Pulse Channel frequency chart: Difference between revisions

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(Genesis!)
 
(Greatly expand the table. Among other things, for a page with "frequency" in the title, we really ought to include the frequencies and not just the periods. :) This also adds PAL periods, and a code block for easier use in new sound drivers.)
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{| border="1" cellpadding="1"
== MIDI Tuning Table ==
|'''Pitch''' || '''Timer High (d2-d0)''' || '''Timer Low'''
 
Using the [https://en.wikipedia.org/wiki/MIDI_tuning_standard MIDI Tuning Standard] with A=440 Hz, we can derive the equivalent period timer value for the two [[APU Pulse | Pulse]] channels. Due to limitations on the 11-bit period's range, the lowest standard MIDI frequency that can be reproduced with acceptable tuning is A-1 (55 Hz) on NTSC, and G#1 (51.91 Hz) on PAL. Here we show the desired frequency for each MIDI index, the closest period value, and the resulting tuning error (in cents) from the standard.
 
'''Note''': The [[APU Triangle | Triangle]] channel can make use of the same 11-bit period values. Due to its longer 32-step sequence, it will sound exactly one octave lower (half of the apparent frequency) compared to the equivalent period on Pulse.
 
{| class="wikitable" style="text-align: right"
|-
|-
| A-1 || 07 || F0
| colspan="3" bgcolor = DDDDDD style="text-align: center; font-weight: bold" | MIDI
|-
| colspan="3" bgcolor = FFDDDD style="text-align: center; font-weight: bold" | NTSC APU Pulse
| Bb1 || 07 || 7C
| colspan="3" bgcolor = DDDDFF style="text-align: center; font-weight: bold" | PAL APU Pulse
|-
| B-1 || 07 || 10
|-
| C-2 || 06 || AC
|-
| C#2 || 06 || 4C
|-
| D-2 || 05 || F2
|-
| Eb2 || 05 || 9E
|-
| E-2 || 05 || 4C
|-
| F-2 || 05 || 01
|-
| F#2 || 04 || B8
|-
| G-2 || 04 || 74
|-
| Ab2 || 04 || 34
|-
| A-2 || 03 || F8
|-
| Bb2 || 03 || BE
|-
| B-2 || 03 || 88
|-
| C-3 || 03 || 56
|-
| C#3 || 03 || 26
|-
| D-3 || 02 || F9
|-
| Eb3 || 02 || CF
|-
| E-3 || 02 || A6
|-
| F-3 || 02 || 80
|-
| F#3 || 02 || 5C
|-
| G-3 || 02 || 3A
|-
| Ab3 || 02 || 1A
|-
| A-3 || 01 || FC
|-
| Bb3 || 01 || DF
|-
| B-3 || 01 || C4
|-
| C-4 || 01 || AB
|-
| C#4 || 01 || 93
|-
| D-4 || 01 || 7C
|-
| Eb4 || 01 || 67
|-
| E-4 || 01 || 53
|-
| F-4 || 01 || 40
|-
| F#4 || 01 || 2E
|-
| G-4 || 01 || 1D
|-
| Ab4 || 01 || 0D
|-
| A-4 || 00 || FE
|-
| Bb4 || 00 || EF
|-
| B-4 || 00 || E2
|-
| C-5 || 00 || D5
|-
| C#5 || 00 || C9
|-
| D-5 || 00 || BE
|-
| Eb5 || 00 || B3
|-
| E-5 || 00 || A9
|-
| F-5 || 00 || A0
|-
| F#5 || 00 || 97
|-
| G-5 || 00 || 8E
|-
| Ab5 || 00 || 86
|-
| A-5 || 00 || 7E
|-
| Bb5 || 00 || 77
|-
| B-5 || 00 || 71
|-
| C-6 || 00 || 6A
|-
| C#6 || 00 || 64
|-
| D-6 || 00 || 5F
|-
| Eb6 || 00 || 59
|-
| E-6 || 00 || 54
|-
| F-6 || 00 || 50
|-
| F#6 || 00 || 4B
|-
| G-6 || 00 || 47
|-
| Ab6 || 00 || 43
|-
| A-6 || 00 || 3F
|-
| Bb6 || 00 || 3B
|-
| B-6 || 00 || 38
|-
| C-7 || 00 || 35
|-
| C#7 || 00 || 32
|-
| D-7 || 00 || 2F
|-
| Eb7 || 00 || 2C
|-
| E-7 || 00 || 2A
|-
| F-7 || 00 || 28
|-
| F#7 || 00 || 26
