Subtractive synthesis starts from a harmonically rich source and removes components with filters

Subtractive synthesis (also called the source-plus-filter model) starts from a harmonically rich source sound and uses filters to remove or attenuate spectral components, sculpting a new timbre out of what remains. It is the inverse of additive synthesis, which builds a timbre up from individual sine partials — you can only subtract components that are already present, which is why the source must have a full spectrum. Canonical sources are classic band-limited waveforms and noise: a sawtooth contains all harmonics, a square or pulse contains only odd harmonics, a triangle contains odd harmonics at steeply falling amplitude, and white noise gives inharmonic/percussive material. A subtractive voice chains an oscillator/noise source, a filter whose cutoff and resonance are modulated over time (typically by an envelope and/or LFO), and an amplitude envelope. Sweeping a low-pass filter progressively removes upper harmonics — the classic synth sound. Digital systems need band-limited sources to avoid aliasing from sharp waveform edges.

Examples

saw~ → resonant low-pass filter with an envelope on cutoff → plucky synth bass or lead. noise~ → low-pass filter with an LFO sweeping the cutoff → classic sweeping noise riser. Moog, Minimoog, Roland Juno, and ARP synths all use subtractive synthesis.

// Sawtooth as a sum of sines (all harmonics):
Mix.fill(~numPartials, {|i| SinOsc.ar(440 * (i+1), mul: (-1**i) * (0.5/(i+1))) })

Assessment

Explain why white noise or a sawtooth makes a better subtractive source than a sine wave, and name the three main stages of a basic subtractive voice. Then predict how a sawtooth’s timbre changes as a low-pass cutoff drops from 10 kHz to 200 Hz — which harmonics are removed and what is the sonic effect? Why does a digital implementation require a band-limited source?