] VIIº 7 6
b
7
CC
! YYY X C CCC W C X C
(in relation 7 1 to root:)
‹7
‹5
VIIº 65
[in
CC
bVb :]
(V6 5) 6
YYY X CCC C W C 7 3
1 6
C C
VIIº 7
6
VIIº 43
I
c)
X X X CCC C WC 7
[in # VI b :] VIIº
3 6
6 (V5 ) 7 6
7
C YYY X CC C X C
C X CC C
#2 #5
C
7 5
VIIº 62
I6
C Y CC C C
#4 #5
5 6
I
d) Brahms, Symphony No. 1/I 9
13
YY X C BC X C C C C C Y ! C CC CC CC # YY C Y C X C C X C Y B
becomes
9
11 (b n = c b)
12 (c
C C CYC YC YC YC X BC C (Y) Y CC C C Y C C B
Y CC Y C Y CC X CC (“I”) enh. (V)6 5 7 6 7 in b : 5 4 5 III V3 4 3 VIIº7 6 7 6 VIIº 53
13
b =b n)
X CC X C g
C
(
C C
X C C X CC C X C C C
enh. in b V: 6
V VII53
b n
(“I”) V
V
b
n
(“I”)
V
)
#
!
g
x2
187
C WC
6
(VIIº 7 ) / IV
[in VI:]
n5
Vb7 2 1
?
YC C
1
b2
V b72
YC h
enharmonic equivalence
bb 52
(VIIº 2) Vb72 1 (bVII 46)
b7
?
Y C C ( X CC ) X C C C YC Y CC
XC C YCYCXCYC h
7th
C Y CC
V 64 53 (VIIº 7 ) III b 52 1
W C (X ) C C C
Ì
enharmonic equivalence
I (bVII) IIIb75
[in VI:]
(VIIº 7) b V 57 6
B YY CC C X CC C
g
188 189 invertible counterpoint
g Y CC C C Y X C Y C Y C C Y C Y C C C W Y CC C ( BC ) Y C C XC XC C
183
1
VIIº7 V 6 I of IV
V 64
XC C C perhaps: aux.
P
XCWC 1
194
5 3
I
¥
g Y CC C C C C C X C (X ) CC X C C (W C )
192
e) apparent enharmonic parentheses: Beethoven, String Quartet Op. 59, No. 3/II
Ex. 8.42 - continued
196
197
g
IN
3rd
[alternative (no PD)]
3rd
V7
4th aug. step = 3rd =
VIIº7
VIIº2 I
VIIº 7 6 5
I
g
IN
3rd
[enh. VIIº 4 in # VI b :] 3 V2 I6 VIIº2 6 4 6 I VIIº5 3
I6
5th
(VIIº56
b :] VIIº 2
V7 I
VIIº2
I6 )
V
69 70
72 * tonic reference
º7 (VII 31
I 6 VIIº2/V
[in I (VI/III):]
2 2
(I 6 4)
76 77
I
CC
CC
2 3
(III 6 4) 1
) 4 3
V7 I
C C C X C C C¥ C C C C C C W CC W CC = X C X CC ¥ C C WC [ C ]
74
d) Mendelssohn, Die Hebriden overture (after N. Wagner)
I
[enh. in b V
C CC = W C W X CC = YX CC Y X CC CC W X CC X YYY CC X C = W C W C X C X C = X C W C XC C Y C C C WC
b)
C X C C X C C W C W C C C C X X CC X X CC C Y C C WW CC CC Y C CXC Y C C C Y X C = W C ! W C W C C C C C (Y) C C C C = X C WC W C DN
c)
I
[enh. in III b :]
DN
YY CCC X CCCC = Y C Y C Y CCC Y CCC = X C X CC Y CC ! YC C
a)
Ex. 8.44: Full enharmonic parentheses within VII º7 via linear progressions
198
I
10
# WWW C C
WWW C ! C
198
(II)
(III) VIIº 7 /[VI]
[enh. in b V:]
5 3 1
b7
(V43
b6 VIIº 53 1 = VIIº 65
h
CC YY CC C C = C =X C
avoided
(in relation to root:)
C X CCC C C 10 10 C WC W C C C WC
C W CC C
g
IN
205
4
6
YC Y CC XC
x2 N
212
216
218
C
4 2 2 7 2 7
“I” 5 3 1
V43 )
3 1
b 56
b7
= VIIº 2
5
Ø6
(“I”)
disalteration YYX CCC YY CCC YY CC C = XW CCC X C W C C W C Y NC X C X C X C X C C C
208
a) Beethoven, Violin Sonata Op. 30, No. 1/III
Ex. 8.45: Open enharmonic parentheses within diminished seventh chords
C C WC h
g
IN
C
C
V64
C C
5 3
C
C
I
C
C
220
199
200
Ex. 8.45 - continued b) Mozart, Piano Concerto K. 595/I 178
180
182
184
CC X C C Y C X CC W C C CC YX CC X C C W C X C W C Y X C W C (X ) C C W C WW C C X CC X CC WW CC X C ! Y BC C C C WC XCX C C Y C C (Y) C XC C (X ) C # YY B 7 5 3 1
(in relation to roots) in bII b: in III:
in V:
6 #6
# (IV 56“I”46 ) # 5 66 57 4 3 2 1
# (IV 65 “I”64 ) 6 5 7 # 5 6 7 5 3 4 3 2 1 1 4 2 VIIº 3 4 3
VIIº 2
I
I IV31 b1(“I” 84 )VIIº 43
Ex. 8.46: Back-relating resolution within enharmonic parentheses in VIIº7 Beethoven, Symphony No. 6/IV
g
68
YY C ! Y Y X CC
72
74 76
78
CCC X X CCC X C CC
back-relating resolution
# YY Y Y W C =Y C X C C X C h [enh. in IV:]
in V:
VIIº 2 V
VIIº 7/V
I
V7 8
=
BC Y C C W CC W C C X C C C C C W (X ) CC BYC YCWC XC h
C
60
N
61
I
(passing º7
(VIIº 6 5 of V
# “I” 6 ) (IV 6 5 4
illusory seventh progression
)
7 ?)
C X C Y C Z C C Z(g?)C Y C
according to inner prolongation
# YY Y B YY
C
64 65
IN
II n
#
V74
3
I
g ant. C C C C C Y CC C C (C )Y C X C (C ) Y C X C C C h ? g C C Y X CC C YC C CC C C Y C X C C C C C C C h C h
g
62
(X ) CC CC C Y Y B ( C ) (X C ) X C Y C C C C C C Y C Z C ! Y Y CC X W CC X C XX CC X Y CC Y C Y C C C Y C X C (f b?)
58
Chopin, Polonaise Op. 26, No. 1
Ex. 8.47: Prolongation of a diminished seventh chord in a special chromatic context
201
#
!
I
(CTCº7 )
pedal point
C
C C C C Y C (W C
C C WC
1
)
I
YC
(CTCº 7 )
C C C
XC
N
3
I
X CC C
WC C C
invertible counterpoint
C C
2
or
a) Brahms, Piano Trio Op. 87/IV
C
I
(“I”)
º7 VIIof V
pedal point
C
C C C YC
3
4
5
(“I”)
V
pedal point removed
6
W C C C C ( CC ) C CC C C C C 6? g C C C C C C W C XC YC XC C C C C C C C CC C C C C C C C
2
C C C C WC
1 as if rebarred
Ex. 8.48: Prolongation of common-tone diminished seventh chords
202
42 49- 57 56 ^ (2)
58
I
V/V
[in V:] Vb
62
66
(III)
( b V)
9th=2nd
X X CC W C YX CC YC XC X CC X C Y C XC C YC
70 ant.
72 ant.
(I)
5 6 5 6 5th quasi-aux.
( n VII)
6
C C C XC C WC C Y W C C X X CC W CC W CCC W CC WW CC X C W C not
(* = occurrence of the VIIº 7 /V) * * *
ant. WWW B C X C g C CC W C C XC ! W CC C X CC # WWW C C ¥ C WC
^ 3
1
a) consonant reading
(II)
5
*
76
C WC
CC X CCC
C
74
V7 )
V6 5 of V (I6
WC
x2
CC WC XC (X ) C
(
86 90
WC
X CC
C
84
Ex. 8.49: Large-scale prolongation of VII º7: Beethoven, Piano Sonata Op. 2, No. 2/I
n
BC
C
C¥ )
88 92 ^2
203
WWW
I
*
62 *
2
(V b)
66
YX CC Y X CC YC
*
b 3^g
I
V/V VIIº of V
C WC h 7 1 2
3
*
60
4
5
*
3rd
YW C C XC 7
b6
C
*
68
YX CC Y X CC YC
64
XC WC C X CCC W C X C Y C X CC X CC X C C C XC C
42 49-56 57
CC X CCC C WC
1
70
ant.
72
ant.
etc.
C C C XC C WC YW C C X X CC W CC W CCC W CC W W CCC XC WC
anticipation
9th=2nd
C C X CCC W C X C W C X C C X CC X Y CC C C C C
58
c) incorrect variant of the prolongation of VIIº7
V
VIIº17
C WC
fp
CC X CCC WC
g
4942 56 57 ^ (2) b 3^
[in V:]
# WWW ¥
!
B
# WWW ¥
!
