07Simple loops, different clocks

Generative rhythm

Evolution does not require constant randomness. Let short deterministic cycles have different lengths; their relative phase produces the long form.

Euclidean lookup

Expression	Density	Good first role
`E(3,8)`	3 hits / 8 steps	slow percussion
`E(5,8)`	5 / 8	dense hat
`E(5,12)`	5 / 12	rolling percussion
`E(7,12)`	7 / 12	high texture
`E(5,16)`	5 / 16	sparse accent
`E(7,16)`	7 / 16	broken hat
`E(9,16)`	9 / 16	busy texture
`E(11,16)`	11 / 16	dense shaker

E(k, n) = spread k hits across n stepsk controls density. n controls cycle length.

Rhythm is a circle

A step grid chooses a left edge. A cyclic rhythm does not: moving the downbeat rotates the same necklace. The gap vector records the clockwise distance from each hit to the next.

E(5,16) · phase 0X..X..X..X..X...

gap vector3 · 3 · 3 · 3 · 4

same necklace · phase +2..X..X..X..X..X.

gap vector3 · 3 · 3 · 3 · 4

rotationsame gaps · different downbeatBoth wheels have gap vector 3 · 3 · 3 · 3 · 4. Their phase differs; their spacing geometry does not.

dᵣₒₜ(A, B) = min Hamming(A, rotate(B, r))Compare every rotation and keep the smallest number of changed cells. This separates a new rhythmic shape from a simple phase shift.

Polymeter

kicklength 16stable reference

basslength 12re-aligns every 48 steps

arplength 7long melodic drift

perclength 11long rhythmic drift

stability4 · 8 · 16 · 32shared factors align often

motion3 · 5 · 6 · 7 · 9 · 11 · 13odd lengths align later

Five-note arp over a sixteen-step bar0 → 3 → 7 → 10 → 7

Harmonic clocks

drums/1immediate pulse

bass/1groove

arp/2surface motion

chord/16phrase

root/32section

mode/64large-scale color

Controlled variation

track12345678910111213141516

main100%XXXX

secondary70%xxxx

ghost20%xxx

fill5%x

priorityphase → velocity → probability → new notesChange articulation before adding information.

The cyclic view, distance geometry and maximally even distributions are drawn from Godfried Toussaint’s The Geometry of Musical Rhythm.