TidalCycles' 'iter' rotates a pattern by a fraction each cycle, and the rotation amount is itself patternable

iter(n) shifts a pattern’s starting point forward by 1/n of a cycle on each repetition, so over n cycles it steps through all rotations and returns to the start. McLean uses it to illustrate the deeper principle that the transformation’s own parameter is a pattern: you can pattern the amount you iterate by, and this is true of every Tidal command. So iter is both a concrete rotation idiom and a worked example of ‘patterns all the way down’ applied to a transformation’s argument.

Examples

Sequence 1 2 3 4 with iter 4 yields 1 2 3 4, then 2 3 4 1, then 3 4 1 2, then 4 1 2 3, then repeats — a rotation each cycle. Patterning the iter amount (e.g. <4 2>) changes the rotation step cycle-to-cycle.

Assessment

Describe what iter(4) does to the sequence a b c d over four cycles. Then explain what it means to ‘pattern the amount you iterate by’ and why that is possible for every Tidal transformation.