REFERENCE - Social Sciences at Hunter College (CUNY)maxweber.hunter.cuny.edu/pub/eres/MUS724_BURSTEIN/Reference.pdf · page 30 Reference Harmony and Figured Bass HARMONY AND FIGURED

REFERENCE

INDEX

Accidentals in four-part harmony, 49 Antecedent-consequent, 65 Apparent seventh chords, 52 Applied Chords, 47, 48 Augmented-six chords, 51 Binary form, 69ff. Cadences, 66 Cadential six-four, 35 Charting Phrases, 66 Choral style, 31 Chord Doublings, 52 Chord Repetition, 46 Consonance and Dissonance, 54 Consonant Three-Part Sonorities, 54 Dominant "13th" chord, 37 Dominant chord with altered fifths, 38 dominant functions, 37 Double-Neighbor Figure, 61 Ending fourth or fifth species

counterpoint, 64 Expansion of phrases, 67 Fifth-Species Counterpoint, 62 Figured Bass, 30 First-Species Counterpoint, 58 Forephrase-afterphrase, 65 Form, 65 Fourth-Species Counterpoint, 61 Harmony and Figured bass, 30 keyboard style, 31 Koch, 66-67 Labeling a Species Counterpoint

Exercise, 57 Leading tone, 32 Melody Rules For Species Counterpoint,

56 Mixture, 46 Modulations, Tonicizations, and Pivot

Chords, 49

Neapolitan 6 Chord, 50 Normal Progressions, 44 Normal Uses of Diatonic Chords, 43 Parallel octaves, fifths, or unisons, 32 Period, 65 Phrases and other groupings, 65 Plagal Use of IV, 41 Rondo form, 74 Second-Species Counterpoint, 59 Sentence structure, 65, 66 Sequences, 45 Sonata Form, 72 Species Counterpoint, 53 Subphrase, 65 Ternary form, 71 Third-Species Counterpoint, 60 Unusual Diatonic Chords, 42 V 4-3, 36 V 8-7, 33 V of V (V/V 48 V6 and Vyg , 34

VI Chord, 39 vii ∅7, 37 vii o 7, 37 Voice-Leading Rules, 32 V4/3 and viio6, 35 I, I6, and V chords, 33 II , 38 II7 and IV7, 39 III chord, 41 IV and II6 chords, 38 IV6 Chord, 40 V chord, 33

page 30 Reference Harmony and Figured Bass

HARMONY AND FIGURED BASS

Figured Bass

Figured bass is a notation used to indicate chords that was developed by composers and music theorists of the Baroque era. A figured bass symbol indicates the appropriate intervals (or their compound equivalents) above the bass. Thus, for instance, the figures: 7 4 2

Indicate one should play a 7th, 4th, and 2nd above the bass (or their compound equivalents, such as an octave plus a seventh or two octaves plus a seventh).

Sometimes a type of shorthand is used to indicate the notes to be played in a

figured bass. According to this shorthand (which must be memorized):

This figure: is shorthand for:

[nothing underneath the bass]; 5; 3; 8 or any combination of these three numbers

5 3

6 6 3

6 5

6 5 3

4 3

6 4 3

4 or 2 2

6 ( remember: don’t double the bass, since there is a “2” 4 among the figures) 2

4 5 4

7 7 [BUT SEE 7 6 below!] 5 3

7 6 7 6 3----- (note: 7/3 chord does not have a 5th above the bass with a 7-6!)

9 9 5 3 (note: 9th of chord must be at least a 9th above the bass and

also a 9th above any doubling of the bass) # 5

#3 4 # 5 -------

4 #3 (note: 4 # does not equal #4! Students often seem to make careless mistakes with this figure!)

6 #

6 #3


8 7 8 --- 7 ( 5 ------) 3 -------

5 2

5 (remember: don’t double the bass!) 2

Note that any accidental (sharp or flat) in front of a number alters that interval above the bass. Thus, for instance, a “#6” means to sharp the 6th above the bass. An accidental alone refers to a third above the bass. A dash in a figured bass symbol means “move the bass only, keep the upper voices stationary.” Usually, a dash is used when the bass line is a passing tone or when the bass line moves by arpeggio.

Doubling in realizing a figured bass: Often a tone will need to be doubled when

realizing a figured bass in four-part harmony. In most such cases, the leading tone should not be the tone that is doubled, nor (in most cases) should a chromaticized tone be doubled. Also, one should not double a dissonance (a seventh above a bass, for instance, is almost always a dissonance). Usually, it is a good idea to double the bass; however, the bass should not be doubled the bass if the number “2” is among the figures (since the bass will be a dissonance), nor should the bass be doubled if it is the leading tone.

Choral style and keyboard style

In four-part choral style format, the treble and alto voices are always written in treble clef, and the tenor and bass are always written in bass clef. The soprano and tenor are always stemmed up, and the alto and bass are always stemmed down. The soprano and alto should be within an octave of one another, and the alto and tenor should be within an octave of one another.

In keyboard style format, the top three voices are all written in the treble clef and there

should be no more than an octave between the alto and tenor (if there were more than an octave, the stretch would be too great for the pianist’s right hand). When there are two different rhythms in the same hand at the same time in keyboard style, they must be stemmed in opposite directions. The example shown in (a) below looks amateurish; it looks as though all of the notes on the downbeats are only an eighth note long. The example in (b) is much better.

(a)

(b)


Basic Voice-Leading Rules for harmony and figured bass exercises (see Aldwell-Schachter, pages 63-77).

Main rules:

(a) Don’t have parallel octaves, fifths, or unisons. Also, note that a perfect fifth may move to a diminished fifth, but a diminished fifth may not move to a perfect fifth.1

(b) Don’t double the leading tone.

(c) Chordal dissonances should resolve down by step and not be doubled. Examples of chordal dissonances include sevenths of seventh chords and the fourth above the bass of a cadential six-four.

(d) Use the proper tones of a chord, with proper accidentals. Remember that

scale-degree 7̂ must be raised to create a leading tone in minor keys. The root or third of a chord may not be omitted.

Secondary rules (a) Use the proper range, avoid notes needing more than one ledger line. (b) Use proper spacing. In chorale style, you should not have more than an octave

between adjacent upper voices. In keyboard style, the upper voices should be within an octave of one another.

(c) The upper voices should move smoothly. The bass voice can leap large intervals (though the bass should not leap the interval of a seventh). However, the upper voices usually do not move more than a third when one chord moves to another chord. (The upper voices usually leap only if there is a chord repetition or in other special circumstances.)

(d) Do not use augmented melodic intervals. In particular, avoid leaping an augmented fourth (even in the bass voice) and avoid moving an augmented second (an interval which may accidentally crop up in between scale degrees ^6 and ^7 in minor).

(e) Avoid hidden fifths or octaves in between the outer voices if the upper voice leaps. Other instances of hidden fifths and octaves are not that faulty. (A hidden interval occurs when the interval is approached in similar motion; a hidden interval is also referred to as a similar or direct interval.)

(f) Usually the bass of a chord should be doubled. If the chord is in first inversion, any voice may be doubled. However, leading tones or dissonances should never be doubled, even if they are in the bass.

(g) Avoid overlap and voice crossing.

1 The only time a diminished fifth may move to a perfect fifth is when a viio6 or V4/3 moves to a I6.


I, I6, and V chords (See Aldwell-Schachter, pp. 81-99.)

Basic Outline: The I and V are the most basic harmonies. The V chord resolves to a I.

Main Uses:

(a) The I and I6 are chords of tonal resolution. A root position I chord should appear at the end of a harmony exercise and at its main cadence points. The I6 can substitute for I in other places in order to provide variety in the bass line.

(b) A V chord resolves to a I or I6 chord (not to a I 6/4 chord!). Specifically, a V chord should (i) resolve to a I or I6; (ii) be followed by another V or similar chord; or (iii) more rarely, a root position (not inverted) V or V7 may move to a root position VI. A V, V7, or similar chord may not move to any other chord.

(c) When a V or V7 resolves to a I, the leading tone (scale degree 7̂, the third of the V chord) must resolve up to the tonic if it is in the soprano voice. If the leading tone is in an inner voice, it need not resolve up to tonic.

(d) A V7 functions in a manner similar to a V triad, except that it is a bit more intense. A V7 is too unstable to appear at a half cadence. The seventh of the V7 (the subdominant scale degree) must resolve down by step to the third of the I chord (the mediant scale degree). V7 may not resolve to a I6.

(e) The fifth of the I, V, or V7 may be omitted. The roots and thirds of these chords may not be omitted, however.

(f) It is most normal to double the bass of the I and V chords. Do not double the

leading tone (7̂, the third of the V chord).

V 8-7

Basic outline: A V 8-7 is simply a V triad moving to a V7 chord. (See Aldwell-

Schachter, p. 90.)

Main uses:

(a) A V triad often is followed directly by the V7 chord. By contrast, a V7 chord almost never moves to the less intense V triad.1

(b) The progression “ V– V7 ” is often written as “ V 8-7 .”

(c) When moving from the V triad to a V7, only one note moves: that is, the root of the chord in an upper voice (not in the bass) moves to the seventh of the chord. (It is also possible for the fifth of the chord to move to a seventh of the chord.) All the other notes can stay the same.

1 This is also true for inversions. That is a V triad in inversion might move to a V7 chord or V7 chord in inversion, but V7 chord or V7 chord in inversion does not progress to a V triad in root position or inversion.


V6 and V y gy g Basic Outline: The V6 and V6/5 are the first inversions of the V and V7 chords, respectively. (See Aldwell-Schachter, pp. 100 ff. and 111.)

Main Uses:

(a) The V6 and V6/5 are used in place of the root position V and V7 in order to create variety in the bass line. These chords function like a V, though they should not be used at important cadences.

(b) V6 and V6/5 resolve to a I chord in root position. (They should not resolve to a I6 chord!)

(c) The V6 and V6/5 can readily interchange with a root position V chord. Thus, for instance, one can have the progression I-V6-V-I or I-V-V6-I.1

(d) Any predominant chord (such as a IV, II, or II6) can move to a V6. Do not leap an augmented fourth in the bass when you approach the V6 or V6/5 (augmented fourths can arise, for instance, when a IV or II6 moves to a V6).

