Sawtooth, square, and triangle waves have distinct harmonic series that determine their timbral character

The three fundamental synthesizer waveforms differ in which harmonics they contain and at what amplitudes. The sawtooth contains all harmonics (fundamental + all integer multiples) at amplitude 1/n, giving a bright, buzzy sound similar to brass and strings. The square wave contains only odd harmonics (1st, 3rd, 5th…) at amplitude 1/n, giving a hollow woodwind-like sound. The triangle wave also contains only odd harmonics but at amplitude 1/n², making the upper harmonics much quieter — the result is a softer, flute-like sound. Understanding this determines which waveform to choose as a starting point for a given instrument character before filtering.

Examples

// Sawtooth (all harmonics): bright, like brass/strings
Saw.ar(440)
// Square (odd harmonics only): hollow, woodwind-like
Pulse.ar(440, width: 0.5)
// Triangle (odd harmonics, 1/n² decay): soft
LFTri.ar(440)

Assessment

Without listening, rank sawtooth, square, and triangle waves from brightest to softest timbre. Justify your ranking by describing the harmonic content of each.