WWW
1 3^
b) alternative: prolongation of VIIº7
Ex. 8.49 - continued
3
9 7
8
ff pp
76 84 2^
I6
WC
x2
V7)
C
WC
C W X CC WC XC C
(
86 90
aux. (V/V
(ff)
g C WC C C CC X CC C X C¥
74
C I35
CB
C
)
88 92
204
# YY Y YY
Y ! Y YYY
(“I” 6 )
C
C
1
g
X¥
C
(problematic unfolding) VIIº 7 /V
C C
C X¥ C
2
C XC
C
3
YC XC YC
C C C C
C
XC C C (C)
CC X C Y C X C
4
Ì
XC
18
c) foreground reading of the initial phrase (after Morgan and Rothstein)
YYYYY
YYYYY
C
C
Ì
4
C XC XC
this line continues Ì
CXC
2
this line does not continue 6 (VIIº 7/V) I5 [passing]
C¥
¥
1
d) alternative: stable point of departure
205
206
Ex. 9.1: Half-diminished seventh chords as inversions of dominant seventh chords
minor 3rd
A
major 3rd dominant seventh chord
Y Y AAAA
g
Ì
!
AAA
minor 3rd
minor 3rd
(inversion of Ex. 7.88a)
0 3 6 T
Ì
Y Y CCC Y YYY CCC C X W CC C YX CC C YY CCC C X C C XC
Ì
T 6 3 0
b) equal division of the octave within a half diminished seventh chord
Ì
a) set class 036T
major 3rd minor 3rd
half-diminished seventh chord
Ø G 7
#
b
Ø Ø B 2 C 43 EØ6 5
Ø G7
Ex. 9.2: Parallellism between minor-minor II7 and half-diminished II7 Grieg, National Song (Lyric Piece, Op. 12, No. 8) 1
!
YYY #
3
4
5
7
minor-minor
8 half-diminished
CC C C C C C C C C C C C XC C C dim. 5th perf. 5th 10 C C C C C C CCC CCC CC YYY ¥ CC CC CCC CCC CCC CC CC XC C dim. 5th perf. 5th h h CC
I
(II 43
7
[in III:] I V I) III
(II 43
Ex. 9.3: Harmonies that emerge in prolongations of II7 (white noteheads: chordal tones [including the seventh]; black noteheads: non-chordal tones)
!
YYY AAA A
Number of foreign tones 0 Number of 4 chordal tones
CCC
AC (X ) CC C A
III
I6
V 64
3 0
2 1
2 1
A A CA (X ) CAA CA quartal
VI64 VII6 harmony 1 1 1 2 2 2
7
X CC ¥C W CC 10C C V
I)
207
Ex. 9.4: Subordinations to II7 true subordinations C.P.E. Bach, Keyboard Sonata Wq. 48, 4/II
a)
5 as (inverted) in
g
Y C C C Y Y CC C C
CC !
h
h
dubious subordinations c) d)
b)
6
C C C C CC C
CC C C CC h
(IV 2 ) (IV 7) (VI 43 ) 7 7 II 57 6 II 53 II 54 3 V I 2 1 2 1 * All abstract configurations possible in major of minor
CC
C CC C C CC h
h
C CC
(I 6 ) 7 II 42 31
from
(I 6 5) 7 II 64 35 2 1
C C C CC C CC I 63 (5) II 7
Ex. 9.5: Third voice exchanges within half-diminished II 7 a)
b)
Beethoven, Piano Sonata Op. 27, No. 2/I
c) Schumann, Symphony No. 1/II
58 not in use
!
C YYY C
# YY CC Y 7 II 53 1
C C
C C
(VI 6 4) 2 2
especially inverted as in:
in use
YYY
1 3
C C
C YYY C
C
C
7 II 53 1
10
WWWW
C C 4 4
(VII7 in relative major? cf. Ex. 9.13c)
3 5
C
C
C
YYY
C
YY Y CC
C
CC WWWW C C II 65
g
(rare form)
4 3
C
7 II 53 1
C C
C C
(nVII 6 ) 6 5 6 7
g
208
Ex. 9.5 - continued d) Mendelssohn, Piano Trio Op. 49/I 1) retransition 2) coda (excerpt) 336
360
! Y B C CC C #Y C B C
g
CC CC CC CC C C C C C WC C C C C C N h N
(I46 ) (I64 ) 7 5 4 5 4 3 3 4 3 4 5 1 2 1 2 1
[in relation to root:]
V
366
7 V II 65 (neighbor harmony)
530 568 569
576 579
572
g
580
g
C CCC C C CC C C C C C C C C C C C C C CC C W CC C C C C C C C C C C C C C C C C C C C C N h
( )
I IV
7 5 3 1 6 II 53 1
4 4
3 4 5 4
2 2
1 3
5 3
2 2
3 1
V7
I
Ex. 9.6: Fifth progressions within half-diminished II7 Mahler, Kindertotenlieder. No. 1: Nun will die Sonn’ so hell aufgehn! a) strophe no. 1 4 5
!Y B C #Y B
g
7 dim. 5th
C C
(not really ? belonging together)
WC C
? (VII 7 ) I [II 2 ?]“VI”
WC C
CC C C
II 2
9
g
N C C C C C CC C C C C dim. 5th
N
CC C C
C C
WC C 4 3
(VI)
11 14
6 5
C
CC C CWC
WC C P
V 64 53
g
C
g
C C
27 dim. 5th
WC C
dim. 5th
dim. 5th
N
dim. 5th
g
dim. 5th
6 5
48
(“I”6)
dim. 5th VE
(“I”64) 4 3 7
C C C C C C
(“I”6)
N (“I”64 )
g
N
6 5
52
I
(“I” 6 )
[inversions not including the pedal point in the bass]
II 7
4 3
(III
6) 3
C
C XC C C C WC C
modified hierarchy (cf. strophe 2)
C C
CC
32
I
C
C C C X C C NC C C X C C C C C C C C C CC notC C C CC CC W C C CC CC W C C X C C C C C C C X C C C C h N N N h
cover tone
II 2
g
29
CC C CC C C C C CC C CC (X ) CC C CC CC C CC C C C C
WC C C C C C WC C
X C C CC
C
C
dim. 5th
(perf. 5th)
WC C
44
I [II 2 ?] “VI”
# Y B
! Y CC C
43
c) strophe no. 3
I[II 2 ?]“VI”
# Y B WC CWC
! Y B C
25
b) strophe no. 2
Ex. 9.6 - continued
209
210
Ex. 9.6 - continued d) strophe no. 4 67
! Y
B
68
C
70
g
CC CC CC
dim. 5th
dim. 5th
C
g
73 76 77 dim. 5th
CC C CC C C C C B B B CC C C not C C C C C W C W C # Y WC ¥ WC WC C C WC C C C B B C h I
C
? (VII 7) [II 2 ?]“VI”
(“I”6 4)
II 43
6 5
V 64 53 I
Ex. 9.7: Seventh progressions within half-diminished II7 a)
b)
c)
g g N YY Y C C C C Y Y X CC C Y Y C C C C C C X CC C Y Y C C C C C C X CC C C ! C C C C CC C C C C C C C illusory 6th h h seventh progression h true seventh progression
I II7
VI
d)
I
(II7) V I
e)
(II7 ) V I
I
f) 3rd p illusory seventh progression
CXC C C C C C Y Y Y C C C CC C ! Y Y CC C C C C C X CCC CCC Y Y CC CC C C C C C CC X CC CC Y Y CCC CC C C h h illusory seventh progression
(
(
II 7
) )
(VII6)I
N true seventh progression ( )
I II7
V I
I II6
6 V I 5
C
enharmonic transformation of Tristan-chord *
h
a b# [not: fb
I
[in relation to the root:]
YC X C C C YY Y Y YY
( bII6 ) a b# c f ] b II 65 (=b7 ) b 66 n57
# YY C Y
II 7
8 7
BO BO
2
b 8 n7 b8 8
(bII)
V 65
I
V
Y CC OY C X CC OO BB OO YY Y ¥ h
323
(V 56 of V) II 65
(empty fourth)
CYCXC
335
4 I 3 (larger context uncertain)
Ì
330-3
Ì
XC
336 349
V
I
g C C C CC C C C C Y C CC X CC C CWC h h ? ?
C
327
c) Schubert, Piano Sonata D. 958/IV
BB O YYY O
b) recomposition of Tristan-chord complex
g YY Y C ( Z =C ) Y C C YYYY Y g C C Y ! C C O C C CB OO C X C C Y CC OX C CC OO C
a)
Ex. 9.8: Filled voice exchange in the 7-8-7 space of a second in half-diminished II7
211
212
b) Chopin, Mazurka Op. 17, No. 2
W
43
45
g
47
g
N
N
C X CC W C C W C X C C Y CC W C C WX CC X C C XC N N h h N N N g N N g N # W C YC X C C C YC C YC XC C C YC C C !
