Harmonic spectrum explained

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

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

Notes and References

1. Benward, Bruce and Saker, Marilyn (1997/2003). Music: In Theory and Practice, Vol. I, p.xiii. Seventh edition. McGraw-Hill. .