Editing Missing fundamental (section)

== Explanation ==
[[Image:Missing fundamental Fourier series 8.png|thumb|150px|The GCD of the frequency of all harmonics is the fundamental (dashed).]]

A low [[pitch (psychophysics)|pitch]] (also known as the pitch of the missing fundamental or virtual pitch<ref>{{cite web | url=http://jjensen.org/VirtualPitch.html | title=Virtual Pitch Algorithm of Terhardt and Extensions }}</ref>) can sometimes be heard when there is no apparent source or component of that frequency. This perception is due to the brain interpreting repetition patterns that are present.<ref>{{cite book
 |title        = Auditory Neuroscience
 |author       = Jan Schnupp, Israel Nelken and Andrew King
 |publisher    = MIT Press
 |year         = 2011
 |isbn         = 978-0-262-11318-2
 |url          = https://mustelid.physiol.ox.ac.uk/drupal/?q=topics/how-many-repetitions-are-required-produce-pitch
 |access-date  = 2018-08-30
 |archive-url  = https://web.archive.org/web/20120318013518/https://mustelid.physiol.ox.ac.uk/drupal/?q=topics%2Fhow-many-repetitions-are-required-produce-pitch
 |archive-date = 2012-03-18
 |url-status     = dead
}}</ref><ref>
{{cite book
 | title = An Introduction to Phonetics and Phonology
 | author = John Clark, Colin Yallop and Janet Fletcher
 | publisher = Blackwell Publishing
 | year = 2007
 | isbn = 978-1-4051-3083-7
 | url = https://books.google.com/books?id=dX5P5mxtYYIC&q=phantom-fundamental+pitch+perception&pg=PA233}}</ref><ref name=plack>
{{cite book
 | title =Pitch: Neural Coding and Perception
 | author = Christopher J. Plack
 | publisher = Springer
 | year = 2005
 | isbn = 978-0-387-23472-4
 | url = https://books.google.com/books?id=n6VdlK3AQykC&q=Pitch&pg=PP1
 }}</ref>

It was once thought that this effect was because the missing fundamental was replaced by distortions introduced by the physics of the ear. However, experiments subsequently showed that when a noise was added that would have masked these distortions had they been present, listeners still heard a pitch corresponding to the missing fundamental, as reported by [[J. C. R. Licklider]] in 1954.<ref>{{cite book | title = Music and Connectionism | author = Peter M. Todd and D. Gareth Loy | publisher = MIT Press | year = 1991 | isbn = 978-0-262-20081-3 | url = https://books.google.com/books?id=NxycaQH6PeoC&q=missing-fundamental+pitch+perception+distortion+noise+masked&pg=PA86}}</ref> It is now widely accepted that the brain processes the information present in the overtones to calculate the fundamental frequency. The precise way in which it does so is still a matter of debate, but the processing seems to be based on an [[autocorrelation]] involving the timing of neural impulses in the auditory nerve.<ref>{{cite journal|last=Cariani|first=P.A.|author2=Delgutte, B.|title=Neural Correlates of the Pitch of Complex Tones. I. Pitch and Pitch Salience|journal=Journal of Neurophysiology|date=September 1996|volume=76|issue=3|pages=1698–1716|pmid=8890286|url=http://www.brainmusic.org/MBB91%20Webpage/Pitch_II_Cariani.pdf|accessdate=13 November 2012|doi=10.1152/jn.1996.76.3.1698}}</ref> However, it has long been noted that any neural mechanisms which may accomplish a delay (a necessary operation of a true autocorrelation) have not been found.<ref name=plack/> At least one model shows a temporal delay to be unnecessary to produce an autocorrelation model of pitch perception, appealing to [[Phase shift#Phase shift|phase shifts]] between [[Cochlea|cochlear filters]];<ref>{{cite journal|last=de Cheveigné|first=A.|author2=Pressnitzer, D.|title=The case of the missing delay lines: Synthetic delays obtained by cross-channel phase interaction|journal=Journal of the Acoustical Society of America|date=June 2006|volume=119|issue=6|pages=3908–3918|pmid=16838534|url=http://audition.ens.fr/dp/pdfs/cheveigne-2006-synthetic_delay.pdf|accessdate=13 November 2012|bibcode = 2006ASAJ..119.3908D |doi = 10.1121/1.2195291 }}</ref> however, earlier work has shown that certain sounds with a prominent peak in their autocorrelation function do not elicit a corresponding pitch percept,<ref>{{cite journal|last=Kaernbach|first=C.|author2=Demany, L.|title=Psychophysical evidence against the autocorrelation theory of auditory temporal processing|journal=Journal of the Acoustical Society of America|date=October 1998|volume=104|issue=4|pages=2298–2306|pmid=10491694|bibcode = 1998ASAJ..104.2298K |doi = 10.1121/1.423742 |s2cid=18133681}}</ref><ref>{{cite journal|last=Pressnitzer|first=D. |author2=de Cheveigné, A. |author3=Winter, I.M.|title=Perceptual pitch shift for sounds with similar waveform autocorrelation|journal=Acoustics Research Letters Online|date=January 2002|volume=3|issue=1|pages=1–6|doi=10.1121/1.1416671|s2cid=123182480 |doi-access=free}}</ref> and that certain sounds without a peak in their autocorrelation function nevertheless elicit a pitch.<ref>{{cite journal|last=Burns|first=E.M.|author2=Viemeister, N.F.|title=Nonspectral pitch|journal=Journal of the Acoustical Society of America|date=October 1976|volume=60|issue=4|pages=863–869|bibcode = 1976ASAJ...60..863B |doi = 10.1121/1.381166 }}</ref><ref>{{cite journal|last=Fitzgerald|first=M.B.|author2=Wright, B.|title=A perceptual learning investigation of the pitch elicited by amplitude-modulated noise|journal=Journal of the Acoustical Society of America|date=December 2005|volume=118|issue=6|pages=3794–3803|pmid=16419824|bibcode = 2005ASAJ..118.3794F |doi = 10.1121/1.2074687 }}</ref> Autocorrelation can thus be considered, at best, an incomplete model.