[in VI:]V VI [in III:] b 6 I II 42
7 5
V etc.
b6
b6
I II b 42
4
7 5
n2
b6
49
g
Wand not C CC W C C W C YX CC C C C W C C W C X C C C C C N h 3rd 3rd N N g 3rd 3rd YC C X C NC C Y C C W C Y C X C C C Y C C C C C N
b6
4
I II 42
7 5
b6 b42
III 53
I
7 5
5 3
(V/VI)
Ex. 9.10: Prolongation of half-diminished II 7 as the product Beethoven, Symphony No. 7/III of mixture in major 33 37 flute+ violins+ clarinets violas x4 x4
41 bassoons, horn, cellos, basses
43,beat 3 45 flute+ tutti oboes
C WC C XC C C W CC C W C Y C ! WC X CC C p reverse hierarchy g ff pp C C Y CC X NC Y CC X NC Y CC ( X(sub.) CC ) C C # YXC C (C ) h (V 7) (V 7) (VII6 I) (VII6 I) Ì
[in V:] V/
V/
4 (II 3b Ì
b
CC
g
g
N
Y CC X CC Y CC X CC h h 4 (II 3b )
) 4
7
V 54
initially sounds as
3 2 1
b 42
3 1
b 42
3 1
I
(II 3b ) V53 1
7
b42
3 1
?
C
Ì
[Wagner notates in E b Major] I # II7
Ì
(V 43
ring/destiny
(II 65 /IV)
(II56 /V+p.p.)(VIIº2 )
273
6) 4
C
CXC
CCC CCC ( W X= C C )
g
274 277
VIIº 7 = 43
Ì
connected?
XC X CC X CC
271
C XC CX C X C Y CC X C Y C CC YY CC C C CC Y C CC X X CC YX C C C CC X CC XX CC YYX C CC C ? C X CC C XC C C (X ) CC C XC Y C X C YC YC C C CYC C YC YC C XC cons. (unclear)
(Rheingold + Rheinmaidens) X2
268
C C C C C C C C C C C C C CC # YY Y Y X C C X C XC YY B C C C C C C
Y ! Y YYYY
ring/destiny
259 265
g
Wagner, Götterdämmerung. Vorspiel (Norns’ scene)
Ex. 9.11: Prolongation of half-diminished attenuated II7 in chromatic context
213
in V:
[in relation to root:]
7 5 3 1 6 II 5
6
4 4 2
3 5 3 4 4 2
5 3 1
6
49
C C C C C C
6
CC CC C C
(I 64 ) (IV 6) (I 64 )
C C CC 6 6 # WWW C C C C
!
WWW
47
a) Beethoven, Cello Sonata Op. 69/III
IV
5 3 1
7
6
2 7
1 6
2 7
(I 6) (II7) (I6)
following
6
5
3 1
C C C C C
5
C C C C C C C C C C 10 10 10 10 10
space filling motion leading
b)
IV6
II 65 IV 6
6 II (5)
C C C C C C C C Y C C
(crossing hierarchies)
21
22
C
V
CC
CC C C C C CC C ( C C ) C C C C C Y C
17-19
c) Bach, Italian Concerto/III
Ex. 9.12: Parallel third progressions in the lower spans of minor-minor II7
214
215
Ex. 9.13: Third- voice exchanges within minor-minor II7 (in major) a)
b) Mozart, c) Piano Concerto K. 595/I 157 159
g
(Cf. Ex. 9.5c)
! CC C C CCC
YY C
YY
# CC C C C * (problematic doubling)
158 160
(Cf. Ex. 9.5a)
C C C C hg C C C C
X2
1/2 + 1
C CC C C C C C
7
6
II 53 6
5 7 V
7 5 3
d) (after Aldwell & Schachter)
! CC # CC
C
C
CC
N
II 7
4 2 2
3 5 4 3
CC
1/2 + 1
(I 6 ) VII7 4 of V(VI 6 ) 4 7 5 3 2 1 1 2 3
6 V 5
II 7
II 7
3
C
4
5 1 3
8 7 5 1 3
6 5
II 65
C CC
C
C
CC C
C C
CC
C C C
(“I” 6) 4 2 2
5 3 3 1 7
V7
]
6 V 5
e) Brahms, Violin Sonata Op. 100/III (after Forte & Gilbert)
WWW C C C C CC
(“I” 6 ) 7 5 3 1
4 4
II 56
WWW
CC
(I6 ) IV7 4 (VI 64 ) 7 5 3 2 1 1 2 3
(VII 6 ) [in relation to root:]
1 + 1/2
1 + 1/2
[local impression:
YYY CC C C CC as hg opposed to C XC YY Y C C C C
CC
( )
2
!
II 71
5
(VI 7)
1
CC CC CC C # WWWW C W C C C C C C
WWWW
1
II 2
CC
CC
22
6 5
7 1
5
(VI 8 7 )
30
1
5
(VI 8 7)
32
33
WWW C
1 Andante
Ì
1
II 65
(VI n
# = V/ ) II(8
(VI)
CC CC W C C C C C C CC XC C C WC XC C C W C C (X ) C C C
3rd
5
7)
Ì
8 10 11 Allegro
V7 I
C C C C C C C C C C C C C ¥
6
b) Schumann, String Quartet, Op. 41, No. 3/I
IN IN C C C C C C C C C C C C C C C C C C C X CC W C C W CC C C C C CC C CC W C C WW C C W C C C C C C C h
25
a) Skryabin, Prelude Op. 11, No. 9
Ex. 9.15: Bass divider within minor-minor II7 harmonized as VI
216
Ì
237
VI
II 65
# WWW C C C
[b
9th=2nd
239 X2
241
245
( b III)
II 65
(“I” 64 )
h
d ?]
C XCWC
c#
CCC (XW) CC C
247- 255 254
not cadential!
X CC X C Y C CC X CC C X C W C C C C C c CC CC W C C C (W ) C W C X CC
X2
WWW C C ! [ C ] CC C C
236
Schumann, String Quartet, Op. 41, No. 3/IV
Ex. 9.16: Large-scale prolongation of minor-minor II 7 266 267
(associative connection) *
269 270 271
281
[in b II:] #6 (IV 51
C XC
( b II) 7 V5 (“I”)64 75
alternative
#
¥C ¥C C ) V6 (II 56 ) V I contained over a pedal point?
WC WC
CC
CCC X W C C C = Y C YX NCC YX CC = W C C X X CC CC CC X ¥ C¥ C C C (X ) C C
263
217
CC CC CC CCC CC WC C C
of V
[in relation to root:]
7 5 1 2 3 3 2 1 6 7 V2 I VII 5
(I46 )
g
50 53 N
X2
[N]
g
55
57
1 after No. 42
I6
[in III:]
V3 7
89
V VII71 7 1 9) 4 3
#6 2 #( 8
(enh. IIø2 )
C C X CC C h
10
10
10
n8
V65
I
I
VII 7
Ø (d # 7
10
W CC W CC
(
X C) C
5 after No. 42
b Ø7
g Ø7
d# Ø7)
V
I
C (X ) C X C W C X C X C W C W C C W CC ( C ) X C C C C equal division of the octave into three
X CC W C C¥ W WW W C ¥ W
10
CC X CC YX CC W C X C X C C W C W C C X C C W Y C Y C C X C C C X C C W C C W C X Y C C X C YW CC Y C XX CC W CC X C CC Y Y C C C C (Y) C [ ] C XC
20
b) Schumann, Piano Quintet, Op.44/I c) Richard Strauss, Der Rosenkavalier , Act 1 51
CC X C X # W W CC C C W C ( C ) X C C YYY C
!
WW
g
18 19
a) Tchaikovsky, Symphony No. 5/II
Ex. 9.17: Prolongation of half-diminished VII7 in major
218
b75
106 parallel 5ths
108
[in relation to local roots:]
3
#
b57 4 b 3 4 3 3 4 b5 4 5 6 4 =IV b 53 I II 56 b31 over a pedal point 6 4 11 nVII b 97 88 b 79 VIIº7 I9 8 IV b 53 b13 V65 [In IV:] 11 I [V b 97 ?] (VI [Riemannian PR] IVm
bb75 b3
bb 35
b 65 b IV b3 1
II6 5
b6 bb43 1
110
b75
4 4
b 35
112
VIIº7
6 IV b 53
6 II b53
[Riemannian R]
I9 8
I
3
4
b31
“I”m
VIIº7 I 9
8
C
C
X CC
113
) IV 7 # 6 V
YY CC Y C YY CC Y C Y C X C C X C g C Y C Y C (X ) C C XC h (X ) Y C C Y C Y C Y C YC XC YC YC XC YC YC XC h
[Riemannian PRP] b III M
I9 8
I
4 4
g CC Y CC C Y C Y CC C X C Y CC C C WW CC WW CC XW CC ZY CC Y C Y C YY CC ! C C C CC (enh. spelled) C Y C C X CC X C Y C YC YX CC C Y C C W C Z C C Y C # C C C YC C W C C C
104
Schubert, Piano Sonata D. 279/I
Ex. 9.18: Prolongation of half-diminished altered IV7
219
3 4
(Vn) IV6 5
I]
Vn
3 2
1 2
1
7 6 7
7 6
2
6
3
7
[IV 53 42 51 24 53 42 51 “I” # n ]
(Vn )IV65(V n)
[or in major: IVb53
b7
#
C
C W ! C h
[ in relation to root: VI
7 b6 5 IV65 b4 3
IV 56 of III
C
C
2
4
1
3
7 6
2 1]
V
V of III
C
C
9
I
III ]
¥
C
CXC C C C C C C WC C C ¥
7
true 7th prog.? Schenker: unfolding
5
=h (verticalization)
C
W ¥
3
1) after Schenker
2
1
7) 6
(IV7)
(8-7 lower counterpoint)
VI 55 (b4 3
h
7
9
V
I
C Xillusory C C C 7thC prog. W C C C C C CC C C
3
2) alternative
b) Beethoven, String Quartet Op. 59, No. 2/IV
[in real-time listening: I
CC C C C C C C C C C C # WWW C C C h N
N
W W W C C C C C C C C C ant. C ! C CC CC CC CC CC CC CC W CC X CC W( CC )
g
1
a) Wolf, Mörike-Lieder. No. 23: Auf ein altes Bild
Ex. 9.19: Prolongation of minor-minor IV7
220
sus.
