Module 14: Modern harmony and rhythmLesson 5advanced⏱ 90 min + 25 min daily for three weeks

Odd meters and polyrhythm

Comp and phrase in 3/4, 5/4, 7/4 and 6/8 by grouping the beats, play 3-against-2 and 4-against-3 with both hands, execute a metric modulation, and carry a motif across the bar line without losing the form.

Why odd meters are a grouping problem, not a counting problem

Since Take Five (1959) and Afro Blue (1959), 5/4, 7/4 and 6/8 have been normal in jazz, and in the contemporary repertoire of Pat Metheny, Brad Mehldau, Kurt Rosenwinkel and Avishai Cohen they are the default rather than the exception. Players who struggle with them almost always make the same mistake: they count to five or seven. That is too slow to feel. The players who sound relaxed in 7 are not counting seven; they are feeling a bar of four plus three (or three plus four), two familiar groups joined together, exactly as a bar of 4/4 is two groups of two. Every meter in this lesson is handled that way: find the grouping, make the groups physical in the thumb or the foot, then comp and phrase inside them.

The second half of the lesson is about polyrhythm: two groupings at once, 3-against-2 and 4-against-3, which are the raw material of the rhythmic language of Elvin Jones, Tony Williams and everyone who followed. Polyrhythm leads directly to metric modulation, in which one of the two layers becomes the new tempo. You need the subdivision work from Time feel, bossa nova and jazz waltz, its basic 3/4 comping, and the quartal shapes from Quartal voicings and modal comping.

3/4: the jazz waltz and the hemiola

You already comp a waltz with the dotted-quarter pair (a chord on 1 and on the and-of-2). Take that one step further: two dotted quarters fill a bar of 3/4, so across two bars there are four of them, and the ear hears four beats where the bass plays six. This is the hemiola, the oldest polyrhythm in Western music and the signature of the modern jazz waltz. In the example the thumb walks strict quarter notes while the fingers play chords on every dotted quarter; the two layers meet on the downbeat of every second bar.

\tempo 150
.
\ts 3 4
\voice :4 3.6{ch "Gm7"} 6.6 5.5 | 1.6 5.5 3.6 | 8.6{ch "C7"} 7.5 3.6 | 6.6 3.6 8.6 | 1.6{ch "Fmaj7"} 5.6 3.5 | 7.5 3.5 1.6 |
\voice (3.4 3.3 3.2).4{d} (3.4 3.3 3.2).4{d} | (3.4 3.3 3.2).4{d} (3.4 3.3 3.2).4{d} | (2.4 3.3 1.2).4{d} (2.4 3.3 1.2).4{d} | (2.4 3.3 1.2).4{d} (2.4 3.3 1.2).4{d} | (2.4 2.3 1.2).4{d} (2.4 2.3 1.2).4{d} | (2.4 2.3 1.2).2{d} |

Practise each layer alone against the metronome set to 3 beats per bar, then together at 100 bpm before raising it. The moment it starts to work you will feel the pull of the "big four" over the bass's six, which is exactly what drummers do with the ride cymbal in a waltz: they play the 3 and imply the 2.

5/4: three plus two

Nearly every 5/4 tune in the repertoire groups the bar as 3 + 2 (a dotted half followed by a half), occasionally as 2 + 3. Make the grouping physical: the thumb plays the root on beat 1 and the 5th on beat 4, and those two attacks are the only thing you count. The fingers then play figures that start on 1 and on 4, with anticipations before them, just as the Charleston anticipates 1 and 3 in 4/4. The vamp is on the quartal Dm11 stacks.

\tempo 132
.
\ts 5 4
\voice 5.5.2{d ch "Dm11"} 5.6.2 | 5.5.2{d} 5.6.2 | 5.5.2{d} 5.6.2 | 5.5.2{d} 5.6.2 |
\voice (5.4 5.3 5.2).4{d} (5.4 5.3 5.2).4{d} (7.4 7.3 8.2).4 :8 r (7.4 7.3 8.2) | (5.4 5.3 5.2).4 :8 r (5.4 5.3 5.2) (-.4 -.3 -.2).4 :4 r (7.4 7.3 8.2) | :8 r (7.4 7.3 8.2) (-.4 -.3 -.2).4 (5.4 5.3 5.2).4 (5.4 5.3 5.2).4{d} (5.4 5.3 5.2).8 | (5.4 5.3 5.2).2{d} (7.4 7.3 8.2).2 |

Lines in 5 follow the same rule: phrase in a three-beat cell and a two-beat cell, and let the accent fall on 1 and 4. The engine checks the line against D Dorian via chordscale, which accepts every note of the chord's first-choice scale, so the 9th and 11th need no special treatment.

