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Topic: Shepard tone

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Shepard scale

Deutsch tritone paradox

Auditory illusion

Pitch (music)

Penrose staircase

Optical illusion

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	Shepard's Tones
		A sequence of Shepard Tones is comprised of twelve tones.
		In contrast to a pure tone, which may be described as a sinusoidal function of a single frequency (see Equation 1), each Shepard Tone is built from several harmonics of a single (fundamental) frequency.
		In a pure tone, the pitch closely corresponds to the frequency of the sinusoid; for complex tones, our pitch judgement is associated with the periodicity of the overall function.
	hebb.mit.edu /courses/9.29/2003/athena/auditory/shepard.html (492 words)

	Shepard tone - Wikipedia, the free encyclopedia
		A Shepard tone is a sound, named after Roger Shepard, 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.
		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.
	en.wikipedia.org /wiki/Shepard_scale (738 words)

	Tritone paradox - Wikipedia, the free encyclopedia
		In the illusion, two Shepard tones exactly half an octave apart, a tritone, are played; Shepard predicted that they 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.
		Diana Deutsch later found that perception of which tone was higher was dependent on the absolute frequencies involved: an individual will tend to consistently find the same tone as higher or lower, and this is determined by the tones' absolute pitch.
		This is consistently done by a large portion of the population, despite the fact that responding differently to different tones must involve the ability to hear absolute pitch, which was thought to be extremely rare.
	en.wikipedia.org /wiki/Deutsch_tritone_paradox (327 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.
		The resulting 'chromatic' tones are represented on a piano by the 12 fl and white keys that span an octave interval.
	www.cameron.edu /~lloydd/webdoc1.html (1517 words)

	[No title]
		Shepard, in an biographical article in The Medium, a London spiritualist publication, said that his first psychic abilities of clairvoyance and psychometry appeared when he was 19.
		She told Olcott Shepard was a charlatan and accused him of having paid a music-master to teach him the Russian songs he sung in the Eddy farmhouse.
		Shepard, the daughter reported, said he was controlled by a bank of Egyptian spirits, the leader of whom had lived on the earth when the pyramids were young.
	artofhacking.com /IET/NEWTECH/MUSICV.TXT (3211 words)

	Spectra and Amplitudes (Site not responding. Last check: 2007-10-23)
		The structure of a tone’s partials (its spectrum) is shown here on a log2-frequency axis, with amplitude shown along the y-axis (using some arbitrary, though relative, scale) and frequency along the x-axis.
		The dotted vertical line represents a Shepard tone that is slightly higher than that represented by the solid line.
		As can be observed, the lower partials have a greater amplitude than their corresponding partials in the first tone, while the higher partials have a lesser amplitude than their corresponding partials in the first tone.
	epsych.msstate.edu /descriptive/Hearing/shepard/shepard6.html (155 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)

	Shepard's Tones
		In 1964, the psychologist Roger N. Shepard published a paper entitled Circularity in Judgements of Relative Pitch in the Journal of the Acoustical Society of America [Shepard-64].
		When the tones contain only two components, it is easy to hear the lower tone come to dominate as the two progress towards the right.
		On the other hand, the pitch is not heard to fall in the transition from the twelfth tone to the first because the component in the middle at that point dominates the tone that disappears from the right end and reappears at the left.
	www.cs.ubc.ca /nest/imager/contributions/flinn/Illusions/ST/st.html (1025 words)

	In part, Shepard explains how the social environment influences the self-concepts and the social identities we form
		In part, Shepard explains how the social environment influences the self-concepts and the social identities we form.
		Shepard argues for fighting those environmental influences in order to find your "true" self and talents.
		"Tone," "resonance," and "perspective" are the signs that you have discovered your genius and have developed the autonomy to live by it, rather than by society’s dictates (p.
	pubpages.unh.edu /~ckb/SHEPARD.html (549 words)

	The Shepard Tone
		The partials of a Shepard Tone are related to each other by a geometrical relationship.
		43, page 96] shows that the auditory paradox created by the Shepard Tone, which is generated according to a Weierstrass function, has become possible due to the self-similarity of the signal.
		Although Shepard applies a formant-like envelope to the frequency domain representation of the signal, this is done for smoothing the perceptual transition and sustaining the paradox effect.
	crca.ucsd.edu /~syadegar/MasterThesis/node35.html (238 words)

