rhythm-permutation.md

Idea 1: numbers as lengths

[2,1,1] could be half, quarter quarter

rhythmPermutations(4);

could yield:

[[1, 1, 1, 1], [1, 1, 2], [1, 2, 1], [1, 3], [2, 1, 1], [2, 2], [3, 1], [4]]

Which runs the permutator with all numbers that fit into the grid size (4). The result can be interpreted as all possible rhythms inside a grid of 4 units.

restrict sizes

rhythmPermutations(4, { allowedSizes: [1, 2, 4] });

could yield:

[[1, 1, 1, 1], [1, 1, 2], [1, 2, 1], [2, 1, 1], [2, 2], [4]]

forbid syncopation

to be able to test if a rhythm syncopates, we need those two helpers:

function sum(path) {
  return path.reduce((sum, size) => sum + size, 0);
}
function positionInGroup(path, groupSize) {
  return sum(path) % groupSize;
}

• sum just adds all given numbers
• positionInGroup tells the position inside a given group size:

positionInGroup([2, 1], 2); // 1 e.g. in quarter grid: after half and quarter note
positionInGroup([1, 1], 2); // 0
positionInGroup([1, 1], 3); // 2
positionInGroup([1, 1, 1], 4); // 3 e.g. in 8ths grid: offbeat on 4ths 8th note (= index 3)
positionInGroup([1, 1, 1, 1], 3); // 1 e.g. 2 of second measure in 3/4

To tell if a syncopation would happen, we can do this:

function exceedsGroup(groupSize) {
  return (path, next) => return positionInGroup(path, groupSize) + next <= groupSize;
}

function isSyncopating(path, next) {
  return (groupSize) => return positionInGroup(path, groupSize) + next <= groupSize;
}

examples:

isSyncopating([1], 2)();

rhythmPermutations(4, { validate: (path, next) =>  });