The N2 denominator of the FM frequency ratio determines which harmonic series members are absent

When c:m = N1:N2, every N2-th harmonic is absent from the spectrum. N2 = 1 gives all harmonics; N2 = 2 (or any even number) gives only odd harmonics (like a square wave or clarinet); N2 = 3 removes every third harmonic. This provides recipes for crafting specific spectral shapes. The mathematical cause is cancellation of Bessel-function terms at specific sideband orders. This mechanism has no direct equivalent in subtractive synthesis and is unique to FM.

Examples

c:m = 5:1 → all harmonics. c:m = 5:2 → 2nd, 4th, 6th, 8th harmonics absent (clarinet-like). c:m = 5:3 → every 3rd harmonic absent.

Assessment

A designer wants an FM patch with only odd harmonics. What constraint on N2 achieves this? Give a concrete c:m ratio example.