mirror of
https://github.com/Michaelangel007/apple2_mockingboard.git
synced 2024-06-07 14:07:25 +00:00
363 lines
14 KiB
C
363 lines
14 KiB
C
/*
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Frequency To/From Mockingboard Tones
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by Michael Pohoreski
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GitHub: https://github.com/Michaelangel007/apple2_mockingboard
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The Mockingboard document at:
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* ftp://ftp.apple.asimov.net/pub/apple_II/documentation/hardware/sound/Mockingboard%20Docs.pdf
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has several incorrect values:
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APPENDIX E
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Course & Fine
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Note Octave Frequency Decimal Hex. Notes
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A 0 27.500 9 20 09 14 Exact 27.5 Hz -- bottom key on Piano
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A# 0 29.135 8 145 08 91
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B 0 30.868 8 22 08 16
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C 1 32.703 7 163 07 A3 <-- should be 7A2
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C# 1 34.648 7 53 07 35 <-- should be 734
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D 1 36.708 6 205 06 CD
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D# 1 38.891 6 108 06 6C <-- should be 66B
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E 1 41.203 6 15 06 0F
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F 1 43.654 5 184 05 B8
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F# 1 46.249 5 102 05 66
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G 1 48.999 5 24 05 18
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G# 1 51.913 4 207 04 CF
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A 1 55.000 4 138 04 8A Exact 55.0 Hz
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A# 1 58.270 4 73 04 49 <-- should be 448
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B 1 61.735 4 11 04 0B
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C 2 65.406 3 209 03 D1
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C# 2 69.296 3 154 03 9A
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D 2 73.416 3 102 03 66
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D# 2 77.782 3 54 03 36 <-- should be 335
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E 2 82.406 3 7 03 07
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F 2 87.308 2 220 02 DC
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F# 2 92.498 2 179 02 B3
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G 2 97.998 2 140 02 8C
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G# 3 103.826 2 103 02 67
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A 3 110.000 2 69 02 45 Exact 110.0 Hz
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A# 3 116.540 2 36 02 24
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B 3 123.470 2 5 02 05
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C 3 130.812 1 232 01 E8
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C# 3 138.592 1 205 01 CD
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D 3 146.832 1 179 01 B3
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D# 3 155.564 1 155 01 9B <-- should be 19A
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E 3 164.812 1 131 01 83
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F 3 174.616 1 110 01 6E
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F# 3 184.996 1 89 01 59
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G 3 195.996 1 70 01 46
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G# 3 207.652 1 51 01 33
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A 3 220.000 1 34 01 22
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A# 3 233.080 1 18 01 12
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B 3 246.940 1 2 01 02
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C 4 261.624 0 244 00 F4 -- Middle C4 --
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C# 4 277.184 0 230 00 E6
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D 4 293.664 0 217 00 D9
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D# 4 311.128 0 205 00 CD
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E 4 329.624 0 193 00 C1 <-- 329.628 Hz
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F 4 349.232 0 183 00 B7 <-- 349.228 Hz
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F# 4 369.992 0 172 00 AC
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G 4 391.992 0 163 00 A3
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G# 4 415.304 0 153 00 99
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A 4 440.000 0 145 00 91 Exact 440 Hz -- Concert Tuning A440
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A# 4 466.160 0 137 00 89
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B 4 493.880 0 129 00 81
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C 5 523.248 0 122 00 7A
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C# 5 554.368 0 115 00 73
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D 5 587.328 0 108 00 6C
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D# 5 622.256 0 102 00 66
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E 5 659.248 0 96 00 60 <-- 659.255 Hz
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F 5 698.464 0 91 00 58 <-- Should be 5B
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F# 5 739.984 0 86 00 56
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G 5 783.984 0 81 00 51
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G# 5 830.608 0 76 00 4C
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A 5 880.000 0 72 00 48 Exact 880 Hz
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A# 5 932.320 0 68 00 44 <-- 932.328 Hz
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B 5 987.760 0 64 00 40 <-- 987.767 Hz
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C 6 1046.496 0 61 00 3D -- every frequency
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C# 6 1108.736 0 57 00 39 -- from this point
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D 6 1174.656 0 54 00 36 -- forward is slightly
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D# 6 1244.512 0 51 00 33 -- off except for 'A'
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E 6 1318.496 0 48 00 30
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F 6 1396.928 0 45 00 2D <--1396.913 Hz
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F# 6 1479.968 0 43 00 2B
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G 6 1567.968 0 40 00 2B <-- Should be 28
