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How did vintage synthesizers create lush, shimmering string ensembles using just a single oscillator? The secret lies in constantly changing the symmetry of a pulse wave.

What is Duty Cycle?

A pulse wave is a discontinuous waveform that alternates between a high and low voltage. The duty cycle is the percentage of one complete cycle that the waveform spends in its high state.
When a pulse wave spends exactly 50% of its time high and 50% low, it is called a square wave. But what happens to the sound when we squeeze that high state into a narrower slice?

Harmonic Spectra of Pulse Waves

A 50% square wave contains only odd harmonics (1f,3f,5f,…1f, 3f, 5f, \dots), which gives it a characteristically hollow, clarinet-like timbre. As you narrow the duty cycle, even harmonics (2f,4f,6f,…2f, 4f, 6f, \dots) enter the spectrum, making the sound brighter and more nasal.
The harmonic recipe follows an exact acoustic rule: whenever a duty cycle is expressed as a fraction 1n\frac{1}{n}, every nthn^{\text{th}} harmonic drops to zero amplitude.
For example, at a 33.3%33.3\% duty cycle (which is 13\frac{1}{3} of the period), harmonics 3, 6, 9, and 12 completely vanish, leaving a distinctive double-reed timbre like an oboe.
Because human hearing detects harmonic amplitude rather than absolute phase polarity, a 25%25\% duty cycle sounds sonically identical to a 75%75\% duty cycle.
A static pulse wave has a fixed tone, but what happens if we continuously move the pulse width back and forth automatically?

Pulse-Width Modulation (PWM)