Chapter Four: Synthesis

### 6. Principles of Audio-rate Frequency Modulation | page 10

Below is the same modulation index as example 2, but with a carrier frequency plotted low enough so that the lower sidebands, starting with the n=4 pair reflect back on top of existing sidebands. In this case, the lower n=2 (green) and n=4 (purple) will sum, n=1(blue) and n=5 (orange) will just about cancel each other out and n=0 (red) and n=6 (dark green) will fight it out, but the stronger n=0 will be heard, but reduced by the value of n=6. The lower n=3 (yellow) plots out at 0 Hz and so is not heard at all.

Here are two audio examples. The first has a C:M ratio of 1:2 creating a harmonic spectrum, the second a C:M ratio of 1:1.31 creating an inharmonic spectrum. In both examples, the modulation index is increased slowly over 10 seconds from 0 (no modulation) to 15. Play these several times and focus on different frequencies as they move through their Bessel functions. Start with the carrier frequency (the first frequency you will hear). Listen as it immediately begins to lose strength, completely disappears and then reappears. Listen to the effects of phase cancellation in the first harmonic example, which will have far fewer discreet frequencies than the inharmonic one.

Click here to play harmonic example (C:M = 1:2, carrier frequency = 200 Hz)

Click here to play the inharmonic example (C:M = 1:1.31, carrier frequency=150 Hz)