Towards a Chowning FM Trumpet

In Figure 17, two carriers are modulated by the same oscillator with a frequency $f_m$.

The index of modulation for the first and second carrier is given by $I_1$ and $I_2/I_1$ respectively.

The value $I_2$ is usually less than $I_1$, so that the ratio $I_2/I_1$ is small and the spectrum does not spread too far beyond the region of the formant.

The frequency of the second carrier $f_{c2}$ is chosen to be a harmonic of the fundamental frequency $f_0$, so that it is close to the desired formant frequency $f_f$,

$$f_{c2} = nf_0 =$$   int$$(f_f/f_0 + 0.5)f_0.$$

This ensures that the second carrier frequency remains harmonically related to $f_0$.

If $f_0$ changes, the scond carrier frequency will remain as close as possible to the desired formant frequency $f_f$ while remaining an integer multiple of the fundamental frequency $f_0$.