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Topic: Shepard scale

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Shepard tone

Tritone paradox

Pitch (music)

Auditory illusion

Musical tuning

Penrose stairs

Note

James Tenney

Tritone

International Organization for Standardization

C Sharp programming language

Hertz

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	Shepard tone - Wikipedia, the free encyclopedia
		Figure 1: Shepard tones forming a Shepard scale, illustrated in a sequencer
		A Shepard tone is a sound, named after Roger Shepard, consisting of a superposition of sine waves separated by octaves.
		The scale as described, with discrete steps between each tone, is known as the discrete Shepard scale.
	en.wikipedia.org /wiki/Shepard_tone (746 words)

	Measuring Similarity
		On the response scale, for example, C differs from A by about half the number of responses as does D, but we cannot say that C twice as similar to A as is D. As for the stimulus scale, there is no reason to assume that wavelength is related to similarity in a simple way.
		Shepard found that by rescaling the abscissa such that data points near 570 nm were pushed horizontally closer together (in addition to similar, smaller changes elsewhere), he could make all the gradients take on approximately the same shape.
		The significance of all this for similarity scaling is that the metric structure of similarity space is initially unknown and it may reflect important properties of inter-object similarity and the cognitive operations involved in computing it.
	www.pigeon.psy.tufts.edu /avc/dblough/measurement.htm (4112 words)

	The David E. Rumelhart Prize: Roger Shepard
		Roger N. Shepard, Professor of Psychology at the University of Stanford, is a particularly appropriate recipient for a prize dedicated to the “Theoretical Foundations of Human Cognition”.
		Shepard also demonstrated that the path of apparent motion could be distorted by the presentation of a curved grey cue [23], again yielding highly regular laws relating motion and path length.
		Roger N. Shepard is a fellow of the American Association for the Advancement of Science and the American Academy of Arts and Sciences, and is the William James Fellow of the American Psychological Association.
	www.rumelhartprize.org /roger.htm (1801 words)

	Learn more about Pitch (music) in the online encyclopedia. (Site not responding. Last check: 2007-10-31)
		The relative pitches of individual notes in a scale may be determined by one of a number of tuning systems.
		In the west, the twelve-note chromatic scale is the most common method of organisation, with equal temperament now the most widely used method of tuning that scale.
		There are several of these, such as the tritone paradox, but most notably the Shepard scale, where a continuous or discrete sequence of specially formed tones can be made to sound like this sequence continues ascending forever, when this in fact is a clever audio illusion.
	www.onlineencyclopedia.org /p/pi/pitch__music_.html (1559 words)

	Tritone Paradox and Spectral-Motion AfterEffects
		Shepard tones consist of 10 components (octaves) and are presented through a Gaussian-shaped spectral filter (see Figure to the right).
		Illusions arise from Deutsch and Shepard tones when the spectral envelopes are held constant and the frequencies components are raised or lowered in pitch.
		After listening to a prolonged presentation of a Shepard scale, perception of the tritone pairs changes depending upon whether the scale was ascending or descending.
	www.cameron.edu /~lloydd/webdoc1.html (1517 words)

	[No title]
		Shepard Function (Barberpole) CV generator Reprinted from: "Lab Notes: Shepard Functions", by John Simonton, Polyphony magazine 2/83 see accompanying files: shepard.gif for figures 1-7 shepard2.gif for figures 8-11 The first audio illusion I ever heard was the Shepard Tone.
		Roger N Shepard's original work used a computer program written by Max Matthews but the same type of effect can be accomplished using analog synthesis equipment controlled by a gadget which, for lack of a better name, we may as well call a "Shepard Function Generator".
		But Shepard Tone generation is not the only application for this circuit; recently the same principles have been applied to other areas of electronic music.
	machines.hyperreal.org /manufacturers/Paia/images/shepard.txt?0046 (1976 words)