V4/2

Basic Outline: The V4/2 is a third inversion V7 chord, respectively. (See pp. 114-15)

Main Uses:

(a) The V4/2 is sometimes used in place of the root-position V7 in order to create variety in the bass line. This chord functions like a V, but should not be used at important cadences.

(b) The V4/2 resolves to a I6 chord (that is, a I in first inversion), since the chordal seventh (which is in the bass) must resolve down by step. The Vrs thus should not resolve

to a I chord in root position!

(c) The V4/2 can (and often does) follow a root position V chord. Thus, for instance, one can have the progression I-V- V4/2 -I6. A V chord cannot follow a V4/2, however; thus, for instance, the progression I- V4/2 -V-I is faulty.

(d) Any predominant chord (such as a IV, II, or II6) can move to a V4/2.

1 Remember, however, that one can move from a triad to a seventh chord but not from a seventh chord to a triad.


V4/3 and viio6

Basic Outline: The V4/3 and viio6 function as dominant chords, usually along with a passing motion in the bass from I to I6 (See Aldwell-Schachter, pp. 112-13 and 101-5).

Main Uses:

(a) The V4/3 and viio6 are used in place of the root position V and V7 in order to create variety in the bass line. These chords function like a V, though they should not be used at important cadences.

(b) These are relatively weak chords and are usually found in weak rhythmic positions.

This is largely because the tone of the V chord with the weakest pull, scale-degree 2̂ , is in the bass.

(c) These chords rarely interchange with other inversions of the V chord. Thus, for instance, one rarely finds a V4/3 or viio6 followed by a V7 or a V7 followed by a V4/3 or viio6.

(d) The V4/3 and viio6 move directly to a I or I6, usually with a passing motion in the bass (as in the progressions I- viio6 -I6 or I6- viio6 –I6).

(e) The melodic succession 3̂- 4̂- 5̂ is often harmonized with the progression I- V4/3 -I6 or the progression I- iio6 -I6.

(f) Any predominant chord (such as a IV, II, or II6) can move to a V4/3 or viio6.

(g) In an exception to an otherwise rarely broken rule, a diminished fifth may move to a perfect fifth when a V4/3 or viio6 moves to a I6.

(h) When the V4/3 and viio6 move to a I or I6, the upper voices almost invariably resolve in a stepwise fashion. In an exception to an otherwise rarely broken rule, when a V4/3 moves to a I6, the 7th of the V4/3 need not resolve down.

Cadential 6/4

Basic outline: The cadential six-four is a chord that contains the notes of a I chord in second inversion and functions as a suspension chord that decorates the V chord.

Main uses:

(a) The notes of a tonic chord in second inversion form a cadential six-four chord.

(b) Almost invariably, in four-part harmony the bass of this chord is doubled Do not double the fourth above the bass (that is, do not double the root of the chord).

(c) The cadential six-four resolves directly to a V or a V7 in root position.

(d) The cadential six-four is often called a V6/4. This term does not imply that the chord is a V chord in second inversion, but rather a implies that the chord involves

intervals of a fourth and a sixth above scale-degree 5̂ in the bass.


(e) The cadential six-four never follows a V, V7, or inversion of V or V7 (or similar chord).

(f) The cadential six-four always appears on a metrically stronger beat than the V or V7 that follows it.

(g) Normally in moving from a cadential 6/4 to a V chord, the notes either are repeated or move down by step (in particular, the fourth above the bass should move down by step, and not up). In moving from a cadential 6/4 to a V chord, the bass either is repeated or else leaps an octave.

ü Summary of the rules for the normal use of a cadential six-four:

Ø The cadential 6/4 should always go to a root position V or V7 chord.

Ø The cadential 6/4should not follow a V or V7 chord.

Ø The cadential 6/4 always appears on a relatively stronger beat than the following

V or V7.

Ø The fourth above the bass in a cadential 6/4should resolve down by step.

Ø Double the bass of a cadential 6/4

V 4-3

Basic Outline: The V4-3 is a V chord decorated by a suspension in which a dissonant 4th above the bass resolves down to a 3d above the bass.

Main uses:

(a) The V4 chord (sometimes called a V sus chord) consists of scale degree 5̂ in the bass,

with scale degrees 1̂, 2̂ and 5̂ in the upper voices (note that in four-part harmony, the

note in the bass of the chord is doubled). The V4 chord is also known as the V 54 chord.

(b) The V4 chord must resolve directly to a V5/3 chord. Since these chords always come

as a pair, the chord progression V4 - V5/3 is labeled V4-3. It can also be labeled

as V 54 _

3

(c)The V4 chord must be on a metrically stronger position than the following V5/3 chord.

(d) In moving from the V4 chord to the V5/3 chord, the 4th above the bass resolves down to the 3rd above the bass.


Other chords that have dominant functions

In addition to V7, inversions of V and V7, and VII6, the following chords function like a V. In other words, they resolve to I, they may be preceded by a predominant, and they may at times interchange with other chords that are similar to V.

vii o 7 (see Aldwell-Schachter, pages 368-72) (a) A common V-like chord is the diminished chord based on the leading tone (one half

step below tonic), which may be used in both major and minor keys in root position and inversions (though it rarely appears in third inversion).

(b) When this chord resolves, care must be taken not to have a diminished 5th move to a perfect 5th.

(c) The seventh of the vii o 7 chord must resolve down by step. Often, it is necessary to double the third of the following I chord in order to avoid voice-leading problems

(d) A vii o 7 may function as an applied chord to any major or minor chord, in which case its root must be one half step below the chord to which it is applied.

vii ∅∅ 7 (vii half-diminished 7) (see Aldwell-Schachter, pages 375-76) This chord functions just like the vii o 7, except that it is used only in major keys and can function as an applied chord only to major chords. V9 and V9-8 (see Aldwell-Schachter, pages 441-45) (a) These chords involve a V7 chord with an added 9th or 9-8 suspension above the root. (b) The chordal ninth should resolve down by step (c) It is important that the ninth of the V9 or V9-8 chord must be at least a ninth above

any root of the chord. (This is true even if the ninth chord is in inversion or if the root of the chord is doubled).

(d) In four-part harmony, it is necessary to omit the 5th of the V9 chord. “Dominant 13th” chord (Aldwell-Schachter, pp. 449-50): This exotic chord may be found in a number of 19th-century compositions. A “dominant 13th chord” is a dominant seventh chord with a sixth above the bass instead of a fifth above the bass.1 The sixth above the bass must resolve down to the tonic; the seventh of the chord must resolve down by step. Usually the sixth above the bass is in the soprano.2 Dominant chord with altered fifths (Aldwell-Schachter, pp. 514-15): In particularly

exotic instances, the fifth of the V or V7 chord (that is, scale-degree 2̂) may be lowered or raised. When a dominant seventh chord with a raised fifth resolves, often the third of the

following tonic chord will often be doubled, because the raised fifth (scale-degree 2̂) must resolve up (to a major third above tonic). In a dominant with a lowered fifth of the

chord, the lowered fifth (scale-degree b2̂) must resolve down to the tonic.

1 For instance, a dominant 13th in C major would be G-B-E (not D) F. 2 Do not confuse this term with a 13th chord of jazz terminology, which would involve a chord of six stacked thirds.


IV and II6 chords Basic outline: The IV and II6 chords are predominant chords; that is, they help lead to a V or similar chord. (See Aldwell-Schachter, pp. 123-35.)

Main uses:

(a) The IV and II6 are similar to each other; they both lead to a V, V7, or to an inversion of a V or V7 (as in the progressions I-IV-V-I or I-II6-V-I).

(b) With both the IV and II6, the bass of the chord will usually be doubled.

(c) When a IV or II6 moves to V, the bass moves up by step and usually each of the upper voices each either stay on the same note or else they move down to the nearest note of the V chord. Indeed, usually when the bass of a chord moves by step, the upper voices normally move in opposite motion from the bass! (This is in order to avoid parallel fifths or octaves).

(d) The IV and II6 can interchange with one another; as in the progression I-II6-IV-V-I or the progression or I-IV-II6-V-I.

(e) The figured bass symbol “5 6” underneath a single bass tone means move from a 53

chord to a 63 chord; The figured bass symbol “6 5” underneath a single bass tone

means move from a 63 to a 53 chord. You will often find these symbols when there is an interchange between IV and II6.

II 53 (See Aldwell-Schachter, pp. 125-26.)

Basic outline: The II chord is a predominant chords; that is, it leads to a V, V7, or similar chord. The II in root position is less common than a II6 or IV.

Main uses:

(a) The II leads to a V, V7, or similar chord, as in the progressions I-II-V-I or I-II-V7-I.

(b) Normally the bass of the II chord is doubled.

(c) The II chord can follow a I or it can follow a IV or II6. Note that while it is common to follow a IV or II6 with a II, it is not common to follow a II with a IV or II6. Indeed, it is far more common for a bass of a chord progression to move down by a third than it is for a bass of a chord progression to move up by a third. Thus, for instance, the progressions I-IV-II-V-I or I-II6-II-V-I are quite common. On the other hand, The progressions I-II-IV-V-I or I-II-II6-V-I are rare.

(d) A II td rarely occurs in minor keys unless it follows a IV or II6 (see p. 126).


II7 and IV7 (and their inversions)

Basic outline: The II7, IV7, and their inversions function as predominant chords. The seventh of the II7 and the IV7 should resolve down by step. (See Aldwell-Schachter, pp. 162-70.)

Main uses:

(a) The II7, IV7, and their inversions function in a manner similar to the II and IV triads and their inversions. That is, they lead to a V, V7, or to an inversion of a V or V7.

(b) The II6/5 is an extremely popular chord and is often used in cadential progressions.

(c) The upper tones of the II7, IV7, and their inversions usually resolve stepwise when moving to a V. When moving from a IV7 to a V, however, often one must leap in an inner voice to avoid a voice-leading problem (see Aldwell-Schachter, p. 175, Example 12-18 a and b).

