生成正确的音调频率值

Question

I have written a perl script to generate a list of note information entries to be used in a C++ header. The script contains contains the following:

#!/bin/perl
use strict;
use warnings;

my @NOTES = ( "C" , "C#", "D", "D#", "E", "F", "F#", "G", "G#", "A", "A#", "B" );

#2*(x/12)
my @CF_VALUES = (1, 1.0594630943592953, 1.122462048309373, 1.189207115002721, 1.2599210498948732, 1.3348398541700344, 1.4142135623730951, 1.4983070768766815, 1.5874010519681994, 1.681792830507429, 1.7817974362806785, 1.8877486253633868);

my @START_FREQS = (27.5,55,110,220,440,880,1760,3520,7040);

my $FREQUENCY = 0;
my $OCTAVE;
my $KEY;
my $INDEX = 12;

print "static const MidiNote_t Notes[" . 8 * 12 . "] = {\n";

#4 times

for ($OCTAVE=0; $OCTAVE<=8; $OCTAVE++)
{
    for ($KEY=0; $KEY<12; $KEY++)
    {
        print "\t{ $INDEX, \"" . @NOTES[$KEY] . $OCTAVE . "\", " . @START_FREQS[$OCTAVE] * @CF_VALUES[$KEY] .  " }";
        if ($KEY == 11 && $OCTAVE == 8) {
            print "\n};";
        } else {
            print ",\n";
        }
        $INDEX++;
    }
}

And the generated output looks like this:

static const MidiNote_t Notes[96] = {
        { 12, "C0", 13.75 },
        { 13, "C#0", 14.5676175474403 },
        { 14, "D0", 15.4338531642539 },
        { 15, "D#0", 16.3515978312874 },
        { 16, "E0", 17.3239144360545 },
        { 17, "F0", 18.354047994838 },
        { 18, "F#0", 19.4454364826301 },
        { 19, "G0", 20.6017223070544 },
        { 20, "G#0", 21.8267644645627 },
        { 21, "A0", 23.1246514194772 },
        { 22, "A#0", 24.4997147488593 },
        { 23, "B0", 25.9565435987466 },
        { 24, "C1", 27.5 },
        { 25, "C#1", 29.1352350948806 },
...

Although, I cannot seem to get the resulting frequencies in the list generated by my script, to align with the base 'A' frequencies.

For example, A4 should correspond to 440 Hz, and A0 should be 27.5 Hz.

How can I align the frequencies properly and multiply each note in each octave with its respective base A note frequency?

Answer 1

Your program is expecting the values in @START_FREQS to be the C frequencies, and not the A frequencies. We can modify the value printed to be based on the A be dividing everything on the A changer like this:

print "\\t{ $INDEX, \\"" . $NOTES[$KEY] . $OCTAVE . "\\", " . $START_FREQS[$OCTAVE] * $CF_VALUES[$KEY] / $CF_VALUES[9] . " }";

This would be the whole program:

#!/bin/perl
use strict;
use warnings;

my @NOTES = ( "C" , "C#", "D", "D#", "E", "F", "F#", "G", "G#", "A", "A#", "B" );

#2*(x/12)
my @CF_VALUES = (1, 1.0594630943592953, 1.122462048309373, 1.189207115002721, 1.2599210498948732, 1.3348398541700344, 1.4142135623730951, 1.4983070768766815, 1.5874010519681994, 1.681792830507429, 1.7817974362806785, 1.8877486253633868);

my @START_FREQS = (27.5,55,110,220,440,880,1760,3520,7040);

my $FREQUENCY = 0;
my $OCTAVE;
my $KEY;
my $INDEX = 12;

print "static const MidiNote_t Notes[" . 8 * 12 . "] = {\n";

#4 times

for ($OCTAVE=0; $OCTAVE<=8; $OCTAVE++)
{
    for ($KEY=0; $KEY<12; $KEY++)
    {
        print "\t{ $INDEX, \"" . $NOTES[$KEY] . $OCTAVE . "\", " . $START_FREQS[$OCTAVE] * $CF_VALUES[$KEY] / $CF_VALUES[9] .  " }";
        if ($KEY == 11 && $OCTAVE == 8) {
            print "\n};";
        } else {
            print ",\n";
        }
        $INDEX++;
    }
}

