Editing Shepard tone (section)

== Construction==
[[File:Shepard tone.jpg|thumb|left|150px|Figure 1: Shepard tones forming a Shepard scale, illustrated in a [[music sequencer|sequencer]]]]
Each square in Figure 1 indicates a tone, with any set of squares in vertical alignment together making one Shepard tone. The color of each square indicates the [[loudness]] of the note, with purple being the quietest and green the loudest. Overlapping notes that play at the same time are exactly one octave apart, and each scale fades in and fades out so that hearing the beginning or end of any given scale is impossible. [[File:Shepard A.ogg|thumb|Shepard tone as of the root note A (A<sub>4</sub> = 440 Hz)]]
[[File:Shepard scale diatonic C.ogg|thumb|Shepard scale, [[Diatonic scale|diatonic]] in [[C major|C Major]], repeated 5 times]]
As a conceptual example of an ascending Shepard scale, the first tone could be an almost inaudible C<sub>4</sub> ([[middle C]]) and a loud C<sub>5</sub> (an octave higher). The next would be a slightly louder C{{music|sharp}}<sub>4</sub> and a slightly quieter C{{music|sharp}}<sub>5</sub>; the next would be a still louder D<sub>4</sub> and a still quieter D<sub>5</sub>. The two frequencies would be equally loud at the middle of the octave (F{{music|sharp}}<sub>4</sub> and F{{music|sharp}}<sub>5</sub>), and the twelfth tone would be a loud B<sub>4</sub> and an almost inaudible B<sub>5</sub> with the addition of an almost inaudible B<sub>3</sub>. The thirteenth tone would then be the same as the first, and the cycle could continue indefinitely. (In other words, each tone consists of two sine waves with frequencies separated by octaves; the intensity of each is e.g. a [[raised cosine]] function of its separation in [[semitone]]s from a peak frequency, which in the above example would be B<sub>4</sub>. According to Shepard, "almost any smooth distribution that tapers off to subthreshold levels at low and high frequencies would have done as well as the cosine curve actually employed."<ref name="Shepard1964">{{cite journal | author-link=Roger N. Shepard | first=Roger N. | last=Shepard | title=Circularity in Judgements of Relative Pitch | journal=Journal of the Acoustical Society of America | volume=36 | issue=12 |date=December 1964 | pages=2346–53 | doi=10.1121/1.1919362 | bibcode=1964ASAJ...36.2346S }}</ref>

The theory behind the illusion was demonstrated during an episode of the BBC's show ''[[Bang Goes the Theory]]'', where the effect was described as "a musical [[barberpole illusion|barber's pole]]".<ref>{{Cite episode
 | title          = Clip from Series 4, Episode 6
 | url            = https://www.bbc.co.uk/programmes/p00gfdg1
 | series         = Bang Goes the Theory
 | network        =BBC
 | date           =18 April 2011
 | quote          = It's like a barber's pole of sound.
 | language       =en
}}</ref>

The scale as described, with discrete steps between each tone, is known as the '''discrete Shepard scale'''. The illusion is more convincing if there is a short time between successive notes ([[staccato]] or [[marcato]] rather than [[legato]] or [[portamento]]).{{citation needed|date=December 2019}}