FM woodwind timbres use a higher carrier harmonic and inverse index-amplitude coupling, causing higher harmonics to lead the attack

Woodwind and organ pipe tones characteristically start with prominent higher harmonics during the attack, which then recede as lower harmonics grow during the steady state — the opposite of brass. In FM, this is achieved by setting the carrier frequency to a multiple of the modulating frequency (e.g., c/m = 3/1 or 5/1) so the carrier sits at a high harmonic position, and by making the index inversely proportional to amplitude. When the index is high at the onset, sidebands fill out below the carrier; as index decreases, the carrier harmonic (sitting at a high position) initially dominates then blends in. Clarinet-like tones additionally require only odd harmonics, achieved with c/m ratios whose denominator is even (e.g., c/m=3/2 gives c/m=1.5, odd harmonics only).

Examples

Chowning’s clarinet patch: c=900Hz, m=600Hz (c/m=3/2), I1=4, I2=2 (index inversely proportional to amplitude), fundamental at 300Hz, predominantly odd harmonics.

Assessment

Explain why c/m=3/2 produces predominantly odd harmonics in an FM spectrum, using the harmonic-number formula k=|N1±nN2|.