Final Projects

Short three-part fugue (32-36 mm). Details in class.

Typically this will be an exposition, three developing phrases, and a recapitulation in which the subject-answer pair is restated entirely in the home key.

The exposition typically consists of one well-formed subject-answer pair imitating at the 5th, a second subject entry imitating at the octave in the third voice, and an episode following that subject entry, in which the third voice utilizes material from the countersubject, sequentially, to reach a full strong cadence in V or III.

In total, the exposition of a 3-part fugue is really two large phrases.

1. The first is the subject-answer pair which together form a progression that tonicizes the dominant and then (with a “linking” passage) returns to the tonic. During the answer, the subject voice continues in invertible counterpoint against the answer; this material is the “countersubject”. The end of the “link” that returns to the tonic is the beginning of the second phrase, where the third voice enters with an imitation of the subject at the octave.

2. The second phrase begins by replicating the chord progression implied by the subject, exactly; it only differs from the opening statement of the subject by having three voices instead of one. During the second subject entry, the voice of the answer makes use of countersubject material (which needn’t be a strict imitation of the countersubject). Rather than proceed to the answer, a sequential treatment of countersubject material in the third voice (called an “episode”) leads to the related key, completing the second phrase with a strong cadence.

3. Just as is the case with 2-part inventions, the cadence is not a stopping point for the piece, but a launching pad for the next phrase.

The remaining phrases of the fugue are structured very much like those of a two-part invention.

Since the answer and countersubject are related to each other as invertible counterpoint, it will now be possible to reiterate the the relationship between them in several new transpositions, and several new part relationships. Fugue 17 (A-flat major) from WTC I is one possible model for a short-subject, tonal-answer fugue; a detailed, hand-written diagram of its phrases was given and discussed in class. Note that this fugue is in four voices, offering plentiful examples of its subject in various stages of development. Your assignment is to write a three-voice fugue, which is a somewhat less daunting task.

Phrases use subject-answer pairs, subject statements alone, and sequential bridges, to progress between related keys. Like two-part inventions, fugues do not cease their rhythmic motion until the end of the last sentence: the recapitulation of the subject-answer pair in the home key area.


Week 9

Due Wednesday, May 27

Read an excerpt of the Kent Kennan textbook, Chapter 13.

Write one short fugue subject (1.5-3 measures) in minor, fitting the criteria of those that tend to produce “tonal answers”. Write a tonal answer to it, a fourth below your subject (i.e. “imitation at the 5th”), and write a good invertible counterpoint above that answer. You should spend no more than 1/2 hour in this process (after you have absorbed the reading) — do your best with what you know, and bring your effort to class on Wednesday for discussion. You will not be asked to turn it in, but I will ask some students to write their work on the board.

Due Friday, May 29

Compose two short fugue subjects (1.5-3 measures, mostly eighth notes), and one long subject (3-4 measures, mostly 16th notes). Write answers to each, at the fifth, and compose invertible counterpoint to each. At least one answer should be tonal and at least one should be “real”; you may use the tonal answer you composed for Wednesday’s meeting, provided you revise it if necessary to reflect Wednesday’s discussion.

Choose one of your three subject-answer pairs, and revise it to connect the answer’s counterpoint (the “countersubject”) to its subject, fluidly. Extend the answer with a very short sequence that reaches a cadence in the tonic.

Optional: you are nearly done with the three-part fugue exposition. Shift the sequence so that, at the tonic resolution of your short sequence,  the “missing” note could be an octave transposition of the first tonic triad note of your subject. If you achieve this, you’ll be ready to

(1) add the third subject entry

(2) extend the “answer” in a manner that loosely imitates the countersuject, and

(3) add a third voice.

When the third subject entry is then extended (along with its two accompanying voices, without deviating from the basic character of the subject), to reach toward a strong cadence in a related key, you have completed a “fugal exposition.”

Fugal expositions count among the most significant musical passages composed by Bach, Haydn, Beethoven, and other composers; they represent a demonstration of a kind of mastery, a balanced synthesis of both the horizontal and vertical dimensions of musical experience, in a single, unified expression. Meanwhile, they provide one of the richest opportunities for melodic development in a short form — each restatement of the subject-answer combination, or fragments thereof, is cast in a new harmonic, registral, and contrapuntal “light”, so that the whole form embodies a unity of concept, or affect, through a narrative of changing perspectives. What a way to end the school year!





