THE BACH PRIMER
Music Theory Classes [Mathews] Peabody Conservatory • JHU
J.S. Bach's Clavier Figured Bass Instructions From the Anna Magdalena Bach Notebook in J.S. Bach's hand • 1725 Bach wrote these instructions into the notebook of pieces he composed for the keyboard instruction of his second wife. Bach intended them as instructions for realizing figured bass extemporare. This translation comes from an appendix to Spitta's The Life of Bach.1 A much better edition/translation of this and the primer assembled by Bach's students has been made by Dr. Poulin.2 In what follows, my comments are italicized. The examples to the right are mine. Whole notes illustrate a chord Bach describes, darkened notes illustrate a likely resolution. Several Rules of Figured Bass. 1.
Each chief note has a chord, either its own or borrowed. "Borrowed" chords are inverted chords.
2.
The proper chord of a fundamental note consists of the 3, 5, and 8. N.B. Of these species none can change except the 3, which may be great or small, according to whether the scale is major or minor. "Species" indicates the members of a chord (root, third, and fifth). The emphasis is original.
1
Philipp Spitta, The Life of Bach, Vol.3, trans. Clara Bell and J.A. Fuller-Maitland (London: Novello,1889.), 347-8. J.S. Bach. J.S. Bach's Precepts and Principles for Playing the Thorough-Bass or Accompanying in Four Parts: Leipzig, 1738, ed. and trans. Pamela L. Poulin (New York: Oxford University Press, 1994).
2
Voice Leading Notes: 2
3.
A borrowed chord is one which consists of species other than the ordinary ones, being placed over a fundamental note, as for instance: &c.
4.
5.
A or alone over a note shows that the third is to be major in the case of a sharp and minor in the case of a flat, the other two species remaining the same.
A 5 alone, as also an 8, betokes the full chord. Typically, a 5 or 8 is taken to indicate the soprano.
6.
A 6 alone may be filled up in three ways. 1st, with the 3 and 8; 2nd, with the doubled 3; and 3rd with the doubled 6 and the 3. N.B.: —Where 6 major and 3 minor occur together over a note, the sixth may not be doubled, because it would sound wrong; but the 8 and 3 must be played instead. Bach's warning about the major sixth and minor third cautions against doubling one of the tendency tones of a tritone: the root of a diminished chord. He indicates that the bass should be doubled (8).
Voice Leading Notes: 3
7.
2 over a note is accompanied with a doubled fifth, and sometimes also with 4 and 5 together... Of course, the doubled fifth would be the root of the chord. This formation is the first part of a 2-3 suspension (in the bass).
8.
The ordinary 4, especially when followed by a 3, is accompanied with the 5 and 8, but if there is a stroke through it the 2 and 6 are played with it. Naturally, a 4-3 suspension. However, the raised four indicates a 3rd inversion applied dominant. Note that the slash indicates raising the tone a halfstep..
9.
The 7 is accompanied in three ways: 1st, with the 3 and 5; 2nd with the 3 and 8; and 3rd, with the doubled 3. Three voicings. The first two are for all sevenths, complete and omitting the fifth, respectively. The third choice assumes a seventh that is suspended, since Bach never doubles the leading tone.
10. The 9 appears to have a similarity to the 2, and indeed by itself it is the 2 doubled, but it is accompanied in quite a different way— viz.: by the 3 and 5; instead of the 5 the 6 is put sometimes, but very rarely. A 9-8 suspension with a root position chord. Naturally, with the 6, the chord would be a first inversion chord and the suspension, while still 9-8 above the bass, would actually be 4-3 against the root. This is, as Bach notes, quite rare.
11.
The takes the 6 as well, and sometimes the 5th in its place. The first instance is the seventh chord in third inversion. The second instance is a 4-3 suspension.
Voice Leading Notes: 4
12.
13.
With the the 8 is taken, and the 4 resolves into the 3.
With the the 3 is taken, whether it be major on minor.
14. With the the 3 is taken.
15. With the
the 3 is taken.
The other points which ought to be remembered are better conveyed by word of mouth than in writing.