Gives this output:

 static const MidiNote_t Notes[96] = {
      { 12, "C0", 16.3515978312874 },
      { 13, "C#0", 17.3239144360545 },
      { 14, "D0", 18.354047994838 },
      { 15, "D#0", 19.4454364826301 },
      { 16, "E0", 20.6017223070544 },
      { 17, "F0", 21.8267644645627 },
      { 18, "F#0", 23.1246514194772 },
      { 19, "G0", 24.4997147488593 },
      { 20, "G#0", 25.9565435987466 },
      { 21, "A0", 27.5 },
      { 22, "A#0", 29.1352350948806 },
      { 23, "B0", 30.8677063285078 },
      { 24, "C1", 32.7031956625748 },
      { 25, "C#1", 34.647828872109 },
      { 26, "D1", 36.7080959896759 },
      { 27, "D#1", 38.8908729652601 },
      { 28, "E1", 41.2034446141087 },
      { 29, "F1", 43.6535289291255 },
      { 30, "F#1", 46.2493028389543 },
      { 31, "G1", 48.9994294977187 },
      { 32, "G#1", 51.9130871974931 },
      { 33, "A1", 55 },
      { 34, "A#1", 58.2704701897612 },
      { 35, "B1", 61.7354126570155 },
      { 36, "C2", 65.4063913251497 },
      { 37, "C#2", 69.295657744218 },
      { 38, "D2", 73.4161919793519 },
      { 39, "D#2", 77.7817459305202 },
      { 40, "E2", 82.4068892282175 },
      { 41, "F2", 87.307057858251 },
      { 42, "F#2", 92.4986056779086 },
      { 43, "G2", 97.9988589954373 },
      { 44, "G#2", 103.826174394986 },
      { 45, "A2", 110 },
      { 46, "A#2", 116.540940379522 },
      { 47, "B2", 123.470825314031 },
      { 48, "C3", 130.812782650299 },
      { 49, "C#3", 138.591315488436 },
      { 50, "D3", 146.832383958704 },
      { 51, "D#3", 155.56349186104 },
      { 52, "E3", 164.813778456435 },
      { 53, "F3", 174.614115716502 },
      { 54, "F#3", 184.997211355817 },
      { 55, "G3", 195.997717990875 },
      { 56, "G#3", 207.652348789973 },
      { 57, "A3", 220 },
      { 58, "A#3", 233.081880759045 },
      { 59, "B3", 246.941650628062 },
      { 60, "C4", 261.625565300599 },
      { 61, "C#4", 277.182630976872 },
      { 62, "D4", 293.664767917408 },
      { 63, "D#4", 311.126983722081 },
      { 64, "E4", 329.62755691287 },
      { 65, "F4", 349.228231433004 },
      { 66, "F#4", 369.994422711634 },
      { 67, "G4", 391.995435981749 },
      { 68, "G#4", 415.304697579945 },
      { 69, "A4", 440 },
      { 70, "A#4", 466.16376151809 },
      { 71, "B4", 493.883301256124 },
      { 72, "C5", 523.251130601197 },
      { 73, "C#5", 554.365261953744 },
      { 74, "D5", 587.329535834815 },
      { 75, "D#5", 622.253967444162 },
      { 76, "E5", 659.25511382574 },
      { 77, "F5", 698.456462866008 },
      { 78, "F#5", 739.988845423269 },
      { 79, "G5", 783.990871963499 },
      { 80, "G#5", 830.60939515989 },
      { 81, "A5", 880 },
      { 82, "A#5", 932.32752303618 },
      { 83, "B5", 987.766602512248 },
      { 84, "C6", 1046.50226120239 },
      { 85, "C#6", 1108.73052390749 },
      { 86, "D6", 1174.65907166963 },
      { 87, "D#6", 1244.50793488832 },
      { 88, "E6", 1318.51022765148 },
      { 89, "F6", 1396.91292573202 },
      { 90, "F#6", 1479.97769084654 },
      { 91, "G6", 1567.981743927 },
      { 92, "G#6", 1661.21879031978 },
      { 93, "A6", 1760 },
      { 94, "A#6", 1864.65504607236 },
      { 95, "B6", 1975.5332050245 },
      { 96, "C7", 2093.00452240479 },
      { 97, "C#7", 2217.46104781498 },
      { 98, "D7", 2349.31814333926 },
      { 99, "D#7", 2489.01586977665 },
      { 100, "E7", 2637.02045530296 },
      { 101, "F7", 2793.82585146403 },
      { 102, "F#7", 2959.95538169308 },
      { 103, "G7", 3135.96348785399 },
      { 104, "G#7", 3322.43758063956 },
      { 105, "A7", 3520 },
      { 106, "A#7", 3729.31009214472 },
      { 107, "B7", 3951.06641004899 },
      { 108, "C8", 4186.00904480958 },
      { 109, "C#8", 4434.92209562995 },
      { 110, "D8", 4698.63628667852 },
      { 111, "D#8", 4978.03173955329 },
      { 112, "E8", 5274.04091060592 },
      { 113, "F8", 5587.65170292806 },
      { 114, "F#8", 5919.91076338615 },
      { 115, "G8", 6271.92697570799 },
      { 116, "G#8", 6644.87516127912 },
      { 117, "A8", 7040 },
      { 118, "A#8", 7458.62018428944 },
      { 119, "B8", 7902.13282009799 }
 };