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]

Approximating a square wave by ${\displaystyle \sin(t)+\sin(3t)/3+\sin(5t)/5}$

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

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

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

See also

• Fourier series
• Harmonic series (music)
• Periodic function
• Scale of harmonics
• Undertone series

References

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.