|-
| G-7 || 00 || 24
|-
| Ab7 || 00 || 22
|-
| A-7 || 00 || 20
|-
| Bb7 || 00 || 1E
|-
| B-7 || 00 || 1C
|-
|-
! Index || Note || Frequency || 11bit Period || Frequency || Tuning || 11bit Period || Frequency || Tuning
|-
| 31 || G-1 || 49.00 || bgcolor=FFDDDD | - || - || - || bgcolor=DDDDFF | $7FF || 50.74 || +60c
|-
| 32 || G#1 || 51.91 || bgcolor=FFDDDD | $7FF || 54.62 || +88c || bgcolor=DDDDFF | $7D1 || 51.90 || +0c
|-
| 33 || A-1 || 55.00 || bgcolor=FFDDDD | $7F1 || 55.00 || +0c || bgcolor=DDDDFF | $760 || 55.01 || +0c
|-
| 34 || A#1 || 58.27 || bgcolor=FFDDDD | $77F || 58.26 || +0c || bgcolor=DDDDFF | $6F6 || 58.28 || +0c
|-
| 35 || B-1 || 61.74 || bgcolor=FFDDDD | $713 || 61.73 || +0c || bgcolor=DDDDFF | $692 || 61.74 || +0c
|-
| 36 || C-2 || 65.41 || bgcolor=FFDDDD | $6AD || 65.42 || +0c || bgcolor=DDDDFF | $634 || 65.40 || +0c
|-
| 37 || C#2 || 69.30 || bgcolor=FFDDDD | $64D || 69.31 || +0c || bgcolor=DDDDFF | $5DB || 69.28 || -1c
|-
| 38 || D-2 || 73.42 || bgcolor=FFDDDD | $5F3 || 73.40 || +0c || bgcolor=DDDDFF | $586 || 73.44 || +0c
|-
| 39 || D#2 || 77.78 || bgcolor=FFDDDD | $59D || 77.79 || +0c || bgcolor=DDDDFF | $537 || 77.78 || +0c
|-
| 40 || E-2 || 82.41 || bgcolor=FFDDDD | $54C || 82.43 || +1c || bgcolor=DDDDFF | $4EC || 82.41 || +0c
|-
| 41 || F-2 || 87.31 || bgcolor=FFDDDD | $500 || 87.32 || +0c || bgcolor=DDDDFF | $4A5 || 87.32 || +0c
|-
| 42 || F#2 || 92.50 || bgcolor=FFDDDD | $4B8 || 92.52 || +0c || bgcolor=DDDDFF | $462 || 92.53 || +1c
|-
| 43 || G-2 || 98.00 || bgcolor=FFDDDD | $474 || 98.04 || +1c || bgcolor=DDDDFF | $423 || 98.03 || +1c
|-
| 44 || G#2 || 103.83 || bgcolor=FFDDDD | $434 || 103.86 || +1c || bgcolor=DDDDFF | $3E8 || 103.81 || +0c
|-
| 45 || A-2 || 110.00 || bgcolor=FFDDDD | $3F8 || 109.99 || +0c || bgcolor=DDDDFF | $3B0 || 109.96 || -1c
|-
| 46 || A#2 || 116.54 || bgcolor=FFDDDD | $3BF || 116.52 || +0c || bgcolor=DDDDFF | $37B || 116.49 || -1c
|-
| 47 || B-2 || 123.47 || bgcolor=FFDDDD | $389 || 123.47 || +0c || bgcolor=DDDDFF | $349 || 123.41 || -1c
|-
| 48 || C-3 || 130.81 || bgcolor=FFDDDD | $356 || 130.83 || +0c || bgcolor=DDDDFF | $319 || 130.87 || +1c
|-
| 49 || C#3 || 138.59 || bgcolor=FFDDDD | $326 || 138.61 || +0c || bgcolor=DDDDFF | $2ED || 138.55 || -1c
|-
| 50 || D-3 || 146.83 || bgcolor=FFDDDD | $2F9 || 146.80 || +0c || bgcolor=DDDDFF | $2C3 || 146.77 || -1c
|-
| 51 || D#3 || 155.56 || bgcolor=FFDDDD | $2CE || 155.58 || +0c || bgcolor=DDDDFF | $29B || 155.56 || +0c
|-
| 52 || E-3 || 164.81 || bgcolor=FFDDDD | $2A6 || 164.74 || -1c || bgcolor=DDDDFF | $275 || 164.94 || +1c
|-
| 53 || F-3 || 174.61 || bgcolor=FFDDDD | $280 || 174.51 || -1c || bgcolor=DDDDFF | $252 || 174.64 || +0c
|-
| 54 || F#3 || 185.00 || bgcolor=FFDDDD | $25C || 184.89 || -1c || bgcolor=DDDDFF | $231 || 184.90 || -1c
|-
| 55 || G-3 || 196.00 || bgcolor=FFDDDD | $23A || 195.90 || -1c || bgcolor=DDDDFF | $211 || 196.06 || +1c
|-
| 56 || G#3 || 207.65 || bgcolor=FFDDDD | $21A || 207.53 || -1c || bgcolor=DDDDFF | $1F3 || 207.83 || +1c
|-
| 57 || A-3 || 220.00 || bgcolor=FFDDDD | $1FB || 220.20 || +2c || bgcolor=DDDDFF | $1D7 || 220.15 || +1c
