Editing Shepard tone (section)

==Variants==
[[File:Shepard Tone spectrum video visualization.webm|thumb|right|Moving audio and video visualization of a rising Shepard–Risset glissando. See and hear the higher tones as they fade out.]]

===Shepard–Risset glissando===
[[Jean-Claude Risset]] subsequently created a version of the scale where the tones glide continuously, and it is appropriately called the '''continuous Risset scale''' or '''Shepard–Risset glissando'''.<ref name="CDM">{{Cite news|url=http://cdm.link/2016/11/jean-claude-risset-reimagined-digital-sound-europe-abroad/|title=Jean-Claude Risset, who reimagined digital synthesis, has died - CDM Create Digital Music|date=2016-11-22|work=CDM Create Digital Music|quote=The sound for which Risset is best known is perhaps the most emblematic of his contributions. Creating a sonic illusion much like M.C. Escher’s optical ones, the Shepherd-Risset glissando / Risset scale, in its present form invented by the French composer, seems to ascend forever.|access-date=2019-12-30|language=en-US}}</ref> When done correctly, the tone appears to rise (or fall) continuously in pitch, yet return to its starting note. Risset has also created a similar effect with rhythm in which tempo seems to increase or decrease endlessly.<ref>{{Cite web|date=12 May 2013|title=Risset rhythm - eternal accelerando|url=http://swiki.hfbk-hamburg.de:8888/MusicTechnology/826}}</ref>
[[File:Risset accelerando beat1 MCLD.ogg|thumb|An example of Risset's accelerating rhythm effect using a [[breakbeat]] loop]]

===Tritone paradox===
{{main|Tritone paradox}}
A sequentially played pair of Shepard tones separated by an [[interval (music)|interval]] of a [[tritone]] (half an octave) produces the [[tritone paradox]]. Shepard had predicted that the two tones would constitute a bistable figure, the auditory equivalent of the [[Necker cube]], that could be heard ascending or descending, but never both at the same time.<ref name="Shepard1964" />
[[File:Paradoxa del tríton.wav|thumb|Sequence of Shepard tones producing the tritone paradox]]
In 1986, [[Diana Deutsch]] discovered that the perception of which tone was higher depended on the absolute frequencies involved and that an individual would usually hear the same pitch as the highest (this is determined by the absolute pitch of the notes).<ref name="Deutsch1986">{{cite journal|last=Deutsch|first=Diana|year=1986|title=A musical paradox|url=http://philomel.com/pdf/MP-1986_3_275-280.pdf|journal=Music Perception|volume=3|issue=3|pages=275–280|doi=10.2307/40285337|jstor=40285337}}</ref> Interestingly, different listeners may perceive the same pattern as being either ascending or descending, depending on the language or dialect of the listener (Deutsch, Henthorn, and Dolson found that native speakers of [[Vietnamese language|Vietnamese]], a [[Tone (linguistics)|tonal]] language, heard the tritone paradox differently from Californians who were native speakers of English).<ref name="Deutsch1992">{{Cite journal 
| last1 = Deutsch | first1 = D. 
| title = Some New Pitch Paradoxes and their Implications 
| doi = 10.1098/rstb.1992.0073 
| journal = Philosophical Transactions of the Royal Society B: Biological Sciences 
| volume = 336 
| issue = 1278 
| pages = 391–397 
| year = 1992 
| pmid = 1354379 
| bibcode = 1992RSPTB.336..391D 
}}</ref><ref>{{Cite journal|last1=Deutsch|first1=Diana|last2=Henthorn|first2=Trevor|last3=Dolson|first3=Mark|date=2004|title=Speech Patterns Heard Early in Life Influence Later Perception of the Tritone Paradox|url=http://dx.doi.org/10.1525/mp.2004.21.3.357|journal=Music Perception|volume=21|issue=3|pages=357–372|doi=10.1525/mp.2004.21.3.357|issn=0730-7829}}</ref>

=== Perpetual melody ===
Pedro Patricio observed in 2012 that, by using a Shepard tone as a sound source and applying it to a melody, he could reproduce the illusion of a continuously ascending or descending movement characteristic of the Shepard Scale. Regardless of the tempo and the [[Envelope (music)|envelope]] of the notes, the auditory illusion is effectively maintained. The uncertainty of the scale the Shepard tones pertain allows composers to experiment with deceiving and disconcerting melodies.<ref>Patricio, Pedro. [https://www.researchgate.net/publication/279236493_From_the_Shepard_tone_to_the_perpetual_melody_auditory_illusion From the Shepard tone to the perpetual melody auditory illusion]. Proceedings of the 9th Sound and Music Computing Conference, SMC 2012. 5-10, 2012.</ref>[[File:Melodia Perpètua.wav|thumb|An example of an ascendent perpetual melody|left]]

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