A Shepard tone, named after Roger Shepard, is a sound consisting of a superposition of sine waves separated by octaves. When played with the bass pitch of the tone moving upward or downward, it is referred to as the Shepard scale. This creates the auditory illusion of a tone that seems to continually ascend or descend in pitch, yet which ultimately gets no higher or lower. [1]
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.
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. a raised cosine function of its separation in semitones 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 show Bang Goes the Theory , where the effect was described as "a musical barber's pole". [2]
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 ]
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. [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 an 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. [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 of Vietnamese, a tonal 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 the 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. [8]
In music, a glissando is a glide from one pitch to another. It is an Italianized musical term derived from the French glisser, "to glide". In some contexts, it is equivalent to portamento, which is a continuous, seamless glide between notes. In other contexts, it refers to discrete, stepped glides across notes, such as on a piano. Some terms that are similar or equivalent in some contexts are slide, sweepbend, smear, rip, lip, plop, or falling hail. On wind instruments, a scoop is a glissando ascending to the onset of a note achieved entirely with the embouchure, except on instruments that have a slide.
In music, an octave or perfect octave is a series of eight notes occupying the interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems". The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave have the same name and are of the same pitch class.
In music theory, a scale is "any consecutive series of notes that form a progression between one note and its octave", typically by order of pitch or fundamental frequency.
A strange loop is a cyclic structure that goes through several levels in a hierarchical system. It arises when, by moving only upwards or downwards through the system, one finds oneself back where one started. Strange loops may involve self-reference and paradox. The concept of a strange loop was proposed and extensively discussed by Douglas Hofstadter in Gödel, Escher, Bach, and is further elaborated in Hofstadter's book I Am a Strange Loop, published in 2007.
In music theory, the tritone is defined as a musical interval spanning three adjacent whole tones. For instance, the interval from F up to the B above it is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B.
Pitch is a perceptual property that allows sounds to be ordered on a frequency-related scale, or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre.
Auditory illusions are illusions of real sound or outside stimulus. These false perceptions are the equivalent of an optical illusion: the listener hears either sounds which are not present in the stimulus, or sounds that should not be possible given the circumstance on how they were created.
In music theory, the circle of fifths is a way of organizing pitches as a sequence of perfect fifths. Starting on a C, and using the standard system of tuning for Western music, the sequence is: C, G, D, A, E, B, F♯/G♭, C♯/D♭, G♯/A♭, D♯/E♭, A♯/B♭, F, and C. This order places the most closely related key signatures adjacent to one another.
The octave illusion is an auditory illusion discovered by Diana Deutsch in 1973. It is produced when two tones that are an octave apart are repeatedly played in alternation ("high-low-high-low") through stereo headphones. The same sequence is played to both ears simultaneously; however when the right ear receives the high tone, the left ear receives the low tone, and conversely. Instead of hearing two alternating pitches, most subjects instead hear a single tone that alternates between ears while at the same time its pitch alternates between high and low.
The glissando illusion is an auditory illusion, created when a sound with a fixed pitch, such as a synthesized oboe tone, is played together with a sine wave gliding up and down in pitch, and they are both switched back and forth between stereo loudspeakers. The effect is that the oboe is heard as switching between loudspeakers while the sine wave is heard as joined together seamlessly, and as moving around in space in accordance with its pitch motion. Right-handers often hear the glissando as traveling from left to right as its pitch glides from low to high, and then back from right to left as its pitch glides from high to low.
The tritone paradox is an auditory illusion in which a sequentially played pair of Shepard tones separated by an interval of a tritone, or half octave, is heard as ascending by some people and as descending by others. Different populations tend to favor one of a limited set of different spots around the chromatic circle as central to the set of "higher" tones. Roger Shepard in 1963 had argued that such tone pairs would be heard ambiguously as either ascending or descending. However, psychology of music researcher Diana Deutsch in 1986 discovered that when the judgments of individual listeners were considered separately, their judgments depended on the positions of the tones along the chromatic circle. For example, one listener would hear the tone pair C–F♯ as ascending and the tone pair G–C♯ as descending. Yet another listener would hear the tone pair C–F♯ as descending and the tone pair G–C♯ as ascending. Furthermore, the way these tone pairs were perceived varied depending on the listener's language or dialect.