|-
| 58 || A#3 || 233.08 || bgcolor=FFDDDD | $1DF || 233.04 || +0c || bgcolor=DDDDFF | $1BD || 232.99 || -1c
|-
| 59 || B-3 || 246.94 || bgcolor=FFDDDD | $1C4 || 246.93 || +0c || bgcolor=DDDDFF | $1A4 || 246.82 || -1c
|-
| 60 || C-4 || 261.63 || bgcolor=FFDDDD | $1AB || 261.36 || -2c || bgcolor=DDDDFF | $18C || 261.75 || +1c
|-
| 61 || C#4 || 277.18 || bgcolor=FFDDDD | $193 || 276.88 || -2c || bgcolor=DDDDFF | $176 || 277.10 || -1c
|-
| 62 || D-4 || 293.66 || bgcolor=FFDDDD | $17C || 293.60 || +0c || bgcolor=DDDDFF | $161 || 293.54 || -1c
|-
| 63 || D#4 || 311.13 || bgcolor=FFDDDD | $167 || 310.72 || -2c || bgcolor=DDDDFF | $14D || 311.12 || +0c
|-
| 64 || E-4 || 329.63 || bgcolor=FFDDDD | $152 || 329.97 || +2c || bgcolor=DDDDFF | $13A || 329.88 || +1c
|-
| 65 || F-4 || 349.23 || bgcolor=FFDDDD | $13F || 349.57 || +2c || bgcolor=DDDDFF | $129 || 348.70 || -3c
|-
| 66 || F#4 || 369.99 || bgcolor=FFDDDD | $12D || 370.40 || +2c || bgcolor=DDDDFF | $118 || 369.80 || -1c
|-
| 67 || G-4 || 392.00 || bgcolor=FFDDDD | $11C || 392.49 || +2c || bgcolor=DDDDFF | $108 || 392.12 || +1c
|-
| 68 || G#4 || 415.30 || bgcolor=FFDDDD | $10C || 415.84 || +2c || bgcolor=DDDDFF | $0F9 || 415.65 || +1c
|-
| 69 || A-4 || 440.00 || bgcolor=FFDDDD | $0FD || 440.40 || +2c || bgcolor=DDDDFF | $0EB || 440.31 || +1c
|-
| 70 || A#4 || 466.16 || bgcolor=FFDDDD | $0EF || 466.09 || +0c || bgcolor=DDDDFF | $0DE || 465.98 || -1c
|-
| 71 || B-4 || 493.88 || bgcolor=FFDDDD | $0E1 || 494.96 || +4c || bgcolor=DDDDFF | $0D1 || 494.82 || +3c
|-
| 72 || C-5 || 523.25 || bgcolor=FFDDDD | $0D5 || 522.71 || -2c || bgcolor=DDDDFF | $0C6 || 522.18 || -4c
|-
| 73 || C#5 || 554.37 || bgcolor=FFDDDD | $0C9 || 553.77 || -2c || bgcolor=DDDDFF | $0BA || 555.68 || +4c
|-
| 74 || D-5 || 587.33 || bgcolor=FFDDDD | $0BD || 588.74 || +4c || bgcolor=DDDDFF | $0B0 || 587.08 || -1c
|-
| 75 || D#5 || 622.25 || bgcolor=FFDDDD | $0B3 || 621.45 || -2c || bgcolor=DDDDFF | $0A6 || 622.23 || +0c
|-
| 76 || E-5 || 659.26 || bgcolor=FFDDDD | $0A9 || 658.00 || -3c || bgcolor=DDDDFF | $09D || 657.68 || -4c
|-
| 77 || F-5 || 698.46 || bgcolor=FFDDDD | $09F || 699.13 || +2c || bgcolor=DDDDFF | $094 || 697.40 || -3c
|-
| 78 || F#5 || 739.99 || bgcolor=FFDDDD | $096 || 740.80 || +2c || bgcolor=DDDDFF | $08B || 742.24 || +5c
|-
| 79 || G-5 || 783.99 || bgcolor=FFDDDD | $08E || 782.24 || -4c || bgcolor=DDDDFF | $084 || 781.30 || -6c
|-
| 80 || G#5 || 830.61 || bgcolor=FFDDDD | $086 || 828.60 || -4c || bgcolor=DDDDFF | $07C || 831.30 || +1c
|-
| 81 || A-5 || 880.00 || bgcolor=FFDDDD | $07E || 880.79 || +2c || bgcolor=DDDDFF | $075 || 880.62 || +1c
|-
| 82 || A#5 || 932.33 || bgcolor=FFDDDD | $077 || 932.17 || +0c || bgcolor=DDDDFF | $06E || 936.15 || +7c
|-
| 83 || B-5 || 987.77 || bgcolor=FFDDDD | $070 || 989.92 || +4c || bgcolor=DDDDFF | $068 || 989.65 || +3c
|-
| 84 || C-6 || 1046.50 || bgcolor=FFDDDD | $06A || 1045.43 || -2c || bgcolor=DDDDFF | $062 || 1049.63 || +5c
|-
| 85 || C#6 || 1108.73 || bgcolor=FFDDDD | $064 || 1107.53 || -2c || bgcolor=DDDDFF | $05D || 1105.46 || -5c
|-