Voice Leading Notes: 5
BASIC NOTES ON CHORALE VOICE LEADING
Music Theory Classes [Mathews] Peabody Conservatory • JHU
ELEMENTS OF CHORD VOICING IN THE CHORALE STYLE The Voices, Their Ranges •
• •
• •
We think of harmony in four voices; we should always remember the four voices were actually choral voices (soprano, alto, tenor and bass or "SATB"), but the designation "voice" has come to mean a moving line that is part of the harmony. Frequently, we refer to the soprano and bass as the "outer voices" and the tenor and alto as the "inner voices." In chorale style, the voices are mostly kept in a specific range: 4 5 o The soprano goes from C to G 3 5 o The alto goes from F to C 3 4 o The tenor goes from C to G 2 4 o The bass goes from F to C In actual chorales, Bach may occasionally exceed these ranges. Moreover, textbooks may give larger or smaller ranges. These ranges reflect the practice in most of the chorales. Naturally, when composed, the chorales were notated on four staves like most choral music. For the sake of convenience, the voices are notated on a grand staff (like a piano): the outer voices have stems pointing down; the inner voices have stems pointing up.
Chord Spacing • • •
•
There can be no more than an octave between the three upper voices (soprano, alto, and tenor). However, the tenor can be as much as two octaves higher than the bass. Voices cannot cross: for example the tenor cannot go above the alto. Keep in mind a distinction between open chords and close chords: o Open chords are spaced such that a chord tone could be placed between any two voices. o Closed chords have the chord tones as close a possible o Some sources call a chord "close" if the upper three voices are close and the bass is lower. Open chords are preferred because they allow for more possibility of movement.
Rhythm • • • • •
Chorale melodies use mostly quarter notes. Quarter notes are frequently subdivided into two eighth notes. Dotted rhythms are used. Half notes occur at cadences. There is a prevailing macrorhythm of quarter notes.
Voice Leading Notes: 6
Line • • • •
The line is balanced, resembling an arch. Stepwise motion predominates, made possible by a liberal use of passing tones. Leaps are balanced by stepwise motion in the opposite direction. The octave is frequently used in the bass to change the register and to accentuate cadences.
Cadences • • • • • •
Half cadences and authentic cadences predominate. A half cadence (HC) will have SD5 in the bass and SD5, SD7, or SD2 in the soprano. An imperfect authentic cadence (IAC) will have SD1 in the bass and SD3, or SD5 in the soprano. A perfect authentic cadence (PAC) will have SD1 in the bass and SD1 in the soprano. The soprano moves to the cadence by step, the bass leaps down a fifth (or up a fourth) to the cadence. Direct motion to fifths or octaves frequently happens at a cadence.
Intervals • • • • •
Every beat has a consonant interval, usually occurring on the strong half of the beat. Occasionally the consonant interval is displaced to the weak half of the beat by accented non-harmonic tones. Thirds (tenths) and sixths predominate. Fifths occur frequently; except at cadences, they are approached by contrary or oblique motion only; never by parallel motion. Octaves are used less frequently. When they occur in a phrase (between cadences), they will be part of a characteristic 10-8-6 voice-exchange.
The Figures in Figured Bass • • •
•
The figures indicate the chord tones above the bass. Each figure is a diatonic distance above the bass; a sixth above the bass is six note classes (or letter names); the quality is not indicated by the figures (i.e., major or minor). The figures indicated the exact distance for a close position chord. In actual practice, the chord tones may appear in any order above the bass and at any distance (within the guidelines of good chord spacing). For example, a six-five-three chord may be voiced with the sixth above the bass, the third a tenth above the bass, and the fifth a twelfth above the bass. The chart below lists the figures, their common forms, and the notes that can be doubled. For examples of the figures and a treatise by J.S. Bach, see the Bach's Primer (also on the class page).
Voice Leading Notes: 7
Common Figure 5 3 6 3
Actual Figure
Notes 3rd cannot be doubled if the bass note is SD5; it is the leading tone (SD7).
—
Bass
5th
3rd
6
6th
3rd
Bass
—
Bass
5th
The seventh can never be doubled. If occurring over SD5, neither the 7th nor the 3rd can be doubled.