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G# 6 1661.216 0 38 00 26
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A 6 1760.000 0 36 00 24 Exact 1760 Hz
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A# 6 1864.640 0 34 00 22
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B 6 1975.520 0 32 00 20
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C 7 2092.992 0 30 00 1E <-- 2093.005 Hz
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C# 7 2217.472 0 28 00 1C
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D 7 2349.312 0 27 00 1B
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D# 7 2489.024 0 25 00 19
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E 7 2636.992 0 24 00 18
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F 7 2793.856 0 22 00 16
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F# 7 2959.936 0 21 00 15
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G 7 3135.936 0 20 00 14
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G# 7 3322.432 0 19 00 13
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A 7 3520.000 0 18 00 12 Exact 3520 Hz
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A# 7 3729.280 0 17 00 11
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B 7 3951.040 0 16 00 10
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C 8 4185.984 0 15 00 0F -- top key on Piano
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C# 8 4434.944 0 14 00 0E
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D 8 4698.624 0 13 00 0D
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D# 8 4978.048 0 12 00 0C
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E 8 5273.984 0 12 00 0C <-- 5274.041 Hz
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F 8 5587.712 0 11 00 0B
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F# 8 5919.872 0 10 00 0A
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G 8 6271.872 0 10 00 0A
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G# 8 6644.864 0 9 00 09
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A 8 7040.000 0 9 00 09 Exact 7040 Hz
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A# 8 7458.560 0 8 00 08
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B 8 7902.080 0 8 00 08
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Here are the correct frequencies and tones
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along with the relative error:
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Note Frequency Tone reproduced Relative Error
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A0 27.500 Hz -> $090F ~ 27.503 Hz (0.012 %)
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A0# 29.135 Hz -> $088D ~ 29.137 Hz (0.005 %)
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B0 30.868 Hz -> $0812 ~ 30.871 Hz (0.012 %)
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C1 32.703 Hz -> $079E ~ 32.708 Hz (0.014 %)
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C1# 34.648 Hz -> $0730 ~ 34.663 Hz (0.044 %)
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D1 36.708 Hz -> $06C9 ~ 36.719 Hz (0.029 %)
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D1# 38.891 Hz -> $0667 ~ 38.914 Hz (0.060 %)
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E1 41.203 Hz -> $060B ~ 41.228 Hz (0.060 %)
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F1 43.654 Hz -> $05B5 ~ 43.655 Hz (0.004 %)
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F1# 46.249 Hz -> $0563 ~ 46.251 Hz (0.004 %)
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G1 48.999 Hz -> $0515 ~ 49.024 Hz (0.050 %)
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G1# 51.913 Hz -> $04CC ~ 51.938 Hz (0.049 %)
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A1 55.000 Hz -> $0487 ~ 55.030 Hz (0.055 %)
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A1# 58.270 Hz -> $0446 ~ 58.300 Hz (0.051 %)
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B1 61.735 Hz -> $0409 ~ 61.743 Hz (0.012 %)
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C2 65.406 Hz -> $03CF ~ 65.416 Hz (0.014 %)
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C2# 69.296 Hz -> $0398 ~ 69.326 Hz (0.044 %)
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D2 73.416 Hz -> $0364 ~ 73.480 Hz (0.086 %)
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D2# 77.782 Hz -> $0333 ~ 77.876 Hz (0.121 %)
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E2 82.407 Hz -> $0305 ~ 82.510 Hz (0.125 %)
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F2 87.307 Hz -> $02DA ~ 87.370 Hz (0.072 %)
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F2# 92.499 Hz -> $02B1 ~ 92.569 Hz (0.076 %)
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G2 97.999 Hz -> $028A ~ 98.123 Hz (0.127 %)
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G2# 103.826 Hz -> $0266 ~ 103.877 Hz (0.049 %)
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A2 110.000 Hz -> $0243 ~ 110.156 Hz (0.142 %)
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A2# 116.541 Hz -> $0223 ~ 116.600 Hz (0.051 %)
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B2 123.471 Hz -> $0204 ~ 123.605 Hz (0.109 %)
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C3 130.813 Hz -> $01E7 ~ 130.966 Hz (0.117 %)
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C3# 138.591 Hz -> $01CC ~ 138.653 Hz (0.044 %)
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D3 146.832 Hz -> $01B2 ~ 146.959 Hz (0.086 %)
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D3# 155.563 Hz -> $0199 ~ 155.942 Hz (0.243 %)
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E3 164.814 Hz -> $0182 ~ 165.234 Hz (0.255 %)
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F3 174.614 Hz -> $016D ~ 174.740 Hz (0.072 %)
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F3# 184.997 Hz -> $0158 ~ 185.408 Hz (0.222 %)
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G3 195.998 Hz -> $0145 ~ 196.247 Hz (0.127 %)
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G3# 207.652 Hz -> $0133 ~ 207.753 Hz (0.049 %)
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A3 220.000 Hz -> $0121 ~ 220.693 Hz (0.315 %)
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A3# 233.082 Hz -> $0111 ~ 233.627 Hz (0.234 %)
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B3 246.942 Hz -> $0102 ~ 247.210 Hz (0.109 %)
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C4 261.626 Hz -> $00F3 ~ 262.470 Hz (0.323 %)
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C4# 277.183 Hz -> $00E6 ~ 277.306 Hz (0.044 %)
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D4 293.665 Hz -> $00D9 ~ 293.918 Hz (0.086 %)
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D4# 311.127 Hz -> $00CC ~ 312.648 Hz (0.489 %)
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E4 329.628 Hz -> $00C1 ~ 330.468 Hz (0.255 %)