| 86 || D-6 || 1174.66 || bgcolor=FFDDDD | $05E || 1177.48 || +4c || bgcolor=DDDDFF | $057 || 1180.83 || +9c
|-
| 87 || D#6 || 1244.51 || bgcolor=FFDDDD | $059 || 1242.90 || -2c || bgcolor=DDDDFF | $052 || 1251.96 || +10c
|-
| 88 || E-6 || 1318.51 || bgcolor=FFDDDD | $054 || 1316.01 || -3c || bgcolor=DDDDFF | $04E || 1315.35 || -4c
|-
| 89 || F-6 || 1396.91 || bgcolor=FFDDDD | $04F || 1398.26 || +2c || bgcolor=DDDDFF | $049 || 1404.23 || +9c
|-
| 90 || F#6 || 1479.98 || bgcolor=FFDDDD | $04B || 1471.85 || -10c || bgcolor=DDDDFF | $045 || 1484.47 || +5c
|-
| 91 || G-6 || 1567.98 || bgcolor=FFDDDD | $046 || 1575.50 || +8c || bgcolor=DDDDFF | $041 || 1574.44 || +7c
|-
| 92 || G#6 || 1661.22 || bgcolor=FFDDDD | $042 || 1669.56 || +9c || bgcolor=DDDDFF | $03E || 1649.41 || -12c
|-
| 93 || A-6 || 1760.00 || bgcolor=FFDDDD | $03F || 1747.83 || -12c || bgcolor=DDDDFF | $03A || 1761.24 || +1c
|-
| 94 || A#6 || 1864.66 || bgcolor=FFDDDD | $03B || 1864.35 || +0c || bgcolor=DDDDFF | $037 || 1855.59 || -8c
|-
| 95 || B-6 || 1975.53 || bgcolor=FFDDDD | $038 || 1962.47 || -11c || bgcolor=DDDDFF | $034 || 1960.62 || -13c
|-
| 96 || C-7 || 2093.00 || bgcolor=FFDDDD | $034 || 2110.58 || +14c || bgcolor=DDDDFF | $031 || 2078.26 || -12c
|-
| 97 || C#7 || 2217.46 || bgcolor=FFDDDD | $031 || 2237.22 || +15c || bgcolor=DDDDFF | $02E || 2210.91 || -5c
|-
| 98 || D-7 || 2349.32 || bgcolor=FFDDDD | $02F || 2330.43 || -14c || bgcolor=DDDDFF | $02B || 2361.66 || +9c
|-
| 99 || D#7 || 2489.02 || bgcolor=FFDDDD | $02C || 2485.80 || -2c || bgcolor=DDDDFF | $029 || 2474.12 || -10c
|-
| 100 || E-7 || 2637.02 || bgcolor=FFDDDD | $029 || 2663.35 || +17c || bgcolor=DDDDFF | $026 || 2664.43 || +18c
|-
| 101 || F-7 || 2793.83 || bgcolor=FFDDDD | $027 || 2796.52 || +2c || bgcolor=DDDDFF | $024 || 2808.46 || +9c
|-
| 102 || F#7 || 2959.96 || bgcolor=FFDDDD | $025 || 2943.71 || -10c || bgcolor=DDDDFF | $022 || 2968.94 || +5c
|-
| 103 || G-7 || 3135.96 || bgcolor=FFDDDD | $023 || 3107.24 || -16c || bgcolor=DDDDFF | $020 || 3148.88 || +7c
|-
| 104 || G#7 || 3322.44 || bgcolor=FFDDDD | $021 || 3290.02 || -17c || bgcolor=DDDDFF | $01E || 3352.03 || +15c
|-
| 105 || A-7 || 3520.00 || bgcolor=FFDDDD | $01F || 3495.65 || -12c || bgcolor=DDDDFF | $01D || 3463.76 || -28c
|-
| 106 || A#7 || 3729.31 || bgcolor=FFDDDD | $01D || 3728.69 || +0c || bgcolor=DDDDFF | $01B || 3711.18 || -8c
|-
| 107 || B-7 || 3951.07 || bgcolor=FFDDDD | $01B || 3995.03 || +19c || bgcolor=DDDDFF | $019 || 3996.65 || +20c
|-
| 108 || C-8 || 4186.01 || bgcolor=FFDDDD | $01A || 4142.99 || -18c || bgcolor=DDDDFF | $018 || 4156.52 || -12c
|-
| 109 || C#8 || 4434.92 || bgcolor=FFDDDD | $018 || 4474.43 || +15c || bgcolor=DDDDFF | $016 || 4517.95 || +32c
|-
| 110 || D-8 || 4698.64 || bgcolor=FFDDDD | $017 || 4660.87 || -14c || bgcolor=DDDDFF | $015 || 4723.32 || +9c
|-
| 111 || D#8 || 4978.03 || bgcolor=FFDDDD | $015 || 5084.58 || +37c || bgcolor=DDDDFF | $014 || 4948.24 || -10c
|-
| 112 || E-8 || 5274.04 || bgcolor=FFDDDD | $014 || 5326.71 || +17c || bgcolor=DDDDFF | $013 || 5195.65 || -26c
|-