2
5th
h
3
C C C
7- 6 7 -6 7- 6
C C
7th
(perhaps should be a 4th) I VI7 II7 V7
# WWWW W ¥ W
C
7- 6
WWWW W ¥ C C C C C C C C CC C ! W
1 ant.
3
I IV 7 6
(VII6 )
V7
¥ C C C C C C C C CC C C C C C sus. sus. etc. genuine 7th (subordination) 7 g - 6 7 - 6 7 - 6 7- 6 7 - 6 7 - 6 7th C C transitive C C C C C ¥ C
1 2
3
I
¥
C
C C
C
C
(VII7 )
C
7th
V7
CC
7- 6 7 - 6 7 - 6 7 - 6 7 - 6 7 - 6 7 - 6
¥ sus.C C sus.C C etc. C C C C CC C C C C C
1 2
a) Bach, The Well-tempered Clavier, Vol.1. Prelude in F # major 2) 3) 1) Schenker endorses (my notation) Schenker refutes (my notation)
Ex. 9.20: Prolongation of minor-minor VI7 in minor
221
8
10
V 4 3 VI 7
(II7 4 3) (II7 )
(VI) (II43 )
( )
or
15 7
8
10
12
II 7 V46 53 I
C C CC C C C C (VI7)
7 4 7 4 3 2 13 4 (or variant: II 3 dominates)
(VI 7) (VI 43 ) 7 V II 42 31 43
(VI 7 )
15
CC ( BCC ) C C ¥
CC
14
7 V6 5 I 43
aux. (or: continuation of V until m. 14?)
C C C C BC C C¥ C C C C CC C C CC C C C C C C¥ C C C C C C C CC C C C C B C CC
14
C C C C C C CC C C C CC ant. C C C C ant. C C C C C C C
12
aux. (or: continuation of V until m. 14?)
C C C C C C C C CC C g CB C C ant. C C C CC C C ant.C # WWWW W W C
WWWW W B W C !
7
b) Skryabin, Mazurka Op. 25, No. 6
Ex. 9.20 - continued
222
7th
6
[In A:]
C C C hC
I IV 73 6 7 9 8 7 I IV73 6 7 9 8 7
# WWW C C C C
N
7th
V76
C
C 5
ant. I
C CC C (8) (8)
III7
[Schenker: C 7
V7 /III
?
7]
7
CYC C C WCXC CWC C
g Ng C CC C NC C C C C CC CC NC C C C C CC C ( CC ) C g Ng C C C # WWW C C C CC C C C C !
274
7th
6
10
V7/III
III5
(“I” 6
Ì
Ì
V n61 )
CYC C C WCXC CWC C
10
C C C CC C C C C C (C) C
g
5
5
272
265 266
269 270
b) Bach, Short Prelude No. 12 (BWV 942) 1) after Schenker 2) alternative
a) Chopin, Scherzo No. 2, Op. 31
Ex. 9.21: Prolongation of non-tonic major-major seventh chords
223
[in V:]
(II 2) [in relation to root:]
130
3 1 6 1
4 2 2
(II34 )
7
3 1 3
(V2) (V2) 7 5 3 4 3 4 1 2 1 2 6 7 6 7 I 53 1 2 1 2
133
(V43 )
5 3
3 1 3
CC CC
C C C C
8 4 3 2 1 2 6 6 1
C C C C XC C C C C C C C C CC CC X CC C C C C C C C CC C C C X C CC X CCC X C CC X CCC XC CC CC XC XC C C
X2
(II 2 ) (II2) 7 5 4 3 4 3 1 2 1 2 7 6 7 6 V 51 2 1 2
# YY C CC X CC C CC
Y C C C Y ! C C C
121 122 126 127
a) Schumann, Humoresque, Op. 20
Ì
Ex. 9.22: Prolongation of major-major I7 (in major) 3
5
7
7 6
I 10
b6
=
9 3
8 2
#5 # 4 n
4
b(7) 2
3 7 1
5th W W W W C CC XX CC X C WC C C C (W ) C eva C C X 4th CC W C C W C X C C Y C C C W WW W C C XC YC C
CC
1
4th
CC
C C W 5thC W C C C C CC
for
b) Ravel, Jeux d’eau (after Salzer)
224
225
Ex. 10.2: Hierarchical status of diatonic and augmented sixths a) normative explanation
b)
c)
(from Aldwell and Schachter)
¥ C WC C C C C WC C Y CC Y C X C ¥ YC C h #
!
becomes
#
B WB A AA W AA
WA A AA W AA
# IV6 6 V
IV # 6 V
I
¥ C CC CC W CC W CC C Y CC C YnotC X C C ¥ YC h #
ant.
6 (IV b5 1 V
C¥
X C¥ I)
V
I
6 (IV b3 1
Ex. 10.3: Perceptions of diatonic versus augmented sixths a)
b)
YY C CC C X CCC Y C ! C C h P
(IV 6)
I (VI)
V
but
g
N
C C W C CC CC X CC C h (VI)
I
# IV 65
V
6 5
ant.
V
C¥
X C¥ I)
V
226
C W CA
h
C
6 V IV (5)
#
g g C C C CWC
51
46
50
51
C C WC C CWC C YC x x y C y CYC C C YC C
44
V [Schenker’s notation, diagonal line mine]
b5 Schenker: #IV 3
in III (G minor): surface b VI b7 harmonies:
# YY A Y
YY g Y C !
YC
50
a) Haydn, Piano Sonata Hob. XVI:52/I Schenker’s reading (Der Tonwille 3)
#6 IV b3 V [“Italian”]
IV b VI
CC Y CC W CC X CCC CYC Y C C
b)
=
IV [“German”]
#6 bIV 5b V
CC W Y C CC CC C Y C X CC WW
WW
I
Trio
100 Minuet repeated transition ant.
53 97
( b VI)
¥ Y¥ h
#6 IV 5b V
¥
I
B
g ¥C X ¥ W C C W ¥B C¥ W CC¥ C C C
Minuet
1
c) Haydn, Symphony No. 104/III
Ex. 10.5: Structural priority of the German augmented sixth over a preceding bVI
227
228
229
230
Ex. 10.8: Third progressions in augmented sixth chords: the middle (major) span a)
b) Chopin, Nocturne Op. 32, No. 1 62 3rd
C W WW ant. CXC C C C Y W CC C C C C W Y X C C C C Y W C C W C C ! VC X C C X CC XX CC C (or: ) hg C C C C C W # YY W W Y C C C C C W WWC C h (enh. #6
b ) III 6 4
IV 53 2 1 2
1 3
V
b7 #
IV b 35
Vb 64 53
W CC C C C XC
YYY
b)
YYY
c)
ant.
YYY
d)
!
#
1
6
2 3
IV 35 4 5 V 1
#6
# IV 53 46 56 5 3 V
# IV 65
5 3 1 (3) 3
(I # ) #6 7 8 5 #5 #6
3 V
#4
# IV 65
3
#4 V
(I 2 ) #6 7 8 5 3 1 2 3
W CC C C C C W CC C CC C W CC C C C XC XC XC # YY C C C C YY C C W C C C YY C X CC W CC C YY C C C C Y C C Y C C Y C C Y C C
YYY
a)
Ex. 10.10: Parallel third progressions in augmented sixth chords
I
B YY
YY C
[ B ]
g
not yet V despite entrance of trombones
ant.
36 37 38 39 40 44
7 7
b IV 3# 2
#8 of V b
8
b3
(V64 I 63 )
*
WC C C
V I
C B
C X C CCC W CC CC W X CC C W X CCC BCC
1-24 25-33 34
e) Bruckner, Symphony No. 1/III [Linz version]
231
perf. 5th
C
dim. 5th
C XC
c)
C C
dim. 5th
C XC CC
# IV 65 4 3 2 1 V
(VII 6 )
5 IV 35 2 41 7 # 36 V
# 6 n6 4 1 2
IV 53 42
(“I”6
#6 7
Y C YY C C 1 3 1 7 #6 3
)
WW
B
(“I”)
C C WC C C
20 24
38
descent continues
C C (X ) C CC
28 33 32
(“I”)
dim. 5th
I VI
V/III V
Ì
CC C W C X C C C WC C XC ¥
X2
25 26 29 30
WW B W C C C C C C C C C WC
X2
(1-)17 18 21 22
d) Tchaikovsky, Album for the Young . No. 2 : A Winter Morning
V [in b:] I Gr-type [in D:] VI common-tone chord
C
C (Y) C C W C X C W C C Y Y C C C X C Y Y C C C WC C Y Y C XC C WC C
C
b)
C C C C C C C # YY Y Y C C YY C
Y W CC Y ! Y
a)
Ex. 10.11: Fifth progressions in German-type augmented sixth chords
232
# in relation #71 6 7 to root: # IV 65 #4 5
V 5
# 8 ‹7 # 8 # ‹ # IV 6 5 6
d) 236
238
V
# 31 b4 # IV 65 1 b2 1
3
V
(“I”64 ) #6 7 #6 IV 53 1 7 1
V
8 #7 8 5 3 1 2 1
# IV 56 V 64
b
6 (“I”64 ) in (“I”4 ) # 6 7 # 6 II 7 6 7 IV 35 = V 53 44 53 1 7 1
C
C
Y CC
e) Mendelssohn, Piano Trio Op. 49/IV
or C C Y YC C Y Y Y C C C WC C C C W C W C (= Y C ) X C C W C C C C CXC C C CXC XC g Y Y Y CC C Y Y CC Z C C C Y Y CC C CC C CC C CC C Y CCC CCC CCC C C C C C C
c)
Y Y C YYWC WC C C YYWC C C XC XC
b)
# YY C C C C YYY C C Y C C
C
Y ! YYWC
a)
Ex. 10.12: Neighbors to German-type augmented sixth chords
233
dim. 3rd ant.
b) (cf. Ex. 10.15d)
c)
d)
# IV 56
dim. 3rd
(III) (“I”)
V
# YY C C C C C Y C C CWC C dim. 10th =
N
dim. 3rd
# IV 65 (V “I”)
dim. 3rd (V
“I”)
( b II)
# V IV 56
CC C C C C C CWC C dim. 10th = # (“I”)
#6
C
V IV 53
CC CC CC C W C
V IV 65
CC Y C Y C X C YC C C
(e # ?)