—
—
6th
If bass is SD7, neither the bass nor the 5th can be doubled.
—
—
4th
If the bass is SD2, neither the 3rd nor the sixth can be doubled.
—
—
2nd
Bass cannot be doubled. If bass is SD4, 4th cannot be doubled.
Bass
—
—
4th is never doubled.
Bass
—
—
4th is never doubled.
Bass
—
—
9th is never doubled.
7 5 3 6 5 3 6 4 3 6 4 2 6 4 5 4
7 6 5 4 3 4 2 6 4 4 9
Best Note to Double Best Second Third
9 9 5 or 6 3 3
Cannot double the bass if the bass is SD7.
———— C H R O M A T I C
M A T E R I A L S —————
I
[7] 5 3#
Bass
5
—
Raises the third of a chord one half step: useful for dominants in minor keys and applied dominants. Frequently occurs under the 7 in applied dominants.
b
5 3b
Bass
5
—
Lowers the third one half step. Mostly found in minor. It may also appear before or after another figure (e.g. b7 ).
n
[7] 5 3
n
Bass
5
—
Raises the third of a chord: useful for minor keys and applied dominants. Frequently occurs under the 7 in applied dominants.
+
Any
—
—
—
\
Any
—
—
—
Raises any figure it appears after one half step. Not typically used with three. Raises any figure it appears through one half step. Typically appears though 6 or 2.
GUIDELINES FOR GOOD VOICE LEADING Following is a list of guidelines for Voice Leading. Some of these guidelines have exceptions that will be explored later. For now, these guidelines represent the safest choices. •
Observe the "law of the shortest way." When moving from chord to chord, move the voices to the nearest chord tone; keep all common tones.
Voice Leading Notes: 8
• • • •
No parallel fifths or octaves between any of the voices. No parallel fifths or octaves by inversion (or "anti-parallels") between any of the voices. Parallel fifths occur in root position chords, particularly when there are two root position chords in a row. Parallel octaves can occur between any two chords with doubling. If a tritone appears in a chord, neither of the The Most Common Errors, notes of the tritone can be doubled. The tritone In Decreasing Severity: must resolve by stepwise motion: an A4 resolves ———————————————— • Parallel Fifths and Octaves out, a D5 resolves in. The following diatonic • Resolution of Tendency Tones chords contain tritones: • Chord Missing Third or Root — a seventh chord built on SD5; • Chord Choice Weak Progression • Bad line or Use of Non-Harmonic Tones — a six-five chord built on SD7; • Hidden Fifths and Octaves — a four-three chord built on SD2; • Voice Crossing and Overlap • Spacing — a four-two chord built on SD4. In each of these chords, the tritone is between SD4 and SD7 (the leading tone). SD7 must resolve up to the tonic; SD4 must resolve down to SD3.
•
Because the leading tone (SD7) resolves up to the tonic, it cannot be doubled. In addition to the previously named chords, where SD7 appears as part of a tritone: — SD7 also appears in the 5-3 chord built on SD5; and — SD7 appears in the 6-3 chord built on SD7 (the leading tone as the bass). In these two chords, SD7 cannot be doubled. — Finally, the leading tone also appears in the 6-3 chord built on SD2; it cannot be doubled in that chord either. However, in this chord, the tritone can resolve freely, with SD7 resolving up to tonic and SD4 resolving up to SD5. This is the only chord where the tritone resolves freely. — In short, SD7 can only be doubled when it appears as the 5th of the 5-3 chord built on SD3 or in the rare case of a 6-3 chord built on SD5.
•
In general, open spaced chords allow for more possibilities than close space chords.
Voice Leading Notes: 9
•
Passing tones are the most common accidentals, and may appear on the beat or off the beat. Neighbor tones also occur with regularity. Appoggiaturas and escape tones appear less frequently.