\tempo 132
.
\ts 5 4
:8 5.5{ch "Dm7"} 7.5 3.4 5.4 7.4 5.3 :4 7.3 5.2 | :4 7.3 :8 5.3 7.4 :4 5.4 :8 3.4 5.5 :4 r |

7/4: four plus three

Seven is usually 4 + 3: a bar of 4/4 with a bar of 3/4 glued on (occasionally 3 + 4, or 2 + 2 + 3 in faster tunes). The comping figure below is a ii–V–I–I in C with one chord per bar; in each bar the four-beat group gets the Charleston-type figure you already know and the three-beat group gets a dotted-quarter pair with the second chord tied through to the next downbeat. Think of it as two bars you already know how to play, one after the other.

\tempo 132
.
\ts 7 4
(5.5 3.4 5.3 5.2).4{d ch "Dm9"} (5.5 3.4 5.3 5.2).4{d} (5.5 3.4 5.3 5.2).4 (5.5 3.4 5.3 5.2).4{d} (5.5 3.4 5.3 5.2).8 (-.5 -.4 -.3 -.2).4 | (3.6 3.4 4.3 5.2).4{d ch "G13"} (3.6 3.4 4.3 5.2).4{d} (3.6 3.4 4.3 5.2).4 (3.6 3.4 4.3 5.2).4{d} (3.6 3.4 4.3 5.2).8 (-.6 -.4 -.3 -.2).4 | (3.5 2.4 4.3 3.2).4{d ch "Cmaj9"} (3.5 2.4 4.3 3.2).4{d} (3.5 2.4 4.3 3.2).4 (3.5 2.4 4.3 3.2).4{d} (3.5 2.4 4.3 3.2).8 (-.5 -.4 -.3 -.2).4 | (3.5 2.4 2.3 3.2).4{d ch "C6/9"} (3.5 2.4 2.3 3.2).4{d} (3.5 2.4 2.3 3.2).4 (3.5 2.4 2.3 3.2).4{d} (3.5 2.4 2.3 3.2).8 (-.5 -.4 -.3 -.2).4 |

For soloing, a ii–V that lasts one bar of 7 gives the ii four beats and the V three: the line below plays D Dorian for the four and G Mixolydian for the three, which is the same vocabulary you have in 4/4 with the dominant bar shortened. Learn to hear the shortened dominant as a push toward the next bar rather than as a missing beat.

\tempo 132
.
\ts 7 4
:8 5.5{ch "Dm7"} 7.5 3.4 5.4 7.4 5.3 7.3 5.2 6.2{ch "G7"} 5.2 7.3 4.3 5.3 2.3 | :4 5.5{ch "Dm7"} :8 r 3.4 5.4 7.4 :4 7.3 :8 5.2{ch "G7"} 6.2 :2 3.6 |

6/8: two big beats, three small ones

A bar of 6/8 has two dotted-quarter beats, each divided into three eighths. The feel is the Afro-Cuban and West African 6/8 of Afro Blue and of the bembé bell pattern, which is the clave of this meter: seven strokes across two bars that every drummer knows. Learn the bell first; it tells you where the 6/8 "clave" falls, and your comping should agree with it.

\tempo 100
.
\ts 6 8
:8 5.3 r 5.3 r 5.3 5.3 | r 5.3 r 5.3 r 5.3 |

\tempo 100
.
\ts 6 8
\voice 5.5.4{d ch "Dm11"} 5.6.4{d} | 5.5.4{d} 5.6.4{d} | 5.5.4{d} 5.6.4{d} | 5.5.4{d} 5.6.4{d} |
\voice :8 (5.4 5.3 5.2) r (5.4 5.3 5.2) r (7.4 7.3 8.2) (7.4 7.3 8.2) | r (5.4 5.3 5.2) r (5.4 5.3 5.2) r (7.4 7.3 8.2) | (5.4 5.3 5.2) r (5.4 5.3 5.2) r (7.4 7.3 8.2) (7.4 7.3 8.2) | r (5.4 5.3 5.2) r (5.4 5.3 5.2) r (7.4 7.3 8.2) |

6/8 contains its own polyrhythm: the six eighths divide into two groups of three (the dotted quarters) or three groups of two (quarter notes). Playing three quarter notes with a finger against the thumb's two dotted quarters is 3-against-2 with no tuplets at all, which makes 6/8 the easiest place to learn it: take the vamp above, replace the chord layer with three evenly spaced quarter notes per bar, and swap the roles between thumb and finger until both directions are automatic.

Polyrhythm in 4/4 and 3/4

3-against-2 in 4/4 is quarter-note triplets against quarter notes: three evenly spaced notes in the time of two beats. Mnemonics help some players, but the reliable way is mathematical: subdivide the half note into six, play the bass on 1 and 4 of those six and the melody on 1, 3 and 5. The example puts the triplets in the upper voice on a Dm7 arpeggio and the bass in quarters.

\tempo 80
.
\ts 4 4
\voice :4 7.3{tu 3 ch "Dm7"} 10.3{tu 3} 5.1{tu 3} 7.3{tu 3} 10.3{tu 3} 5.1{tu 3} | 7.3{tu 3} 10.3{tu 3} 5.1{tu 3} 7.3{tu 3} 10.3{tu 3} 5.1{tu 3} |
\voice :4 5.5 5.5 5.6 5.6 | 5.5 5.5 5.6 5.6 |

4-against-3 is easiest in 3/4, where four dotted eighths fill the bar exactly against three quarter notes. Subdivide the bar into twelve sixteenths: the bass falls on 1, 5 and 9, the melody on 1, 4, 7 and 10. This is the rhythm Elvin Jones plays under a waltz, and the one that makes a 3/4 solo sound like it is floating over the bar.