(“I”)
C
C
(“I”)
C
C
4 V
C
C
5
C h
C
5
3
# 6 # 6 #56 4 (IV )(IV ) (IV )
C
VI (“I”)
C
53
C
V
ant.
48 50
CCC W C CC W NC C CC W C C CC W C C C C C C
47 51 53 47 (after N. Wagner) or
e) Tchaikovsky, The Seasons . No. 1: January
W C NC NC C W C YY C YC C XC N Y ! W C C C C C W C C C C C W C X C W C C W C C C C CC W C CC W CC C CC W C C C C C C C C XC C XC C C XC C C CXC ant.
(a-d all set in C minor)
a)
Ex. 10.13: Support for motion that prolongs German-type augmented sixth chords
234
235
Ex. 10.14: Wide prolongation of a German augmented sixth chord Beethoven, Piano Trio Op. 1, No.3/I a) prolongation of augmented sixth chord 294
hypermetric unit dim. 12th = dim. 5th (problematic inner segmentation)
C YY Y W CC XX CCCC X C CCC ! ff # YY C C (X ) C Y (V
#6 IV [5]
C XC CC X C CC C
CC C
3rd
C CC C CC
CC X CC Y CC CC C C
C XC
C
C XC
298
299
CC (Y) CC W C C C C C C C C CC
C X CC C
“I”) 5
V 64
5 3
b) alternative 294
g
299
295
W CCC XX CCCC CC XC C ! Y ff C C (X ) C # YY Y h YY
hypermetric unit
10th = 3rd
C CC X X CCC C C
IV# 6 V
C
CC
C CC C CC
CC X CC Y CC CC C C
C XC
C
C XC
CC (Y) CC W C C C C C C C C
CCC X CC C
(“I”)
c) recomposition that guarantees prolongation of the German chord
!
294
YYY # YY Y
W ¥¥¥ OOO ff ¥O
#6 IV [5]
298
hypermetric unit
hypermetric unit
dim. 12th = dim. 5th (problematic inner segmentation)
CC X CC C C C X CC X C CC CC X(X ) CCC CCC C C C C CC C C (X ) C C C C XC (V
CCCC XC CC Y CCC CCC CCC W ¥ O¥ O ¥O ¥ C C XC C C O
“I”) 5
O ¥¥¥ OO ¥O
¥O X ¥¥ OO ¥O
V46
5 3
236
b) Schubert, Piano Sonata D. 845 (Op. 42)/I (after Proctor) 10
14
5^ 6^
18
^ ^ 5^ 5 6 N
C CC C ! C C C C W CC C C C (W C )C #
N
C C
C
C C
20
g
CC Y CC C CC C Y C YC CYC C = Y C W C Y CC Y CC W C C CCC X C C CC C ( C ) W C C ( Y C ) YX CC C WC 5^
^5 6^
C C C h
(inner V 7 unconnected to boundaries?) 5^
C
enh. 7 [in b II:] (V5
V
24 5^
^ 5 6^ N
(VI)
6 4 # 6 (‹ 5?) IV 53
C
I 64
C n6 4 4
C C C C C 5 #6 5 6 3 V4
7 5
) 3
(f # )
104
# YY Y
b
# IV 65
II:] V 73
h
g C
C
C
6 4 +consonant support
(“I”)
YC
C YC
107
C C (V73
C YC YC
g
N =
112
g
114
6 4 +consonant support
5 “I”) 3 7 3
V46
5 3
YC WC XC CC Y CC Y C C C C C CC Y C C CC X C CC X X CC YC C
110
Ì
I
[enh. in
B
C
7
BC Y C Y CC Y CC Y C Y C YY C C Y !
100
a) Beethoven, Piano Sonata, Op.10, No. 1/III (coda)
Ex. 10.16: Consonant b II within prolongation of augmented sixth chords
(
I
C
C
C)
115
237
! 6 7 6 #7? 6
[enh. in
b II:] V 2 IV b73
55 56
228
229 231
V46 35 I
I
[enh. in
7 5
#V IV 6
b II:]
CWC C C C C C C W C W W C C C W CC W CC W C CC h
I6 (V2 I6 ) V2
X2
230 232
233
234 235
c) Mendelssohn, String Quartet, Op. 44, No. 2/I
6 ) V2 3 b73
(
CC V64 53 I
Y C (W C ) X C XC YC C
(“I” 64
C
W C C C C YC X C CCC (X ) CCC W C C C C C C WC C C W CC ( ) XX CC WC
(whole tones)
6 7 7 7# 6 b (7) 10
W C
from
57
CC CC CC CC W CC W C C
52
CC W C X C C Y C C Y C C X C C C C X CXC C XC C
7 6 7
C C C C C C X C XC C C
(e #)
C
[in V:] I
# W
W
not 7-6 suspensions!
49 51
46
42
b) Beethoven, Piano Sonata Op. 109/II
Ex. 10.16 - continued
)
238
239
Ex. 10.17: Back-relating resolution within enharmonic parentheses in a diminished-third chord Schubert, Moment Musical, D. 780 (Op. 94), No. 6 (after Laufer)
65
65, beat3
Y ! Y YY YC CC
Y CC
67, beat 2
g
69
70
YC ZY CC ZY CC Y C Z Y CC ZY CC Y CC YX BC
Y C
# YY Y C Y
68
X C (= Z C ) Y C Y C Z C Y C Y C Y B h h back-relating tonic
[enh. in b II:] II 65
4 3
V2 IV# 17
I6
I
V 64
5 3
Ex. 10.18: Expanded enharmonic parentheses within augmented sixth chords a) Mendelssohn, Piano Trio No. 1, Op. 49/III 65
82
93
C W C (X =C ) X C C (X ) CC C WC C C
WW C !
90
C
6
# WW C C
C
[enh. in
b II/III:]
[in III:] I
h
C
C C
V7
# IV
6 5
94 X2
96
98
100 106
= ( X CC ) W C W C C C C X CC W C C C W CC C C W C X CC WW CC C g 5 6 5 6 C C (X ) C C C C C W C C WC
(“I”) 1 4
(
2 5
3 6
)
# 57 n78 V
I
YC C YC
84
C
X3
92
C YC
85
96
99 100
C
[in VI:]
[= enh.in b VII:] [= in b II/VI:]
IV 15
#6
back-relating tonic V7 “I”
[not yet]
#1 2
6 (V5 / n6 #2
C YY CC Y CC Y CC (X ) CC C (outer parallelism; no structural connection) C C C C # YY C YC C YC XC C C XC Y
Y C !YY
81
b) Mozart, Horn Concerto No. 3, K. 447/I
Ex. 10.18 - continued
C
Ì
104
V
C WC XC XC YC C C X C C C X CC Y C C C WC XC XC YC C
VI) 5 #6 3 1
C
CC
C
103
# IV 65
[in b II:] V 7
(“I”) VI
V 65
6 3 V
#4
YC = Y C XC X CC W CC ( Y C ) X C Y C ( =W C ) X C C YC YC C C C YC YC YC C XC
112
c)
240
b
#
!
enh. notation
129
# I (IV #71 ) V 46 (IV 56
7 V3 1
not bn !
!
131
133
4 5 7
4
(VII º 6 4)
YC not e n 3 1
)
C XC 5 3
I
C
CYC CYC C C C W C (XW) CC C
C YC C YC C C C C C
[enh. in b II:]
¥WC
¥
C
126
184
[enh. in b II( b):] #6 I IV 53 44 53 1
b2
1
V7 1 ( b)2 1
(VIIº 2)
avoided [I]
inner tendency:
188
190
n V 64 35 I
Samiel’s plan C YC XC C C YYY C X C C C enharmonic positive tragic fate Y C majic fate C C avoided bullets achieved C YC YC YYY C Y C =X C X C X C = XC h
X2 context: Agatha’s love
182
Ex. 10.19: Enharmonic parentheses within the German augmented sixth without reaching II a) Beethoven, Cello Sonata Op. 102, No. 1/I b) Weber, Der Freischütz . No. 9 (Terzett)
241
242
Ex. 10.19 - continued c) Tchaikovsky, Orchestral Suite No. 3/II 278
!
