Overtone Series

Physics: The harmonic series is f_n = n·f₁, where f₁ is the fundamental. Brass instruments overblow through these harmonics: a bugle plays harmonics 2,3,4,5,6,8. The 7th harmonic is approximately 31 cents flat from equal temperament, and the 11th harmonic is a tritone (+49¢). Harmonics 4-8 form a major triad. Fourier (1822) proved any periodic signal decomposes into sinusoidal harmonics. The "missing fundamental" effect: the brain infers f₁ even when only f₂, f₃, f₄... are present, because it detects the common difference frequency.