Harmonic spectrum

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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."{{Cite book |last=Benward |first=Bruce |url={{google books|plainurl=y|id=-iK8PwAACAAJ&dq=978-0-07-294262-0}} |title=Music in Theory and Practice |last2=White |first2=Gary |date=1999 |publisher=McGraw-Hill Higher Education |isbn=978-0-697-35375-7 |language=en|volume= 1 |p=xiii|edition=7}}

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

:$\backslash \{\backslash dots,\; -2\backslash omega,\; -\backslash omega,\; 0,\; \backslash omega,\; 2\backslash omega,\; \backslash dots\backslash \}.$

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