| 113 || F-8 || 5587.65 || bgcolor=FFDDDD | $013 || 5593.04 || +2c || bgcolor=DDDDFF | $012 || 5469.10 || -37c
|-
| 114 || F#8 || 5919.91 || bgcolor=FFDDDD | $012 || 5887.41 || -10c || bgcolor=DDDDFF | $011 || 5772.94 || -44c
|-
| 115 || G-8 || 6271.93 || bgcolor=FFDDDD | $011 || 6214.49 || -16c || bgcolor=DDDDFF | $010 || 6112.53 || -45c
|-
| 116 || G#8 || 6644.88 || bgcolor=FFDDDD | $010 || 6580.05 || -17c || bgcolor=DDDDFF | $00F || 6494.56 || -40c
|-
| 117 || A-8 || 7040.00 || bgcolor=FFDDDD | $00F || 6991.30 || -12c || bgcolor=DDDDFF | $00E || 6927.53 || -28c
|-
| 118 || A#8 || 7458.62 || bgcolor=FFDDDD | $00E || 7457.39 || +0c || bgcolor=DDDDFF | $00D || 7422.35 || -8c
|-
| 119 || B-8 || 7902.13 || bgcolor=FFDDDD | $00D || 7990.06 || +19c || bgcolor=DDDDFF | $00C || 7993.30 || +20c
|-
| 120 || C-9 || 8372.02 || bgcolor=FFDDDD | $00C || 8604.68 || +47c || bgcolor=DDDDFF | $00B || 8659.41 || +58c
|-
| 121 || C#9 || 8869.84 || bgcolor=FFDDDD | $00C || 8604.68 || -53c || bgcolor=DDDDFF | $00B || 8659.41 || -42c
|-
| 122 || D-9 || 9397.27 || bgcolor=FFDDDD | $00B || 9321.73 || -14c || bgcolor=DDDDFF | $00A || 9446.63 || +9c
|-
| 123 || D#9 || 9956.06 || bgcolor=FFDDDD | $00A || 10169.16 || +37c || bgcolor=DDDDFF | $009 || 10391.29 || +74c
|-
| 124 || E-9 || 10548.08 || bgcolor=FFDDDD | $00A || 10169.16 || -63c || bgcolor=DDDDFF | $009 || 10391.29 || -26c
|-
| 125 || F-9 || 11175.30 || bgcolor=FFDDDD | $009 || 11186.08 || +2c || bgcolor=DDDDFF | $008 || 11545.88 || +56c
|-
| 126 || F#9 || 11839.82 || bgcolor=FFDDDD | $008 || 12428.98 || +84c || bgcolor=DDDDFF | $008 || 11545.88 || -44c
|-
| 127 || G-9 || 12543.85 || bgcolor=FFDDDD | $008 || 12428.98 || -16c || bgcolor=DDDDFF | $007 || 12989.12 || +60c
|}
== Code Friendly Tables ==
Here are the period values from the above table in ca65 syntax, split into low/high byte halves for convenient indexing.
'''Note''': These include every MIDI index from 0-127. This means the first ~32 entries in the table contain nonsense values, as the equivalent periods are larger than the range of the 11-bit timer. Programmers may wish to trim these early entries to save space.
=== NTSC Periods ===
<pre>
ntsc_period_low:
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $f1, $7f, $13, $ad, $4d, $f3, $9d
  .byte $4c, $00, $b8, $74, $34, $f8, $bf, $89
  .byte $56, $26, $f9, $ce, $a6, $80, $5c, $3a
  .byte $1a, $fb, $df, $c4, $ab, $93, $7c, $67
  .byte $52, $3f, $2d, $1c, $0c, $fd, $ef, $e1
  .byte $d5, $c9, $bd, $b3, $a9, $9f, $96, $8e
  .byte $86, $7e, $77, $70, $6a, $64, $5e, $59
  .byte $54, $4f, $4b, $46, $42, $3f, $3b, $38
  .byte $34, $31, $2f, $2c, $29, $27, $25, $23
  .byte $21, $1f, $1d, $1b, $1a, $18, $17, $15
  .byte $14, $13, $12, $11, $10, $0f, $0e, $0d
  .byte $0c, $0c, $0b, $0a, $0a, $09, $08, $08
ntsc_period_high:
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $06, $06, $05, $05
  .byte $05, $05, $04, $04, $04, $03, $03, $03
  .byte $03, $03, $02, $02, $02, $02, $02, $02
  .byte $02, $01, $01, $01, $01, $01, $01, $01
  .byte $01, $01, $01, $01, $01, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
</pre>
=== PAL Periods ===


