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A harmonic spectrum is a
A harmonic spectrum is a spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...
containing only frequency components whose frequencies are whole number multiples of the fundamental frequency
The fundamental frequency, often referred to simply as the ''fundamental'', is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. I ...
; such frequencies are known as harmonics. "The individual partials are not heard separately but are blended together by the ear into a single tone."Benward, Bruce and Saker, Marilyn (1997/2003). ''Music: In Theory and Practice'', Vol. I, p.xiii. Seventh edition. McGraw-Hill. .
In other words, if is the fundamental frequency, then a harmonic spectrum has the form
:
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
A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which repeat at intervals of 2\pi radians, are periodic functions. Periodic functions are used throughout science to des ...
* Scale of harmonics
The scale of harmonics is a musical scale based on the noded positions of the natural harmonics existing on a string. This musical scale is present on the guqin, regarded as one of the first string instruments with a musical scale.Yin, Wei. ''Z ...
* Undertone series
In music, the undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the physical production of music on instruments, undertones must ...
References
{{Signal-processing-stub Functional analysis Acoustics Sound