maia-util/es6/farey.js

Utility math and music functions supporting various applications by Music Artificial Intelligence Algorithms, Inc.

import get_unique from './get_unique'

/**
 * This function returns the Farey sequence of order *n*.
 *
 * @author Tom Collins
 * @comment 21st January 2018
 * @param {number} n - Order of the Farey sequence
 * @return {number[]} Farey sequence, deduplicated and in ascending order
 *
 * @example
 *     farey(6);
 * →
 * [0, 0.16667, 0.25, 0.33333, 0.5, 0.66667, 0.75, 0.83333, 1]
 */
export default function farey(n){
  var out_arr = [];
  for (let m = 2; m <= n; m++){
    var fracs = [];
    for (let i = 1; i < m; i++){
      // Round to 5 d.p. and push to fracs.
      fracs.push(Math.round(100000*i/m)/100000);
    }
    out_arr = out_arr.concat(fracs);
  }
  // Sort and get unique elements.
  out_arr = get_unique(out_arr.sort(function(a, b){return a - b;}));
  // Stick 0 at the front and 1 at the end.
  out_arr.unshift(0);
  out_arr.push(1);
  return out_arr;
};