The idea
A fugue is not a shape you pour music into. The source course states it flatly: "A fugue is not a form. A fugue is a procedure" (Source course, Lesson 8). There is no template. There is a way of working. A subject is stated alone, imitated in the other voices, developed, and brought to an end.
That procedure is available to you with a guitar, a piano and a bass, and it costs nothing. What it demands is a subject built to two competing specifications. It has to be compact enough to recognise instantly when buried under two other parts, and rich enough in interval and rhythm to survive sequencing, inversion, fragmentation and stacking for four minutes.
A good riff meets the first requirement. Most fail the second, because a riff is designed to loop rather than develop. Making a riff that can also be a fugue subject is this lesson's real work.
Watch
Why Every Jazz Pianist Should Learn Bach (https://www.youtube.com/watch?v=Aa_BpDisgFs)
- Greg names the A minor Prelude as one of three pieces in his routine, then says "not the fugue, I haven't quite gotten there yet" [00:46]. Fugues are slow to learn, and you are learning to write one, not to perform the repertoire.
- "You can do any Bach" [01:21]. The catalogue is open. Pick by what you can play. Learn to play Bach in 1 Hour (https://www.youtube.com/watch?v=473fw73Jlag)
- The metronome ladder he actually runs on camera: 62, 70, 80, 93, 101, going up only after a clean pass [00:00]–[07:04]. Use it on your own exposition.
- "Positioning the center of the weight of my arm over each individual note" [01:07]–[01:22], at slow tempo too, because the slow version is what the fast version becomes.
- He drops the sheet music partway up the ladder [05:24], and starts hard material at 40 with the click on eighths [09:46]. A three-voice texture is hard material.
Why Every Jazz Pianist Should Learn Bach
- the A minor Prelude, and Greg's honest note that he has not got to the fugue yet
Learn to play Bach in 1 Hour
- the metronome ladder that gets a fugal exposition under your hands inside a week
Listen
Bach, Fugue in C minor, BWV 847. Three voices, thirty-one bars, 4/4. Five passes.
- No score. Hear three separate entries at the start.
- Follow the subject in whichever voice has it, singing along.
- Follow the countersubject, the unbroken sixteenths arriving with the second entry.
- Find the episodes, where nobody states the subject in full, and ask what they are made of.
- Listen to the last three bars. Something in the bass stops moving.
Mehldau, "Paranoid Android," solo piano. Rusch's transcription gives exact bars. The head of the second solo section runs mm. 162–177, its first half doubling the upper voice with the bass. From m. 170 the "Rain down" melody runs in parallel tenths with the bass while the former top voice drops into the alto, producing 9–8 suspensions at mm. 170 and 172. A third soprano voice arrives at m. 178, and mm. 207–210 thin four voices back to melody and accompaniment. Listen for the number of voices, not the notes.
Modern Jazz Quartet, "Vendome." John Lewis writes a compact, driving subject and runs a formal exposition: vibes state it, piano answers, bass takes it in the lowest register. Listen to what happens to the improvisation. Milt Jackson improvises lines holding a contrapuntal relationship to what Lewis plays, rather than soloing over changes (Source course, Lesson 8).
The comparison
The exact parallel. A fugal exposition and a band arrangement that stacks entrances are the same event. One line arrives alone, a second arrives with the first still going, a third arrives under both. The composer buys the listener's attention by spending it one voice at a time. The source course puts it in the triple-fugue lesson: introduce three unfamiliar melodies at once and the ear has nothing to parse, so it hears a blur (Source course, Lesson 9). Bands learn this when everyone comes in on bar one.
Where it breaks, and it breaks on the answer. Bach's second entry is never a straight copy. It arrives transposed to the dominant, and it is often adjusted on the way. In BWV 847 the alto states the subject alone in bar one: after an eighth rest, C and B natural in sixteenths, then C, then down to G, up to A flat, then C and B natural again, then C, then D, landing on G at the start of bar two. The soprano answers in bar three: G, F sharp, G, then C, then E flat, then G, F sharp, G, then A. A strict transposition up a fifth would have put a D on that fourth note. Bach writes C instead, so the answer does not drag the music into the dominant's dominant this early. That is a tonal answer, and the adjustment is a harmonic decision, not a mistake.
Riff idiom has no equivalent constraint, because a riff in a metal or math-rock context often has no functional key to protect. Transposing your riff for the second entry is a choice of colour and register, not a defence of a tonic. Your answer therefore carries less structural weight than Bach's, so form has to come from texture, from the entries themselves, and from where the density peaks.
Where it breaks, second break. Bach's countersubject is the subject's permanent companion, written to fit above or below in invertible counterpoint, with a rhythm deliberately unlike the subject's. In BWV 847 the subject moves in eighths with sixteenth-note pairs while the countersubject under the answer is a continuous stream of descending sixteenths. Different density, same bar. Bands differentiate by instrument instead, which is a weaker guarantee than it looks, because two distorted guitars in one octave are effectively one timbre. Write for two guitars by rhythmic density first, register second, and treat timbre as a bonus.
Two corrections to the source course, from the score. The course says the bass enters in bar three of BWV 847. The score has the bass entering in bar seven, with the subject at the original pitch an octave below the alto. The course also says Bach deploys a stretto at the end. There is no stretto in this fugue. The closing device is a tonic pedal: a C, doubled at the octave and tied, starts in the second half of bar 29 and holds through bar 31, with the final subject entry sounding in the soprano above it and the last chord carrying an E natural. Learn the difference, because "pedal under a final entry" is a device you can use next week and stretto is not.
The course also describes the subject two ways across two lessons, once as a rising half step and once as a plunging chromatic descent. Neither matches the score. Use the notes above.
