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{{Short description|Fixed series of tones that appear to ascend or descend endlessly in pitch}}
[[Pitch]] is often defined as extending along a one-dimensional continuum from high to low, as can be experienced by sweeping one’s hand up or down a piano keyboard. This continuum is known as pitch height. However pitch also varies along a circular dimension, known as [[pitch class]]: As you go up a keyboard in semitone steps you play C, C#, D, D#, E, F, F#, G, G#, A, A#, B, and then you reach C again, but now the note is an octave higher. Tones that stand in octave relation, and are so of the same pitch class, have a certain perceptual equivalence. So all Cs sound in some sense alike, as do all D#s, and so on.▼
[[File:Impossible staircase.svg|thumb|[[Penrose stairs]], visual metaphor for pitch circularity<ref>{{Cite web |url=http://deutsch.ucsd.edu/psychology/pages.php?i=213 |title=Diana Deutsch's page on Pitch Circularity |access-date=2012-10-20 |archive-date=2012-09-05 |archive-url=https://web.archive.org/web/20120905015746/http://deutsch.ucsd.edu/psychology/pages.php?i=213 |url-status=live }}</ref>]]
 
'''Pitch circularity''' is a fixed series of [[Musical note|tones]] that are perceived to ascend or descend endlessly in [[pitch (music)|pitch]]. It's an example of an [[auditory illusion]].
Researchers have shown that by creating banks of tones whose note names are clearly defined perceptually but whose perceived heights are ambiguous, one can create scales that appear to ascend or descend endlessly in pitch. [[Roger Shepard]] achieved this ambiguity of height by creating banks of complex tones, with each tone composed only of components that stood in octave relationship. In other words, the components of the complex tone C consisted only of Cs, but in different octaves, and the components of the complex tone F# consisted only of F#s, but in different octaves. <ref>{{cite journal | author=[[Roger N. Shepard]] | title=Circularity in Judgements of Relative Pitch | journal=Journal of the Acoustical Society of America | volume=36 | issue=12 | year=1964 | month=December | pages=2346–53 | doi=10.1121/1.1919362 | url= }}</ref> When such complex tones are played in semitone steps the listener perceives a scale that appears to ascend endlessly in pitch. [[Jean-Claude Risset]] achieved the same effect using gliding tones instead, so that a single tone appeared to glide up or down endlessly in pitch.<ref>{{cite journal | author = [[Jean-Claude Risset]] | title=Pitch control and pitch paradoxes demonstrated with computer-synthesized sound | journal=Journal of the Acoustical Society of America | volume=46 | year=1969 | pages=88 | doi=10.1121/1.1973626}}</ref>▼
==Explanation==
Circularity effects based on this principle have been produced in orchestral music and electronic music, by having multiple instruments playing simultaneously in different octaves. ▼
▲[[Pitch]] is often defined as extending along a one-dimensional [[continuum (theory)|continuum]] from high to low, as can be experienced by sweeping one’s hand up or down a piano keyboard. This continuum is known as pitch height. However pitch also varies alongin a circular dimensionfashion, known as [[pitch class]]: Asas youone goplays up a keyboard in semitone steps you play, C, C{{music|#}}, D, D{{music|#}}, E, F, F{{music|#}}, G, G{{music|#}}, A, A{{music|#,}} and B, andsound thenin yousuccession, reachfollowed by C again, but nowone [[octave]] higher. Because the noteoctave is anthe octavemost higher.consonant interval after the [[unison]], Tonestones that stand in octave relation, and are so of the same pitch class, have a certain perceptual equivalence. So &mdash;all Cs sound inmore somealike senseto alikeother Cs than to any other pitch class, as do all D{{music|#}}s, and so on; this creates the auditory equivalent of a [[Barber's pole]], where all tones of the same pitch class are located on the same side of the pole, but at different heights.
 
