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FM Tone Generation
Appendix
Most sounds are made up of multiple tones that are different than the pitch (frequency). Within these multi-
ple tones, the one that determines the pitch of the entire sound is called the fundamental tone (fundamental
frequency). All the tones besides the fundamental tone are called harmonics or overtones.
When all the harmonics that are related to a particular fundamental tone are arranged in order, it is called a
harmonic series. Each tone in the harmonic series is given a name in order, with the fundamental tone being
one, followed by the second harmonic, third harmonic and so on.
The frequency of each harmonic in the harmonic series is a natural number multiple of the frequency of the
fundamental tone. Overtones that have frequencies that are not natural number multiples of the fundamental
are called unharmonic overtones.
Generally, the more harmonics the tone has, the brighter the sound. On the other hand, if the amount of har-
monics is reduced, the tone will sound darker. Furthermore, the voice will change a lot according to the type
and volume of the harmonics. For example, if there are a lot of high pitched harmonics in the tone, it will
have a brilliant, crisp sound. On the other hand, a tone with a large amount of lower harmonics will have a
rather “fat,” warm sound.
Harmonics
Harmonics
Level
Waveform
Time
Natural Harmonic Series
(when C1 is the fundamental tone)
Eighth Harmonic
Seventh Harmonic
Sixth Harmonic
Fifth Harmonic
Fourth Harmonic
Third Harmonic
Second Harmonic
Fundamental
Fourth Harmonic
Third Harmonic
Second Harmonic
Fundamental
Harmonics
Level
Fundamental Wave
Second Harmonic
Third Harmonic
Frequency
Harmonic
Fundamental and
Harmonics (graph)