Introduction to Computer Music: Volume One

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

Computing the sideband strengths • the modulation index (I)

As with ordinary complex waveforms, the timbre perceived by the listener is determined not only by the frequencies present, but also by their relative strengths. The upper and lower sidebands of each sideband pair have the same strength. In order to calculate the strength of each sideband pair relative to the others, we first must look at the main factor that determines it. As we have seen above, when the carrier is modulated, its frequency rises and falls with the amplitude of the modulating wave. The greater the amplitudes of the modulating wave are at its peaks, the greater the maximum distance the carrier is pushed off its center frequency. At sub-audio rate, we would perceive this as the depth of a vibrato. When using a pure sine wave and linear modulation, these peaks will be an equal number of Hz above and below the carrier's center frequency. The number of cycles above or below the center frequency is called the peak deviation (or p.d., or delta (Δ) ƒ). As the amplitude of the modulating wave is increased or decreased by some means, perhaps using an envelope generator, so too does the peak deviation change. It is this parameter, the changing strength of the modulating wave, that allows us to create dynamic, time-varying spectra of a sort very different from subtractive filtering, and one that can, under certain circumstances, mimic the complexity of real-world sound characteristics using only two oscillators.

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