FM percussive sounds use inharmonic c/m ratios with index decaying from dense to sparse spectrum

Percussive sounds (bells, drums) are characterized by inharmonic spectra and a decay from spectral complexity to simplicity. FM models this by using irrational or non-integer c/m ratios (producing inharmonic partials) and coupling the modulation index directly to a decaying amplitude envelope. At the onset, a high index produces a dense, complex spectrum; as amplitude decays, index decays in tandem, leaving a simpler, sparser spectrum that converges toward the carrier frequency alone at full decay. This spectral contraction matches the perceptual character of struck bells and drums. The exponential decay envelope is natural for percussive sounds (cf. physical spring/capacitor analogues).

Examples

Bell: c=200Hz, m=280Hz (c/m≈1/1.4, inharmonic), I1=0, I2=10, exponential decay over 15 seconds. As the bell fades, the spectrum simplifies to near-pure 200Hz carrier. Drum: same c/m but shorter duration and lower I2=2.

Assessment

Modify the FM bell patch to produce a higher-pitched, shorter metallic chime. Which two parameters do you change, and in which direction?