Spectrum view of ascending Shepard Tones(linear frequency scale)

descending, logarithmic frequency scale

A Shepard tone, named after Roger Shepard, is a sound consisting of a superposition of sine waves separated by octaves. Roger Newland Shepard (born January 30, 1929 in Palo Alto, California) is a cognitive scientist and author of Toward a Universal Sound' is Vibration transmitted through a Solid, Liquid, or Gas; particularly sound means those vibrations composed of Frequencies In Music, an octave ( is the the use of which is "common in most musical systems When played with the base pitch of the tone moving upwards or downwards, it is referred to as the Shepard scale. Pitch represents the perceived Fundamental frequency of a sound 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. An auditory illusion is an Illusion of hearing, the aural equivalent of an optical illusion the listener hears either sounds which are not present in the stimulus ^[1]

Construction of a Shepard scale

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

The illusion can be constructed by creating a series of overlapping ascending or descending scales. A music sequencer (also MIDI sequencer or just sequencer) is software or hardware designed to create and manage computer-generated music 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 created by Lionel Penrose and his son Roger Penrose. This article is about visual perception See Optical Illusion (Album for information about the Time Requiem album Maurits Cornelis Escher (17 June 1898 – 27 March 1972 usually referred to as M Ascending and Descending is a lithograph print by the Dutch artist M A barber's pole is a type of Sign used by Barbers a pole with white and red stripes

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. Loudness is the quality of a Sound that is the primary psychological correlate of physical strength (amplitude 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). C or Do is the first Note of the fixed-Do Solfege. In Western Music, the expression " Middle C " refers to the note 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. (In other words, 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 normal distribution, also called the Gaussian distribution, is an important family of Continuous probability distributions applicable in many fields A semitone, also called a half step or a half tone, is the smallest Musical interval commonly used in Western tonal music and it is considered the )

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). In Musical notation, the Italian word staccato (literally detached, plural staccatos or staccati) indicates that notes Marcato is a Bowing technique for playing a stringed instrument such as Violin, Viola, Cello, and the Double bass. In Musical notation the Italian word legato (literally meaning "tied together" indicates that musical notes are played or sung smoothly Portamento is a Musical term primarily denoting a vocal slide between two pitches and its emulation by instruments such as the violin and in 16th century 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.

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. Jean-Claude Risset ( March 18, 1938 in Le Puy France) is a French Composer, best known for his pioneering contributions to Computer music 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. Rhythm (from Greek ῥυθμός - rhythmos, "any measured flow or movement symmetry" is the variation of the length and accentuation of ^[2]

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). James Tenney ( August 10, 1934 - August 24, 2006) was 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) is the Research organization For Ann (rising is a piece of Electronic music created by James Tenney in 1969. 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 ratio, which would make each lower first-order combination tone of each successive pair coincide with subsequently spaced, lower, tones. A ratio is an expression which compares quantities relative to each other In Mathematics and the Arts two quantities are in the Golden ratio if the Ratio between the sum of those quantities and the larger one is the A combination tone, also called a sum tone or a difference tone, can be any of at least three similar Psychoacoustic phenomena

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. A Day at the Races is a rock album by English band Queen released in December 1976 Queen were an English rock band formed in 1970 in London by guitarist 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". Melissa Arnette "Missy" Elliott (born July 1 1971 is a five-time Grammy Award -winning American rapper, singer, Songwriter, and ) "Echoes", a 23-minute song by Pink Floyd, concludes with a rising Shepard tone. " Echoes " is a song by Pink Floyd, including lengthy instrumental passages sound effects and Musical improvisation. Pink Floyd are The Shepard tone is also featured in the fading piano outro to "A Last Straw", off Robert Wyatt's 1974 opus Rock Bottom. Robert Wyatt (born Robert Wyatt-Ellidge, 28 January 1945 in Bristol) is an English Musician, and founding member of the influential Rock Bottom is the second solo album (the first post- Soft Machine) by Robert Wyatt.

In his book Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter explains how Shepard Scales can be used on Bach's Endlessly Rising Canon for making the modulation end in the same pitch instead of an octave higher. Gödel Escher Bach an Eternal Golden Braid (commonly GEB) is a Pulitzer Prize -winning book by Douglas Hofstadter, described Douglas Richard Hofstadter (born February 15 1945 in New York New York) is an American academic whose research focuses on consciousness thinking and creativity WikipediaWikiProject Composers#Lead section.2 This article is written in British English including maximised use of "-ise" In Music, modulation is most commonly the act or process of changing from one key ( tonic, or tonal center) to another

Another independent discovery, in classical music, occurs in the Fantasy and Fugue in G minor for organ, BWV 542, by Bach. BWV is also the SIL code for the Language Bahau River Kenyah spoken in Borneo. 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. In Music theory, the circle of fifths (or '''circle of fourths''') shows the relationships among the twelve tones of the Chromatic scale, their corresponding 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. An organ stop (or just stop) is a component of a Pipe organ which admits pressurized air (known as wind) to a set of Organ pipes Its name

Chopin's Etude no. 3, op. 10 contains Shepard tone-like sequences in the middle section. Étude Op10 No3 in E major is a solo piano work composed by Frédéric Chopin.

An example in modern culture of the Shepard tone is in the video game Super Mario 64; the tone accompanies the never-ending staircase. is a Platform game developed by Nintendo Entertainment Analysis and Development and published by Nintendo for the Nintendo 64. ^[3] However, this may not be a true Shepard tone, as the tone only takes on three note values within an octave and the transition to the third is not always perceived as being in the same direction.

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. Antonio Carlos Brasileiro de Almeida Jobim ( January 25, 1927 in Rio de Janeiro &ndash December 8, 1994 in Brazil) also " Waters of March " ( Portuguese: " Águas de Março " is a Brazilian Song composed by Antonio Carlos Jobim.

A Shepard-Risset glissando can be found at the end of the Muse song "Ruled by Secrecy. In Greek mythology, the Muses ( Ancient Greek, hai moũsai: perhaps from the Proto-Indo-European root * men- "think" are Absolution is the third Studio album by English alternative Rock band Muse. "

Example

References

1. ^ Roger N. Shepard (December 1964). Roger Newland Shepard (born January 30, 1929 in Palo Alto, California) is a cognitive scientist and author of Toward a Universal "Circularity in Judgements of Relative Pitch". Journal of the Acoustical Society of America 36 (12): 2346-53. doi:10.1121/1.1919362. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.  
2. ^ Risset rhythm
3. ^ YouTube: "Super Mario 64: Endless Stairs Glitch and Ending"

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
• Demonstration of the Shepard Scale of the Infinite Staircase in Super Mario 64