euclidean-gate

euclidean-gate gates your notes through a Euclidean rhythm: you propose the onsets, the grid decides which of them sound.

Godfried Toussaint observed that the Euclidean algorithm, asked to spread k pulses as evenly as possible over n steps, generates a startling share of the world’s rhythms: k=3 n=8 is the tresillo of Cuban son, 10010010. The effect runs an endless grid of steps pulse long, with k open steps spread as evenly as possible over every n, the whole pattern shifted by rotation. The grid is anchored at the first note-on the effect ever sees: that note lands in step zero and fixes where every later step falls, for good. It never re-anchors, so after a pause you re-enter wherever the running pattern happens to be; with the default rotation=0 step zero is open, and the anchoring note itself sounds.

A note arriving in a closed step is handled by mode. With "defer", the default, it waits and sounds at the start of the next open step, so a steady stream of playing comes back already phrased as the pattern; a note arriving inside an open step sounds immediately. With "drop" it simply vanishes, its release swallowed with it. A note deferred into the future keeps its release ordered after it (the note-off is held to at least 10ms past the emitted note-on), so nothing sticks.

Parameters

pulse= takes a duration string like "250ms" or "1.5s", or beats= against the tempo, never both; left out entirely, the step is a quarter of a beat. See Time and tempo.

Parameter	Type	Default	Range
k	integer	required	1..=64, at most n
n	integer	required	1..=64
rotation	integer	0	0..=n-1
pulse	duration string	a quarter beat	positive, "250ms" or "1.5s" form
beats	number	none (instead of pulse)	finite, greater than 0
mode	string	"defer"	"defer", "drop"

Example

miditool.kdl

input "Roland"
output virtual="miditool Out"

tempo 100

euclidean-gate k=3 n=8 beats=0.5      // the tresillo, an eighth note per step

Play even eighths and they come back as the tresillo; play freely and every onset is pulled onto the nearest open step ahead of it.

Try this

Turn the gate into a sieve in time. With mode="drop", whatever misses the pattern is gone, and your own accuracy becomes the instrument:

tempo 110

euclidean-gate k=5 n=16 beats=0.25 mode="drop"

Then nudge rotation=3 to shift where the open steps fall against your downbeat, or follow the gate with accent-groups so the survivors get phrased as well as placed.