Pulse Width Modulation

Overview

A square wave at 50% duty cycle sounds hollow and thin. Change that ratio—make the high portion wider or narrower—and the harmonic content shifts dramatically. The SID chip could sweep through duty cycles in real-time, creating dynamic, living sounds from simple waveforms.

Understanding duty cycle

Duty cycle	Sound character
12.5%	Thin, nasal, clarinet-like
25%	Hollow, woody
50%	Pure square, hollow
75%	Same as 25% (inverted)

The duty cycle determines which harmonics are present:

50%: Only odd harmonics (1, 3, 5, 7...)
Other ratios: Mix of odd and even

SID implementation

Register layout

The SID stores pulse width as a 12-bit value across two registers per voice. The high register only uses bits 0-3:

Register	Bits	Function
`$D402` (PWLO1)	7:0	Voice 1 pulse width, low 8 bits
`$D403` (PWHI1)	3:0	Voice 1 pulse width, high 4 bits
`$D409` (PWLO2)	7:0	Voice 2 pulse width, low 8 bits
`$D40A` (PWHI2)	3:0	Voice 2 pulse width, high 4 bits
`$D410` (PWLO3)	7:0	Voice 3 pulse width, low 8 bits
`$D411` (PWHI3)	3:0	Voice 3 pulse width, high 4 bits

The duty cycle is PW / 4096. Values of 0 or 4095 cause the pulse output to stick high or low — silence. Stay clear of the edges if you're modulating right up to the rails.

Setting pulse width

    lda #$00
    sta $d402        ; PW low byte
    lda #$08         ; 50% duty cycle ($800 = 2048 = 4096/2)
    sta $d403        ; PW high nibble

Sweeping (PWM)

pulse_sweep:
    lda pulse_lo
    clc
    adc #$10         ; Increment
    sta pulse_lo
    sta $d402
    lda pulse_hi
    adc #$00
    and #$0f         ; Keep in range
    sta pulse_hi
    sta $d403
    rts

Musical applications

Brass sounds

Fast PWM sweep creates brassy attack:

Attack:  Sweep 12% → 50% quickly
Sustain: Hold at 50% or slow sweep

String pads

Slow, subtle PWM creates warmth:

Continuous slow sweep: 25% ↔ 50% over 2-4 seconds

Lead sounds

Moderate PWM adds movement and interest to melodic lines.

NES pulse channels

The NES has four fixed duty selections per pulse channel. Hardware-wise the four sequences are 12.5%, 25%, 50%, and "25% negated" — the 25-negated waveform is 1 0 0 1 1 1 1 1, which sounds the same as a 75%-duty pulse (six-eighths high) and is universally referred to as "75%" in tracker UIs.

DD bits	Sequence (8 steps)	Audible duty
00	`0 1 0 0 0 0 0 0`	12.5%
01	`0 1 1 0 0 0 0 0`	25%
10	`0 1 1 1 1 0 0 0`	50%
11	`1 0 0 1 1 1 1 1`	25% negated (= 75% audible)

There is no continuous sweep: the duty selector is two bits in $4000 (or $4004 for pulse 2), so you can only switch between the four presets. Famicom musicians fake PWM-like motion by alternating between 25% and 50% on adjacent rows.

Tracker notation

Pulse-width commands vary by tracker:

Tracker	Command	Notes
GoatTracker (C64)	`Wxx`	Sets pulse width directly (high nibble of PWHI:PWLO)
GoatTracker (C64)	`1xx` / `2xx`	Pulse width slide up / down at speed `xx`
FamiTracker (NES)	`Vxy`	Sets duty cycle preset (0-3)

Combining with other effects

PWM layers beautifully with:

Combination	Result
PWM + Filter sweep	Rich, evolving pads
PWM + Vibrato	Organic lead sounds
PWM + Arpeggio	Shimmering chords

The "SID sound"

PWM is central to the distinctive SID character:

Rob Hubbard's brass stabs
Martin Galway's warm pads
Tim Follin's aggressive leads

Shaping square waves