(d) It is important to be vigilant in setting a IV7-V progression; when setting this progression, take special care that you do not have parallel fifths, a doubled leading tone, or an unresolved seventh.

VI Chord

Basic outline: The VI chord functions as a predominant. It often follows a I chord, but can follow a V in a deceptive cadence or in a similar progression.

Main uses of VI: (See Aldwell-Schachter, pp. 150-54)

(a) The VI chord can move to V as part of a I-VI-IV-V or I-VI-II6-V progression (creating a brief descending arpeggio motion in the bass).

(b) The III chord moves to V as part of a VI-II-V progression (creating a cycle of fifths progression leading to the dominant chord.

(c) In rare instances, a VI can move directly to a V, V7, V6 or V6/5 chord.

(d) In its main uses, the VI chord always appears as a root position chord.

V-VI (See Aldwell-Schachter, pp. 185-88)

(a) Sometimes a root position V or V7 will move to a root position VI. (Of course, normally a V will move to a I or I6). If a V or V7 moves to a VI at a cadence, this progression forms what is known as a “deceptive cadence.” Note: in this progression, both the V and VI chords must be in root position!

(b) In a typical four-part harmony setting of the V-VI progression (or V7-VI progression), two voices move up, two voices move down, and the third of the VI chord is doubled. Note the unusual features of this special progression: in most other progressions when the bass ascends by step, all the voices will move in


opposite direction.1 Also, in almost all other progressions, one avoids doubling the third of a root position chord. This special treatment of the V (7)-VI progression should be memorized.

(c) After the V or V7 moves to a VI, the VI chord then proceeds in a normal fashion to a IV-V, II6-V, II-V, or even (though rarely) directly to a V or inversion of a V.

IV6 Chord

Basic outline: The IV6 chord functions as a predominant. It functions much like a VI chord, except that a IV6 can more easily move straight to a root position V chord (without creating parallel fifths) than can a VI chord.

Main uses of IV6: (See pages Aldwell-Schachter, pp. 155-59.)

(a) The IV6 chord can move to V via another predominant chord (such as a II6 or a IV) or it can move straight to a V chord.

(b) The IV6 often moves straight to a V, V6, V7, or V6/5 chord.

(c) The IV6 often follows a I. It also often follows a VI (the progression I-VI-IV6-V is quite common).

(d) A Phrygian cadence occurs when IV6 moves to a root position V at a cadence in a minor key.

(e) A IV6 does not normally decorate a I chord in the same manner that a IV chord decorates a I (see below regarding “Plagal Use of IV”). That is, though I-IV-I is common (see below) a I-IV6-I progression is not normal. The progression I-IV6-I6 in which the bass descends is a normal progression, however, especially in

harmonizing the melodic succession 3̂- 4̂- 5̂ (see Aldwell-Schachter, pp. 183-84).

Plagal Use of IV

Basic outline: Often a IV chord can decorate a I or I6. (See pages 179-82)

Main uses of the plagal IV: (a) The IV often decorates a I or I6 chord as part of a I-IV-I progression (or as part of a I-

IV-I6, I6-IV-I, or a I6-IV-I6 progression). In such instances, the IV does not act as predominant, but simply as a decorative chord sandwiched in between two I chords.

This progression often harmonizes the succession 3̂- 4̂- 3̂ and 5̂- 6̂- 5̂ (b) The progression from IV to I at a cadence is known as a plagal cadence.

1 Such a strategy occasionally may be found in V-VI progressions in major keys, though never with V-VI progressions in minor keys.


III Chord (See Aldwell-Schachter, pp. 212-18.)

Basic outline: The III chord is rarely used in major keys. The III chord will be used more frequently in minor keys, since in minor keys there will often be a modulation to the key of III (the relative major). The III chord shares two notes in common with the I chord and two notes in common with the V chord. In most cases where students use a III chord to harmonize a melody they are making a questionable decision; it would be better in most of these cases to harmonize the melody note with a I chord or a V chord. In the rare instances where a III chord does appear in a major key, it usually functions as a predominant.

Main uses of III:

(a) The III chord can move to V via a III-IV-V or III-II6-V progression (creating a rising stepwise motion in the bass).

(b) The III chord can move to V via a III-VI-II-V progression (creating a cycle of fifths progression leading to the dominant chord).

(c) In rare instances, a III can move directly to a V or inversion of a V chord.

(d) Remember that a III is used rarely in major keys; in most cases, a I or V chord would be preferable. A III chord is used a bit more often in minor keys; in minor keys, the III chord appears as a major triad, not as an augmented triad (that is, do not raise the leading tone of the III chord in minor keys).

(e) In its main uses, the III chord always appears as a root position chord.

Advanced uses of III: (a) The III chord is sometimes used as a tonic substitute; a kind of I chord with an embellishing tone; see

Aldwell-Schachter, p. 220 and 236). (b) The III6 chord is sometimes used as a dominant substitute (a kind of V chord with an embellishing

tone; see p. 279-80).

(c) The special progression I-III-IV-I sometimes harmonizes the melodic succession ^8-

^7-

^6 -

^5 (pp. 218-19).


Unusual Diatonic Chords

(a) III6 : The III6 is sometimes used as a type of V chord with an embellishing tone (see Aldwell-Schachter, page 278, bottom). It should not be used by students in simple harmony exercises.

(b) VI6 : The VI6 is sometimes used as a type of I chord with an embellishing tone(see Aldwell-Schachter, page 278, bottom). It is also used as a pivot chord leading to the key of V (see Aldwell-Schachter, page 200, regarding I 5-6).1 The VI6 should not be used by students in simple harmony exercises, however.

(c) II6/4, III6/4, VI6/4, VII6/4 : Six-four chords are dissonant chords, and they can be used only in specific contrapuntal contexts (such as when they are functioning as cadential six-fours, passing six-fours, arpeggiated six-fours, or neighbor six-fours). The II6/4, III6/4, VI6/4, and VII6/4 have no special function outside of these specific contrapuntal contexts. As a result, the chords labeled as II6/4, III6/4, VI6/4, andVII6/4 chords should not be used in harmony exercises.

(d) bVII (that is, in a minor key a chord whose root is the subtonic): This chord has three functions: (1) The bVII can function as a V of III, the relative major. This is a common function. (2) The bVII can function as part of a cycle of fifths, in the progression I-IV-VII-III-VI-II-V-I. (3) The bVII can also function as a type of predominant, leading to a V, V7, or V chord in inversion. (See Aldwell-Schachter, pp. 221-23.)

(e) vii o 5/3 (i.e., a chord whose root is the leading tone of a major or minor key): (1) In major keys this chord can function as part of a cycle of fifths, in the progression I-IV-VII-III-VI-II-V-I. (2) In analyzing compositions, you will occasionally come across a VII 5/3 that functions as a V6. You should label such a chord as V6. Students should not use a leading tone viio5/3 in harmony exercises, however (see Aldwell-Schachter, pages 223-24).

(f) Remember that not every simultaneity (group of tones sounding at the same time) will produce a functional harmony. In analyzing a piece, one should not simply label the Roman numeral of a chord unless it forms part of a logical harmonic progression. If it does not, the chord would be better understood as a contrapuntal sonority .

1 Because a VI6 can function as the II6 of V, an extremely common chord.


Summary of Normal Uses of Diatonic Chords (a) I and I6 chords are goal chords of tonal rest; they can be followed by any chord. (b) II and II6 chords are pre-dominant chords that lead to the V chord, inversions of V,

or similar chords (such as VII6). A II6 can move through a IV or a II before moving to a V chord (as in the progressions II6-IV-V or II6-II-V). A II in root position is less common than a II6, especially in minor keys.

(c) A III is a rarely used chord, especially in major keys. It functions as a pre-dominant, moving to a V (or inversion of a V) either directly or (more normally) through a IV, II6, or VI-II progression. The III6 is a contrapuntal chord that functions as type of V chord with an embellishing tone; a III6 should not be used in simple harmony exercises.

(d) A IV functions much like a II6; in other words, it is a pre-dominant that moves to a V or similar chord. It can also move through a II6 or II before moving to V (as in the progressions IV-II6-V or IV-II-V). Furthermore, a IV can function as a type of embellishing chord by moving directly to a I chord within a I-IV-I progression. (When used within the I-IV-I progression, the IV is known as a plagal IV). A IV6 also functions as a predominant. Usually, a IV6 moves directly to a V or V6, or else it moves through a II6 or IV to a V (as in the progression IV6-IV-V or IV6-II6-V).

(e) AV moves directly to a I or I6. A root position V may also resolve deceptively to a root position VI. A V6 functions like a V, except that it does not usually appear at important cadences. A V6 resolves to a I chord (a V6 may not resolve to a I6). Furthermore, V ad V6 may interchange with one another (so that a V can move to a V6 and V6 can move to a V).

(f) VI is a pre-dominant chord. Usually it moves to a V through a IV, II6, or II (as in the progressions VI-IV-V, VI-II6-V, or VI-II-V). At times, it may also move directly to a V or V6. A VI6 is a contrapuntal chord that functions as type of I chord with an embellishing tone; sometimes it functions as a type of pivot chord leading to the key of V (where a VI6 in the original key functions as a II6 the new key). Aside from this pivot function, a VI6 should not be used in simple harmony exercises.

(g) A viio t d t d (whose root is the leading tone) sometimes appears within a cycle of fifths

sequence (as in the progression I-IV-viio-iii-vi-ii-V-I). Otherwise, a root position viio td triad should not be used in simple harmony exercises. A viio6, on the other hand, is quite common. It functions like a V chord, and directly to a I or I6. Any pre-dominant chord that can move to a V (such as a IV, II6, or I) may also move to a viio6 chord.

(h) The 6/4 chords all have a contrapuntal function, and should only be used in specific contrapuntal contexts. These include use as appogiaturas (as in the cadential 6/4 ), as neighbor tones (as in the I-IV6/4-I progression) or as passing tones (as in the I-V6/4-I6 or I6-V6/4-I progressions). 6/4 may not be used freely; they do not function in the same manner as their root position or first inversions counterparts.


