A pulse wave's duty cycle sets its harmonic content: 50% is a pure square of odd harmonics, and moving away introduces even harmonics and thins the timbre

A square wave is a pulse at 50% duty cycle — equal on and off time — the widest, richest form, containing only odd harmonics at full amplitude. Moving the duty cycle away from 50% (narrowing the pulse) introduces even-numbered harmonics alongside the odd ones, making the spectrum resemble a sawtooth but with a different harmonic decay, and progressively cancels or thins harmonics so the tone becomes thinner, more nasal or metallic. Narrow pulses (roughly 10–20% width) produce a bright, crisp, hollow sound with an undulating harmonic pattern — useful for plucked-string imitations or edge on a lead — and at extremes the wave approaches a low-energy spike. Because thinning removes low-mid energy, narrow pulses sit well above a sub-bass without competing. The control is variously labelled ‘PW’, ‘Pulse Width’, or ‘Duty Cycle’. In SuperCollider’s Pulse.ar(freq, width), width ranges 0–1: 0.5 is a square, smaller is narrower.

Examples

SuperCollider — sweep square to narrow pulse: {Pulse.ar(440, width: 0.5) !2}.play {Pulse.ar(440, width: 0.1) !2}.play {Pulse.ar(440, width: MouseX.kr(0.1, 0.5)) !2}.play // mouse-controlled width

On a soft-synth (e.g. Diva INIT), raise PW from 0 toward 70: full and buzzy at low PW, progressively thinner as it rises; combine with a high-pass filter to compound the hollowing.

Assessment

Starting from a 50% square wave, describe how the harmonic content changes as pulse width narrows toward 10–20% (which harmonics appear). Predict the interaction with a high-pass filter at 80 Hz, and explain why slowly oscillating the width produces a chorus-like effect.