Waveforms and harmonics
Why a saw sounds bright and a square sounds hollow: every waveform is a recipe of pure tones.
A sine wave is the only sound with a single frequency in it — one lonely line on the spectrum. Every other sound is a stack of sines: a strong one at the pitch you perceive (the fundamental) plus quieter ones at exact multiples of it — 2×, 3×, 4×… — called harmonics. Your ear fuses the stack into one note with a character. Timbre is the recipe: which harmonics are present, and how loud.
The four classic recipes
- Sine — fundamental only. Pure, soft, disappears in a mix. The atom everything else is built from.
- Triangle — odd harmonics (1×, 3×, 5×…), falling off very fast. Still soft, slightly reedy.
- Square — odd harmonics, falling off slowly. Hollow, woody, clarinet-like; the missing even harmonics are the hollowness.
- Sawtooth — every harmonic, falling off slowly. The brightest and richest of the four; the default raw material of subtractive synthesis, because there is the most to carve away.
Watch the spectrum this time. Sine: one bar. Triangle/square: bars at 1×, 3×, 5×… of the fundamental. Saw: a full picket fence. Then sweep the frequency and watch the whole comb slide together — the recipe moves with the pitch.
Where this lesson lives on the hardware — machines that let you choose or morph the recipe directly, and the sampler view of the same idea (a sample is a recorded recipe; retuning it slides every harmonic together, exactly like the frequency slider above):