Week 7

Due Friday, May 22

Read Gauldin Chapter 11: “Introduction to Three-Voice Texture…”

In two of the three examples given in class (see handout <— modified 10:45 pm, Wednesday 5/20), write two independent voices of counterpoint, using a mostly quarter-note texture, to the given lines. Make certain that the two new voices are relatively independent by including mixtures of oblique, parallel, and contrary motion. Use occasional eighth-notes or half notes in order separate the rhythmic motion of one voice from another.  

Create at least 3 “7”, “6/5”, “4/3”, and “4/2” chords in each phrase; you will need to begin with a clear sense of the harmonic possibilities, including secondary dominants. Make sure each line ends with a clear and conclusive cadence. 

Finally, write a third example of 3-part harmony in a similar style, without a given bass note. You may want to draw on, or make an elaboration on, a chord progression from your “baroquized” melody, if you have completed that assignment with a satisfactory sense of harmony.


PROJECT TWO: Two-Part Invention

Using the technique of invertible counterpoint, invert, transpose, and develop a single basic two-part theme into a full-fledged form. Model your work after the four Bach examples discussed in class and in labs, and incorporate feedback given on your sequence assignment (Week 5) and invention-practice phrase assignment (Week 6).

Your composition can take any of several overall forms, including but not limited to:

PHRASE 1: 4-8 bars, melody with counterpoint, tonicizing V, v, i, or III with a weak cadence.

PHRASE 2: a transposition of phrase 1, with bass and treble parts switched. Begin with a tonicized key related to the end-point of phrase 1. Modify the cadence to tonicize a new related key, or return to the tonic.

SEQUENCE: based on a fragment of phrase 1, 4-6 bars in length, reaching a cadence in a key opposite the mode of the tonic.

PHRASE 3: a third version of the basic phrase, in the key reached by the sequence (opposite the mode of the tonic), possibly extended 1-2 bars in additional length, or intensified through a widened or contrasting range.

SEQUENCE: based on the same fragment as the first sequence, moving as necessary to return to the tonic.

PHRASE 4: restatement of the first phrase in its original key, and ending on the tonic with a stronger, more conclusive cadential ending.


Week 6

Due Wednesday, May 13

To continue your work on writing Two-part Inventions:

  1. Read pp 126-132 [pdf in fair use] of Kent Kennan’s Counterpoint
  2. Following the guidelines in the reading, and the guidelines of last week’s reading (Gauldin Ch 6-8 excerpts, see below)— Compose three contrasting musical sentences (using different meters, motifs, and keys) using the technique of invertible counterpoint, restricting your use of 5ths and anticipating that the example’s parts will be switched. Where possible, continue in the spirit of your sequence assignment due last week, using mobile and active rhythms in both voices. These sentences will all be candidates to become the basic theme of your Two-part Invention project due May 18.
  3. Pick one of the sentences above, and re-write it with a new harmonic purpose, with the treble and bass parts switched. Do not change the original key signature, but begin at a different diatonic position (for example vi or V in major; III, v, or VI in minor … but of course those are not the only options!), and modify the cadence so that it “lands” in a sensible harmonic area for the chosen key of the original.

Examples: each of the inventions 1, 5, 9, and 14 begin with 4- to 8-bar “invertible” sentences — when the parts are exchanged, only slight modifications are called-for to produce excellent counterpoint. In invention 5, the first sentence tonicizes V. The second sentence begins in bar 5, at the dominant position — but rather than continuing to tonicize II (V/V), as it would if everything were left alone, Bach modifies the cadence to tonicize vi. (The same principle is at work in Inventions 1, 9, and 14.)

The sentences you write might not end up being the “first two sentences” of your finished composition; but you will be able to modify them further, transpose them, and fragment them into sequences, in order to weave together a satisfying musical whole.

Extra credit (+3) due Monday, May 11: Bring your best phrase from step 2 above, on transparency sheet for overhead projection. And please RSVP.