W #W
295
C
C
CC
CC C C C
C
C h
C
298
g
C
C WC
I
321
C
CC
6
C
[enh. in # VI # 5:
[enh. in b II?:
314
C Y Y CC X W CC X CC W CC (X ) CC (X ) C (X ) CC C W C Y C Y C octatonic CC
C
304 308
5 3 1
IV
tethrachord? 5
WC
V6
V7
#6
[=7
C
I
b III6 bb 6] # b63 [= n # 5] 3
6
XC
C
C
VI 6 ] V7 ] (III6 ) 8 7 Vn 63 5#
n6
#6 n1
1
I
Ex. 10.20: Apparent enharmonic parentheses within augmented sixth chords b) Schubert, Die Winterreise . No. 12: Einsamkeit (key of later version)
a) *
Y Y CC Y CC Y ! Y C CC # YY Y C Y b II
29 ^3
*
Y CC W CC XX CC Y C CC X CC C h
(V/ b II)
# (IV 6 ) 5
31
WW C Y C C * C C XCXCXC >C WW C C h
V
VI 8
(V/ b II 64 ) 7
32 ( b ^2)
n ^2 *
XC C > C
C
C
Ì
[again] ( b II 64 )
W PC C # (IV 56 )
34 ^1
WC C WC C C C C C V
I
243
Ex. 10.21: Hybrid combinations of enharmonic parentheses Beethoven, Piano Sonata Op. 2, No. 2/IV b) a) 139
146
157
#
(a ) (a # ?) Y C # WWW C CC YX CC X CC X CC X X CC X CC W C W CC h (VIIº2 V7 “I”64 V7 “I”46 V7 VII º2 ) of V of V 6 6 I (VIIº 5 / II6
enh. in b II: V7 ( 64
# IV 6 65
Ì
OR enh. in bVI:
6 V7 “I” 6 V7 ) 4
# (V 7 “I”4 I b65 b 1
I
b n
164 165
C C C Y CC Y C C XC YC Y Y CC C Y CC Y CC C C (d# ) C XC XC XC XC XC XC XC XC
W W W C C C C X C C X C X CC X C W C ! C XC C C YC Y C WC XC
enh. in bVI:
158
7 6 7 ) 3 4 3
6 (7 4 3
X CC X C C WC X C WC C
6 ) VIIº 7 4 of II * V
n
b
(= VIIº 65 /V)
II6
Ex. 10.22: Prolongations of French-structured augmented sixth chords a) Grieg, Stimmungen, Op. 73. No. 5: Study 8
12
15
YY YY C C C X C C (Y) C W CC C W C C C C C C C C ! X CC X CC W C g C C # Y Y Y CC WC X C Y C Y XC YC h #3
[in relation to root:]
8 7 5
4
#6
[in V:]
I
II 43 1
7 7
C C C WC C
C
C C
4
5
#3
4
C C CC
4 1
#6
C C
3 5
7
#6 V
7
1
244
Ex. 10.22 - continued c)
b)
aug. 4th
Y ! Y Y W CC X C
C X C C W CC C
# YY C X C W C Y C h C
h
aug.
(VI # 5 )
#6 ##5 #4 5 6 II 4 3
C CC
C C C
dim. 5th aug. 4th
Y CC Y CC W CC X CC Y CC Y CC (XY) CC
C X CC C
dim. 5th
aug.
# ( n VII 5)
(inaccurate vertical spellings; weakened tonal identity)
#6
II 43
V
W CC X CC Y CC Y C (X ) C Y C C C YC C WC
2 2
1
1 3
V6
d) Beethoven, String Quartet, Op. 59, No. 3/I 1) after Free Composition , 2) alternative Fig, 148, 3
!
150 167
YC C
Ib
168 169
C W CC YC
#6 b1
II 43
C
170
150
167 168
C
YC
YC C W CC Y C
CC V
(
C Ib
169
170
C
C
ant. )
# (IV 65 ) b1
CC V
245
Ex. 10.22 - continued
e) Mussorgsky, Be Bored 1) after Russ 28
!
WW
28
29
N
B W BB # WW X C O W C g in relation to root:
29
2) recomposition that fits Russ’s reading
Vb53 7
CC
C W CC C W CCC C C XC C
N
1
6 4 2
#6 b1
7 5 2
V 34
N
b5
3 1
#6 4 b1
I# I#
BB WB XCO
WC
b V 53 7
g
C
C
CC
N
1
6 4 2
#6 b
7 5 2
V 34
1
W CC C XC
C
W CCC C
b5
I#
#6 4 b1
I#
3 1
246
Ex. 10.24: Prolongation of rare types of augmented-sixth seventh chords a) recomposition of R. Strauss, Till Eulenspigels lustige Streiche 46
47
b) Schubert, Schwanengesang No. 5: Aufenthalt
48
49
51
52
C C C W C C C W C T Y X C (Y) C C C C ! W BB O CC B O WC C C (Y) Y BB O C W BC O C C (X ) CC W #Y C C (enh. [in relation to root:]
VII b
4
5
4
#3 b 65 # 13
4
4 3
4
54
55
[also m. 48]
IV ø7 III # IVø 56 III # IVø7 )
#3 b17 5 #6
53
C
C
CC CC C C C C W C C X C C CC
h
CC
Y CC C
C
#3
5 #6 b43 I
[in III:]
# ( ) III (IV 55 6 (6) 6) V64 53 b n 1 1 [=V ] 8 7
I
c) Bruckner, Symphony No. 9/II 1) 2) real-time listening strategy 3
13 23
27 31
43
3
C C W C C WW CC W V CC W W C Y C ! aug. 2nd aug. 4th
perf. 4th
dim. 5th P
VII
(º7 º7
ø6 5
V7/bV)
(#) 8 2 # 3 # # 4 # ‹4 # 57 (#)# 86 ##27 (#)28 (#)28 3
(#)6
4
(#) VII #53 46 #
7
1 2
5
6
31
35
(X W) CC ( X CC ) W W W W C X C C WX C C W CC V CC X CC V CC CC CC WC
WWWW W C W C W C X C Y C Y C ) (= ! W CC W CC W C C W Y CC CC C C Y C X CC (ant.?)
[in relation to root:]
13 23 27
might have been
perf. 5th aug. 2nd
dim. 3rd
35
7
#1 # 2 ‹2 # 75 (#)# 76 (#)#76 #3 4 b5 1
CC
h
W CC C
CC W C C C
C
#5 (#)83 7
#3 (#) 86
# ( b II 6 VIIº 6)II 4 V7 8 I 4* 5 3 5 3 5 6 * = added 6th of IV of V 6
I
7 5
[V I]
INDEX OF MUSIC EXAMPLES Bach, Carl Philipp Emanuel Keyboard Sonatas W48,1/I 53–54 8.40e W48,4/I 3–6 9.4a W57,6/I 58–62 8.13h Rondo W56,5 mm. 140–54 8.31e BACH, JOHANN SEBASTIAN Chorales 69 melodies, No. 30—Gott, wie gross ist deine Güte 2.14b Riem. 59— Herzliebster Jesu, was hast du 2.2a Riem. 80—O Haupt voll Blut und Wunden 3.21 Chromatische Fantasie for Keyboard, m. 31 8.6e English Suites No. 2/Bourrée No. 2, m. 1 2.15b No. 4/Sarabande 7.95b2 No. 6/Gigue 3.9 French Suites No. 2/Sarabande, mm. 1–5 7.36 No. 6/Sarabande, mm. 13–20 6.12b Fugue BWV 948 for Keyboard (attributed), 65–83 8.33b Inventions (3-part) E minor, 37–44 8.32d F minor, m. 1 1.12
Italian Concerto for Keyboard/III 17–22 9.12c Motet No. 5—Komm, Jesu, Komm, m. 14 3.16 Organ Works Allabreve, BWV 589 2.3c Das Orgelbüchlein. No. 5— Puer natur in Bethlehem, 12– 13 8.35 Preludes for Keyboard BWV 924 (12 short preludes, No. 1), 7–18 7.23c BWV 942 (12 short preludes No. 12), 5–7 9.21b Sonata for Violin, No. 1 Adagio, mm. 18–19 8.19d Fugue mm. 47–52 7.81c St. John Passion/Chorale— O grosse Lieb, m. 10 2.2a St. Matthew Passion/Chorale—O Haupt voll Blut und Wunden, m. 1 3.21 Suites for Cello No. 4/Prelude, 15–27 8.10a No. 5/Prelude, 27–30 2.9c
248
Index of Musical Examples
BACH, JOHANN SEBASTIAN—contd. The Well-tempered Clavier, Vol. 1 Prelude in C major, 24–31 7.64 Prelude in Cƒ minor, 30–31 3.13 Fugue in F major, 1–4 7.27d Prelude in Fƒ major, 1–4 9.20a Fugue in A minor, 80–83 7.96a Fugue in Bß minor, 55–62 8.23c The Well-tempered Clavier, Vol. 2 Fugue in E major, 38–40 7.43b BEETHOVEN, LUDWIG VAN Ah, Perfido!, Op. 65, 118–21 7.31d ______, 156–60 10.7a Allegretto for Piano, WoO 53, 141–69 8.39b Bagatelles for Piano Op. 33,7 theme 6.4a Op. 119,1 mm. 25–29 3.20 Op. 119,11 mm. 7–9 6.24a Concerto for Piano, No. 5 (Emperor)/I 6–9, 363–364 7.45b Fantasy for Piano, Op. 77, transition to Allegretto (142–57) 7.91 Leonore Overture No. 3 Leonore No. 3, 570–614 7.83 Quartets (Strings) Op. 18,1/I 14–15 8.3d _______ 282–4 7.38b Op. 18,2/IV 7.115 Op. 59,2 (Razumovsky 2)/IV 1–9 9.19b Op. 59,3 (Razumovsky 3)/I introduction 1–29 8.27c _____ 30–43 7.32b _____ 126–37 7.97c _____ 150–70 10.22d ____/II 183–194 8.42e Op. 127/I 7–10 6.21c Op. 131/I 18–20 8.10d