Summary of Normal Progressions

II6 IV

VI IV6

II

V, V7 or inversions (V6 , V6/5,V4/2) V 6/4-5/3 , V 4-3 V 8-7 viio6 viio7 or inversions

r

I or I6 (I-IV-I) (I-IV6/4 -I)

• A root position V or V7 can go to a root position VI. • A V7 can’t resolve to I6. • • III is rarely used; when is used, III usually functions as a type of predominant (usually going through IV, II6,

or VI-II to a V; more rarely going straight to a V or inversion of a V). • III6, VI6, and most 6/4 chords are not normal functional chords; they should not be used or labeled in a

simple harmony exercise. • II6/5 functions like a II6; IV7 functions like a IV; II7 functions like a II. You may move from a triad to a

seventh chord with the same root, but not vice versa. • Inversions of a V chord must resolve stepwise in the bass. • It is more normal for a bass or root to move down by a third or down by a fifth than it is for a root or bass to

move up by a third or up by a fifth. • A Neapolitan six functions like a II6; augmented six chords are all predominant chords. • A I chord can move to any other chord.

Predominant chords Dominant chords

Tonic chords


Sequences Basic outline: Sequences consist of a progression that repeats a specific harmonic motion. (pp. 246-69, 380-85, 410-18). Main uses: (h) In a sequence, a specific harmonic motion is repeated a number of times. Usually,

every other chord of the sequence will be similar. (For instance, see p. 585. Note that in each example, the 1st, 3rd, 5th, and 7th chords are similar to one another—albeit transposed by step—and likewise the 2nd, 4th, 6th and 8th chords are similar to one another).

(i) In a sequence, not only does the bass line repeat, but usually all of the upper voices repeat in a pattern as well.

(j) The specific Roman numerals of the chords in the middle of the sequence usually do not matter; the sequence creates its own sense of harmonic propulsion.

(k) The most common sequence is the descending fifth sequence, in which the roots of the chords in the sequence descend by fifths (or ascend by fourths, or both).

(l) Another common sequence is the ascending fifth sequence, in which the roots of the chords in the sequence ascend by fifths (or descend by fourths, or both); do not use a diminished chord within an ascending fifth sequence.

(m) Another common sequence is the ascending 5-6 sequence, in which the roots of the chords alternate by descending a third, then ascending a fourth (some people call this the “down a third, up a fourth sequence”).

(n) A less common sequence is the descending 5-6 sequence, also known as the “down a fourth, up a step” sequence or (in slang terminology) the “Pachelbel canon” sequence.

(o) Within the middle of the sequence, scale-degree 7̂ may be doubled (since the scale

degree 7̂ does not function as a leading tone within the middle of a sequence). On the other hand, one may not have illegal parallels, unresolved sevenths, or other rule violations in the middle of a sequence.

(p) Any sequence (including those mentioned above) may be varied by using inversions, chromaticisms, and chordal sevenths. For instance, one may have not only a sequence of descending fifths, but also a sequence of descending fifths in which every other chord is a seventh chord in first inversion.

(q) Seventh chords may be used within sequences; in such cases, the seventh of the chords must resolve down. In four-part harmony, in a descending fifth sequence with seventh chords, in every other chord the fifth will be omitted and the seventh doubled (see example below).


Chord Repetition

Basic Outline: One can always repeat a chord in harmony exercises from a strong to a weak beat. This is known as “chord repetition.” When a chord repeats, the upper voices can leap freely.

Main concepts:

(a) When moving between two chords, the upper voices usually should not leap more than a third. When chord repeats, however, the upper voices may leap freely!

(b) A chord can always be repeated from a strong beat to a weak beat (only rarely may a chord be repeated from a weak beat to a strong beat; see pp. 91-92).

Examples: (Note: in each case of the following cases, upper voices can leap when the

chord repeats, but usually move stepwise when the chord changes.)

Mixture

Basic Outline: Mixture occurs when there is a shift between parallel major and minor keys (see Aldwell-Schachter, pages 355-65).

Main Uses:

(a) A piece in a major key can shift to the parallel minor (and vice versa) for a section, phrase, or even a single chord. This is known as mixture.

(b) In major keys, mixture usually involves the lowering of scale-degrees 3̂, 6̂ or both.1

1 For instance, the IV chord in a major key normally is a major chord. But if scale-degrees

^̂6 is lowered, the IV

chord will become minor (as the IV chord is in a minor key). Similarly, the II chord in a major key is usually a minor chord, but if ^6 is

lowered, the II will become a diminished chord.


(c) Chords altered by mixture function the same way as unaltered chords. (For instance, a iv chord functions the same way as a IV chord does.)

(d) Scale-degree b 7̂ rarely is involved in mixture. (For instance, one rarely finds a minor

V chord in a minor key, since a minor V chord would involve a b 7̂. Similarly, one will rarely find a minor V chord involved in mixture within a major key context.)

(e) As an exception to item (d) above, the bIII chord—when used as a mixture chord—

will include scale-degrees b^̂7 . That is, the bIII must be a major triad, not an augmented triad. (For instance, the lowered-III of C major is Eb-G-Bb, not Eb-G-B.)

(f) Similarly, the bIII should be a major triad, not an augmented triad (for instance, the lowered-VI of C major is Ab-C-Eb, not Ab-C-E).

(g) In minor keys, mixture takes place when the I chord (which should be a minor chord) is transformed into a major triad by means of a Picardy third.

(h) Mixture can arise on the deeper levels of structure, as when there is a modulation to a key involving mixture. For instance, in a piece in C major, a modulation to F minor (as opposed to F major) would be a modulation that involves mixture.

(i) “Secondary mixture” takes place when a chord is altered by an accidental that is not borrowed from the parallel major or minor key (see Aldwell-Schachter, pages 363-364).

Applied Chords

Basic outline: An applied chord (sometimes referred to as a secondary dominant) momentarily tonicizes (i.e., makes into a tonic) a chord other than the I chord (see Aldwell-Schachter, pages 195-97 and 397-409).

Main uses:

(a) Any major or minor chord can be preceded by its own V, V7, viio7, or similar chord. For instance, you may precede a V chord by a “V/V” (that is, a V in the key of V;. this chord can also be labeled as “V of V”).

(b) An applied chord either moves to the chord to which it is applied or to a similar chord. For instance, a V of V will usually go to a V, but it can also progress to a V7, a V6, a viio 6 (which is like a V).

(c) Usually, the raised tone of an applied chord functions as a local leading tone. This tone should not be doubled. In harmonizing a melody, consider that a raised tone in the melody might function as part of an applied chord.

(d) Be careful to check the use of accidentals when using an applied chord. Remember that an applied V should be a major triad, an applied V7 should be a major chord with a minor 7, and an applied VII should be a diminished chord.

(e) Remember that the root of an applied V or V7 will be a perfect 5th above the chord to which it is applied.

(f) Remember that the root of an applied VII will be a minor second below the chord to which it is applied.


Examples: (A) What is the V/V in E major? (a) The V of E major is a B chord. (b) The V chord of B is a perfect fifth above B; that is, it is an F# major chord. (c) Therefore, the V/V in E major is F#, A#, C#. (The F# and C# are already in the key of E major, but you will have to add an accidental to A#, the leading

tone of B). (B) What is the VIIo7/II in C? (a) The II of C is a D chord. (b) The VII of D is C# (not C!; the

VII is always a half step below the tonic). (c) Therefore, the VIIo7/II in D is C#, E, G, Bf.

V of V (V/V); harmonizing scale-degrees 5̂- sharp4̂-natural 4̂

(a) A V/V is equivalent to major II# chord and includes the pitch #$, which is the third of

the chord. (The scale-degree sharp-4̂, of course, is the leading tone of the dominant).

(b) A V/V (or V7/V) normally leads to a V chord or V6. It is also possible, however, for a V/V to lead to a C6/4 –V or to a V7.

(c) Normally, the third of the V/V (the raised subdominant) will lead up to the dominant when V/V progresses to a V triad. If a V/V progresses to a V7, however, it might instead lead downward to the natural subdominant. Indeed, the common melodic

figure 5- sharp4̂-natural 4̂ is often harmonized with the harmonic progression I-V/V-V7.

Other Common Applied Chords (see Aldwell-Schachter, page 397-409).

(a) A V7/IV requires a lo (as the seventh of the V7/IV). Indeed, the appearance of f& in a melody most often will be harmonized with a V7/IV chord. The V7/IV is the only common applied chord in a major key that requires the use of a lowered tone (as opposed to the use of a raised tone, which is found in all other common applied chords in a major key).

(b) The V7/IV in a minor key will require a raised- 4̂.

(a) In minor keys, the V/III or V7/III will have b7̂ (the subtonic) as its root. Though in

minor keys the 7̂ is usually raised to become the leading tone, one should not raise &

within the V/III or V7/III, since within these chords the 7̂ does not function as a leading tone. (For instance, in A minor, the root of the V/III is G-natural, not G-sharp.)

(b) The V/III will have the same notes as a major triad built on the subtonic (that is, the bVII chord). (For instance, the V of III in C minor is Bb-D-F.)

(c) The V/II involves # 1̂ (7̂ of II); the V/VI involves #5̂; in major keys, the V/III (a

rarely found chord) involves both # 2̂ (7̂ of III) and # 4̂.

(d) Notice that a raised tone in the melody will function as a 7̂ of the tonicized chord in most cases. (For instance, since #

^5 is a half step below

^6, therefore it can function as the leading tone of

^6. As

a result, # ^5 in the melody will often be harmonized with a V/VI chord.)

(e) Since the vii o chord is a diminished chord, there cannot be an applied chord to vii o.


