Pulse Width Modulation

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”

Pulse modulation is the most common way C64 players give an instrument its timbre, and it goes back to the first routines. Rob Hubbard’s first player — used for Thing on a Spring, Commando, Thrust and International Karate — stores a single “pulse speed” byte per instrument. Its pulsework routine sweeps the width between square and “very rectangular” at that speed, reversing direction whenever it hits either extreme, on every frame. Anthony McSweeney’s disassembly of the Monty on the Run player describes it as the most common way of creating timbre on the chip. In October 1985 Hubbard told Zzap!64 that his own utility had been “perfected over the last four months” and that he changed it constantly to customise sounds; the drums alone, an attempt at a Simmons-style electronic kit, “took two weeks to perfect”.

The general form, as Cadaver sets it out, is four parameters per instrument: an initial pulse width, a modulation speed, and low and high limits. The player initialises the width at the start of each note (or leaves it running from the previous one), adds or subtracts the speed each frame, and turns round at the limits. The limits matter: if the 12-bit width wraps from $FFF back to $000, “an ugly sound is heard”.

Shaping square waves