Op. 132/I bridge 7.103 Rondo a Capriccio for Piano, Op. 129, 149–62 7.98 ___, 260–379 7.102 Sonatas for Cello and Piano No. 3, Op. 69/I 1–5 6.18b __/III 47–49 9.12a No. 4, Op. 102,1/I 128–135 10.19a No. 5, Op. 102,2/transition to III 7.97d Sonatas for Piano Op. 2,1/III 1–4 7.95a2 Op. 2,2/I 42–92 8.49 ______/I retransition 215–24 7.75d5 ____/IV 139–46, 157–65, 10.21 Op. 2,3/IV 282–308 7.108 Op. 10,1/III coda 10.16a Op. 10,2/I m. 111 3.17 _____/III 23–85 10.6a Op. 10,3/II 1–9 2.17a ____/III 1–8 6.8 Op. 14,1/III 1–4 6.24b Op. 14,2/III 160–89 7.18b Op. 26/III 1–18 2.17b Op. 27,2 (Mondlicht)/I 1–5 6.16c ______ 48–49 7.95a1 ______ m. 58 9.5b Op. 28/I 77–91 8.36 _____/III 25–49 6.15a Op. 49,1/I 12–17 6.24c Op. 53 (Waldstein)/I bridge 6.7 Op. 54/II 130–3 8.13e Op. 57 (Appassionata)/I exposition bridge, 23–33 7.62d _____ 54 6.20b _____ 238 6.20a _____ 242–5 8.16 Op. 78/I 20–27 8.39c
249
Index of Musical Examples
BEETHOVEN, Sonatas (piano)–contd. Op. 81a (Les Adieux)/I transition from introduction 12–21 7.106c _____/I 47–49 7.79c _____/I dev. 7.106a-b Op. 90/II 41–43 7.6b _______ 261–7 8.23d Op. 101/II 1–7 7.44 ______/III 79–80 7.38a Op. 106 (Hammerklavier)/I bridge 5.13 Op. 109/II 42–57 10.16b Op. 109/III 103–4 10.15c Op. 110/I bridge 6.13d ______/II 45–47 3.14 Op. 111/I 5–11 8.33a Sonatas for Violin and Piano No. 6, Op. 30,1/III 198–220 8.45a No. 9, Op. 47 (Kreutzer)/III 100–52 4.17 ____ 317 7.31f Songs Mit einem gemalten Band, Op. 83,3 21–24 7.27a Vom Tode, Op. 48,3 15–17 10.9a Symphonies No. 2/I coda 8.33c ____/IV theme 7.110c No. 3 (Eroica)/I development 7.105 _____/III 236–8 6.3c No. 4/I 203–17 5.15 No. 5/IV 265–6 6.2c No. 6 (Pastoral)/I development 6.12c __________ 468–70 7.80b ________/IV 68–78 8.46 No. 7/I 142–51 6.21a ____/III 1–10 5.10b _______ 33–45 9.10 No. 8/I theme 7.67b
No. 9/I 142–43 3.12 __/II 117–26 3.11 ____ trio 466–75 7.16 Trio for Piano and Strings, Op.1,3 /I 294–99 10.14 32 Variations for Piano in C minor, WoO 80, Var. 9 3.8. Berlioz, Hector Benvenuto Cellini overture, 284–99 8.28d BRAHMS, JOHANNES Concerto for Violin and Cello, Op. 102/I 71–89 7.68c ____ 180–93 8.20g Fest- und Gedenksprüche, Op. 109. No. 2, mm. 36–41 8.19a Piano Works Op. 4 (Scherzo) trio No. 2 7.10c Op. 5 (Sonata no. 3)/V 9–10 7.40a Op. 24 (Variations and Fugue on a theme by Handel). Fugue, mm. 7–8 7.33c Op. 76,4 (Intermezzo) 7.113 Op. 116,1 (Capriccio) 7.109 Op. 116,3 (Capriccio) outer sections 7.112 Op. 116,6 (Intermezzo), mm. 13–14 8.9d Op. 118,3 (Ballade) 15–17 6.1c Schicksalslied 152–72 8.27b Sonatas for Violin and Piano No. 1, Op. 78/I m. 10 7.39f _____ bridge 7.3c No. 2, Op. 100/III 3–4 9.13e Symphonies No. 1/I 9–13 8.42d ____ 327–9 1.8b ____ retransition 7.21 No. 2/I 14–41 8.12 ______ 78–82 7.14b ______ coda 7.108b
250
Index of Musical Examples
BRAHMS, Symphonies—contd. No. 2/IV 7–24 6.12e No. 4/I theme 8.13f ___ 27–31, 113–17 6.26b Trio for Piano and Strings, Op. 87/IV theme 8.48a Variations on a Theme by Haydn Var. 7 7.84d Bruckner, Anton Symphonies No. 1 [Linz version]/III 25–44 10.10e No. 9/II 1–43 10.24c CHOPIN, FREDERICK FRANCISZEK Ballades No.1, Op. 23 27–28, 68–71 8.38f No.3, Op. 47 theme 7.77c __________ coda 7.77a No.4, Op. 52 92–99 8.36b Barcarolle, mm. 28–33 7.28d Berceuse, mm. 3–7 3.19 Bolero, mm. 155–72 4.23b Etudes Op. 10,3 22–42 7.29d Op. 10, 3 38–41 8.34c Op. 10,5 23–40 7.3d Op. 10,12 m. 28 10.1 Trois nouvelles Études No. 2 coda 61–63 7.47 Mazurkas Op. 17,2 43–49 9.9b Op. 17,3 17–25 8.9f Op. 24,2 75–88 6.21b Op. 50,2 1–8 7.2b Op. 59,2 97–101 7.97b Nocturnes Op. 9,2 3–4 7.68e Op. 15,2 middle section 7.71a Op. 27,1 m. 17 4.22c _______ 65–83 8.7g Op. 27,2 18–25 7.8d _______ 38–46 8.24c
Op. 32,1 m. 62 10.8b Op. 62,2 1–7 3.23b Polonaises Op. 26,1 33–41 7.99c _______ 54–56 6.25d Op. 26,1 58–65 8.47 Prelude Op. 28,9 m. 6 6.12d Scherzos No. 1, Op. 20 37–44 8.10f _____ 112–27 8.6a _____ 332–41 7.101a No. 2, Op. 31 53–56 7.54c _____ 265–74 9.21a _____ coda 736–55 7.39c Sonata No. 2/I 122–25 7.31e Waltzes Op. 34,1 1–17 7.8c Op. 34,3 9–17 7.28c Op. 69,1 55–6 7.76a2 Couperin, François Pièces de Clavecin 1, Ordre 3. La Favorite m. 3 7.76b3 Dvořak, Antonin Silhuoutte for Piano, Op. 8,5 40 Fauré, Gabriel Songs Arpège, Op. 76,2 7.78a Chanson, Op. 57,1 7.95b1 La fleur qui va sur l'eau, Op. 85,2 32–34 7.79f Mirages, Op. 113. No. 1–Cygne sur l'eau m. 10 6.9d Gluck, Christoph Willibald Orfeo ed Euridice/Aria: Che faró 7.24c Grieg, Edvard Lyric Pieces Op. 12,8 (National Song) 1–8 9.2 Op. 38,1 (Berceuse) 51–61 7.93a Stimmungen, Op. 73. No.5– Study, 8–15 10.22a
251
Index of Musical Examples
Halévy, Jacques François Fromental La Juive. Overture 107–29 8.4f Handel, Georg Friedrich The Messiah, No. 3—Every Valley Shall Be Exalted m. 39 7.6c Suites for Keyboard (collection 1), Suite No. 3/Prelude 7.99b /Allemande m. 18 6.9a Hassler, Leo Lustgarten. Chorale No. 24 1–12 4.13 HAYDN, JOSEPH Die Schöpfung. Die Vorstellung des Chaos 3–5 2.4 Quartets (Strings) Op. 20,2/I 64–76 8.10c ______/II 23–26 8.27a Op. 33,3/IV 59–62 6.25c Op. 55,1/I dev. 7.107a Op. 55,2/IV dev. 7.107b Op. 64,3/I 132–8 7.49 Op. 64,3/IV theme 7.50c ___ 35–59, 162–96 7.50a-b Op. 71,3/I coda 284–300 8.10e Op. 76,4/I 128–9 7.70a _______/II 70–71 8.38a Op. 76,6/II 74–80 7.42c Sonatas for Piano Hob. XVI:22/I 60–67 7.19f Hob. XVI:26/I 11–14 6.1b Hob. XVI: 32/III 147–50 6.23a Hob. XVI: 43/I 28–32 7.26a ________/III 50–56 6.15b Hob. XVI: 52/I 44–51 10.5a Symphonies No. 92 (Oxford)/I rcp. bridge 155–70 7.78f No. 94 (Surprise)/I transition from slow introduction 7.82b