Modulations, Tonicizations, and Pivot Chords A modulation or tonicization occurs when the key of a composition changes in the middle; that is, when the tonal center shifts from one tone to another. Though the terms are used somewhat interchangeably, modulation usually refers to a lengthy key change (one that is confirmed by a cadence) and tonicization usually refers to a brief key change (one that is not confirmed by a cadence). Modulations and tonicizations almost invariably involve the use of accidentals; that is, sharps, flats, and naturals not found in the original key. For instance, consider the typical modulation is to the key a perfect fifth above the initial tonic. Such a modulation

will require a raised scale-degree # 4̂,the leading tone of the new key. For instance, a

modulation from C major to G major requires an F# (leading tone of G, raised- 4̂ of C) in order to lead to G major. A modulation can arise suddenly, as when one section ends in one key and the following phrase immediately begins in another. A smoother effect can be realized if the modulation takes place by means of a pivot chord. A pivot chord is a chord that occurs as a normal diatonic chord in both the initial key and the key to which there is a modulation. For example, in modulating from C major to G major, an A minor chord (among others) may function as a pivot chord. After all, an A minor chord is a vi chord in C major a ii chord in G major; that is, the A minor chord functions naturally in both keys. On the other hand, a D major chord may not function as a pivot chord between C and G major: though an D major chord is a V chord in G major, it is not a normal diatonic chord in C major. (See Aldwell-Schachter, pages 198-203.) Accidentals in four-part harmony Here are the most common functions of pitches with accidentals in normal harmonic usage:

(a) Raised scale-degrees 6̂ and 7̂ are quite common in minor keys; they are normal components of the ascending melodic minor scale.1

(b) Raised tones in major keys (and raised 4̂ and 3̂ in minor) often function as parts of applied chords. These raised tones will usually be leading tones to the key a half step

above. For instance, in C major, an F# (scale-degree #4̂) can function as a leading tone to G (the V of C) and thus function as an applied chord to V.

(c) A lowered scale-degree 7̂ in a major key will often function as part of an applied chord to IV.2

1 A raised

^7 is particularly common in minor keys. When

^7 is not raised in minor, a modulation to the

relative major key is implied (unless the lowered ^7 clearly forms part of a descending melodic minor

scale).

2 Note the lowered ^7 is the only normal chromaticism in a major key that implies an applied chord and yet

does not involve a raised tone.


(d) A lowered scale-degree 2̂ in minor often implies use of a Neapolitan 6 chord (see below).

(e) Lowered scale-degrees 6̂ and 3̂ in major keys often imply the use of mixture; a raised

3̂ in minor at a cadence can imply use of a Picardy third. (f) A chromaticism might merely form part of an ornamental embellishing motion,

especially when it is used in an obviously incidental manner. (g) If a specific note is chromaticized in a consistent and persistent manner, or if it

appears at a pivotal cadence within a piece, a modulation might be implied. Many a modulation will involve a pivot chord (see above).

(h) Remember that a raised tone will most likely function as a local leading tone. Thus, for instance, in the key of C major, an A major chord (with a C#) suggests a tonicization of D (because C# is the leading tone of D) and not a tonicization of A major!

Neapolitan 6 Chord Basic outline: The Neapolitan 6 chord is a bII6 chord that functions as a predominant. (See Aldwell-Schachter, pages 456-60.) Layout and main uses: (a) The Neapolitan 6 chord is almost exclusively found in minor keys. (If a Neapolitan 6

were found in a major key, it would be an extreme example of mixture). (b) The root of the Neapolitan 6 is scale-degree ^2. (That is, the root is the lowered second

scale degree. For instance, the root of the Neapolitan 6 in A minor is B-flat, and the root of the Neapolitan 6 in E minor is F-natural).

(c) The Neapolitan 6 is always a major triad. (d) The third of the Neapolitan 6 should be in the bass and should be doubled. (e) The Neapolitan 6 chord functions in a manner similar to a II6, that is, it moves to a V,

V7, or similar chord. It may also move through a IV, cadential six-four, or V6/V, vii7/V, or similar chord before progressing to the dominant.

(f) When the Neapolitan 6 progresses to the following chord, b ^2 must resolve down (it cannot move up to natural ^2 !).

(g) This chord is sometimes referred to as a Phrygian II6.

Examples

:

☺ L


Augmented-six chords

Basic outline: Augmented six chords are special predominant chords that have a powerful drive towards V or V7. (See pp. 477ff.)

Layout and main uses:

(a) The bass of an augmented six chord is a minor second above the dominant.

(b) One of the upper voices will be a minor second below the dominant (this will create the interval of an augmented sixth with the bass).

(c) Another upper voice will be the tonic.

(d) In four-part harmony, the fourth voice will usually be either a doubling of the tonic, scale-degree ^2, a minor third above the tonic, or an augmented second above the tonic.

(d) If the fourth voice is a doubled tonic (or if the chord has only three voices as described in a-c above), the chord is called an Italian augmented six chord.

(e) If the fourth voice is scale-degree ^2 (i.e., an augmented fourth above the bass) the chord is called a French augmented six (sometimes abbreviated as Fr 6/4/3).

(f) If the fourth voice is either scale-degree ^3 (i.e., lowered third scale degree in major, normal third scale degree in minor; this will be a perfect fifth above the bass) or scale degree # ^2 (in major keys only; this will produce a doubly augmented fourth above the bass) the chord is called a German augmented six (sometimes abbreviated as either Ger. 6/5/3 or Ger. 6/4/3, respectively).

(g) These chords should resolve to a V5/3 or C6/4-V (possibly to a V7). The German augmented sixth almost always resolves to a C6/4-V; rarely does a German augmented six resolve straight to a V or V7.

(h) The minor second above the dominant and the minor second below the dominant should resolve by step. (If augmented sixth resolves to a V7, # ^4 will move down to natural-^

4 rather than up to ^5.

(i) Notice that there is no real “root position” for these chords. The Fr 6/4/3 is not an “inversion,” nor are the Ger. 6/4/3 or Ger6/5/3 “inversions;” these are the normal positions for the chord with the minor second above the dominant in the bass.

(j) These chords are usually used only at pivotal, dramatic parts of a composition, such as right before the end of the bridge section or transition section of a sonata-form movement.


Apparent seventh chords and other uses of seventh chords

Basic outline: There are chords that are literally seventh chords but don’t function as such. Also, sometimes the resolution of a seventh chord might be masked.

Examples:

(a) With a true seventh chord, the seventh functions as an “essential dissonance” that must resolve down by step. With “apparent seventh chords,” either the apparent seventh is an embellishing tone (as in Example 1 below) or the apparent root is an embellish tone (as in Example 2). In these chords, there is no true dissonant seventh that must resolve down.

(b) Sometimes the seventh of a true dissonance will be transferred while the seventh chord is being prolonged (Example 3), or—more radically—the resolution will transferred into another voice as the chord resolves (Example 4) or the resolution will be implied (Example 5).

(c) Sometimes the seventh chord will be prolonged, so that the seventh of the chord is “extended” (Example 6) or so that its resolution will be “delayed” (Example 7).

Chord Doublings (a) One should not double strong tendency tones in a chord. Thus do not double the

leading tone (that is the scale degree 7), even if it is in the bass. Likewise, do not double a chordal dissonance (such as the seventh of a seventh chord or the fourth above the bass in a C6/4 ), even if it is in the bass.

(b) With a root position chord, it is usually best to double the bass (unless the bass is the

leading tone). One notable exception occurs with the progression V-VI. That is, with the progression V-VI, one often doubles the third of the VI chord, even though the VI chord is in root position.

(c) With a second inversion chord, it is also usually best to double the bass. One notable

exception occurs with the second-inversion V chord, where one can double either the bass or the root.

(d) With a first inversion triad, one can usually double any note of the chord (except for the leading tone).

page 53 Reference Species Counterpoint

SPECIES COUNTERPOINT

Species counterpoint is a teaching tool developed over the centuries to help students learn the technique of writing for two or more voices at the same time. Species counterpoint rules are stricter than the rules for real composition (much as the rules for grammatical exercises are stricter than the rules for grammar in poetry). Haydn, Mozart, Beethoven, Chopin, and many other famous composers studied species counterpoint.

In traditional species counterpoint exercises, the teacher provides a melody, known as a cantus firmus. Against this cantus firmus, the student writes a countermelodies, know as the counterpoints. In a good counterpoint exercise, each part must have a viable melody and be able to stand on its own. The harmonic intervals must be treated carefully, especially perfect consonances (which may not be approached in parallel motion) and dissonances.

In first species the rhythms of the counterpoint and the cantus firmus are the same; in first species, all the notes must be consonant.

In second species, there are two notes of the countermelody for every one note of the cantus firmus. Dissonant passing tones are allowed on the weak beats; the strong beats must be consonant.

In third species, there are four notes of the countermelody for every one note of the cantus firmus. Dissonant passing tones and neighbor tones are allowed on the weak beats; the strong beats must be consonant.

In fourth species, there are notes of the countermelody are (for the most part) syncopated against the cantus firmus. Dissonant suspensions are allowed on the strong beats; the weak beats must be consonant. The suspensions must be prepared by a consonance which is held over to become a dissonance that resolves down by step.

In fifth species, the countermelody has a variety of rhythms against the cantus firmus. The dissonances must be weak beat passing tones, weak beat neighbor tones, or suspensions.

In each species, perfect intervals must not be approached by parallel motion. Intervening passing tones or suspensions will not eradicate faulty parallel motion. Similar motion into perfect intervals is tolerated only in special circumstances. Oblique or contrary motion into perfect intervals are acceptable.


Consonance and Dissonance

Much of species counterpoint hinges on treatment of consonances and dissonances. Consonant means “harmonically stable,” dissonant means “harmonically unstable.” Classification of intervals as consonant or dissonant varies between cultures and can also change somewhat from one style period to another. In species counterpoint exercises, however, the classification of harmonic intervals as consonant or dissonant is clear cut:

Perfect Consonances Imperfect Consonances Dissonances

Perfect unison Perfect 8ve Perfect 5th

Major and minor 6ths Major and minor 3rds

Major and minor 2nds Major and minor 7ths Perfect 4ths between the bass

and an upper voice All Augmented and diminished

intervals between the bass and an upper voice

Perfect 4ths and augmented and diminished intervals are treated as consonances

between upper voices in counterpoint exercises of three or more parts.

