Harmonic Series

Physics: Fourier (1822): any periodic signal = sum of harmonics at f₀, 2f₀, 3f₀, ... Square wave: odd harmonics only (1/n amplitude) — spectrum has gaps at even multiples. Sawtooth: all harmonics at 1/n. Triangle: odd harmonics at 1/n². The missing fundamental: perceived pitch at f₀ even if that component is absent (the brain infers it from upper harmonics). Timbre difference between instruments is entirely spectral content — a violin and flute on the same note have the same f₀ but different harmonic amplitudes.