music tones: guess how many notes should be in one octave

gistfile1.txt

#!/usr/bin/perl -w

use strict;
use Data::Dumper;

my $besterr = 1000;
foreach my $i ( 5..100 ) {
    my ($err, $notes) = find_all( 2**(1/$i), qw(3/2 4/3 5/4 6/5 9/8) );
    next if $err > 1.5*$besterr;

    $besterr = $err if $err < $besterr;

    print "2^$i: $err: ".Dumper($notes);

    
};




sub find_all {
    my ($base, @ratios) = @_;

    my $maxerr = 0;
    my %notes;
    foreach (@ratios) {
        my ($pow, $err) = ratio_diff( $base, $_ );
        $notes{$_} = $pow;
        if ($err > $maxerr) {
            $maxerr = $err;
        };
    };
    return ( $maxerr, \%notes );
};


sub ratio_diff {
    my ($base, $ratio) = @_;

    $ratio =~ m{(\d+)/(\d+)}
        and $ratio = $1/$2;

    my $pow = int ((log ($ratio) / log ($base)) + 0.5);
    my $appr = $base ** $pow;

    my $err = abs ($ratio - $appr) / abs ($ratio);

    return ($pow, $err);
};