Compound intervals have the same classification as simple equivalents. For instance a major 10th , like a major 3rd, is an imperfect consonance. You should memorize the relation between simple intervals and their compound equivalents:

9th = 2nd plus an octave 10th = 3rd plus an octave 11th = 4th plus an octave 12th = 5th plus an octave

13th = 6th plus an octave 14th = 7th plus an octave 15th = 8ve plus and octave

Consonant Three-Part Sonorities

There are only a limited number of sonorities in three-parts that are consonant. The best of these sonorities are (1) a major or minor 5/3 chord; (2) a major, minor, or diminished chord; (3) a sixth with the bass doubled [8/6] and (4) a third with the bass doubled [8/3] . Also acceptable are (5) a sixth with the upper voice doubled or (6) a third with the upper voice doubled.1

The interval of a fifth with a note doubled or a three-part sonority with the bass tripled sound hollow, and should be avoided except for the first and last bars of an exercise. All other three-note sonorities are dissonant.

1 Avoid doubling the leading tone, however, especially in the penultimate bar.



Melody Rules For Species Counterpoint

(1) The melodies should be mostly stepwise. (a) The melody should have a few, but only a few, skips or leaps. (b) Do not have a melodic leap of a 7th or an interval over an octave. (c) Don’t have a melodic leap an augmented or diminished interval. Be especially

careful not to leap an augmented fourth. (d) After a large leap (of an 8ve, 6th, 5th, or maybe even a 4th) the melody should

move in the opposite direction, preferably by step. Thus, for instance, a leap up of a 6th should be followed by a downward melodic step.

(e) Avoid a melodic motion by a chromatic step. Thus, for instance, avoid moving melodically from C to C#.

(2) Leading tones should be treated with care.

(a) The leading tone should not be the highest tone of the melody. (b) A leading tone should not be approached by a melodic interval of a fourth

or larger.

(3) The melody must have some variety. (a) Change directions at least twice per exercise. (b) The melody should have a range of at least a fifth. (c) Avoid repeating any note or melodic motive too frequently. (d) Avoid moving more than five notes in one direction. (e) Avoid moving more than an octave in one direction. Also, avoid moving a

seventh or an augmented or diminished interval in one direction. (f) Avoid having too many arpeggios.

(4) The melody should have a climax. (a) The climax is the highest tone of a melody, or (if the melody is in the bass) the

climax can be the lowest tone of the melody. (b) Each melody should have one climactic point. (c) If a climax is approached by a leap, it should be left by step, and vice versa.


Labeling a Species Counterpoint Exercise

Labeling a counterpoint exercise can help a to see better (and thus hear better) what is written.

Once you learn how to label carefully and correctly, you will find completing species counterpoint exercises to be relatively easy.

(1) Label each and every interval.

(a) Don’t omit any interval, even ones you consider to be obvious.

(b) For the most part, you don’t have to label the quality of the intervals. But do check to see if a 5th is perfect (therefore consonant) or diminished (therefore possibly dissonant).

(c) You may refer to compound intervals by their simple equivalent. For instance, if the interval is a 10th, you may call it a 3.

(d) In 3-part counterpoint (i) in the space below the alto clef, write the intervals that are found between the bass voice and the alto voice; (ii) in the space below the treble clef, write the intervals that are found between the bass voice and the treble voice; and (iii) label the intervals between the alto and treble above the treble staff.

(2) Label each and every dissonance.

(a) Place a triangle around every dissonant interval.

(b) Place a triangle around every dissonant note. (For some reason, unfortunately, students often neglect this important labeling suggestion.)

(3) Label each and every perfect consonance.

(a) Circle every perfect interval. (Unlike with dissonances, you do not have to circle the notes involved in the perfect interval; simply circle the interval number).

(b) Label how each perfect interval is approached (by parallel, similar, oblique, contrary, or stationary motion). Remember to double-check every similar interval: an interval that you might think is approached in similar motion might actually be approached in parallel motion.

(4) Do not label how 3rds or 6ths are approached; do not circle 3rds or 6ths.


Rules For Three-Part First-Species Counterpoint (see Salzer-Schachter, pages 25-34)

Each pair of voices must be considered in constructing a three-part counterpoint. In other words, one must consider the intervals between (a) the bass and alto, (b) the bass and treble, and (c) treble and alto. Dissonances (1) Don’t use any dissonant harmonic intervals in first species counterpoint. (2) Dissonant harmonic intervals are 2nds, 7ths, and their compound equivalents. (3) Also, between the bass and an upper voice, 4ths and augmented and diminished

intervals are treated as dissonances. (4) However, between the upper voices, 4ths and diminished and augmented intervals are

treated as consonances. Perfect intervals (1) Approach perfect consonances (unisons, 5ths, 8ves, and their compound equivalents)

in contrary or oblique motion. (2) Never approach perfect consonances in parallel motion!

(3) Similar motion into a perfect fifth or octave is not so bad in three-part counterpoint. This is especially true if (a) there is stepwise motion in the upper voice of the two voices involved in the similar motion; (b) the similar motion involves an inner voice (that is, it is between the alto and soprano or the alto and the bass); and (c) the third voice (that is, the voice not involve in the similar motion into a perfect fifth or octave) moves in contrary motion to the other two voices. This chart sums up these concepts:

Similar motion into a perfect fifth or octave in 3-part counterpoint is better if:

Similar motion into a perfect fifth or octave in 3-part counterpoint is less good if:

Upper voice moves by step ☺ Upper voice moves by leap L

Involves an inner voice ☺ Involves two outer voices L

Third voice moves in contrary motion ☺ Third voice moves in similar motion L (4) You may move from a perfect 5th to a diminished 5th without creating parallel fifths.

On the other hand, in three-part counterpoint you may move from a diminished 5th to a perfect 5th only in the upper voices and only if all three voices move up by step.


Example of three-part first species:

Rules For Three-Part Second-Species Counterpoint (see Salzer-Schachter, pp. 51-53).

Dissonances (1) Dissonant intervals are not allowed on the first beat of a measure.

(2) Dissonant intervals are allowed on the second half note of a bar only if the second half note of the counterpoint is a passing tone. Remember, a passing tone must be (a) both approached and left by step and (b) approached and left in the same direction.

Perfect intervals

(1) Perfect consonances on the first beat of a bar may not be approached in parallel motion.

(2) Avoid approaching perfect consonances between the bass and treble in similar motion if the upper voice leaps (see rules of first species regarding when it is allowable to approach perfect intervals by similar motion).

(3) Two measures in a row may start with the same perfect interval if one of the voices is in second species and if its second note is a consonance.

(4) Except for the first and last bar, avoid having a sonority with all perfect intervals on the downbeat.


Rules For Three-Part Third-Species Counterpoint

Basic Strategy: The teacher provides a cantus firmus in all whole note values. Against this cantus firmus, the student will write a countermelody in all quarter notes, creating a counterpoint of 4-against-1 (i.e., four notes of counterpoint for every one note of cantus firmus). This species of counterpoint help demonstrate two types of dissonant embellishment, that is, the passing tone and the neighbor tone.

Dissonances

(1) If there is a dissonant interval between the cantus firmus and the counterpoint, we must assume that the note of the counterpoint is the dissonant note.

(2) Dissonant notes are not allowed on the first beat of a measure.

(3) A dissonant notes is allowed only on the weak beats of a bar and only if it is (a) a passing tone, (b) a neighbor tone, (c) part of a double-neighbor figure (double-neighbors will be discussed below) or (d) part of a cambiata (cambiatas will be discussed in class). The weak beats are beats 2, 4, and even beat 3 (which is relatively weak). You may have two passing tones in a row. You may not have a passing tone directly followed by a neighbor tone, however, nor may you have a neighbor tone directly followed by a passing tone.

Perfect Intervals

(1) Perfect intervals on the downbeat of a bar must be approached in contrary motion. Perfect intervals on the first beat of a bar may not be approached in parallel motion; furthermore, one should avoid approaching perfect intervals on the first beat of a bar in similar motion (see rules for first species regarding when it is allowable to approach perfect intervals in similar motion).

(2) If there is a perfect interval on the downbeat of a measure, avoid having the same perfect interval in the previous measure, especially on the last two beats (For instance, if there is a perfect fifth on the downbeat of a measure, there should not be a perfect fifth on the third beat of the previous measure).

(3) You may freely use any perfect intervals on the second, third, and fourth beats of a measure. After all, such intervals will always be approached in oblique motion (since only the counterpoint—not the cantus firmus—moves on the weak beats).

(4) Except for the first and last bar, avoid having a sonority with all perfect intervals (a so-called “open fifth” sonority”) on the downbeat.

Melody

(1) Melody must sound decent; obey melody rules shown on earlier page. In particular, avoid going too many notes in one direction.

(2) Avoid “leaping over the bar line.” That is, you should try to have a stepwise motion from the fourth beat of one measure to the first beat of the next.

(3) You may not repeat a note twice in a row.


Double-Neighbor Figure

(1) A double-neighbor figure is made up of four notes. The first and last notes of this figure are the same. One of the middle two notes is a step above these outer notes, the other is a step below (see example below).

(2) The two middle tones function as neighbor tones and thus may be dissonant. Note that only with the double-neighbor figure (and the cambiata, to be discussed in class) may you leap to or from a dissonance in third species.

Example of two-part third species:

Rules For Three-Part Fourth-Species Counterpoint

Basic Strategy: The teacher provides a cantus firmus in all whole note values. Against this cantus firmus, the student will write a countermelody in half notes, most of which are tied over the bar. This creates syncopations, which cross the bar line. This species of counterpoint helps demonstrate the important dissonant embellishment known as the suspension. A suspension is a dissonance that is tied to and that resolves downwards by step to a consonance (See Salzer-Schachter, pages 78-87). Dissonances (4) In this species, dissonant notes allowed only on the first beat of a measure. (5) Dissonant notes must be tied to. (6) Dissonant notes must resolve (a) down, (b) by step (c) to a consonance. However,

a 7th must never resolve down to an 8ve, and a 2nd must never resolve down to a unison.

(7) Though the first beat of a measure may be dissonant, it does not have to be dissonant. In other words, one may tie to a consonant half note on the first beat of a measure.

