The sawtooth wave produces a brassy, harmonically rich sound because it contains all harmonics

A sawtooth wave’s amplitude rises linearly then drops sharply each cycle, a shape that decomposes into a full harmonic series: fundamental plus all integer multiples (2nd, 3rd, 4th… partial), with amplitude decreasing as 1/n. The result is a dense, bright, brassy sound often described as characteristic of string-machine or brass synthesis. Because it is harmonically saturated, the sawtooth is the default starting material for subtractive synthesis: a low-pass filter can then carve out a large variety of timbres by removing upper harmonics. Almost all classic analog lead and bass patches begin with a sawtooth.

Examples

Patch a sawtooth VCO into a spectrum analyser in VCV Rack; observe that harmonics continue up the spectrum with none missing. Then open a low-pass filter cutoff from low to high to hear how removing upper harmonics transforms the timbre from muffled to bright.

Assessment

Describe the harmonic content of a sawtooth wave and explain why it is the default starting waveform for subtractive synthesis rather than, say, a square or sine wave.