Harmonic spectrum

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

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 ${\displaystyle \omega }$ 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; White, Gary (1999). Music in Theory and Practice. Vol. 1 (7 ed.). McGraw-Hill Higher Education. p. xiii. ISBN   978-0-697-35375-7.