Programming Polyrhythms: Three Against Four and Layered Counterpoint
Three against four starts with a shared twelve-step grid, then each layer has to count on its own.
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Find the shared grid first
Three against four shares twelve steps: from the first step, the three layer lands every four steps and the four layer every three, then they realign after the twelfth. Five against four needs twenty steps; three against two needs only six. Work out that number before choosing a grid resolution. Drawn on straight sixteenths, three against four always leaves one layer between grid lines; cut the bar into twelve and both layers land on whole steps. Get the number wrong once and every alignment after it drifts.
Each track keeps its own grid
Keep the kick and bass on the 4/4 sixteenth grid and put the other track on triplets or quintuplets. The meter stays put; what changes is each track's grid and note values. Quantise both tracks to the same grid and the counterpoint is erased, so let at least one track keep some of its played deviation. A DAW's tuplet setting usually applies only to the active track; check the grid when you switch tracks, or triplets end up drawn on straight sixteenths.
Layer against layer
| Ratio | Shared steps | Sound | Common writing |
|---|---|---|---|
| 3:2 | 6 | Rolling, swaying | 6/8 against 3/4, jazz eighths |
| 4:3 | 12 | Stable but suspended | Left-hand triplets, right-hand sixteenths |
| 3:4 | 12 | Opposite weight | Drums against melody |
| 5:4 | 20 | Tense, hard to count | Modern scores, prog rock |
3:4 and 4:3 share the same grid; the difference is who starts first and who is denser. Complexity is not a virtue by itself: 3:2 is enough to give a 4/4 section a second centre of gravity, while 5:4 at a fast tempo mostly reads as confusion. Decide which layer anchors before deciding where the other one leans.
Hear each layer alone, then together
Listen to each layer on its own and check that it counts. Then put them together and hear whether the shared hit lands where it should. The low layer usually anchors, so keep it simple; put the complex layer in the midrange where it has room. Check in mono so width does not hide a clash. Add a third layer only after two already stand, and give three or more layers a clear hierarchy, or every layer fights for the ear.
Where it breaks
The usual failure is quantising both tracks to sixteenths: triplets get pulled straight, the counterpoint disappears, and only a syncopated rhythm remains. The second failure is too many layers, with everything moving and nothing for the ear to hold. The third is frequency collision: if both layers occupy the low end, even a correct shared grid will not be heard. Build two layers, confirm each stands alone, then consider a third.
Listen in the library
All tracks from midicn-lib — inline badge is the license tier (C1 commercial / C2 non-commercial / C3 study only).
Along the same line
Sources
- Peter Magadini, Polyrhythms — The Musician's Guide（教材）
- Toussaint, The Geometry of Musical Rhythm（节奏结构教材）
- Ableton Live 用户手册，网格分辨率与连音符（软件文档）