|}
<pre>
<br>
pal_period_low:
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $d1, $60, $f6, $92, $34, $db, $86, $37
  .byte $ec, $a5, $62, $23, $e8, $b0, $7b, $49
  .byte $19, $ed, $c3, $9b, $75, $52, $31, $11
  .byte $f3, $d7, $bd, $a4, $8c, $76, $61, $4d
  .byte $3a, $29, $18, $08, $f9, $eb, $de, $d1
  .byte $c6, $ba, $b0, $a6, $9d, $94, $8b, $84
  .byte $7c, $75, $6e, $68, $62, $5d, $57, $52
  .byte $4e, $49, $45, $41, $3e, $3a, $37, $34
  .byte $31, $2e, $2b, $29, $26, $24, $22, $20
  .byte $1e, $1d, $1b, $19, $18, $16, $15, $14
  .byte $13, $12, $11, $10, $0f, $0e, $0d, $0c
  .byte $0b, $0b, $0a, $09, $09, $08, $08, $07


The timer-low value is stored at $4006 (Pulse-2) or $4002 (Pulse-1). The timer-high value is stored at $4007 (Pulse-2) or $4003 (Pulse-1), possibly after further modification of d7-d3.
pal_period_high:
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $06, $06, $06, $05, $05, $05
  .byte $04, $04, $04, $04, $03, $03, $03, $03
  .byte $03, $02, $02, $02, $02, $02, $02, $02
  .byte $01, $01, $01, $01, $01, $01, $01, $01
  .byte $01, $01, $01, $01, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
</pre>

