Figure 1: Shepard tones forming a Shepard scale, illustrated in a sequencer

A Shepard tone, named after Roger Shepard, is a sound consisting of a superposition of sine waves separated by octaves. When played with the base pitch of the tone moving upwards or downwards, it is referred to as the Shepard scale. This creates the auditory illusion of a tone that continually ascends or descends in pitch, yet which ultimately seems to get no higher or lower.^[1] Shepard Tone Illustration File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Shepard Tone Illustration File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... In the field of electronic music, a sequencer was traditionally a device or piece of software that allows the user to record, play back and edit musical patterns. ... Roger Newland Shepard (born January 30, 1929 in Palo Alto, California) is a cognitive scientist and author of Toward a Universal Law of Generalization for Psychological Science. ... Sound is a disturbance of mechanical energy that propagates through matter as a wave. ... For other uses, see Octave (disambiguation). ... Pitch is the perceived fundamental frequency of a sound. ... An auditory illusion is an illusion of hearing (sense), the sound equivalent of an optical illusion: the listener hears either sounds which are not present in the stimulus, or impossible sounds. ...

Construction of a Shepard scale

The illusion can be constructed by creating a series of overlapping ascending or descending scales. Similar to the Penrose stairs optical illusion (as in M.C. Escher's lithograph Ascending and Descending) or a barber's pole, the basic concept is shown in Figure 1. The Penrose stairs is an impossible object devised by Lionel Penrose and his son Roger Penrose and can be seen as a variation on his Penrose triangle. ... An optical illusion. ... Hand with Reflecting Sphere (Self-Portrait in Spherical Mirror), 1935. ... Ascending and Descending, an M. C. Escher lithograph print Ascending and Descending is a lithograph print by the Dutch artist M. C. Escher which was first printed in 1960. ... Barber pole, ca. ...

Each square in the figure indicates a tone, 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. As a conceptual example of an ascending Shepard scale, the first tone could be an almost inaudible C(4) (middle C) and a loud C(5) (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 D(4) and a still quieter D(5). The two frequencies would be equally loud at the middle of the octave (F#), and the twelfth tone would be a loud B(4) and an almost inaudible B(5) with the addition of an almost inaudible B(3). The thirteenth tone would then be the same as the first, and the cycle could continue indefinitely. (More accurately, each tone consists of ten sine waves with frequencies separated by octaves; the intensity of each is a gaussian function of its separation in semitones from a peak frequency, which in the above example would be B(4).) The horizontal axis shows frequency in Hz Loudness is the quality of a sound that is the primary psychological correlate of physical intensity. ... In Western music, the expression middle C refers to the note C or Do located exactly between the two staves of the grand staff, quoted as C4 in note-octave notation (also known as scientific pitch notation). ... Probability density function of Gaussian distribution (bell curve). ... A semitone (also known in the USA as a half step) is a musical interval. ...

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 instead of legato or portamento). As a more concrete example, consider a brass trio consisting of a trumpet, a horn, and a tuba. They all start to play a repeating C scale (C-D-E-F-G-A-B-C) in their respective ranges, i.e. they all start playing C's, but their notes are all in different octaves. When they reach the G of the scale, the trumpet drops down an octave, but the horn and tuba continue climbing. They're all still playing the same pitch class, but at different octaves. When they reach the B, the horn similarly drops down an octave, but the trumpet and tuba continue to climb, and when they get to what would be the second D of the scale, the tuba drops down to repeat the last seven notes of the scale. So no instrument ever exceeds an octave range, and essentially keeps playing the exact same seven notes over and over again. But because two of the instruments are always "covering" the one that drops down an octave, it seems that the scale never stops rising. In musical notation, the Italian word staccato (literally detached, plural staccatos or staccati) indicates that notes are sounded in a detached and distinctly separate manner, with silence making up the latter part of the time allocated to each note. ... Marcato in the context of bowed string instruments is an arco technique for playing such a stringed instrument, such as violin, viola, cello, and the double bass, also called contrabass, bass viol, or upright bass. ... In musical notation legato indicates that musical notes are played smoothly. ... Portamento is a musical term currently used to mean pitch bending or sliding, and in 16th century polyphonic writing refers to a type of musical ornamentation. ...

Jean-Claude Risset subsequently created a version of the scale where the steps between each tone are continuous, and it is appropriately called the continuous Risset scale or Shepard-Risset glissando. When done correctly, the tone appears to rise (or descend) 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.^[2] Jean-Claude Risset (March 13, 1938 in Le Puy, France) is a French composer of electronic music. ... Rhythm (Greek = flow, or in Modern Greek, style) is the variation of the length and accentuation of a series of sounds or other events. ...

