Editing Additive synthesis (section)

===Inharmonic form===
Additive synthesis can also produce [[Inharmonicity|inharmonic]] sounds (which are [[aperiodic]] waveforms) in which the individual overtones need not have frequencies that are integer multiples of some common fundamental frequency.<ref name=smith05>
{{Cite book     
 | last1        = Smith III | first1 = Julius O.
 | last2        = Serra     | first2 = Xavier
 | year         = 2005
 | chapter      = Additive Synthesis
 | chapter-url   = https://ccrma.stanford.edu/~jos/parshl/Additive_Synthesis.html
 | title        = PARSHL: An Analysis/Synthesis Program for Non-Harmonic Sounds Based on a Sinusoidal Representation
 | url          = https://ccrma.stanford.edu/~jos/parshl/
 | series       = Proceedings of the International Computer Music Conference (ICMC-87, Tokyo), Computer Music Association, 1987
 | publisher    = [[Center for Computer Research in Music and Acoustics|CCRMA]], Department of Music, Stanford University
 | access-date   = 11 January 2015
}} ([https://ccrma.stanford.edu/STANM/stanms/stanm43/stanm43.pdf online reprint])</ref><ref name=smith11>
{{Cite book     
 | last         = Smith III | first = Julius O.
 | year         = 2011
 | chapter      = Additive Synthesis (Early Sinusoidal Modeling)
 | chapter-url   = https://ccrma.stanford.edu/~jos/sasp/Additive_Synthesis_Early_Sinusoidal.html
 | title        = Spectral Audio Signal Processing
 | url          = https://ccrma.stanford.edu/~jos/sasp/
 | publisher    = [[Center for Computer Research in Music and Acoustics|CCRMA]], Department of Music, Stanford University
 | isbn         = 978-0-9745607-3-1
 | access-date   = 9 January 2012
}}</ref> While many conventional musical instruments have harmonic partials (e.g. an [[oboe]]), some have inharmonic partials (e.g. [[bell (instrument)|bells]]).  Inharmonic additive synthesis can be described as

: <math>y(t) = \sum_{k=1}^{K} r_k(t) \cos\left(2 \pi f_k t + \phi_k \right),</math>

where <math>f_k</math> is the constant frequency of <math>k</math>th partial.
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| [[File:Inharmonic additive synthesis spectrum.png|280px]]
| <span style="font-size:85%;line-height:130%;">Example of inharmonic additive synthesis in which both the amplitude and frequency of each partial are time-dependent.</span>
[[File:Inharmonic additive synthesis.ogg|noicon|150px]]
<span style="font-size:70%;line-height:130%;font-style:italic;">Problems listening to this file? See [[Media help]]</span>
|}