Revision as of 11:54, 23 September 2024

MIDI Tuning Table

Using the MIDI Tuning Standard with A=440 Hz, we can derive the equivalent period timer value for the two Pulse channels. Due to limitations on the 11-bit period's range, the lowest standard MIDI frequency that can be reproduced with acceptable tuning is A-1 (55 Hz) on NTSC, and G#1 (51.91 Hz) on PAL. Here we show the desired frequency for each MIDI index, the closest period value, and the resulting tuning error (in cents) from the standard.

Note: The Triangle channel can make use of the same 11-bit period values. Due to its longer 32-step sequence, it will sound exactly one octave lower (half of the apparent frequency) compared to the equivalent period on Pulse.

MIDI NTSC APU Pulse PAL APU Pulse
Index Note Frequency 11bit Period Frequency Tuning 11bit Period Frequency Tuning
31 G-1 49.00 - - - $7FF 50.74 +60c
32 G#1 51.91 $7FF 54.62 +88c $7D1 51.90 +0c
33 A-1 55.00 $7F1 55.00 +0c $760 55.01 +0c
34 A#1 58.27 $77F 58.26 +0c $6F6 58.28 +0c
35 B-1 61.74 $713 61.73 +0c $692 61.74 +0c
36 C-2 65.41 $6AD 65.42 +0c $634 65.40 +0c
37 C#2 69.30 $64D 69.31 +0c $5DB 69.28 -1c
38 D-2 73.42 $5F3 73.40 +0c $586 73.44 +0c
39 D#2 77.78 $59D 77.79 +0c $537 77.78 +0c
40 E-2 82.41 $54C 82.43 +1c $4EC 82.41 +0c
41 F-2 87.31 $500 87.32 +0c $4A5 87.32 +0c
42 F#2 92.50 $4B8 92.52 +0c $462 92.53 +1c
43 G-2 98.00 $474 98.04 +1c $423 98.03 +1c
44 G#2 103.83 $434 103.86 +1c $3E8 103.81 +0c
45 A-2 110.00 $3F8 109.99 +0c $3B0 109.96 -1c
46 A#2 116.54 $3BF 116.52 +0c $37B 116.49 -1c
47 B-2 123.47 $389 123.47 +0c $349 123.41 -1c
48 C-3 130.81 $356 130.83 +0c $319 130.87 +1c
49 C#3 138.59 $326 138.61 +0c $2ED 138.55 -1c
50 D-3 146.83 $2F9 146.80 +0c $2C3 146.77 -1c
51 D#3 155.56 $2CE 155.58 +0c $29B 155.56 +0c
52 E-3 164.81 $2A6 164.74 -1c $275 164.94 +1c
53 F-3 174.61 $280 174.51 -1c $252 174.64 +0c
54 F#3 185.00 $25C 184.89 -1c $231 184.90 -1c
55 G-3 196.00 $23A 195.90 -1c $211 196.06 +1c
56 G#3 207.65 $21A 207.53 -1c $1F3 207.83 +1c
57 A-3 220.00 $1FB 220.20 +2c $1D7 220.15 +1c
58 A#3 233.08 $1DF 233.04 +0c $1BD 232.99 -1c
59 B-3 246.94 $1C4 246.93 +0c $1A4 246.82 -1c
60 C-4 261.63 $1AB 261.36 -2c $18C 261.75 +1c
61 C#4 277.18 $193 276.88 -2c $176 277.10 -1c
62 D-4 293.66 $17C 293.60 +0c $161 293.54 -1c
63 D#4 311.13 $167 310.72 -2c $14D 311.12 +0c
64 E-4 329.63 $152 329.97 +2c $13A 329.88 +1c
65 F-4 349.23 $13F 349.57 +2c $129 348.70 -3c
66 F#4 369.99 $12D 370.40 +2c $118 369.80 -1c
67 G-4 392.00 $11C 392.49 +2c $108 392.12 +1c
68 G#4 415.30 $10C 415.84 +2c $0F9 415.65 +1c
69 A-4 440.00 $0FD 440.40 +2c $0EB 440.31 +1c
70 A#4 466.16 $0EF 466.09 +0c $0DE 465.98 -1c
71 B-4 493.88 $0E1 494.96 +4c $0D1 494.82 +3c
72 C-5 523.25 $0D5 522.71 -2c $0C6 522.18 -4c
73 C#5 554.37 $0C9 553.77 -2c $0BA 555.68 +4c
74 D-5 587.33 $0BD 588.74 +4c $0B0 587.08 -1c
75 D#5 622.25 $0B3 621.45 -2c $0A6 622.23 +0c
76 E-5 659.26 $0A9 658.00 -3c $09D 657.68 -4c
77 F-5 698.46 $09F 699.13 +2c $094 697.40 -3c
78 F#5 739.99 $096 740.80 +2c $08B 742.24 +5c
79 G-5 783.99 $08E 782.24 -4c $084 781.30 -6c
80 G#5 830.61 $086 828.60 -4c $07C 831.30 +1c
81 A-5 880.00 $07E 880.79 +2c $075 880.62 +1c
82 A#5 932.33 $077 932.17 +0c $06E 936.15 +7c
83 B-5 987.77 $070 989.92 +4c $068 989.65 +3c
84 C-6 1046.50 $06A 1045.43 -2c $062 1049.63 +5c
85 C#6 1108.73 $064 1107.53 -2c $05D 1105.46 -5c
86 D-6 1174.66 $05E 1177.48 +4c $057 1180.83 +9c
87 D#6 1244.51 $059 1242.90 -2c $052 1251.96 +10c
88 E-6 1318.51 $054 1316.01 -3c $04E 1315.35 -4c
89 F-6 1396.91 $04F 1398.26 +2c $049 1404.23 +9c
90 F#6 1479.98 $04B 1471.85 -10c $045 1484.47 +5c
91 G-6 1567.98 $046 1575.50 +8c $041 1574.44 +7c
92 G#6 1661.22 $042 1669.56 +9c $03E 1649.41 -12c
93 A-6 1760.00 $03F 1747.83 -12c $03A 1761.24 +1c
94 A#6 1864.66 $03B 1864.35 +0c $037 1855.59 -8c
95 B-6 1975.53 $038 1962.47 -11c $034 1960.62 -13c
96 C-7 2093.00 $034 2110.58 +14c $031 2078.26 -12c
97 C#7 2217.46 $031 2237.22 +15c $02E 2210.91 -5c
98 D-7 2349.32 $02F 2330.43 -14c $02B 2361.66 +9c
99 D#7 2489.02 $02C 2485.80 -2c $029 2474.12 -10c
100 E-7 2637.02 $029 2663.35 +17c $026 2664.43 +18c
101 F-7 2793.83 $027 2796.52 +2c $024 2808.46 +9c
102 F#7 2959.96 $025 2943.71 -10c $022 2968.94 +5c
103 G-7 3135.96 $023 3107.24 -16c $020 3148.88 +7c
104 G#7 3322.44 $021 3290.02 -17c $01E 3352.03 +15c
105 A-7 3520.00 $01F 3495.65 -12c $01D 3463.76 -28c
106 A#7 3729.31 $01D 3728.69 +0c $01B 3711.18 -8c
107 B-7 3951.07 $01B 3995.03 +19c $019 3996.65 +20c
108 C-8 4186.01 $01A 4142.99 -18c $018 4156.52 -12c
109 C#8 4434.92 $018 4474.43 +15c $016 4517.95 +32c
110 D-8 4698.64 $017 4660.87 -14c $015 4723.32 +9c
111 D#8 4978.03 $015 5084.58 +37c $014 4948.24 -10c
112 E-8 5274.04 $014 5326.71 +17c $013 5195.65 -26c
113 F-8 5587.65 $013 5593.04 +2c $012 5469.10 -37c
114 F#8 5919.91 $012 5887.41 -10c $011 5772.94 -44c
115 G-8 6271.93 $011 6214.49 -16c $010 6112.53 -45c
116 G#8 6644.88 $010 6580.05 -17c $00F 6494.56 -40c
117 A-8 7040.00 $00F 6991.30 -12c $00E 6927.53 -28c
118 A#8 7458.62 $00E 7457.39 +0c $00D 7422.35 -8c
119 B-8 7902.13 $00D 7990.06 +19c $00C 7993.30 +20c
120 C-9 8372.02 $00C 8604.68 +47c $00B 8659.41 +58c
121 C#9 8869.84 $00C 8604.68 -53c $00B 8659.41 -42c
122 D-9 9397.27 $00B 9321.73 -14c $00A 9446.63 +9c
123 D#9 9956.06 $00A 10169.16 +37c $009 10391.29 +74c
124 E-9 10548.08 $00A 10169.16 -63c $009 10391.29 -26c
125 F-9 11175.30 $009 11186.08 +2c $008 11545.88 +56c
126 F#9 11839.82 $008 12428.98 +84c $008 11545.88 -44c
127 G-9 12543.85 $008 12428.98 -16c $007 12989.12 +60c