Shepard scales in music

Although it is difficult to recreate the illusion with acoustic instruments, James Tenney, who worked with Roger Shepard at Bell Labs in the early 1960s, has created a piece utilizing this effect, For Ann (rising). The piece, in which up to twelve closely but not quite consistently spaced computer-generated sine waves rise steadily from an A pitched below audibility to an A above, fading in, and back out, of audible volume, was then scored for twelve string players. The effect of the electronic work consists both of the Shepard scale, seamless endlessly (rising) glissandos, and of a shimmering caused by the highest perceivable frequency and the inability to focus on the multitude of rising tones. Tenney has also proposed that the piece be revised and realized so that all entrances are timed in such a way that the ratio between successive pitches is the golden mean, which would make each lower first-order combination tone of each successive pair coincide with subsequently spaced, lower, tones. James Tenney (August 10, 1934 in Silver City, NM) is an American composer and influential music theorist. ... Bell Laboratories (also known as Bell Labs and formerly known as AT&T Bell Laboratories and Bell Telephone Laboratories) was the main research and development arm of the United States Bell System. ... For Ann (rising) is a piece created by James Tenney in 1969. ... A ratio is a quantity that denotes the proportional amount or magnitude of one quantity relative to another. ... In philosophy (especially that of Aristotle), the golden mean is the felicitous middle between two extremes, one of excess and the other of deficiency; for this meaning, see golden mean (philosophy). ... Also called a Tartini tone, a combination tone is a usually lower pitch produced inside the inner ear by the presence of two external pitches. ...

An independently discovered version of the Shepard tone appears at the beginning and end of the 1976 album A Day At The Races by the band Queen. The piece consists of a number of electric-guitar parts following each other up a scale in harmony, with the notes at the top of the scale fading out as new ones fade in at the bottom. Lose Control by Missy Elliott also seems to feature an ascending Shepard tone as a recurring theme (via the sampled synthesizers from Cybotron's song "Clear".) "Echoes", a 23-minute song by Pink Floyd, concludes with a rising Shepard tone. The Shepard tone is also featured in the fading piano outro to "A Last Straw", off Robert Wyatt's 1974 opus Rock Bottom. This article does not cite any references or sources. ... Queen are an English rock band formed in 1970 in London by guitarist Brian May, singer Freddie Mercury and drummer Roger Taylor, with bassist John Deacon joining the following year. ... Melissa Arnette Elliott (born July 1, 1971 in Portsmouth, Virginia), better known as Missy Elliott, is an American rapper, singer, songwriter, MC, and record producer. ... Clear (1990) Cybotron was a techno group formed in 1980 by Juan Atkins and Richard 3070 Davis in Detroit, Michigan. ... This article is about the Pink Floyd song. ... Pink Floyd are an English rock band that initially earned recognition for their psychedelic rock music, and, as they evolved, for their progressive rock music. ... Robert Wyatt (born Robert Wyatt-Ellidge, 28 January 1945, in Bristol) is an English musician, and a former member of the influential Canterbury scene band Soft Machine. ... Year 1974 (MCMLXXIV) was a common year starting on Tuesday (link will display full calendar) of the 1974 Gregorian calendar. ... Rock Bottom can mean: Rock bottom, an all time low Rock Bottom (album), an album by Robert Wyatt Rock Bottom (SpongeBob SquarePants episode), the SpongeBob SquarePants Episode Rock Bottom Restaurants Inc. ...

Another independent discovery, in classical music, occurs in the Fantasy and Fugue in G minor for organ, BWV 542, by Bach. Following the first third movement of the Fantasy there is a descending pedal bass line under a chord sequence which traverses the circle of fifths. The gradual addition of stops up to full organ sound creates something akin to a barber-pole pattern with an illusion of ever-deeper descent, even though the bass line actually skips octaves. This effect is only possible on organs with electric consoles and would have been impossible in Bach's time, as it is hard to throw an organ stop in mid-play^{[citation needed]}. Bach-Werke-Verzeichnis (Bach Works Catalogue) is the numbering system used to identify musical works by Johann Sebastian Bach. ... “Bach” redirects here. ... In music theory, the circle of fifths (or cycle of fifths) is an imaginary geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale. ... The choir division of the organ at St. ...

A good example in modern culture is in the video game Super Mario 64; a Shepard scale accompanies the never-ending staircase. For the Nintendo DS enhanced remake, see Super Mario 64 DS. Super Mario 64 ) is a top-selling platform game developed by Nintendo Entertainment Analysis and Development and published by Nintendo for the Nintendo 64. ...

Antonio Carlos Jobim's Waters of March has descending orchestration that is intended to represent the continual flow of water to the ocean; the effect is very much like Shepard tones. Antônio Carlos Brasileiro de Almeida Jobim (January 25, 1927 in Rio de Janeiro – December 8, 1994 in New York City), or Tom Jobim (as he is fondly known in his home country), was a Brazilian composer, arranger, singer, pianist/guitarist and one of the primary forces behind the creation... Waters of March (Águas de Março) is a bossa nova song composed by Antonio Carlos Jobim. ...

Example

Image File history File links DescenteInfinie. ...

References

1. ^ Roger N. Shepard (December 1964). "Circularity in Judgements of Relative Pitch". Journal of the Acoustical Society of America 36 (12): 2346-53. DOI:10.1121/1.1919362. 
2. ^ Risset rhythm

Roger Newland Shepard (born January 30, 1929 in Palo Alto, California) is a cognitive scientist and author of Toward a Universal Law of Generalization for Psychological Science. ... A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ...

External links

• The partials of a Shepard tone
• Audio demonstration of the discrete Shepard Tone
• Demonstrating an audio example of a continuous "endlessly descending" tone
• Demonstration of discrete Shepard tone (requires Macromedia Flash)
• Visualization of the Shepard Effect using Java