Aspectrogram of ascending Shepard tones on a linear frequency scale
AShepard tone, named afterRoger Shepard, is a sound consisting of asuperposition ofsine waves separated byoctaves. When played with the basspitch of the tone moving upward or downward, it is referred to as theShepard scale. This creates theauditory illusion of a tone that seems to continually ascend or descend in pitch, yet which ultimately gets no higher or lower.[1]
Figure 1: Shepard tones forming a Shepard scale, illustrated in asequencer
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 theloudness 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.
As a conceptual example of an ascending Shepard scale, the first tone could be an almost inaudible C4 (middle C) and a loud C5 (an octave higher). The next would be a slightly louder C♯4 and a slightly quieter C♯5; the next would be a still louder D4 and a still quieter D5. The two frequencies would be equally loud at the middle of the octave (F♯4 and F♯5), and the twelfth tone would be a loud B4 and an almost inaudible B5 with the addition of an almost inaudible B3. 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. araised cosine function of its separation insemitones from a peak frequency, which in the above example would be B4. 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."[1]
The theory behind the illusion was demonstrated during an episode of the BBC's showBang Goes the Theory, where the effect was described as "a musicalbarber's pole".[2]
The scale as described, with discrete steps between each tone, is known as thediscrete Shepard scale. The illusion is more convincing if there is a short time between successive notes (staccato ormarcato rather thanlegato orportamento).[citation needed]
Jean-Claude Risset subsequently created a version of the scale where the tones glide continuously, and it is appropriately called thecontinuous Risset scale orShepard–Risset glissando.[3] 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.[4]
A sequentially played pair of Shepard tones separated by aninterval of atritone (half an octave) produces thetritone paradox. Shepard had predicted that the two tones would constitute a bistable figure, the auditory equivalent of theNecker cube, that could be heard ascending or descending, but never both at the same time.[1]
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).[5] 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 ofVietnamese, atonal language, heard the tritone paradox differently from Californians who were native speakers of English).[6][7]
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 theenvelope 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.[8]
The ending ofThe Beatles' "I Am the Walrus" incorporates a Shepard tone with a chord progression built on ascending and descending lines in the bass and strings that line up to create the auditory illusion.[10]
The ending ofPink Floyd's "Echoes" from their 1971 albumMeddle features an ascending Shepard tone created using a feedback technique involving two tape recorders sharing a single tape, with one set to play and the other to record.[11]
TheDeep Note sound trademark ofTHX, introduced in 1983, uses a Shepard tone.[14]
In 1995, Ira Braus argued that the final sequence ofFranz Liszt's 1885 piano pieceBagatelle sans tonalité could be continued to produce a Shepard scale using Hofstadter's technique.[15]
In a 1967AT&T film by Shepard and E. E. Zajac, a Shepard tone accompanies the ascent of an analogousPenrose stair.[16]
In the video gameSuper Mario 64 (1996) for theNintendo 64 console, a piece that plays when the player tries to climb the neverending stairs located in the penultimate room of Peach's Castle incorporates a slightly modified Shepard scale played in the background. This auditory illusion complements the spatial loop effect, seemingly giving the impression that the stairs never end.[17]
InGodspeed You! Black Emperor's "The Dead Flag Blues" from their 1997 albumF♯ A♯ ∞, a section mainly consisting ofslide guitar is briefly looped into itself to create a downward Shepard tone.
On their 1998 albumLP5, English electronic duoAutechre employed a decelerating Risset rhythm for the track "Fold4,Wrap5".
Austrian composerGeorg Friedrich Haas incorporates Shepard tones at various points in his orchestral piecein vain (2000/02).[18]
Christopher Nolan said in an interview that the soundtrack of his 2006 filmThe Prestige (composed by David Julyan) explores the potential of Shepard tones as a fundamental basis for compositions.[19] This is fully realised in his 2017 filmDunkirk where a Shepard tone is used to create the illusion of an ever increasing moment of intensity across intertwined storylines.[20]
InStephin Merritt's 2007 song "Man of a Million Faces", composed forNPR's "Project Song", the Shepard tone is a key aspect.[21]
In the 2008 filmThe Dark Knight and its 2012 followupThe Dark Knight Rises, a Shepard tone was used to create the sound of the Batpod, a motorcycle that the filmmakers did not want to change gear and tone abruptly but to accelerate constantly.[22]
InLucrecia Martel's feature filmZama (2017), there is extensive use of the Shepard tone creating a "loud and shreechy soundscape, in order to achieve closeness to the viewer", according to the director.[24]
The 2018 track "Always Ascending" byFranz Ferdinand from the album of the same name features a rising Shepard tone throughout the song. The video for the song echoes the effect, with the camera apparently rising continually throughout.[25]
The track "Neuron Activator" from theCruelty Squad soundtrack uses a constantly repeating Shepard tone, in line with the intentionally crude and semi-Dadaist nature of the game's soundtrack.
^"Jean-Claude Risset, who reimagined digital synthesis, has died - CDM Create Digital Music".CDM Create Digital Music. 22 November 2016. Retrieved30 December 2019.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.
^Stephin Merritt: Two Days, 'A Million Faces' (video). NPR. 4 November 2007. Retrieved9 October 2015.'It turns out I was thinking about a Shepard tone, the illusion of ever-ascending pitches.'