(8) Remember that all dissonant tones in fourth species must fulfill five requirements. Namely, in fourth species, dissonant tones must be

may be dissonant

may be dissonant


(a) on the first beat (b) tied to; and resolve (c) down (d) by step (e) to a consonance (with no 7-8 or 2-1 resolutions allowed).

Perfect Intervals

(4) If perfect interval that is tied to appears on the first beat of a measure, that note will necessarily be approached in oblique motion. Approaching a perfect interval in oblique motion is always permitted.

(5) If a perfect interval is formed by a note that is not tied to, it should be approached in contrary motion. Perfect intervals on the first beat of a bar may not be approached in parallel motion; furthermore, one should avoid approaching perfect intervals in similar motion (see rules of first species regarding when it is allowable to approach perfect intervals by similar motion).

(6) Dissonant suspensions do not break up parallel octaves. Thus, for instance, the interval succession 8ve-9th-8ve creates faulty parallel octaves.

Example of two-part fourth species counterpoint:

Rules For Three-Part Fifth-Species Counterpoint Basic Strategy: The teacher provides a cantus firmus in all whole note values. Against this cantus firmus, the student will write a countermelody in mixed rhythms. All dissonant embellishing tones must be unaccented neighbor tones, unaccented passing tones, or suspensions. All perfect intervals should be approached in contrary or oblique motion. (See Salzer-Schachter, pages 51-53.) Dissonances: Dissonances must be unaccented passing tones, unaccented neighbor tones, or suspensions.

(1) No dissonances are allowed on the first beat unless they are tied to. (2) Dissonant half notes on the weak beat must be passing tones. (3) Dissonant quarter notes on the weak beats must be passing tones, neighbor

tones, part of a double-neighbor figure, or part of a cambiata. (4) Dissonances on the downbeat must be tied to, and they must resolve

(a) down, (b) by step (c) on the third beat (see discussion below on “decorating suspensions”), and (d) preferably to an imperfect consonance (a 7th should not resolve down to an 8,

nor should a 2nd resolve down to a unison). (5) Do not tie from a dissonance!


Perfect Intervals (1) All perfect intervals should be approached in contrary or oblique motion; never

approach a perfect interval in parallel motion. (2) Avoid approaching a perfect interval in similar motion, especially if the upper

voice moves by leap (see rules of first species regarding when it is allowable to approach perfect intervals by similar motion)..

(3) If a perfect interval is attacked on the downbeat, the same perfect interval should not be in the previous measure.

(7) A dissonant suspension will not remove would-be illegal parallels (see rules for fourth species).

Rhythms in Fifth Species (1) The following rhythms may be used freely: (a) four quarter notes in a bar; (b) two

half notes in a bar; (c) two half notes in a bar of which either or both are tied to a half note in another bar; (d) a half note followed by two quarter notes; or (e) two quarter notes followed by a half note that is tied to the next bar.

(2) Do not use syncopations, such as a quarter note followed by a half note and then another quarter note. (quarter-half-quarter = L).

(3) Do not use two quarter notes followed by a half note; this important rule is often forgotten by students! (quarter -quarter-half = L). Contrast this rule with rule (1e) above.

(4) You may not tie from a quarter note! (5) Try to vary the rhythms in this species, creating a flowing rhythmic feel. (1) Some teachers allow the use eighth notes; even so, eighth notes should be used

sparingly, if at all. If eighth notes are used, (a) there should be at most one pair of eighth notes per bar; (b) each eighth note should be approached and left by step; and (c) use the eighth notes on either beat 2 or beat 4.

Decorating Suspensions (Tying to a Quarter Note) (see Salzer-Schachter, pages 03-4) (1) Though one may not tie from a quarter note, one may tie to a quarter note. (2) If there is a tie to a quarter note that is a dissonance, the dissonance must resolve

down on the third beat of the measure. The second beat of the bar will be called the decoration of the suspension. On this second beat, there may either be (a) two stepwise eighth notes, or (b) a consonant quarter note.

Example of two-part fifth species counterpoint:


Suggested ending for three-part exercise in fourth or fifth species counterpoint 1. In the last 2½ bars, the fourth species (or fifth species) part should end with a (a)

half-note tonic tied to another half note tonic; (b) followed by a half-note leading tone; (c) ending with a whole note tonic.

Example:

2. If the fourth or fifth species voice is in the bass, the first species voice should end

with a 5̂ moving to a 3̂

3. If the cantus firmus is in the bass, the first species voice should end with a 4̂

moving to a 3̂.

4. If the first species part is in the bass, it should end 5̂-1̂. Some other possibilities exist, but the solution offered above will always work.

page 65 Reference Form

FORM

Phrases and other groupings A phrase is a short complete musical gesture, one that is usually about four or

eight bars long. It should frame a complete harmonic progression and end with a cadence.

A subphrase is a musical gesture that is shorter than a phrase. Often, a phrase can be subdivided into two or more subphrases. A subphrase need not frame a complete progression or end with a cadence. In many cases, deciding whether a musical gesture is a phrase or a subphrase is largely subjective. Within each composition, however, one should try to be roughly consistent with the length of segments that one labels as phrases or subphrases.

A period consists of a grouping of two phrases. Again, deciding whether a musical gesture is a phrase or a period in many cases will be largely subjective. A parallel period occurs when the two phrases of a period begin in a similar manner.1 Often a parallel period takes the form of an antecedent-consequent construction. In such a construction, the first phrase of the period (the antecedent) will end incomplete (with a half cadence or an incomplete authentic cadence). The second phrase of the period (the consequent) will “answer” the first phrase by ending with a perfect authentic cadence. An antecedent-modulating consequent construction occurs when the consequent phrase ends with a perfect authentic cadence in a new key.

Many times the two phrases of a period will not begin in a similar manner. In such cases, the second phrase will nevertheless seem to “answer” the first phrase. (This is especially true if the first phrase ends with a half cadence and the second phrase ends with an authentic cadence). Such a period is often referred to as a forephrase-afterphrase.

The shortest musical segment is a motive. A motive is distinctive musical fragment, one that returns (perhaps a number of times) in a significant fashion within a composition. A motive can consist of a distinctive (a) interval or group of intervals, (b) contour, (c) rhythm, (d) group of notes or scale degrees, (e) or a combination of these items.

A sentence structure, in its ideal format, is an eight-bar phrase with the following structure: (1) two bars present an idea; followed by (2) two bars that repeat (possibly in transposed or varied form) the material of the first two bars; concluding with (3) four bars that continue the phrase by developing motives from the opening four bars (usually by breaking down or “liquidating” these motives) and then driving towards a cadence.

classic sentence structure: x (2 bars); x’ (2 bars); y [developed from x, leading towards a cadence] (4 bars, ending with cadence) [see example on next page]

classic antecedent-consequent: x (2 bars); y (2 bars, ending with incomplete cadence) // x (2 bars); y’ (2 bars, ending with complete cadence) [see example on next page] 1 Note: some theorists use the terms “period” and “parallel period” interchangeably.

page 66 Reference Form Example of sentence structure and antecedent-consequent period structure Here is a classic example of a phrase in sentence structure:

Here is a classic example of a antecedent-consequent period:

Charting Phrases and Cadences

In charting phrases, subphrases, periods, and other such musical groupings, it is important to note that these segments must be hierarchic, non-overlapping, and all-inclusive.

Here is an example of a properly charted form of an imaginary piece: Here is an example of an imaginary piece that is charted correctly: bar 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Here is an example of an imaginary piece that is charted poorly: bar 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 note overlap and lack note: not all- of hierarchy! inclusive

L L

page 67 Reference Form A cadence occurs at the end of a phrase. Here are the cadences that occur in mainstream Western music:

(a) A weak cadence is one that ends on a weak beat. A strong cadence is one that ends on a strong beat.

(b) A half cadence (HC) is a cadence that ends on a V chord. In almost all cases, a half cadence ends with a root position V triad. (A half cadence normally does not end with an inverted V chord or with a V7 chord).

(c) An authentic cadence ends with a V-I (or V7-I) progression. A perfect authentic cadence (PAC) involves root-position V and I chords, with the tonic in the top voice of the final I. In an imperfect authentic cadence (IAC) , either the V or I are not in root position, the tonic is not in the top voice of the final I, or both.1

(d) A deceptive cadence ends with a root position V (or V7) progressing to a root position VI.

A plagal cadence ends with a IV-I progression. A Phrygian cadence is a type of half cadence in a minor key that ends with a IV6-V progression. The plagal and Phrygian cadences are relatively rare.

Note that the number of bars in a phrase is usually 4, 8, or 16 bars (that is, multiples of 4). A phrase may be shortened, however, through devices such as phrase overlap. A phrase also may be lengthened through devices such as interpolations or extensions, which may appear at the beginning, middle, or end of phrases (see next page for demonstrations of these devices as indicated by the eighteenth-century music theorist Heinrich Koch).

1 Note that whereas you may have an authentic cadence may be perfect or imperfect, there is no such thing as a perfect or imperfect half cadence. Likewise, there is no such thing as a perfect or imperfect plagal, Phrygian, or deceptive cadence.


Examples of how a phrase may be rhythmically expanded may be seen in the following example by the eighteenth-century theorist Heinrich Koch:

page 69 Reference Form Binary form

Binary form is a two-part form that derives historically from dance movements of the Baroque era. The two parts of the form (each of which is usually repeated) must somehow relate to one another. Binary form can frame an individual piece, a movement of a piece, or a section of a movement. Binary form can be divided into various subcategories, which differ from each other in subtle yet important ways.

Symmetrical binary form arises when the two parts of the form are approximately the same length. Asymmetrical binary form arises when the second part of the form is approximately twice the length of the first part.

In simple binary form, the two parts of the form will not share any specific thematic material. The two parts of a simple binary form movement will share motives and various textural features, however. Simple binary form may be diagramed like this:

Simple binary

||: A :||: B :||

If the first part of the binary form ends with a harmonically stable cadence (that is, an authentic cadence in the original key), then it is known as sectional. If the first part ends with a harmonically unstable cadence (such as on a half cadence or on authentic cadence in a non-tonic key), then it is known as continuous.

