Timbre Synthesis

Physics: Timbre = spectral envelope + temporal evolution (ADSR). Spectral centroid = Σ(f·A)/ΣA, measuring the "brightness" of a sound. Flute: mostly fundamental + 2nd harmonic; clarinet: odd harmonics only (cylindrical bore, closed end → behaves like half-open pipe); trumpet: rich in high harmonics; violin: complex with formant-like peaks from body resonances; oboe: strong 2nd harmonic. ADSR (Attack-Decay-Sustain-Release) shapes loudness over time — attack of ≈20ms makes strings sound plucked vs bowed.