Frequency modulation (FM)   

also known as FM. used in both analogue and digital systems. 

a carrier is modulated by a program or modulating source/oscillator. the amount of modulation is called the “index’ and determines the extent of the timbral change.

fm example
in linear or digital systems which use sine waves, the sidebands or additional tones which are generated as the index changes from 0 are predictable and coherent. 
if the modulator frequency is sub-audio we refer to this phenomenon as vibrato. by using envelopes to control the amplitude of the carrier and the modulator it is possible to create a vary diverse range of sounds using linear FM. 

FM was made popular in the academic world by composer John Chowning and in the world of popular culture by Yamaha who bought the rights to FM from Chowning and developed a large series of digital synthesizers based on this synthesis algorithm. (DX7, TX802, TX81Z, etc.)

Frequency modulation in its simplest form involves the modulation of the instantaneous frequency of one waveform, the carrier, by another signal called the modulator. 
If the modulating signal is a sine wave and operating at a sub-audio frequency the result will be vibrato If the modulator is operating at audio frequencies new frequencies are created called sidebands
Depth of modulation, or modulation index, is a function of the amplitude of the modulator. 
Frequency modulation has the advantage over both multiplicative (ring) and amplitude modulation in that the amplitudes of the individual sidebands vary as the modulation index is changed with each component varying according to a Bessel function. The result is a dynamic spectrum achieved by simply varying the amplitude of the modulator. 
These sidebands occur above and below the carrier frequency and are spaced at integer multiples of the modulator frequency.  If the lower sidebands fall below 0 Hz into a negative value they are reflected back, or folded under the zero point, in a positive direction. 
See Also:
additive synthesis  granular synthesis 
subtractive synthesis  wavetable synthesis