Waveform shape determines timbre — the tonal quality distinguishing instruments at the same pitch

Timbre is the perceptual quality that lets a listener distinguish a middle C on a guitar from the same note on a saxophone, even when frequency and amplitude are equal. Timbre is determined primarily by the waveform shape — the distribution and relative amplitudes of spectral partials. A sine wave has the purest, most flute-like timbre (one partial). A sawtooth has all harmonics and sounds bright and rich. A square wave has only odd harmonics and sounds hollow. In digital synthesis, choosing and modifying the waveform (or its spectral content) is the primary tool for timbre design. Envelope shape also contributes, especially in the attack transient.

Examples

cycle~ produces a pure sine → flute-like. saw~ produces a sawtooth → string/brass-like. rect~ at 50% duty cycle → square wave → clarinet-like hollow quality.

Assessment

Two sounds are played in succession: a 440 Hz sine wave, then a 440 Hz sawtooth. Same frequency and amplitude. What perceptual parameter differs, and why?