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F4 349.228 Hz -> $00B6 ~ 350.441 Hz (0.347 %)
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F4# 369.994 Hz -> $00AC ~ 370.816 Hz (0.222 %)
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G4 391.995 Hz -> $00A2 ~ 393.705 Hz (0.436 %)
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G4# 415.305 Hz -> $0099 ~ 416.865 Hz (0.376 %)
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A4 440.000 Hz -> $0090 ~ 442.919 Hz (0.663 %)
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A4# 466.164 Hz -> $0088 ~ 468.973 Hz (0.603 %)
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B4 493.883 Hz -> $0081 ~ 494.421 Hz (0.109 %)
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C5 523.251 Hz -> $0079 ~ 527.110 Hz (0.737 %)
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C5# 554.365 Hz -> $0073 ~ 554.611 Hz (0.044 %)
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D5 587.330 Hz -> $006C ~ 590.558 Hz (0.550 %)
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D5# 622.254 Hz -> $0066 ~ 625.297 Hz (0.489 %)
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E5 659.255 Hz -> $0060 ~ 664.378 Hz (0.777 %)
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F5 698.456 Hz -> $005B ~ 700.882 Hz (0.347 %)
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F5# 739.989 Hz -> $0056 ~ 741.631 Hz (0.222 %)
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G5 783.991 Hz -> $0051 ~ 787.411 Hz (0.436 %)
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G5# 830.609 Hz -> $004C ~ 839.214 Hz (1.036 %)
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A5 880.000 Hz -> $0048 ~ 885.837 Hz (0.663 %)
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A5# 932.328 Hz -> $0044 ~ 937.945 Hz (0.603 %)
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B5 987.767 Hz -> $0040 ~ 996.567 Hz (0.891 %)
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C6 1046.502 Hz -> $003C ~1063.005 Hz (1.577 %)
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C6# 1108.731 Hz -> $0039 ~1118.952 Hz (0.922 %)
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D6 1174.659 Hz -> $0036 ~1181.116 Hz (0.550 %)
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D6# 1244.508 Hz -> $0033 ~1250.594 Hz (0.489 %)
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E6 1318.510 Hz -> $0030 ~1328.756 Hz (0.777 %)
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F6 1396.913 Hz -> $002D ~1417.339 Hz (1.462 %)
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F6# 1479.978 Hz -> $002B ~1483.262 Hz (0.222 %)
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G6 1567.982 Hz -> $0028 ~1594.507 Hz (1.692 %)
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G6# 1661.219 Hz -> $0026 ~1678.428 Hz (1.036 %)
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A6 1760.000 Hz -> $0024 ~1771.674 Hz (0.663 %)
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A6# 1864.655 Hz -> $0022 ~1875.890 Hz (0.603 %)
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B6 1975.533 Hz -> $0020 ~1993.133 Hz (0.891 %)
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C7 2093.005 Hz -> $001E ~2126.009 Hz (1.577 %)
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C7# 2217.461 Hz -> $001C ~2277.867 Hz (2.724 %)
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D7 2349.318 Hz -> $001B ~2362.232 Hz (0.550 %)
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D7# 2489.016 Hz -> $0019 ~2551.211 Hz (2.499 %)
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E7 2637.020 Hz -> $0018 ~2657.511 Hz (0.777 %)
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F7 2793.826 Hz -> $0016 ~2899.103 Hz (3.768 %)
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F7# 2959.955 Hz -> $0015 ~3037.156 Hz (2.608 %)
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G7 3135.963 Hz -> $0014 ~3189.014 Hz (1.692 %)
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G7# 3322.438 Hz -> $0013 ~3356.856 Hz (1.036 %)
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A7 3520.000 Hz -> $0012 ~3543.348 Hz (0.663 %)
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A7# 3729.310 Hz -> $0011 ~3751.781 Hz (0.603 %)
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B7 3951.066 Hz -> $0010 ~3986.267 Hz (0.891 %)
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C8 4186.009 Hz -> $000F ~4252.018 Hz (1.577 %)
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C8# 4434.922 Hz -> $000E ~4555.734 Hz (2.724 %)
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D8 4698.636 Hz -> $000D ~4906.175 Hz (4.417 %)
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D8# 4978.032 Hz -> $000C ~5315.023 Hz (6.770 %)
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E8 5274.041 Hz -> $000C ~5315.023 Hz (0.777 %)
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F8 5587.652 Hz -> $000B ~5798.206 Hz (3.768 %)
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F8# 5919.911 Hz -> $000A ~6378.027 Hz (7.739 %)
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G8 6271.927 Hz -> $000A ~6378.027 Hz (1.692 %)
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G8# 6644.875 Hz -> $0009 ~7086.697 Hz (6.649 %)
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Reference:
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* https://en.wikipedia.org/wiki/Piano_key_frequencies
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* http://www.sciencebuddies.org/Fi les/3443/5/Phys_img024.jpg
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*/
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#include <stdio.h>
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#include <math.h>
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// Every 64th cycle is stretched to be a 65th cycle
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//const double _1MHz_NTSC = 14318180.0 / 14.0; // 1,022,727 Hz
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const double _1MHz_NTSC = 1020484.32; // Avg Hz, Table 3.1, Page 3-5, UtA2E, Jim Sather
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//const double _1MHz_PAL = 14250000.0 / 14.0;
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//const double A2_FREQ = 1023000.0; // common incorrect value
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/*
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Mockingboard:
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Tone Freq = A2 Clock Freq / ((256*Course + Fine) * 16)
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6502:
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Master = 14.31818 MHz
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NTSC Cycle = 14.31818 / 14 = 1.0227271429... MHz = 1022727 Hz