A special type of continuous binary form is known as balanced binary form. In a balanced binary form, the two parts end with similar thematic material. In the first part, the concluding thematic material will appear in a non-tonic key. The second part will seem to “answer” the first part by transposing this concluding material into the tonic key. In some cases, the second part of a balanced binary form piece will also start with material similar to the beginning of the first part, so that the entire second part of a balanced binary form movement will be a type of variation of the first half. In each case, however, the two parts a balance binary form movement will differ harmonically: whereas the first part of a balanced binary form movement moves from harmonic stability to harmonic instability, the second half moves from harmonic instability to harmonic stability. Balanced binary form may be diagramed like this:

Balanced binary thematic content: ||: A :||: A’ :|| harmonic content: stability---àinstability, instability-------àstability tonic key-ànon-tonic key, non-tonic key--àtonic key


In rounded binary form, the first part of the form returns at the end of the second part. In asymmetrical rounded binary form, the second part of the form begins with new material and then repeats the entire thematic material from the first part. (In many cases, this material from the first part is altered harmonically when it returns.) A typical asymmetrical rounded binary form can be diagramed like this:

Asymetrical rounded binary ||:A :||: B A’ :|| (The first A section ends with an authentic cadence or a half cadence in the original key or in a new key.)

(Typically, the B section ends with a half cadence in the original key.)

(The return of the A section ends with a perfect authentic cadence in the original key.)

In symmetrical rounded binary form (a.k.a. quatrain form), the first part is an antecedent-consequent (or antecedent-modulating consequent) period. The second half begins with new material that is about the same length as the antecedent phrase and that ends with a half cadence in the original key. This is followed by a repeat of the consequent phrase that ends with a perfect authentic cadence in the original key. A typical symmetrical rounded binary form may be diagramed like this: Symetrical rounded binary |: A :|: B A’ :| 1 antecedent , consequent HC PAC in new

key or in original key

new material consequent HC PAC in original key

To sum up the three basic binary forms: Simple binary may be either continuous or sectional and may be either

symmetrical or asymmetrical. Balanced binary must be continuous and may be either

symmetrical or asymmetrical. Rounded binary may be either continuous or sectional and may be either

symmetrical or asymmetrical.

In practice, there are many exceptions to the basic formats described above. For instance, often the repeats are omitted. At other times, the repeats are written out (rather than being indicated by a repeat sign). Sometimes the form is expanded by transitional material or by the use of a codetta. In these and other such cases, one must be flexible in applying the terms associated with binary form.

1 HC = half cadence, PAC = perfect authentic cadence.


Ternary form

Ternary form is a three-part, sectional form in which the last part is a repetition of the first part. The two outer sections are in the same key; the middle section is often in a contrasting key or mode. Each part usually will be tonally closed; that is, each part usually ends with a perfect authentic cadence in its own key. Sometimes a transitional passage will link the middle section with the return of the opening material.

Ternary form can be diagramed like this:

Ternary form A || B || A (Typically, the first A section ends with a perfect authentic cadence in the original key.)

(The B section will often be in a contrasting key or mode. Typically, It will end with a perfect authentic cadence in this key or mode.)


Notice the difference between the typical ternary form and rounded binary form:1

Asymmetrical rounded binary from ||: A :||: B A’ :|| (The first A section ends with an authentic cadence or a half cadence in the original key or in a new key.)

(The B section ends with a half cadence in the original key.)


These differences may be summed up as follows: Rounded binary form Ternary form The B and the return of A’ form a single, larger section.

The B and the A’ do not form a single, larger section.

Usually the A section is repeated, as is the B-A’ section.

The A section is not repeated. The B and return of A are also not repeated.

The first A section can end in a new key or on a half cadence.

The first section usually does end with a perfect authentic cadence in the original key.

The B section usually ends with a half cadence in the original key.

The B section usually ends with a perfect authentic cadence in a new, contrasting key or mode.

Because of the layout of the cadences and repetitions, the A and B sections may not be regarded as discrete sections.

The A and B sections may be regarded as discrete and closed off from one another, often as though they formed separate movements.

1 Confusingly, some theorists refer to rounded binary form as ternary form—go figure!


Sonata Form

Sonata form is an important form that governs many movements of the late-Classical period and the Romantic period. (It is not found in the works of the high-Baroque period or earlier.) It governs movements not only from sonatas, but also of symphonies, string quartets, and many other genres.

The general layout of sonata form is as follows:

(Introduction) ||: Exposition :||: Development , Recapitulation (:||) (Coda)

Sometimes a large sonata form movement will begin with a slow introduction in the tonic key. Introduction sections usually end with the V of the main key and they are not repeated.

EXPOSITION The exposition, which is usually repeated, can be divided into various subsections:

First group (sometimes called the first theme group): The first group consists of a theme or group of themes that are in the tonic key or that center around the tonic key, ending with a motion towards the second key area. The first group can consist of a single phrase, a half of a phrase, or many phrases. The opening phrase(s) of the first group are sometimes called the first theme. The last part of the first group is known as the bridge or transition.

The bridge or transition is the final phrase (or phrases) of the first group during which a motion toward the second key area takes place. The bridge can introduce a new theme, though often it uses the same thematic material seen earlier during the first group. In many pieces, the bridge section functions as a type of modulating consequent to the first group. The transition usually ends on the V of the key of the second group or on a V of the original key. The typical bridge section often can be subdivided into the following subsections:

(a) The bridge will begin in the tonic key, either introducing new material or developing material heard in the previous phrase.

(b) In the middle of the bridge phrase, tensions will increase, perhaps hinting at a modulation to a new key.

(c) A dramatic motion to a V of the new key or V of the original key will take place. Often this motion will entail a chromatic motion in the bass or top voice, and the half cadence will be preceded by an augmented sixth chord or by an applied dominant.

(d) The V or V of V of the new key will be reiterated a number of times, concluding with “hammer strokes” and followed by a clear pause or by a sudden decrease in texture.

page 73 Reference Form Second group (sometimes called the second theme group): The second group consists of a group of themes in a secondary key, usually the key of V or (if the movement is in minor) in the key of the relative major. The second theme usually(but not always) has three subsections (a) The second theme is the first part of the second group. (b) The closing theme is the part of the second group that follows the first firm cadence in the new key and that has a closing function. (c) The codetta is a short passage at the end of the second group that “wraps up” the section, following the second big cadence in the new key. If there more or less than three big cadences during the second group, then classifying the sections with a standard designation will be difficult, if not impossible.

The second group is usually firmly demarcated from the preceding bridge, often by means of a short pause. The second group often begins somewhat harmonically unstable. It need not introduce a new theme: sometimes, the second group is based on thematic material that clearly is based on material from the first group.

DEVELOPMENT and RECAPITULATION These two parts make up the second big section of sonata form. They usually are repeated in the sonata form movements of Haydn, Mozart, and their contemporaries. In the sonata form movements of Beethoven and his successors, however, these sections rarely are repeated.

The development section usually modulates through many keys, developing thematic material seen earlier and introducing new thematic material. This section often starts with a brief, introductory-like phrase. This is frequently followed by increasingly intense passages that are filled with sequences. The development section typically ends with a retransition that leads to a V of the original key (or, more rarely, leads to a V of VI of the original key).

The recapitulation repeats the material of the exposition. The main difference, however, is that, the second group appears in the tonic key in the recapitulation. Accordingly, the bridge section is often drastically rewritten so as not to effect a modulation. There also might be small changes in the first group as well.

Sometimes the recapitulation is followed by a coda; that is, a tail section that wraps up the entire piece in the tonic key. The coda usually starts after all the material first seen in the exposition has reappeared in the recapitulation.


One might diagram the standard sonata form structure like this:

EXPOSITION DEVELOPMENT RECAPITULATION

(many keys)

Of course, this chart is a bit simplistic; it is intended only as a rough guide. In actual practice, composers show great flexibility in capturing the spirit of sonata form while diverting from this rigid formula in many specifics. As a result, few of the many pieces classified as sonata form adhere to all of the aspects detailed in the sonata form blueprint diagramed above.

Rondo form

Rondo form involves a theme in the tonic key that alternates with a series of contrasting themes that often are in contrasting modes or keys. An early form of rondo is the rondeau, a form that is found in many French Baroque dance suites. In a rondeau, a short refrain alternates with a succession of short “couplets.” There is no set number of couplets allowed in a rondeau. Typically, both the refrain and couplets are about eight or sixteen bars long. The refrain is always in the tonic key; the couplets often are in contrasting modes or keys:

Rondeau form:

A B A C A D A . . .

1st theme (tonic key)

2nd group (non-tonic key)

bridge (modulates)

1st group (tonic key)

2nd group (tonic key)

bridge (doesn’t modulate)

1st group 1st group


A 5-part rondo form appears a slow movement in classical sonata, as well as in other types of compositions. The 5-part rondo has the following structure:

5-part rondo form

A B A C A (in the tonic key)

(often in a contrasting key or mode)

(in the tonic key; usually shorter than the first A section)

(often in a contrasting key or mode; usually longer than the B section)

(in the tonic key; usually about the same length as the first A section)

A 7-part rondo form often appears as the final movement in classical sonata, as well as in other types of compositions. The 7-part rondo has the following structure:

7-part rondo form

A B A C A B’ A (in the tonic key)

(in a non-tonic key, usually the key of the dominant or the relative major)

(in the tonic key)

(in a contrasting key or keys)

(in the tonic key)

(in the tonic key)

(in the tonic key)

A “7-part rondo” can also take the form of ABACAB or ABACBA.

A 7-part rondo can also take the form of a “sonata rondo” if the initial A and B sections are structured like a sonata-form exposition, the C section is structured like a sonata form development section, and the A and B sections following the C section are structured like a recapitulation.

Documents

REFERENCE - Social Sciences at Hunter College (CUNY)maxweber.hunter.cuny.edu/pub/eres/MUS724_BURSTEIN/Reference.pdf · page 30 Reference Harmony and Figured Bass HARMONY AND FIGURED