Deutsch's scale illusion is an auditory illusion in which two series of unconnected notes appear to combine into a single recognisable melody, when played simultaneously into the left and right ears of a listener.
Jean-Claude Raoul Olivier Risset was a French composer, best known for his pioneering contributions to computer music. He was a former student of André Jolivet and former co-worker of Max Mathews at Bell Labs.
For Ann (rising) is a piece of electronic music composed by American composer and music theorist James Tenney in 1969. The piece incorporates the Shepard tone concept, named after Tenney's colleague at Bell Labs, psychologist Roger Shepard. The technique which the piece uses is more properly described as a continuous Risset scale, or a Shepard-Risset glissando (Polansky 2003).
Diana Deutsch is a British-American psychologist from London, England. She is a professor of psychology at the University of California, San Diego, and is a prominent researcher on the psychology of music. Deutsch is primarily known for her discoveries in music and speech illusions. She also studies the cognitive foundation of musical grammars, which consists of the way people hold musical pitches in memory, and how people relate the sounds of music and speech to each other. In addition, she is known for her work on absolute pitch, which she has shown is far more prevalent among speakers of tonal languages. Deutsch is the author of Musical Illusions and Phantom Words: How Music and Speech Unlock Mysteries of the Brain (2019), the editor for Psychology of Music, and also the compact discs Musical Illusions and Paradoxes (1995) and Phantom Words and Other Curiosities (2003).
Illusory conjunctions are psychological effects in which participants combine features of two objects into one object. There are visual illusory conjunctions, auditory illusory conjunctions, and illusory conjunctions produced by combinations of visual and tactile stimuli. Visual illusory conjunctions are thought to occur due to a lack of visual spatial attention, which depends on fixation and the amount of time allotted to focus on an object. With a short span of time to interpret an object, blending of different aspects within a region of the visual field – like shapes and colors – can occasionally be skewed, which results in visual illusory conjunctions. For example, in a study designed by Anne Treisman and Schmidt, participants were required to view a visual presentation of numbers and shapes in different colors. Some shapes were larger than others but all shapes and numbers were evenly spaced and shown for just 200 ms. When the participants were asked to recall the shapes they reported answers such as a small green triangle instead of a small green circle. If the space between the objects is smaller, illusory conjunctions occur more often.
Psychoacoustics is the branch of psychophysics involving the scientific study of the perception of sound by the human auditory system. It is the branch of science studying the psychological responses associated with sound including noise, speech, and music. Psychoacoustics is an interdisciplinary field including psychology, acoustics, electronic engineering, physics, biology, physiology, and computer science.
Pitch circularity is a fixed series of tones that are perceived to ascend or descend endlessly in pitch. It's an example of an auditory illusion.
A constant timbre at a constant pitch is characterized by a spectrum. Along a piece of music, the spectrum measured within a narrow time window varies with the melody and the possible effects of instruments. Therefore, it may seem paradoxical that a constant spectrum can be perceived as a melody rather than a stamp.
Interindividual differences in perception describes the effect that differences in brain structure or factors such as culture, upbringing and environment have on the perception of humans. Interindividual variability is usually regarded as a source of noise for research. However, in recent years, it has become an interesting source to study sensory mechanisms and understand human behavior. With the help of modern neuroimaging methods such as fMRI and EEG, individual differences in perception could be related to the underlying brain mechanisms. This has helped to explain differences in behavior and cognition across the population. The present study using MRS provides direct evidence showing that the excitatory process in the suprasensory areas is linked to the individual differences in visual motion perception. The neurotransmitter concentration in the higher areas that execute cognitive functions is related to the interindividual variability in the perception of visual motion. Common methods include studying the perception of illusions, as they can effectively demonstrate how different aspects such as culture, genetics and the environment can influence human behavior.
It's like a barber's pole of sound.
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.
'It turns out I was thinking about a Shepard tone, the illusion of ever-ascending pitches.'
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