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PAL Cycle = 14.25 / 14 = 1.0178571429... MHz = 1017857 Hz
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n = Floor( 1,022,727 / freq )
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Course = Floor( n / 4096 )
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Fine = (n - (4096*Course)) / 16
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*/
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// Convert Frequency into Mockingboard Tone Period
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// ========================================================================
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int MockingboardGetTone( double freq_hz )
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{
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const int n = (int) (_1MHz_NTSC / freq_hz);
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const int hi = n / 4096;
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const int lo = (n - (hi * 4096)) / 16;
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return (hi*256) + lo;
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}
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// Convert Mockingboard Tone Period into Frequency
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// ========================================================================
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double MockingboardGetFreq( int tone_period )
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{
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// / 256 = >> 8
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// * 4096 = << 12
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// int n = ((tone_period & 0xFF00) << 4) + ((tone_period & 0x00FF) << 4);
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return _1MHz_NTSC / (double) (tone_period << 4);
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}
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// ========================================================================
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int main( const int nArg, const char *aArg[] )
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{
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(void) nArg;
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// 0freq = asm low byte
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// 1freq = asm high byte
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int is_asm = 1*(aArg[0][0] == '0') +
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2*(aArg[0][0] == '1') ;
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const char *names[ 12 ] =
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{
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"A ", // 2^( 0/12)
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"A#", // 2^( 1/12)
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"B ", // 2^( 2/12)
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"C ", // 2^( 3/12)
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"C#", // 2^( 4/12)
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"D ", // 2^( 5/12)
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"D#", // 2^( 6/12)
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"E ", // 2^( 7/12)
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"F ", // 2^( 8/12)
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"F#", // 2^( 9/12)
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"G ", // 2^(10/12)
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"G#" // 2^(11/12)
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};
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double halfstep_freq[12];
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for( int half_step = 0; half_step < 12; half_step++ )
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halfstep_freq[ half_step ] = pow( 2.0, (half_step / 12.0) );
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for( int octave = 0; octave < 8; octave++ )
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{
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double octave_freq = 440.0 * pow( 2.0, (octave - 4.0));
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for( int half_step = 0; half_step < 12; half_step++ )
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{
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double actual = octave_freq * halfstep_freq[ half_step ];
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int tone = MockingboardGetTone( actual );
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double measure = MockingboardGetFreq( tone );
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double rel_err = (measure - actual) / actual * 100.0;
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if( is_asm )
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printf( "%*s.byte $%02X ; %c%d%c %8.3f Hz\n"
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, 8, " "
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,(tone >> ((is_asm-1) * 8)) & 0xFF
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, names[ half_step ][0]
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, octave + (half_step > 2)
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, names[ half_step ][1]
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, actual
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);
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else
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printf( "%c%d%c %8.3f Hz -> $%04X (%3d %3d) ~%8.3f Hz (%5.3f %%)\n"
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, names[ half_step ][0]
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, octave + (half_step > 2)
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, names[ half_step ][1]
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, actual
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, tone
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, (tone >> 8) & 0xFF
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, (tone >> 0) & 0xFF
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, measure
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, rel_err
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);
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if( half_step == 2 )
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printf( "\n" );
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}
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}
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printf( "\n" );
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return 0;
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}
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