FM

carrier frequency

modulation frequency

modulation index

phase modulation

instantaneous frequency

scales and, as a consequence, the control over a time continuum ranging from

the milliseconds to the tens of seconds. There are psychoacoustic effects that can

be easily experimented by using this algorithm, for example crumbling effects

and waveform fusions, which have the corresponding counterpart in the effects

of separation and fusion of tones.

tion (FM). In electrical communications, FM has been used for decades, but its

use as a sound synthesis algorithm in the discrete-time domain is due to John

Chowning [23]. Essentially, Chowning was doing experiments on different ex-

tents of vibrato applied to simple oscillators, when he realized that fast vibrato

rates produce dramatic timbral changes. Therefore, modulating the frequency

of an oscillator was enough to obtain complex audio spectra.

phase modulation because it is the instantaneous phase that is driven by the

modulator. However, when both the modulator and the carrier are sinusoidal,

there is no substantial difference between phase modulation and frequency mod-

ulation. The instantaneous frequency of (16) is

frequency controls a phasor~ unit generator. This block generates the cyclical

phase ramp that, when given as index of a cosinusoidal table, produces the same

result as the osc unit generator. However, this decomposition of the oscillator

into two parts (i.e., the phase generation and the table read) allows to sum the

output coming from the modulator directly to the phase of the carrier.

of the resulting sound. This analysis is based on the trigonometric identity [1]