Mehldau. His own account of why Bach is his model is a composer's statement, not an analyst's. Writing about After Bach II, he calls the constant choice "how to negotiate between harmony and melody," notes that in Bach "the harmonic movement comes about through simultaneous melodies" while each melody "expresses harmonic implication monophonically, in a single line," and states the payoff: "In my improvised solos, I want to make melodic phrases which carry harmonic implication, and create harmony that moves in a melodic fashion." His departure is metrical. Andres documents Bach's regular 3/8 becoming 20/16 in the After Bach "Rondo," and Mehldau told Rusch the C major groove in "Paranoid Android" is heard in 7/4. Bach achieved that fusion inside a fixed metre. Mehldau keeps the fusion and breaks the metre.
At the piano
Learn the BWV 847 exposition, bars 1 to 9 only. Alto alone, then soprano, then bass, hands separate first. Ladder: 40 with the click on eighths, then 50, 62, 70. Do not go past bar 9 this month.
Play the three entries as three separate melodies. The alto's bars 1 to 2, the soprano's 3 to 4, the bass's 7 to 8, each as a tune. Say out loud each time which note differs in the answer and why.
Voicing three parts in two hands. The middle voice belongs to whichever hand can reach it, and it changes hands. Pencil the assignments into the score before you practise and never change them once marked. A hand stretching for a note it should have given away is a hand that clenches. If you feel it, stop and re-mark the passage.
The left hand carries a line, not a root. That is the Mehldau lesson and the Evans lesson before it. Play any tune in the right hand while the left walks a melodic line that never doubles the right hand's contour and never just states the root on beat one.
Exercises
1. Build a subject that passes both tests
Do. Write eight candidate riffs, six to twelve notes each, no longer than two bars. Answer in writing for each: can I recognise it under two other parts, and does it hold two separable components I can develop independently?
Done when: at least two candidates pass both tests, and you can say which component of each one you would sequence and which you would invert.
2. Real answer and tonal answer
Do. Take your best subject. Write a real answer, transposing every interval exactly up a fifth. Then write a tonal answer, adjusting one or two notes so the answer stays inside the home key.
Done when: you can play subject and both answers, and you can state in one sentence what the adjusted note bought you.
3. Countersubject in invertible counterpoint
Do. Write a countersubject to go under the answer. If the subject moves in longer values the countersubject moves in shorter ones, and if the subject leaps the countersubject steps. Then swap them, changing nothing.
Done when: both positions are playable with no unintended strong-beat dissonance. Rewrite until the swap survives.
4. The three-voice exposition, at the piano
Do. Write a full exposition, twelve to sixteen bars. Voice 1 states the subject alone. Voice 2 enters with the answer while voice 1 takes the countersubject. Voice 3 enters with the subject in the lowest register while the other two continue.
Done when: you can play the whole exposition at 60 bpm with correct hand assignments and no tension, and you can sing any one of the three lines while playing the other two.
5. The exposition for guitar and piano
Do. Re-score the same exposition. Guitar takes the first entry, piano right hand the answer, piano left hand the third. Keep guitar and piano right hand at least a sixth apart wherever they overlap. Print both parts from Sibelius.
Done when: you can play the piano part while singing the guitar part in time, and the guitar part is playable at tempo by you on the guitar.
6. Pedal point ending
Do. Write a final passage of four bars in which the bass holds one note, tonic or dominant, while the upper voices state the subject one last time above it.
Done when: you can play it, and you can say which note you chose and what it does to the tension.
7. The left hand as a voice
Do. Record two minutes on one tune with the left hand walking a melodic line, then transcribe your own left hand.
Done when: the transcription reads as a melody on its own and you can play it without the right hand.
Compose
Write a fugal exposition and one episode, ninety seconds of music, for guitar, piano and bass.
Constraints: one subject stated in all three instruments in turn; one countersubject appearing with at least two entries and working in both positions; one episode after the third entry, built only from subject fragments, shifting the tonal centre once; an ending on a bass pedal point with the subject above it.
The subject must be a riff you would use in a piece anyway. If it is not good enough to loop, it is not good enough to be a subject.
Checkpoint
- Play bars 1 to 9 of BWV 847 at 62 bpm with the hand relaxed, and name the bar in which each of the three voices enters.
- State the BWV 847 subject by note name, identify the one note where the answer departs from a strict transposition, and say why Bach did that.
- Play your own three-voice exposition at 60 bpm and sing each line over the other two.
- Hand over the guitar-and-piano score of that exposition, printed from Sibelius, plus a recording of you playing the piano part.
- Explain what a pedal point does and where it happens in BWV 847.
- Play two minutes over a tune with a left hand that is a line rather than a root pattern.
Read
- Source course, Lesson 8 (/library/garnett-course.pdf). Subject, answer, countersubject, exposition, episode, stretto, pedal point, and the parallel with Rosen on sonata form. Read after the five listening passes.
- Source course, Lesson 9, for the rule you will use in every arrangement you ever write: introduce independent lines one at a time.
- Brad Mehldau, liner note to After Bach II, https://www.bradmehldaumusic.com/after-bach-ii. Two pages on melody that carries harmonic implication, and the clearest statement by a living pianist of why this module exists.
- René Rusch, MTO 19/4 (2013), https://mtosmt.org/issues/mto.13.19.4/mto.13.19.4.rusch.html. Read it with the recording, alongside Appendix 2, her bar-numbered transcription. Footnote 14 is where Mehldau supplies the 7/4 reading.
- Score of BWV 847. Colour the three entries, the countersubject, and the pedal point differently.