Code Friendly Tables

Here are the period values from the above table in ca65 syntax, split into low/high byte halves for convenient indexing.

Note: These include every MIDI index from 0-127. This means the first ~32 entries in the table contain nonsense values, as the equivalent periods are larger than the range of the 11-bit timer. Programmers may wish to trim these early entries to save space.

NTSC Periods

ntsc_period_low:
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $f1, $7f, $13, $ad, $4d, $f3, $9d
  .byte $4c, $00, $b8, $74, $34, $f8, $bf, $89
  .byte $56, $26, $f9, $ce, $a6, $80, $5c, $3a
  .byte $1a, $fb, $df, $c4, $ab, $93, $7c, $67
  .byte $52, $3f, $2d, $1c, $0c, $fd, $ef, $e1
  .byte $d5, $c9, $bd, $b3, $a9, $9f, $96, $8e
  .byte $86, $7e, $77, $70, $6a, $64, $5e, $59
  .byte $54, $4f, $4b, $46, $42, $3f, $3b, $38
  .byte $34, $31, $2f, $2c, $29, $27, $25, $23
  .byte $21, $1f, $1d, $1b, $1a, $18, $17, $15
  .byte $14, $13, $12, $11, $10, $0f, $0e, $0d
  .byte $0c, $0c, $0b, $0a, $0a, $09, $08, $08

ntsc_period_high:
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $06, $06, $05, $05
  .byte $05, $05, $04, $04, $04, $03, $03, $03
  .byte $03, $03, $02, $02, $02, $02, $02, $02
  .byte $02, $01, $01, $01, $01, $01, $01, $01
  .byte $01, $01, $01, $01, $01, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00

PAL Periods

pal_period_low:
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $ff, $ff, $ff, $ff, $ff, $ff, $ff, $ff
  .byte $d1, $60, $f6, $92, $34, $db, $86, $37
  .byte $ec, $a5, $62, $23, $e8, $b0, $7b, $49
  .byte $19, $ed, $c3, $9b, $75, $52, $31, $11
  .byte $f3, $d7, $bd, $a4, $8c, $76, $61, $4d
  .byte $3a, $29, $18, $08, $f9, $eb, $de, $d1
  .byte $c6, $ba, $b0, $a6, $9d, $94, $8b, $84
  .byte $7c, $75, $6e, $68, $62, $5d, $57, $52
  .byte $4e, $49, $45, $41, $3e, $3a, $37, $34
  .byte $31, $2e, $2b, $29, $26, $24, $22, $20
  .byte $1e, $1d, $1b, $19, $18, $16, $15, $14
  .byte $13, $12, $11, $10, $0f, $0e, $0d, $0c
  .byte $0b, $0b, $0a, $09, $09, $08, $08, $07

pal_period_high:
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $07, $07, $07, $07, $07, $07
  .byte $07, $07, $06, $06, $06, $05, $05, $05
  .byte $04, $04, $04, $04, $03, $03, $03, $03
  .byte $03, $02, $02, $02, $02, $02, $02, $02
  .byte $01, $01, $01, $01, $01, $01, $01, $01
  .byte $01, $01, $01, $01, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
  .byte $00, $00, $00, $00, $00, $00, $00, $00
Retrieved from "https://www.nesdev.org/w/index.php?title=Pulse_Channel_frequency_chart&oldid=22073"