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Friday
Sep282012

2:1 Writing in the 18th-century Style

Basic principles of 2:1 Counterpoint in the 18th-c style 

Before composing 18th-century style counterpoints in 2:1 relationships to accompanying lines, two concepts must be understood. Both are discussed in detail in Kent Kennan’s reading from the prior week.

(1) Non-chord tones (NCTs)—any notes that deviate from the essential, and usually consonant, intervals formed between the bass and the treble in a composition. We call them non-chord tones or non-harmonic tones because they are not part of the chord or implied harmony in which essential intervals participate. See Kent Kennan’s p 40-43 for a full description of the possibilities. (Most NCTs are dissonant, but resolutions from a 6th to 5th above the bass can qualify as NCT->CT resolutions.)

(2) Essential Intervals—the harmonic intervals that define the relationship between a bass line and an additional line above it. These intervals are usually consonant and they form part of a chord that’s clearly implied as part of a progression.

1. Chords and NCTs: 2:1 writing 

a. 3 possibilities:

i. Thesis CT -> Arsis NCT. A chord occurs plainly on the strong beat, and on the weak beat, a non-chord tone connects to the next strong beat.

ii. Thesis CT -> Arsis CT. Usually both CTs are consonant against the bass, so they are often a skip of a third. Note: 

iii. Thesis NCT -> Arsis CT. This possibility creates “accented NCTs,” especially accented passing tones, neighbor tones, and appogiaturas. (This is a very good thing; the presence of the NCT on the strong beat increases our attention to the resolution and can intensify harmony and motion.

b. In all of the above possibilities, non-chord tones are resolved by step, except in the case of escape tones. NOTE: Appogiaturas and escape tones involve three notes: the outer two notes are both chord tones, and are not the same tone. The escape tone (E) is a step away from the first note; an appogiatura (App) is a step away from the second note. (Usually the step and the leap on either side of an App or E are in opposite directions.)

c. Suspensions:

 i. All suspensions consist of a consonant preparation note (P), a dissonant NCT (Sus or S), and a step-wise resolution (R).

ii. In 2:1 counterpoint, P occurs on a weak beat (arsis), S on the following strong beat (thesis), and R on the following arsis.

iii. In more complex rhythmic situations (with triplets, 16ths, etc.) the preparation may not be shorter than the NCT. 

2. Step-Skip rules

     a. Avoid “step-skipping” (moving by step, and then immediately by skip in the same direction), such that the skip lands on a thesis. This has the effect of “halting” the melody or disorienting us to the meter.

     b. When step-skipping in the same direction to land on arsis, compensate the skip, with a step in the opposite direction. This has the effect of being awesome.

3. Interval Succession:

a. Build your counterpoint on a structure of imperfect consonances (ICs). 3rds and 6ths guiding the relationship between bass and treble. This does not mean that ICs always fall in metrically strong positions, but PCs (5ths & 8ves) on strong beats should be avoided, and dissonances (2nds, 4ths, 7ths, and tritones) on strong beats should generally resolve immediately to ICs. It’s often useful to start out writing a counterpoint as an interesting (non-repetitive) series of ICs, which you then connect with other intervals via passing and ornamental gestures.

b. PCs 

i. - do not write parallel 5ths or 8ves from arsis to thesis or from thesis to thesis. Exceptions are possible when one interval (especially a 5th) is a non-essential interval. (Kennan p 48.)

ii. - a 5th followed by an octave, or an 8ve followed by a 5th, should also be avoided, except when the succession is part of a standard cadence. (5^ in the bass and 2^ in the soprano forms a fifth; both notes can move to 1^, forming an 8ve, if this gesture is cadential. But other movements from PC to PC are not acceptable.)

iii. - avoid approaching PCs by similar motion, except at cadences (called “direct” or “hidden” 5ths & 8ves)

iv. - avoid PCs on strong beats, except at cadences

v. - avoid approaching PCs by leaps in both voices

4. Harmonic movement and clarity

a. Avoid V-IV; maintain harmonic movement that keeps the variety of chords on a trajectory to the dominant, increasing the resolution

b. 6/4 chords are unstable, due to the P4 above the bass, and they must have a passing, arpeggiating, or neighbor-note role. DO use them in these ways:

i. in a bass arpeggiation: when the bass part moves through all the notes of the triad of the harmony it supports, it will obviously assume the 5th of that triad at one or more points, resulting in a 6/4 chord. It works because usually one of the other bass notes is the “real” bass for that part of the harmonic progression.

ii. in a pedal progression: when a root-position triad is proceeded and/or followed by simultaneous upper neighbor tones to both the 3rd and the 5th of the chord. It works because although the upper neighbors form a 6/4, they function as ornaments to the 5/3.

iii. in a cadential 6/4 construction (K6/4): this is a variant on the pedal progression, with the 5/3 chord functioning as cadential V. It’s worth a special mention because the 6/4 upper neighbor notes can be passing notes, appogiaturas, or suspensions, or a combination of two NCT types. (Most of those alternatives are not so elegant when they fall outside this cadential formula.

iv. in a passing progression: When bass notes a third apart are bridged by a passing tone, and the outer pair are part of the same harmony, the bridging note often forms a 6/4 chord with other notes that work well as passing tones. It works because, like examples i-iii, the chord is a collection of ornaments between two stronger chords.

 

c. Avoid repeating the bass note in a counterpoint, either from arsis->thesis, or from thesis->thesis. (in other words, from one thesis to the next, the bass should be in some kind of motion.) Common exceptions: when the bass voice forms a suspension or anticipation, or at the beginnings of pieces, where the tonic chord is being established for the first time.

d. Avoid implying a suspension (by tying a note from weak to strong) where there is no suspension (see 1c above)

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