NON HARMONIC TONES •
•
•
•
Passing Tone (PT): o Dissonant step (or steps) between two consonant tones; approached and left in the same direction. o PT fills in a third, or a pair of PTs fill in a fourth (as in SDs 8-7-6-5). o Passing tones can be accented (APT) or unaccented (UPT); unaccented are far more common. Neighbor Tone (NT): o Dissonant step above or below a consonant tone. o Lower neighbors are more common. o A complete NT (returns to the note from which it approaches) is typically in a weaker metrical position. Anticipation (A): o The same pitch as its following harmonic tone, thus anticipating the note of resolution. o It is commonly in the soprano voice. o Frequently used at authentic cadences. Suspension (X-Y figures above bass): o A three-part pattern: preparation, suspension and resolution. o The preparation is always on a weak beat: it is the same note that is suspended. The preparation is still consonant on the weak beat; it's not dissonant until the suspension. o Resolution is always down by step. o In vocal (choral) style, preparation is as long as suspension o 4-3: suspended note is a fourth above the bass and resolves to a third. o 7-6: suspended note, a seventh above the bass, resolves into an inverted triad: to the root of a first inversion triad or, less commonly, to the third of a 6-4 chord. o 9-8: suspended note resolves to an octave doubling of root position triad. o 2-3: a bass suspension, where the bass resolves down by step to form a third (tenth) above a higher note.
Voice Leading Notes: 10
FIGURED BASS
Thorough Bass or Figured Bass is the principle of determining the members of a chord over the lowest note, or bass note. To some degree, figured bass is a method of notation that makes possible the practice of extemporizing a keyboard part. However, the principle of figured bass as a harmonic system is deeply ingrained in the practice of composers. By the start of eighteenth century, there were many manuals that taught the figures of figured bass. These manuals were written primarily for keyboardists. Every musician alive during the Baroque period was thoroughly versed in the principles of figured bass. We know that J.S. Bach taught figured bass to his keyboard students and that he wrote a primer on figured bass when teaching his second wife, Anna Magdalena Bach. However, figured bass also shaped the instruction of composition. For example, there are many examples of fugue exercises that begin with the subject and countersubject followed by a long figured bass. In these exercises, such as the ones Handel wrote for Princess Anne, the student had to complete the fugue following the figures.
FUNDAMENTAL BASS
MUSIC THEORY ONETWO 710.111.10 [Mathews] Peabody Conservatory / JHU
The number of chords represented by figures more than doubled in the first half of the eighteenth century. Many theorists were seeking ways to better organize the chords represented by the figures. A breakthrough came in 1722 with the publication of Rameau's Traité de l'harmonie. In this famous treatise, Rameau argued that there were only two kinds of chords: triads and seventh chords. All other chords represented by figures were simply inversions of these two basic types, or chords that were decorated by controlled dissonance (e.g. a suspension). Rameau suggested that the progression of chords in music moved primarily by fifths and underneath all chords a hypothetical fundamental bass could be constructed to show the actual roots of the chords (as opposed to the bass notes). While this may seem a fanciful observation, it is the very thing we do when analyze music with Roman Numerals. Rameau's ideas met with opposition in some parts of Germany and were the source of some notable debates. It is unclear whether Bach new Rameau's work, but he had some familiarity with the concepts.
SPECIES COUNTERPOINT
PEDAGOGICAL APPROACHES TH TO 18 CENTURY COUNTERPOINT
In 1725, Johan Joseph Fux published Gradus ad Parnassum a wholly unique approach to counterpoint. Fux, who was trying to model the counterpoint of Renaissance composers, suggested that all counterpoint was best learned in a series of steps, or species. In the first species, one note of counterpoint is set against one note of a cantus firmus, or given line. In second species counterpoint, two notes are set against one note of the cantus firmus. Fux's text was not influential for Baroque composers. However, it was the single most-important textbook on counterpoint for the Classical and Romantic periods. Haydn, Mozart, and Beethoven all learned and taught species counterpoint. The advantage of species counterpoint is that it is very easy to teach and learn. The disadvantage is that it tends to produce slightly artificial compositions that little resemble either the Baroque or Renaissance composers. In the late 20th century, species counterpoint was emphasized in music theory because it tends to prepare the student for an understanding of Schenkerian Analysis.
