Harmonic spectrum

A harmonic spectrum is a spectrum containing only frequency components whose frequencies are whole number multiples of the fundamental frequency; such frequencies are known as harmonics. "The individual partials are not heard separately but are blended together by the ear into a single tone."^[1]

In other words, if $\omega$ is the fundamental frequency, then a harmonic spectrum has the form

\{\dots ,-2\omega ,-\omega ,0,\omega ,2\omega ,\dots \}.

A standard result of Fourier analysis is that a function has a harmonic spectrum if and only if it is periodic.

^ Benward, Bruce and Saker, Marilyn (1997/2003). Music: In Theory and Practice, Vol. I, p.xiii. Seventh edition. McGraw-Hill. ISBN 978-0-07-294262-0.

[1] Benward, Bruce and Saker, Marilyn (1997/2003). Music: In Theory and Practice, Vol. I, p.xiii. Seventh edition. McGraw-Hill. ISBN 978-0-07-294262-0.

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