An integer c/m ratio N1/N2 fixes the fundamental and which harmonics appear in an FM spectrum

When the carrier-to-modulator ratio is a ratio of integers c/m = N1/N2 (all common factors removed), the FM spectrum is harmonic and its components fall in the harmonic series of fundamental f0 = c/N1 = m/N2. The position of each side frequency is given by the harmonic number k = |N1 ± nN2| for side-frequency order n. From this follow useful rules: (1) the carrier is always the N1th harmonic; (2) if N1 = 1 all harmonics are present and the fundamental sits at the modulating frequency (e.g. 1/1, 2/1); (3) if N2 is even only odd-numbered harmonics appear (e.g. 1/2, 3/2); (4) if N2 = 3 every third harmonic is missing. A common error is to assume the fundamental is always at the carrier — for N1 > 1 the carrier is a higher harmonic and, at small index, the fundamental may be absent entirely. (The inharmonic case, c/m irrational, is a separate atom.)

Examples

c/m = 1/1: full harmonic series, fundamental at m. c/m = 1/2: only odd harmonics (clarinet-like). c/m = 4/1: carrier is the 4th harmonic and the fundamental only becomes significant once the index exceeds 2.

Assessment

Given c/m = 3/2, identify the fundamental as a fraction of m, which harmonic the carrier sits on, and whether any harmonics are systematically absent.