	Pitch (music)
		People with a sense of these relationships are said to have relative pitch while people who have a sense of the actual frequencies independent of other pitches are said to have absolute pitch, less accurately called perfect pitch.
		In the west, the twelve-note chromatic scale is the most common method of organization, with equal temperament now the most widely used method of tuning that scale.
		Pitches are named with integers because of octave and enharmonic equivalency (for example, C# and Db are the same pitch while C4 and C5 are functionally the same).
	www.brainyencyclopedia.com /encyclopedia/p/pi/pitch__music_.html (1635 words)

	Visualization of the Shepard Effect (Site not responding. Last check: 2007-10-31)
		Much like MC Escher's picture "Treppauf und treppab" portrays the optical illusion of a never ending staircase, the Shepard effect is an acustical illusion that gives the listener the impression of an endlessly rising melody.
		By abusing certain weaknesses in the way the human brain processes sound, it can be tricked into believing that it hears an ever rising scale or melody.
		By cleverly fading the four scales into and out of each other, the listener won't notice that they are actually hearing the same 12 chords again and again.
	www.netalive.org /tinkering/shepard-effect (153 words)

	Acoustical Society of America - Circularity in Pitch Judgement (Site not responding. Last check: 2007-10-31)
		One of the most widely used auditory illusions is Shepard's (1964) demonstration of pitch circularity, which has come to be known as the "Shepard Scale" demonstration.
		The result is an "ever-ascending" scale, which is a sort of auditory analog to the ever-ascending staircase visual illusion.
		R. Shepard (1964), "Circularity in judgments of relative pitch," J. Acoust.
	asa.aip.org /demo27.html (234 words)

	Shepard's Phenomenon (Site not responding. Last check: 2007-10-31)
		Roger N. Shepard of Bell Laboratories first demonstrated this phenomenon in the 1960s but it had been described ten years earlier by L.S. and Roger Penrose of the University of London.
		We decided to follow Shepard's example [5] of making each tone from a fundamental plus nine harmonics [6] though research shows that a much simpler combination will suffice.
		As the envelope of harmonics slides slowly up the scale, its highest frequency is slid off the top of the range of human hearing.
	www.ee.washington.edu /conselec/CE/sp95reports/other_labs/shep.htm (885 words)

	Ninfinger Productions: Scale Models
		Monogram's re-release of Revell's Mercury and Gemini spacecraft in 1/48 scale in the mid '80s brought back a flood of childhood memories to this spacecadet.
		The escape rocket nozzles (parts No. 7) were reduced on the inside to scale thickness and Evergreen 1/8" diameter plastic tube was used to create a stiffening ring at their base.
		The hatch used on Shepard's spacecraft was thicker and heavier than on those used on the orbital vehicles.
	www.ninfinger.org /~sven/models/rms_tips/mr3.html (4503 words)

	Pitch (music) - Wikipedia, the free encyclopedia
		There are several of these, such as the tritone paradox, but most notably the Shepard scale, where a continuous or discrete sequence of specially formed tones can be made to sound as if the sequence continues ascending or descending forever.
		In it, the pitch ratio between any two successive notes of the scale is exactly the twelfth root of two (or about 1.05946).
		Various systems of musical tuning have also been used to determine the relative frequency of notes in a scale.
	en.wikipedia.org /wiki/Pitch_(music) (2232 words)

	Postviews - past SF reviews, by author, S to Sp (Site not responding. Last check: 2007-10-31)
		Shepard's style has been compared often with Latin mystic realism, with the feel of vast forces at work on an intense and hallucinatory canvas and use of Hispanic settings.
		Shepard has visited this country before in the excellent "Scalehunters Beautiful Daughter" : an oddly anachronistic medieval land of superstitions and law courts with juries, subtle and unseen magic, and slumbering hyperintelligent dragons who some say are just ordinary mountainsides.
		Shepard wisely keeps the magic more spoken of than seen and there's one plot twist that is improbable, but all in all it's a good read.
	homepage.cs.latrobe.edu.au /agapow/Postviews/past_s-sp.html (6519 words)

	Lecture Notes
		In the Shepard's scale the frequency of the partials are increased in half steps.
		In the Descending scale of Jean-Claude Risset the partials are decreased continuously.
		This illusion is constructed from an ascending and descending major scales with notes switching from channel, as shown in the Figure B below.
	www.colorado.edu /physics/phys4830/phys4830_fa01/lab/n1204.htm (1253 words)

