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Frequency modulation synthesis

Frequency modulation synthesis (or FM synthesis) is a form of audio synthesis where the timbre of a simple waveform is changed by frequency modulating it with a modulating frequency that is also in the audio range, resulting in a more complex waveform and a different-sounding tone.

Often, the modulating signal has a harmonic relationship to the original signal. As the amount of FM modulation increases, the sound grows progressively more complex.

The technique was invented by John Chowning at Stanford University in the early 1970s, and later licensed to Yamaha.

FM synthesis is very good at creating 'clang', 'twang' or 'bong' noises, and is also easy to implement digitally. As a result, FM synthesis was the basis of some of the early generations of digital synthesizers from manufacturers such as Yamaha.

FM synthesis is now used in most modern synthesizers, usually in conjunction with additive, subtractive and sometimes sampling techniques.

The harmonic distribution of a simple sine wave signal modulated by another sine wave signal can be represented with Bessel functions - this provides a basis for a simple mathematical understanding of FM synthesis.

Reference:

J. Chowning, "The Synthesis of Complex Audio Spectra by Means of Frequency Modulation," Journal of the Audio Engineering Society 21(7), 1973