HARMONIC SERIES & MUSIC

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.