	Lucius Shepard, Colonel Rutherford's Colt (Site not responding. Last check: 2007-10-23)
		Lucius Shepard's latest short novel (less than 200 pages) is about a couple who earn their living by selling guns at shows on a West Coast circuit.
		The novel changes in tone and direction when a woman gives the couple a Colt.45 revolver on consignment and instructs them not to sell it to a right-wing militiaman named Raymond Borchard.
		Shepard's economical technique makes his accomplishment even more impressive.
	www.rambles.net /shepard_colt02.html (406 words)

	Acoustical Society of America - Circularity in Pitch Judgement (Site not responding. Last check: 2007-10-23)
		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 tones are cosinusoidally filtered to produce the sound level distribution shown below, and the frequencies of the partials are shifted upward in steps corresponding to a musical semitone (= ~ 6 %).
		R. Shepard (1964), "Circularity in judgments of relative pitch," J. Acoust.
	asa.aip.org /demo27.html (234 words)

	electro-music.com :: View topic - Tritone Paradox and Spectral-Motion AfterEffects
		Shepard tone paradox (after its inventor, Roger Shepard), one's perception is that each note in a forever on going series of notes is higher in pitch than the preceding note.
		Shepard tones consist of 10 components (octaves) and are presented through a Gaussian-shaped spectral filter.
		The tones used in the tritone paradox have 6 components (octaves) and are presented through a bell-shaped spectral envelope.
	electro-music.com /forum/post-4010.html (415 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)

	A paradox of musical pitch
		Playing two of these ambiguous tones in succession, Shepard gauged whether listeners heard the second note as ascending or descending, and found their judgments were related to the position of the notes on the pitch class circle.
		Even more interesting was that when Shepard played tones as they repeatedly moved clockwise around the pitch class circle, the tones appeared to endlessly ascend; when moving counterclockwise through the 12 ambiguous notes, the pattern appeared to endlessly descend--the auditory equivalent of Escher's endless staircase.
		Twenty years later, Deutsch added another dimension to Shepard's illusion by giving participants pairs of ambiguous tones, one played after the other, that were related by a tritone (for example, C followed by F#).
	www.apa.org /monitor/julaug01/musicpitch.html (1443 words)

	Ascending Tones (Site not responding. Last check: 2007-10-23)
		This observation suggests that by exaggerating the aspect of chroma, “one might be able to bring about a breakdown of transitivity in judgements of relative pitch”; (R. Shepard, “Circularity in Judgements of Relative Pitch”;, Journal of the Acoustical Society of America, 36(12), pp.
		However, after a while the sensation of ascending tone begins to weaken until you perceive that indeed the tone has not risen at all.
		Notice that while each ascending Shepard tone seems to be higher than the previous one, it seems that, over the long run, the quality of ascent is ambiguous at best.
	epsych.msstate.edu /descriptive/Hearing/shepard/shepard4.html (244 words)

	Shepard tone
		of a tone that continually ascends or descends in pitch, yet which ultimately seems to get no higher or lower.
		Each square indicates a tone, any set of squares in vertical alignment together making one Shepard tone.
		An independently discovered version of the Shepard tone appears at the beginning and end of the album "A Day At The Races" by the band Queen.
	www.mp3.fm /Shepard_tone.htm (499 words)

	An Improved Model of Tonality Perception Incorporating Pitch Salicne and Echoic Memory
		The vertical axis indicates how well, on average, each pitch-class (realized as a Shepard tone) is judged to follow or fit with a preceding diatonic chord progression in C major or C minor.
		The effect of spectral dominance on the pitch of complex tones was studied experimentally by Plomp (1967) and Ritsma (1967).
		4.25) adjusted the calculated salience of tone sensations within a sonority in such a way that the sum of the saliences of all tone sensations evoked by a sonority equals the calculated multiplicity of that sonority, that is, the estimated mean number of simultaneously noticed tones.
	dactyl.som.ohio-state.edu /Huron/Publications/Tonality/tonality.text.html (7134 words)

	Comments Archive - Phase 11
		As the tones were dichotically presented, the results indicated that the central auditory system could distinguish between consonant and dissonant intervals without initial processing of pitch-pitch relations in the cochlea.
		Shepard believed that the illusion of ascension was due to the tones' proximity.
		Shepard's tones (1964) established the notion of a flat "pitch circle", and many experiments conducted since then have reproduced its result-- however, it has been universally assumed that a difference in height naturally causes a difference in chroma, leading to helical models of pitch that spiral around to octave equivalence.
	www.aruffo.com /eartraining/research/phase11comment.htm (18859 words)