	Shepard tone
		apart, and each scale should fade in and fade out, so that it is impossible to hear the beginning or end of any given scale.
		The scale as described, with discrete steps between each tone, is known as the discrete Shepard scale, but, after Shepard,
		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.
	www.mp3.fm /Shepard_tone.htm (499 words)

	[No title]
		Shepard tones exhibit the peculiar property of _circular pitch_ in the sense that if one constructs a musical scale out of them, the pitches eventually repeat themselves when the notes of the scale are played consecutively upward or downward.
		Shepard created this effect by synthesizing a complex tone consisting only of components that are equally spaced on a log frequency scale.
		It sounds like Shepard tones could be done with a little thought on the K2000, with its function-based processing, and it would be my guess that it would be difficult on most other digital machines, and perhaps just barely possible on an old-style patch-programmed analog machine.
	www.ibiblio.org /emusic-l/back-issues/vol068/issue06.txt (2819 words)

	About "Akustische Täuschungen/Acoustic illusions" (Site not responding. Last check: 2007-10-31)
		Perhaps the most popular is the effect that was discovered by Shepard: A scale that gives the listener the impression of an endlessly rising melody - but in fact the pitch of the tones does not rise.
		Demonstration of an endlessly rising scale on a vibraphone; J. Bach's canon per tonus.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /library/view/7552.html (101 words)

	September 16 (Site not responding. Last check: 2007-10-31)
		A problem with such a model is that it cannot account for perceived similarities between pitches that are not next to each other on a one-dimensional scale.
		Shepard (1964) surmised that if one could take pitch height out of the equation, then listeners would hear only chroma.
		When listeners hear an ascending chromatic scale (ex.1) using Shepard tones, they hear the scale rising, rising, rising, rising, and rising, but never getting any higher.
	ccat.sas.upenn.edu /music/music55/sept16.html (469 words)

	For Ann (rising) - Wikipedia, the free encyclopedia
		For Ann (rising) is a piece of electronic music created by James Tenney in 1969.
		The piece is based upon the Shepard scale concept, named after Tenney's colleague at Bell Labs psychologist Roger Shepard, though the technique which the piece uses is more properly described as a continuous Risset scale or Shepard-Risset glissando.
		Each rising sine-wave-like glissando, between twelve and fifteen rising at any time, fades in and out, all entering a minor sixth below their predecessors, rising from the infrasonic to ultrasonic range, from below to above the ability to perceive pitch.
	en.wikipedia.org /wiki/For_Ann_(rising) (313 words)

	Shepard tone - One Language (Site not responding. Last check: 2007-10-31)
		OneLang.com lets you search a huge database of reference and product information to find relevant, specific information on almost any topic.
		Audio demonstration of the discrete Shepard Tone (http://asa.aip.org/demo27.html)
		Demonstartion of discrete Shepard tone (requires Macromedia Flash) (http://www.exploratorium.edu/exhibits/highest_note/ex.about.fr.html)
	www.onelang.com /encyclopedia/index.php/Shepard_tone (542 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		Weatherly, G.T., A. Bouvier, D.L. Lydiard, J. Chapline, I. Henderson, J.L. Schrimsher and S.R. Shepard.
		Shepard, S.R., G.T. Weatherly, A. Bouvier, I. Henderson and J. Schrimsher.
		Shepard, S.R., ISPE Fall Seminars, Durham, N.C. September 11-12, 2000.
	www.diosynthbiotechnology.com /pdf/20040811PublicationsAbstractlist.doc (2116 words)

	Ninfinger Productions: Scale Models
		Like the Shepard figure, the Yeager figure consists of 7 resin pieces on rectangular carriers, a circular base, and a bit of steel wire for the PLSS antenna.
		The blue flag field on the US flag decals is a bit off-register (the flag decals in the Shepard kit also suffer from this), but that can be fixed by cutting it out and applying it separately from the red and white bars.
		This kit includes a large decal to use as the flag, and a steel wire to serve as the flagpole.
	www.ninfinger.org /~sven/models/evamods_rvw.html (1685 words)

