Pythagorian and harmonic music scales using functionnal PHP and a lazy collection

music-scale.php

<?php

/**
 * @file
 * Example/demo file.
 * @see https://github.com/drupol/collection
 */

declare(strict_types=1);

include 'vendor/autoload.php';

use drupol\collection\Collection;

// From: https://stackoverflow.com/questions/14330713/converting-float-decimal-to-fraction
function float2rat(float $value, $tolerance = 1.e-12) {
    $num=1; $h2=0;
    $den=0; $k2=1;

    if ($value === 0) {
        return 0;
    }

    $b = 1/$value;
    do {
        $b = 1/$b;
        $a = floor($b);
        $aux = $num; $num = $a*$num+$h2; $h2 = $aux;
        $aux = $den; $den = $a*$den+$k2; $k2 = $aux;
        $b -= $a;
    } while (abs($value-$num/$den) > $value*$tolerance);

    return $num . '/' . $den;
}

// Harmonic scale serie generator
$harmonic = static function ($value) {
    $s = 1;

    for ($i = 1; $i <= $value; $i++) {
        $s += 1 / $i;
    }

    return $s;
};

// Pythagorian scale serie generator
$pythagorian = static function ($value) {
    return (3/2) ** $value;
};

$scale = Collection::range(0, 12)
    // Choose the scale: $harmonic or $pythagorian
    ->map($harmonic)
    // Scale the values between the interval 1 and 2 (logarithmic)
    ->map(
        static function (float $value) {
            while ($value > 2) {
                $value /= 2;
            }

            return $value;
        }
    )
    // Sort values ASC
    ->sort(static function ($a, $b) {return $a <=> $b;})
    // Convert float to rational numbers (fraction)
    ->map(static function ($value) {return float2rat($value);});

print_r($scale->all());

/*
 Pythagorian:
 Array (
    [0] => 1/1
    [1] => 2187/2048
    [2] => 9/8
    [3] => 19683/16384
    [4] => 81/64
    [5] => 177147/131072
    [6] => 729/512
    [7] => 3/2
    [8] => 6561/4096
    [9] => 27/16
    [10] => 59049/32768
    [11] => 243/128
 )

 Harmonic:
 Array (
    [0] => 1/1
    [1] => 111431/110880
    [2] => 5/4
    [3] => 17/12
    [4] => 37/24
    [5] => 197/120
    [6] => 69/40
    [7] => 503/280
    [8] => 1041/560
    [9] => 9649/5040
    [10] => 9901/5040
    [11] => 2/1
 )
 */