APU period table

APU Pulse and APU Triangle use "period" values to set the pitch of the note. But some people might not know the piano key frequencies or how to convert them to periods for the NES. Fortunately, this has been done for you.

Lookup table

Here's a lookup table from note numbers to the values to write to the pulse and triangle period registers. For the triangle channel, the first value corresponds to the lowest key on a standard piano (an A). The pulse waves sound one octave higher.

; NTSC period table generated by mktables.py
.export periodTableLo, periodTableHi
.segment "RODATA"
periodTableLo:
  .byt $f1,$7f,$13,$ad,$4d,$f3,$9d,$4c,$00,$b8,$74,$34
  .byt $f8,$bf,$89,$56,$26,$f9,$ce,$a6,$80,$5c,$3a,$1a
  .byt $fb,$df,$c4,$ab,$93,$7c,$67,$52,$3f,$2d,$1c,$0c
  .byt $fd,$ef,$e1,$d5,$c9,$bd,$b3,$a9,$9f,$96,$8e,$86
  .byt $7e,$77,$70,$6a,$64,$5e,$59,$54,$4f,$4b,$46,$42
  .byt $3f,$3b,$38,$34,$31,$2f,$2c,$29,$27,$25,$23,$21
  .byt $1f,$1d,$1b,$1a,$18,$17,$15,$14
periodTableHi:
  .byt $07,$07,$07,$06,$06,$05,$05,$05,$05,$04,$04,$04
  .byt $03,$03,$03,$03,$03,$02,$02,$02,$02,$02,$02,$02
  .byt $01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01,$01
  .byt $00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00
  .byt $00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00
  .byt $00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00
  .byt $00,$00,$00,$00,$00,$00,$00,$00

Table generator

This Python program generated the above lookup table. You can use it to make a table for a PAL NES, which has a different CPU clock rate.

#!/usr/bin/env python3
#
# Lookup table generator for note periods
# Copyright 2010, 2020 Damian Yerrick
#
# Copying and distribution of this file, with or without
# modification, are permitted in any medium without royalty
# provided the copyright notice and this notice are preserved.
# This file is offered as-is, without any warranty.
#
assert str is not bytes
import sys

lowestFreq = 55.0
ntscOctaveBase = 39375000.0/(22 * 16 * lowestFreq)
palOctaveBase = 266017125.0/(10 * 16 * 16 * lowestFreq)
maxNote = 80

def makePeriodTable(filename, pal=False):
    semitone = 2.0**(1./12)
    octaveBase = palOctaveBase if pal else ntscOctaveBase
    relFreqs = [(1 << (i // 12)) * semitone**(i % 12)
                for i in range(maxNote)]
    periods = [int(round(octaveBase / freq)) - 1 for freq in relFreqs]
    systemName = "PAL" if pal else "NTSC"
    with open(filename, 'wt') as outfp:
        outfp.write("""; %s period table generated by mktables.py
.export periodTableLo, periodTableHi
.segment "RODATA"
periodTableLo:\n"""
                    % systemName)
        for i in range(0, maxNote, 12):
            outfp.write('  .byt '
                        + ','.join('$%02x' % (i % 256)
                                   for i in periods[i:i + 12])
                        + '\n')
        outfp.write('periodTableHi:\n')
        for i in range(0, maxNote, 12):
            outfp.write('  .byt '
                        + ','.join('$%02x' % (i >> 8)
                                   for i in periods[i:i + 12])
                        + '\n')

def makePALPeriodTable(filename):
    return makePeriodTable(filename, pal=True)

tableNames = {
    'period': makePeriodTable,
    'palperiod': makePALPeriodTable
}

def main(argv):
    if len(argv) >= 2 and argv[1] in ('/?', '-?', '-h', '--help'):
        print("usage: %s TABLENAME FILENAME" % argv[0])
        print("known tables:", ' '.join(sorted(tableNames)))
    elif len(argv) < 3:
        print("mktables: too few arguments; try %s --help" % argv[0])
    elif argv[1] in tableNames:
        tableNames[argv[1]](argv[2])
    else:
        print("mktables: no such table %s; try %s --help" % (argv[1], argv[0]))

if __name__=='__main__':
    main(sys.argv)

The following are exercises for the reader:

• Adapt to FDS audio and other mapper sound chips by changing ntscOctaveBase and the formula for periods
  • Hint: fdsOctaveBase = lowestFreq * 65536 * 64 * 22.0 / 39375000.0 and octaveBase * freq
• Adapt to other musical tuning systems by changing the formula for relFreqs
• Adapt to assemblers other than ca65

See also

• Celius' NTSC table
• Celius' PAL table