Frequency modulation synthesis

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In audio and music 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. The frequency of an oscillator is altered or distorted, "in accordance with the amplitude of a modulating signal." (Dodge and Jerse 1997, p.115)

For synthesizing harmonic sounds, the modulating signal must have a harmonic relationship to the original carrier signal. As the amount of frequency modulation increases, the sound grows progressively more complex. Through the use of modulators with frequencies that are non-integer multiples of the carrier signal (i.e. non harmonic), bell-like dissonant and percussive sounds can easily be created.



The technique, which was discovered by John Chowning (Chowning 1973, cited in Dodge and Jerse, p.115) at Stanford University in 1967-68, was patented in 1975 and later licensed to Yamaha.

The implementation commercialized by Yamaha (US Patent 4018121 Apr 1977 or U.S. Patent 4,018,121) is actually based on phase modulation.

FM synthesis is very good at creating both harmonic and inharmonic ("clang", "twang" or "bong" noises) sounds. Complex (and proper) FM synthesis using analog oscillators is not generally feasible due to their inherent pitch instability, but FM synthesis (using the frequency stable phase modulation variant) is easy to implement digitally. As a result, FM synthesis was the basis of some of the early generations of digital synthesizers from Yamaha, with Yamaha's flagship DX7 synthesizer being ubiquitous throughout the 1980s. Yamaha had patented its hardware implementation of FM, allowing it to nearly monopolize the market for that technology. Casio developed a related form of synthesis called phase distortion synthesis, used in its CZ series of synthesizers. It had a similar (but slightly differently derived) sound quality as the DX series.

Don Buchla implemented FM on his instruments in the mid-1960s, prior to Yamaha's patent. His 158, 258 and 259 dual oscillator modules had a specific FM control voltage input, and the model 208 (Music Easel) had a modulation oscillator hard-wired to allow FM as well as AM of the primary oscillator. These early applications used analog oscillators.

With the expiration of the Stanford University FM patent in 1995, FM synthesis is now part of the synthesis repertoire of 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.

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