No. 104 (London)/I retransition 97–98 7.75d4 ____/II exposition. bridge 7.104a _____ rcp. bridge 7.104b ________/III background 10.5c Humperdinck, Engelbert Hänsel und Gretel. Hexenfahrt 47–50 7.72 Liszt, Franz Blume und Duft (song), mm. 1–4 7.88d Piano Works Années de Pèlerinage. 2nd year. Sonetto 104 del Petrarca 1–5 7.92b Sonata in B minor introduction 8.34d ______ 415–31 7.74d Unstern 7.93b Mahler, Gustav Kindertotenlieder. No. 1—Nun will die Sonn’ so hell aufgehn 9.6 MENDELSSOHN, FELIX Die Hebriden 69–77 8.44d Die Hochzeit des Camacho, 247–63 7.27c Quartets (Strings) Op. 13/I beginning of dev. 85– 99 8.31a ______ 234–6 6.21d Op. 44,2/I 228–35 10.16c Quintet (Strings), Op. 18/I end of exposition 8.37f Songs Morgengruß, Op. 47,2 m. 30 7.54b Reiselied, Op. 34,6 45–48 7.15 Songs Without Words Op. 30,4 theme 7.67a Op. 53,1, mm. 1–24 7.65e Op. 62,1 4.21 Op. 62,3, mm. 21–26 8.26c
252
Index of Musical Examples
MENDELSSOHN, Songs without Words—cntd. Op. 67,1 18–23 8.5f Op. 102,2 8–9 1.6b Symphony No. 4 (Italian)/III trio 77–92 7.96b Trio for Piano and Strings, No. 1, Op. 49/I retr. + coda 9.5d _____/III 65–106 10.18a _____/IV 236–40 10.12e MOZART, WOLFGANG AMADEUS Adagio for Piano, K. 540 m. 30 6.4c Concertos for Horn No. 1, K.412/I 86–89 7.75c1 No. 2, K. 417/I 81–112 10.18b Concertos for Piano K. 491/I 220–40 8.31d K. 595/I 157–60 9.13b ______ 178–84 8.45b Operas Die Zauberflöte. No. 3—Dies Bildniss 1–6 5.6a ___ No. 15—In diesen heil’gen Hallen 1–2 6.22a Quartets (Strings) K. 421/I beginning of dev. 10.6b K. 464/I 1–37 10.4a ______ retansition 7.52e Quintets (Strings) K. 593/I transition to dev. 6.26c _____/IV 128–32 6.26d Rondo for Piano, K. 485 (esp. retr.) 4.19c; 6.23c Sonatas for Piano K. 280/I 13–17 7.4b K. 284/I 29–34 6.9b; 9.14b K. 331/III 3–4 9.14a K. 332/III 96–101 7.56 K. 333/I dev. 6.13c ______ 147–8 7.95a3 K. 533/II 63–71 7.46 K. 576/I 152–3 8.7d
Symphonies No. 35, K. 385 (Haffner)/I 1– 13 4.4b ____ 56–57 7.48b No. 36, K. 425 (Linz)/I 7.8a No. 38, K. 504 (Prague)/II 1– 35 10.4b No. 40, K. 550/I theme 5.6b ____ 150–52 7.74b Puccini, Giacomo Tosca. Act 1, scene 1 37–39 7.13b Ravel, Maurice Jeux d’eau, mm. 1–7 9.22b Rubinstein, Anton Das fallende Sternlein 29–34 8.3f Scarlatti, Domenico Sonata for Keyboard K. 471 51– 54 6.22b Schoenberg, Arnold Gurrelieder. No. 1—Nun dämpft die Dämmerung jeden Ton 6.24d Pierrot Lunaire. No. 8— Nacht, m. 8 3.24 SCHUBERT, FRANZ Dances for Piano Ecossaise D, 781,8, mm. 9–14 7.7 German Dance D. 783 (Op. 33),11 5–8 1.11 Impromptus for Piano D. 899 (Op. 90),1 18–20 8.8c ______,2 2.13a ______,3 40–46 8.6f Moments Musicaux for Piano, D. 780 (Op. 94) No. 2 1–36 6.19c No. 6 65–70 10.17 Quartet (Strings), D. 887 (Op. 161)/I bridge 7.92a Sonatas for Piano D. 279/I 104–13 9.18 D. 575 (Op. Posth. 147)/III middle section 6.13b
253
Index of Musical Examples
SCHUBERT, Sonatas (piano)—contd. D. 664 (Op. 120)/III 67–79 7.14c D. 784 (Op. 143)/I 158–60 7.5b D. 845 (Op. 42)/I 10–24 10.15b ____ bridges 7.17 D. 894 (Op. 78)/I 52–54 7.12b D. 958/IV 145–69 1.4 ______ 323–49 9.8c D. 959/I theme 1–13 7.31g ____ retr. m. 197 7.11 _____/II 73–83 7.39b D. 960/III 1–8, 77–84 7.8b Songs Daß sie hier gewesen, D. 775 (Op. 59,2), mm. 1–2 8.3c Die Wintereise, D. 911. No. 12—Einsamkeit 29–34 10.20b _____. No. 20—Der Wegweiser 41–67 8.29 Schwanengesang, D. 957. No. 5—Aufenthalt 51–55 10.24b _____. No. 11—Die Stadt 2.13b Wandrers Nachtlied, D. 224 (Op. 4,3) m. 2 7.5a Symphony No. 4 [Tragic]/I theme 30–39, 156–60 8.19c Trio for Piano and Strings No. 1, D. 898 (Op. 99)/I 207–18 7.111d Schumann, Clara Romance Op. 11,2 7.76a6 SCHUMANN, ROBERT Piano Works Albumblätter, Op.124. No. 9— Impropmptu, mm. 1–4 7.70e Album für die Jugend, Op. 68. No. 3—Trällerliedchen m. 1 2.16 Davidsbündlertänze, Op. 6. No. 6, mm. 41–48 8.9c
Fantasy Piece, Op. 12,2— Aufschwung 1–2 6.18a Faschingsschwank aus Wien, Op. 26/III 97–102 7.40b Humoresque, Op. 20 121–31 9.22a Kinderscenen, Op. 15 __. Nos. 2–5 7.114 __. No. 8—Am Kamin 9–16 7.51 __. No. 13—Der Dichter spricht mm. 10–12 8.11c Novelettes, Op. 21. __. No. 2 83–90 7.87c __. No. 3 42–45 6.26e __. No. 5 222–8 7.73d __. No. 8 1–4 8.25 Waldscenen, Op. 82 __. No. 1—Eintritt 8–17 7.82c __. No. 4—Verrufene Stelle 12–13 7.71e Quartet (Strings), Op. 41,3/I 1–11 9.15b ____/IV 236–81 9.16 Quintet for Piano and Strings, Op. 44/I 50–57 9.17b ____retransition 7.37b Songs Dichterliebe, Op. 48. No. 7— Ich grolle nicht 9–11 7.22d Frauenliebe und -Leben, Op. 42. No.2—Er, der herrlichster von Allen 28–31 7.39g Liederkreis, Op. 39. No. 8—In der Fremde 1–17 7.101b Symphony No. 1/II 10 9.5c Trio for Piano and Strings, No. 3, Op. 110/I 32–38 7.94 Skryabin, Alexander Enigme Op. 52,2 10.23 Mazurka for Piano, Op. 25,6 7–15 9.20b
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Index of Musical Examples
Skryabin, Alexander—contd. Preludes for Piano Op. 11,9 9.15a Op. 11,22 5–6 7.9d Strauss, Richard Der Rosenkavalier. Act 1, 1–5 after no. 42 9.17c Till Eulenspiegels lustige Streiche 46–49 10.24a __ 67–68 7.73c Stravinsky, Igor Concerto for Piano and Winds/I rehearsal number 11 3.18 Le Sacre du Printemps. Introduction 1–9 3.23a Tchaikovsky, Pyotr Il’yich Album for the Young No. 2—A Winter Morning 21– 38 10.11d No. 12—The Peasant Plays the Accordion 7.100 No. 19—Nursery's Tale 10.7c Orchestral Suite No. 3/II coda 278–321 10.19c Symphony No. 5/II 9.17c The Seasons. No. 1—January 47–53 10.13c Verdi, Giuseppe Otello. Act 4 23–26 7.12c
Wagner, Richard Die Meistersinger von Nürnberg. Act 2, scene 3 7.86 Der Ring des Nibelungen. Götterdämmerung. Prologue (Norns’ scene) 259–77 9.11 Parsifal. Prelude to Act 3 1–4 and background 8.50 8–43 8.13g Tristan und Isolde Prelude 3–4 6.26a ______ 79–89 3.25 Act 2, Scene 2, mm. 546–550 7.19h ____ 554–77 7.41d Act 3, Scene 1 3.7 Weber, Carl Maria von Der Freischütz No. 9—Terzett 10.19b No.10 (Act 2, Finale)/Die Wolfsschlucht scene 13–35 8.48b Wolf, Hugo Mörike songs No. 18—Citronenfalter in April 1–4 7.57b No. 22—Seufzer 1–10 10.7d No. 23—Auf ein altes Bild 1–4 9.19a Spanish Songbook. Spiritual Song No. 9—Herr, was trägt der Boden hier 1–6 7.48c