\tempo 90
.
\ts 3 4
\voice :8 7.3{d ch "Dm7"} 10.3{d} 5.1{d} 10.1{d} | 7.3{d} 10.3{d} 5.1{d} 10.1{d} |
\voice :4 5.5 5.6 5.5 | 5.5 5.6 5.5 |

Metric modulation

A metric modulation changes the tempo by making one note value of the old tempo equal to a different note value of the new one. The most common in jazz: the quarter-note triplet becomes the new quarter note, so the new tempo is one and a half times the old (120 becomes 180). Played well, the listener hears the band "shift gears" without anything being counted off. The reverse (the dotted quarter becomes the new quarter) slows the music to two thirds of the tempo, and a half-note triplet becoming the new quarter gives three quarters of it.

In the example the first two bars are at 120 with the chords on quarter-note triplets; at bar 3 the tempo marking changes to 180 and the same chord continues on quarter notes at exactly the same speed. If you play it with the metronome at 120 for bars 1-2 and switch it to 180 at bar 3, the chord attacks should not change at all.

\ts 4 4
(5.5 7.4 5.3 6.2).4{tu 3 ch "Dm7"} (5.5 7.4 5.3 6.2).4{tu 3} (5.5 7.4 5.3 6.2).4{tu 3} (5.5 7.4 5.3 6.2).4{tu 3} (5.5 7.4 5.3 6.2).4{tu 3} (5.5 7.4 5.3 6.2).4{tu 3} | (5.5 7.4 5.3 6.2).4{tu 3} (5.5 7.4 5.3 6.2).4{tu 3} (5.5 7.4 5.3 6.2).4{tu 3} (5.5 7.4 5.3 6.2).4{tu 3} (5.5 7.4 5.3 6.2).4{tu 3} (5.5 7.4 5.3 6.2).4{tu 3} | \tempo 180 (5.5 7.4 5.3 6.2).4 (5.5 7.4 5.3 6.2).4 (5.5 7.4 5.3 6.2).4 (5.5 7.4 5.3 6.2).4 | (5.5 7.4 5.3 6.2).4 (5.5 7.4 5.3 6.2).4 (5.5 7.4 5.3 6.2).4 (5.5 7.4 5.3 6.2).4 |

To practise a modulation: play the polyrhythm (here 3-against-2) until the triplet layer is rock steady, then stop playing the old layer and let the triplet layer be the beat. Going back is the same in reverse: feel the old quarter note as a triplet grouping of the new tempo (two new beats make three old ones), then re-enter it. Ask the drummer to practise this with you; it is a band skill.

Playing over the bar line

The last technique is the simplest and the most useful on a gig: take a short motif whose length is not the bar length and repeat it. A three-beat motif in 4/4 starts on beat 1, then beat 4, then beat 3, then beat 2, and lands back on beat 1 after three bars; a five-beat motif takes five bars. The listener hears the motif float across the bar lines while the form stays intact underneath. The example repeats a three-beat cell four times over Dm7; count the bar numbers aloud while you play it so the form never disappears.

\tempo 140
.
\ts 4 4
:8 5.5{ch "Dm7"} 7.5 :4 3.4 :8 r 7.4 5.5 7.5 | :4 3.4 :8 r 7.4 5.5 7.5 :4 3.4 | :8 r 7.4 5.5 7.5 :4 3.4 :8 r 7.4 | :1 5.5 |

The rule that keeps this from becoming chaos: know where you will land. Decide in advance that the motif ends on the downbeat of bar 4 (or bar 6 for a five-beat cell) and make sure the rhythm section can hear that landing. Over-the-bar-line playing that does not land is just losing the form.

Exercises

1. Hemiola waltz as written at 100, 130, 160 bpm; then over the chords of any waltz standard you know, chart in front of you.
2. 5/4 vamp for four minutes without stopping at 132; then the 5/4 line, then improvise on Dm7 in 5 using only three-beat and two-beat cells.
3. 7/4 comping as written, then the 7/4 line; then improvise a chorus of a ii–V–I in 7, one chord per bar, at 120.
4. 6/8: the bell on a muted string for two minutes; the vamp for four minutes; the 3-against-2 example until you can swap the layers between thumb and finger.
5. Polyrhythm: the 3-against-2 and 4-against-3 examples at 60, 80, 100 bpm; then tapped on the knees away from the guitar.
6. Metric modulation with the metronome switched by hand from 120 to 180 at bar 3, ten times; then the reverse (start at 180 in quarters, modulate to 120 by hearing the quarters as triplets).
7. Over the bar line: the three-beat motif; then invent a five-beat motif and make it land on the downbeat of bar 6.

Quiz