In FM, c/m controls spectral position (harmonic vs. inharmonic) while I controls spectral density

Chowning’s summary rule: the carrier-to-modulator ratio (c/m) determines where the spectral components fall (which harmonic numbers, or whether they are inharmonic), while the modulation index (I = d/m) determines how many components have significant amplitude. These two parameters are therefore largely independent controls over spectral character: c/m sets the tonal quality (tonal/metallic/organ/clarinet etc.) and I sets the brightness or richness. A patch designer can first fix c/m to determine the harmonic character of the sound, then sweep I to control brightness and spectral complexity. This two-parameter decomposition is the central design insight of FM synthesis and underlies all DX7/Dexed operator programming.

Examples

A bassoon-like patch uses c/m=5/1 (high carrier harmonic, sparse lower harmonics) with small I. A bright brass patch uses c/m=1/1 (full harmonics) with large I sweeping from 0 to 5 over the note duration.

Assessment

Explain what happens to a patch’s timbre when you (a) double the modulating frequency while keeping c/m and I constant, and (b) keep c/m fixed but increase I from 1 to 4.