midi number to frequency using Werckmeister I (III) temperament

werckmeister.js

// by https://github.com/zz85
// http://en.wikipedia.org/wiki/Werckmeister_temperament
// Werckmeister I (III): "correct temperament" based on 1/4 comma divisions

var werckmeister = [
    1, // c
    256/243, // c#
    64 / 81 * Math.pow(2, 1/2), // d 
    32/27, // d#
    256 / 243 * Math.pow(2, 1/4), // e
    4/3, //f
    1024 / 729, // f#
    8/9 * Math.pow(8, 1/4), // g
    128/81, // g#
    1024 / 729 * Math.pow(2, 1/4), // a
    16/9, // a#
    128/ 81 * Math.pow(2, 1/4) // b
    
];

var baseCFrequency = 415 / werckmeister[9];

// midi number to frequency using werckmeister's tuning 
function werckmeisterFrequency(midi) {
    
    var middle_c_midi = 60;
    var semitones, noteIndex, ocatve;
    if (midi < middle_c_midi) {
        semitones = middle_c_midi - midi;
        noteIndex = semitones % 12;
        if (noteIndex>0) noteIndex = 12 - noteIndex;
        octave = -Math.ceil( semitones/12 );
    } else {
        semitones = midi - middle_c_midi;
        noteIndex = semitones % 12;
        octave = Math.floor( semitones/12 );
    }
    
    var freq = werckmeister [ noteIndex ] * Math.pow( 2, octave ) * baseCFrequency;
    
    return freq;
}