==Research on pitch perception==
Recently, [[Diana Deutsch]] and colleagues have shown that pitch circularity can be created using a bank of single tones; here the relative amplitudes of the odd and even harmonics of each tone are manipulated so as to create ambiguities of height.
▲Researchers have showndemonstrated that by creating banks of tones whose note names are clearly defined perceptually but whose perceived heights are ambiguous, one can create scales that appear to ascend or descend endlessly in pitch. [[Roger Shepard]] achieved this ambiguity of height by creating banks of complex tones, with each tone composed only of components that stood in octave relationship. In other words, the components of the complex tone C consisted only of Cs, but in different octaves, and the components of the complex tone F{{music|#}} consisted only of F{{music|#}}s, but in different octaves. <ref>{{cite journal | author=[[Roger N. Shepard]] | title=Circularity in Judgements of Relative Pitch | journal=Journal of the Acoustical Society of America | volume=36 | issue=12 | yeardate=December 1964 | month=December | pages=2346–53 | doi=10.1121/1.1919362 |bibcode url= 1964ASAJ...36.2346S }}</ref> When such complex tones are played in semitone steps the listener perceives a scale that appears to ascend endlessly in pitch. [[Jean-Claude Risset]] achieved the same effect using gliding tones instead, so that a single tone appeared to glide up or down endlessly in pitch.<ref>{{cite journal | author = [[Jean-Claude Risset]] | title=Pitch control and pitch paradoxes demonstrated with computer-synthesized sound | journal=Journal of the Acoustical Society of America | volume=46 | year=1969 | issue=1A | pages=88 | doi=10.1121/1.1973626|bibcode = 1969ASAJ...46...88R | doi-access=free }}</ref>
<ref name="phil-355">{{cite journal | author=[[Diana Deutsch]], Dooley, K., and Henthorn, T. | title=Pitch circularity from tones comprising full harmonic series | journal=Journal of the Acoustical Society of America | volume=124 | pages=589-597 | year=2008 | doi=10.1121/1.2931957 }} [http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASADL&smode=strresults&sort=rel&maxdisp=25&threshold=0&pjournals=ARLOFJ%2CJASMAN%2CNOCOAN%2CSOUCAU%2CPMARCW%2CATCODK%2CASASTR&possible1=henthorn&possible1zone=article&OUTLOG=NO&viewabs=JASMAN&key=DISPLAY&docID=1&page=0&chapter=0 Weblink] [http://philomel.com/pdf/JASA-2008_124_589-597.pdf PDF Document]
▲Circularity effects based on this principle have been produced in orchestral music and electronic music, by having multiple instruments playing simultaneously in different octaves.
</ref>Using this algorithm, gliding tones that appear to ascend or descend endlessly are also produced. This development has led to the intriguing possibility that, using this new algorithm, one might transform banks of natural instrument samples so as to produce tones that sound like those of natural instruments but still have the property of circularity. This development opens up new avenues for music composition and performance.
 
Normann et al.<ref name="nor-2001">{{cite journal | author=Normann, I., Purwins, H., Obermayer, K.| title= Spectrum of Pitch Differences Models the Perception of Octave Ambiguous tones | journal= Computer Music Conference | pages=274–276 | year=2001 }} [http://mtg.upf.edu/files/publications/Normann_ICMC_2001_SpecPitchDiff.pdf PDF Document] {{Webarchive|url=https://web.archive.org/web/20211205035721/http://mtg.upf.edu/files/publications/Normann_ICMC_2001_SpecPitchDiff.pdf |date=2021-12-05 }}</ref> showed that pitch circularity can be created using a bank of single tones; here the relative amplitudes of the odd and even harmonics of each tone are manipulated so as to create ambiguities of height.
A different algorithm that creates ambiguities of pitch height by manipulating the relative amplitudes of the odd and even harmonics, was developed by [[Diana Deutsch]] and colleagues.<ref name="phil-355">{{cite journal | author=[[Diana Deutsch]], Dooley, K., and Henthorn, T. | title=Pitch circularity from tones comprising full harmonic series | journal=Journal of the Acoustical Society of America | volume=124 | pages=589–597 | year=2008 | doi=10.1121/1.2931957 | pmid=18647001 | issue=1|bibcode = 2008ASAJ..124..589D }} [https://archive.today/20130112052940/http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASADL&smode=strresults&sort=rel&maxdisp=25&threshold=0&pjournals=ARLOFJ,JASMAN,NOCOAN,SOUCAU,PMARCW,ATCODK,ASASTR&possible1=henthorn&possible1zone=article&OUTLOG=NO&viewabs=JASMAN&key=DISPLAY&docID=1&page=0&chapter=0 Weblink] [http://philomel.com/pdf/JASA-2008_124_589-597.pdf PDF Document] {{Webarchive|url=https://web.archive.org/web/20110527040222/http://philomel.com/pdf/JASA-2008_124_589-597.pdf |date=2011-05-27 }}</ref> Using this algorithm, gliding tones that appear to ascend or descend endlessly are also produced. This development has led to the intriguing possibility that, using this new algorithm, one might transform banks of natural instrument samples so as to produce tones that sound like those of natural instruments but still have the property of circularity. This development opens up new avenues for music composition and performance.<ref name="phil-445">{{cite journal | author=[[Diana Deutsch]] | title=The paradox of pitch circularity | journal=Acoustics Today | volume= 6| pages=8–15 | year=2010 | doi=10.1121/1.3488670 | issue=3 }} [http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASADL&smode=strresults&sort=rel&maxdisp=25&threshold=0&pjournals=ARLOFJ%2CJASMAN%2CNOCOAN%2CSOUCAU%2CPMARCW%2CATCODK%2CASASTR&possible1=The+paradox+of+pitch+circularity&possible1zone=article&OUTLOG=NO&viewabs=ATCODK&key=DISPLAY&docID=1&page=0&chapter=0 Weblink] {{Webarchive|url=https://web.archive.org/web/20240503071707/https://pubs.aip.org/ |date=2024-05-03 }} [http://philomel.com/pdf/Acoustics_Today_2010_Jul.pdf PDF Document] {{Webarchive|url=https://web.archive.org/web/20110715082127/http://philomel.com/pdf/Acoustics_Today_2010_Jul.pdf |date=2011-07-15 }}</ref>
 
==See also==
*[[Chromatic circle]]
*[[Shepard tone]]
*[[Tritone paradox]]
 
==References==
{{Reflist}}
 
{{Pitch (music)}}
 
[[Category:Auditory illusions]]
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