The pitch of the missing fundamental, usually at the [[greatest common divisor]] of the frequencies present,<ref>{{cite journal|last=Schwartz|first=D.A.|author2=Purves, D.|title=Pitch is determined by naturally occurring periodic sounds|journal=Hearing Research|date=May 2004|volume=194|issue=1–2|pages=31–46|doi=10.1016/j.heares.2004.01.019|pmid=15276674|s2cid=40608136|url=http://www.purveslab.net/publications/schwarrtz_purves_pitch.pdf|archive-url=https://web.archive.org/web/20121208222727/http://www.purveslab.net/publications/schwarrtz_purves_pitch.pdf|url-status=dead|archive-date=2012-12-08|accessdate=4 September 2012}}</ref> is not, however, always perceived. Research conducted at [[Heidelberg University]] shows that, under narrow stimulus conditions with a small number of harmonics, the general population can be divided into those who perceive missing fundamentals, and those who primarily hear the overtones instead.<ref>{{cite journal |last=Schneider |first=P. |author2=Sluming, V. |author3=Roberts, N. |author4=Scherg, M. |author5=Goebel, R. |author6=Specht, H. |author7=Dosch, H.G. |author8=Bleeck, S. |author9=Stippich, C. |author10=Rupp, A. |title=Structural and functional asymmetry of lateral Heschl's gyrus reflects pitch perception preference |journal=Nature Neuroscience |date=August 2005 |volume=8 |issue=9 |pages=1241–1247 |doi=10.1038/nn1530 |url=http://lumiere.ens.fr/Audition/P2web/eval2006/ALG_nnRupp.pdf |pmid=16116442 |s2cid=16010412 |access-date=2012-07-22 |archive-date=2017-08-09 |archive-url=https://web.archive.org/web/20170809032034/http://lumiere.ens.fr/Audition/P2web/eval2006/ALG_nnRupp.pdf |url-status=dead }}</ref> This was done by asking subjects to judge the direction of motion (up or down) of two complexes in [[Melody|succession]]. The authors used structural [[MRI]] and [[Magnetoencephalography|MEG]] to show that the preference for missing fundamental hearing correlated with left-hemisphere lateralization of pitch perception, where the preference for spectral hearing correlated with right-hemisphere lateralization, and those who exhibited the latter preference tended to be musicians.

In ''Parsing the Spectral Envelope: Toward a General Theory of Vocal Tone Color'' (2016) by [https://www.ianhowellcountertenor.com/ Ian Howell], He wrote that although not everyone can hear the missing fundamentals, noticing them can be taught and learned.<ref>Howell, I. (2017). ''Parsing the Spectral Envelope: Toward a General Theory of Vocal Tone Color''[Doctoral Thesis, New England Conservatory of Music]''.'' https://www.nats.org/_Library/So_You_Want_To_Sing_Book_Series/HOWELL-Parsing-the-spectral-envelope-PROQUEST-FINAL.pdf</ref> [[Robert Ladd (linguist)|D. Robert Ladd]] et al. have a related study that claims that most people can switch from listening for the pitch from the harmonics that are evident to finding these pitches spectrally. <ref>{{Cite journal |last=Ladd |first=Robert |date=2013 |title=Patterns of Individual Differences in the Perception of Missing Fundamental Tones |url=https://supp.apa.org/psycarticles/supplemental/a0031261/a0031261_supp.html |journal=Journal of Experimental Psychology |volume=39 |issue=5 |pages=1386–1397 |doi=10.1037/a0031261 |pmid=23398251 |hdl=11858/00-001M-0000-0010-247B-4 |via=Pubmed|hdl-access=free }}</ref>