	The importance of scale in ecology - Travis Shepard - Biology 6000 Seminar - Events Calendar
		The importance of scale in ecology - Travis Shepard - Biology 6000 Seminar - Events Calendar
		The importance of scale in ecology - Travis Shepard - Biology 6000 Seminar
		Travis Shepard, BSc, UNB Saint John Biology, will present "The importance of scale in ecology."
	www.unb.ca /news/event-details.cgi?id=75 (57 words)

	samt-lsa (Site not responding. Last check: 2007-10-31)
		The advanced grid operations includes such operation like scale operations (up-scale, down-scale, Shepard, Zoom2), focal operations and the calculation of distance.
		The Shepard interpolation is a widely used spatial interpolation method.
		It is suitable to up-scale a grid using interpolation between grid cells.
	www.zalf.de /home_samt-lsa/samt1/advanced_grid.html (479 words)

	Find the Highest Note
		But although the keyboard appears to play an endlessly rising scale, it is actually only a single set of 12 tones.
		Each tune is a chord, comprised of six notes of the same pitch, but from six different octaves.
		Because of this volume shift, the visitor interprets the sounds as an ascending scale, a phenomenon known as the Shepard Scale.
	www.exploratorium.edu /cmp/exhibits/f/find_note.html (96 words)

	Flexagon Re'flex'ions - Music Measures (Site not responding. Last check: 2007-10-31)
		The Shepard Scale can enhance the magic-making musical moebius 'band' (Blues Moebius Band, The Dirty Dozen Moebius Band, Marching Moebius Band, Symphonic Moebius Band....).
		A blues scale common utilizes the following nine notes plus the octave with the flatted third and flatted seventh sometimes sliding anywhere in-between the full flat and the third or seventh.
		1, 2, b3, 3, 4, 5, 6, b7, 7, 8 or for C it would be C, D, Eb, E, F, G, A, Bb, B, C. There is not one specific form as a one and only blues scale like there is the specific form to a major scale.
	members.aol.com /verndrei/blues01.html (169 words)

	Las Vegas Weekly (Site not responding. Last check: 2007-10-31)
		And in the Shepardian universe—often a dramaturgy of desolation and damnation in both the setting and the soul, raw and relentless in True West, Cowboy Mouth, Fool for Love, The Tooth of the Crime and Buried Child—the sheer electricity of anger unleashed can be a show's crutch, a distraction from its weaknesses.
		But in tackling one of Shepard's most intense, scorched-earth dramas in the desert—human misery blowing by like tumbleweeds buffeted by the winds of a gathering storm—director Ernest Hemmings and his four-person cast (including himself) provide compensatory pleasures even while smothering the smoldering core of Shepard's incendiary incest tragedy.
		It takes actors who, beyond rafter-rattling, can strike the softer notes on the Shepard scale of scarred emotion, so their enormous vulnerabilities—these are, after all, walking shells of human wreckage—are exposed like raw meat.
	www.lasvegasweekly.com /2004/07/08/theater.html (810 words)

	Starship Modeler - EVA's Alan Shepard Figures
		Early on the morning of friday the 5th of February he and Ed Mitchell guided their Lunar Module Antares to a safe landing in the Fra Mauro highlands.
		Later that morning Shepard would become the 5th human being to walk on the surface of a planet other than Earth.
		All that remains is to have a small brass plaque engraved with Al's name and the dates of his Apollo 14 mission, and to attach it to the display.
	www.starshipmodeler.com /real/ps_shep.htm (923 words)

	week 11 (Site not responding. Last check: 2007-10-31)
		Shepard tones, similar to the ones shown in the movie "a pair of paradoxes".
		Play the Shepard's scale more than once to realize that beginning and end are the same.
		Further down in the page are examples of a Bach canon played on various Shepard's-type scales.
	www.physics.umd.edu /courses/Phys102/brill/wk11.html (84 words)

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