	Conclusions and Speculations
		The Shepard tone is a sound whose internal constraints are not that of the harmonic relationship.
		It seems apparent that the internal constraints of such tones create an integrity in the sound which can be used as a tool for the communication of musical thought.
		If, in fact, the reason for the illusion of the Shepard tone is the self-similar structure in the sound, we may be able to conclude that we can detect and relate to self-similarity in the auditory domain.
	www-crca.ucsd.edu /~syadegar/MasterThesis/node37.html (485 words)

	Music 220: Cognitive Musicology
		A Shepard's Tone is a complex tone constructed using octave-spaced partials spanning the complete range of hearing.
		The two tones begin in precise unison -- with the result that the tones fuse together and are perceived as a single tone, rather than as two distinct tones.
		Nevertheless, the two tones remain fused and are perceived as a single tone whose frequency lies mid-way between the two physical tones.
	www.music-cog.ohio-state.edu /Music220/exam_questions_answers.html (6588 words)

	Timbral Prototypes
		If you interpolate between a tone with a fast attack and a slow attack, the resulting file will have two attacks, one fast and one slow, rather than a medium-speed attack.
		Shepard tones are special tones that "wrap around" to the exact same tone when played an octave higher or lower.
		Shepard tones consist of a series of octave-spaced partials (not the usual harmonic series, but rather the 1st, 2nd, 4th, 8th, 16th, 32nd...
	www.cnmat.berkeley.edu /CAST/Server/timbralprotos.html (1590 words)

	Apathy :wq
		Exploring the Shepard tone sequence in more detail, this site has computer generated cycles in linear and logarithmetic varieties, with both sound clips and Quicktime color movies so you can see with your eyes how your ear is being fooled.
		Complex octave-related tones and how distinguishing between overlaid octave sound waves is rather difficult.
		Shepard's tones have always intrigued me, ever since I first read Douglas Hofstadter's intelligence and self-consciousness masterwork, Gödel, Escher, Bach.
	apathy.pitas.com /bachandtone.html (1069 words)

	[No title]
		It is interesting because Shepard Tones are constructed out of a particular set of partials and this affects the way that we perceive their pitch.
		Each tone is made out of 10 partials, each partial is separated by an octave — this is not a natural overtone series of a complex tone — in which the partials are separated by the fundamental frequency.
		Shepard Tones - construction Each of the (12) pitches in the scale is created by shifting the previous pitch’s partials up by a semitone and changing its energy.
	www.csis.ul.ie /ccmcm/cs5611/lect06_psych4.doc (2483 words)

	Creating a Multimedia CD-ROM
		For example, to illustrate how sound energy interacts when two tones are sounded simultaneously, a 1000 Hz tone is sounded for four seconds, followed by a 1004 Hz tone, then both are sounded together.
		Shepard, Diana Deutsch, and Jean Claude Risset assisted in confirming that the auditory processes involved in music listening involve cognitive interpretation.
		Many textbooks refer to the Shepard tone or Deutsch's tritone paradox-often describing the manner in which these stimuli were created in minute detail-then go on to discuss the relevance of the experimental results.
	music.utsa.edu /tdml/conf-IV/IV-Lipscomb_et.al.html (1398 words)

	Spectral Texturing
		As with spectral texturing one has control over the amount and kind of frequencies and dependencies in the texture, spectral textures could prove to be a powerful tool for examining the mechanisms of human texture perception.
		The Shepard tone is a tone which appears to rise or fall continuously.
		This is achieved by composing the tone of a sum of sine waves which all increase or decrease in frequency over time.
	www.kyb.tuebingen.mpg.de /bu/people/berger/spectraltexturing (1219 words)

	Sometimes higher is lower \| MetaFilter
		June 14, 2006 9:30 AM An audio illusion called the tritone paradox is based on Shepard Tones, a finite self-similar sequence of tones that seem to contiually rise or fall in pitch.
		The details of the research seem to describe using one tone at a time, and yet these are still called "ambiguous" in terms of pitch height.
		The odd thing is, the Shepard tone illlusion is, at least for me, very easy to re-create in your head...just think of an ever increasing, or decreasing tone, and you get much the same effect.
	www.metafilter.com /mefi/52302 (1691 words)

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