c++ - 生成正确的音调频率值

Question

我编写了一个 perl 脚本来生成要在 C++ header 中使用的注释信息条目列表。该脚本包含以下内容:

#!/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++;
    }
}

生成的输出如下所示:

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 },
...

尽管如此，我似乎无法在我的脚本生成的列表中获得结果频率，以与基本“A”频率对齐。

比如A4对应440Hz，A0对应27.5Hz。

如何正确对齐频率并将每个 Octave 音阶中的每个音符与其各自的基音 A 音符频率相乘？

Answer 1

您的程序期望 @START_FREQS 中的值是 C 频率，而不是 A 频率。我们可以将打印的值修改为基于 A 将所有内容除以 A 转换器，如下所示:

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

这就是整个程序:

#!/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++;
    }
}

给出这个输出:

 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 }
 };