sieve

sieve forces every note onto a sieve: a set of keys defined by arithmetic.

Sieves are the residue-class lattices Xenakis built pitch scales from for Jonchaies and Akrata: instead of listing notes, you write conditions on the key numbers, and the keys that satisfy them are the scale. Members pass untouched; everything else snaps to the nearest member, up, down, or drops entirely. Because a sieve’s period need not be an octave, the “scale” can shift shape as it climbs, something no key signature can say.

The mapping is deterministic, no seed. Note-offs map the same way as their note-ons, so held notes always release correctly; with snap="up", "down", or "drop", a dropped note-on takes its note-off with it.

Parameters

sieve takes the expression as one bare string argument.

Parameter	Type	Default	Range
expression	string argument	required	non-empty, must match at least one key
snap	string	"nearest"	"nearest", "up", "down", "drop"

"nearest" breaks ties downward and always finds a member. "up" and "down" drop the note past the last member in their direction. "drop" passes members and silences the rest, a blocked-keys written as arithmetic.

The expression grammar

An atom M@R names every key where key % M == R: 12@0 is every C, 12@7 every G, 2@0 every even key. The modulus M is 1..=127 and the residue R must be less than M.

Atoms combine with three operators, plus parentheses; whitespace is free:

• ! complement (within keys 0..=127), binds tightest
• & intersection, binds next
• | union, binds loosest

So !3@0 & 4@1 | 12@7 reads as ((!3@0) & 4@1) | 12@7. An expression that matches no key at all is rejected.

Some sieves:

• 12@0 | 12@4 | 12@7: the C major triad in every octave.
• 2@0: every even key, the whole-tone scale on C.
• !12@1 & !12@6: everything except C sharps and F sharps.
• 8@0 | 8@3 | 11@5: two interlocking periods, 8 and 11, that only realign every 88 keys, so the scale never quite repeats as it climbs. This is the Jonchaies-flavored sieve from examples/serial.kdl.

Example

miditool.kdl

input "Roland"
output virtual="miditool Out"

sieve "8@0|8@3|11@5" snap="up"

Run the same line up and down the keyboard and listen to the scale change shape under your fingers.

Try this

Turn the keyboard into a triad, then thin it to a filter:

sieve "12@0 | 12@4 | 12@7"

Everything you play snaps onto C major triad tones; smashed clusters come out as voicings. Then add snap="drop" and only the notes already on the sieve survive, holes and all.