Additive synthesis — build any timbre from pure sine waves
Any periodic sound = sum of harmonics: f(t) = Σ Aₙ sin(2πnf₀t).
Square wave: odd harmonics only (1/n). Sawtooth: all harmonics (1/n). Triangle: odd harmonics (1/n²).
The harmonic series is the origin of musical consonance and the overtone structure of all instruments.