diana deutsch - deutsch's musical illusions
TRANSCRIPT
5/14/08 10:18 PMDiana Deutsch - Deutsch's Musical Illusions / Tritone paradox
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Deutsch's Musical Illusions
Introduction
Technical Note
Memory for pitch and music
Octave illusion
Scale illusion
Chromatic illusion
Glissando illusion
Tritone paradox
Mysterious melody
Cambiata illusion
Tritone paradox
The tritone paradox was first described by Deutsch at a meeting of the Acoustical Society of America (Deutsch, 1986)and first published by Deutsch, Music Perception, 1986. The basic pattern that produces the this illusion consists of twocomputer- produced tones that are related by a half-octave. (This interval is called a tritone). When one tone of a pair is played,followed by the second, some people hear an ascending pattern. But other people, on listening to the identical pair of tones,hear a descending pattern instead. This experience can be particularly astonishing to a group of musicians who are all quitecertain of their judgments, and yet disagree completely as to whether such a pair of tones is moving up or down in pitch.
The tritone paradox has another curious feature. In general, when a melody is played in one key, and it is thentransposed to a different key, the perceived relations between the tones are unchanged. The notion that a melody might changeshape when it is transposed from one key to another seems as paradoxical as the notion that a circle might turn into a squarewhen it is shifted to a different position in space.
But the tritone paradox violates this rule. When one of these tone pairs is played (such as C followed by F#) a listenermight hear a descending pattern. Yet when a different tone pair is played (such as G# followed by D), the same listener hearsan ascending pattern instead. (Another listener might hear the C-F# pattern as ascending and yet hear the G#-D pattern asdescending.)
The tones that are used to create the tritone paradox are so constructed that their note names (C, C#, D and so on) areclearly defined, but they are ambiguous with respect to which octave they are in. For example, one tone might clearly be a C,but in principle it could be middle C, or the C an octave above, or the C an octave below. This ambiguity is built into the tonesthemselves. So when someone is asked to judge, for example, whether the pair of tones D-G# is ascending or descending inpitch, there is literally no right or wrong answer. Whether the tones appear to move up or down in pitch depends entirely on themind of the listener. (Ambiguous tones such as these were used by others, particularly Roger Shepard and Jean-ClaudeRisset, to create illusions of endlessly ascending or descending pitches.)
The way that any one listener hears the tritone paradox varies depending on the names of the notes that are played. The musical scale is created by dividing the octave into twelve semitone steps, and each tone is given a name: C, C#, D, D#, E,F, F#, G, G#, A, A# and B. The entire scale, as it ascends in height, consists of the repeating occurrence of this succession ofnote names across octaves. So when you move up a piano keyboard in semitone steps beginning with C, you go first to C#,then D, then D#, and so on, until you get to A#, then B, and then C again. At this point you have reached an octave, and youbegin all over, repeating the same series of note names in the next octave up the keyboard.
Because all Cs sound in some sense equivalent, as do all C#s, all Ds, and so on, we can think of pitch as varying bothalong a simple dimension of height and also along a circular dimension of pitch class - a term that musicians use to describenote names. So, for example, all Cs are in pitch class C, all C#s are in pitch class C#, and all Ds are in pitch class D.
Let us suppose that listeners mentally arrange pitch classes as a circular map, like a clockface. To explain differentlisteners' perceptions of the tritone paradox, Deutsch conjectured that one person might orient his or her clockface so that C isin the 12 o'clock position, C# is in the 1 o'clock position, and so on around the circle. This listener would tend to hear the patternC-F# (as well as B-F, and C#-G) as descending, and the pattern F#-C (as well as F-B and G-C#) as ascending. But anotherperson might orient is or her clockface so that F# is in the 12 o'clock position, G is in the 1 o'clock position, and so on. Thislistener would instead tend to hear the pattern C-F# (as well as B-F, and C#-G) as ascending, and the pattern F#-C (as well asF-B and G-C#) as descending. In other words, differences between listeners in perception of the tritone paradox could be dueto differences in the way they orient their maps of the pitch class circle.
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In one experiment, listeners were played many such pairs of tones, and they judged in each case whether they heard anascending or a descending pattern. Then the proportion of times that each listener heard a descending pattern was plotted as afunction of the pitch class of the first tone of the pair.
The results supported Deutsch’s conjecture - the judgments of most listeners varied systematically depending on thepositions of the tones along the pitch class circle: Tones in one region of the circle tended to be heard as higher, and tones inthe opposite region as lower.
In addition, the orientation of the pitch class circle varied strikingly from one listener to another. To illustrate thesedifferences, the judgments of two subjects are shown below. These subjects heard the tritone paradox in a very pronouncedfashion. The first subject clearly heard tone pairs C#-G, D-G#, D#-A and E-A# as ascending, but F#-C, G-C#, G#-D, A-D#,A#-E, and B-F as descending. The second subject, in contrast, heard tone pairs B-F, C-F#, C#-G, D-G#, D#-A, and E-A# asdescending, and F#-C, G-C#, G#-D, and A-D# as ascending. So for the most part when the first subject heard an ascendingpattern the second subject heard a descending one, and vice versa. The upper part of the figure shows the two orientations ofthe pitch class circle with respect to height which were derived from the judgments of these subjects. For the first subject, pitchclasses G# and A stood at the top of the circle, but for the second subject, C# and D stood in this position instead. To furtherillustrate the differences between listeners in perception of the tritone paradox, the judgments of four more subjects are shownbelow.
5/14/08 10:18 PMDiana Deutsch - Deutsch's Musical Illusions / Tritone paradox
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Another surprising consequence of the tritone paradox concerns absolute pitch - the ability to name a note just fromhearing it. This faculty is generally considered to be very rare. But the tritone paradox shows that the large majority of people infact possess a form of absolute pitch, since we hear tones as higher or as lower depending simply on their pitch classes, ornote names.
Why do people orient their maps of the pitch class circle in different ways? Deutsch conjectured that the answer mightlie in the speech patterns that we hear. When people from other countries visited her laboratory in California, they often heardthis pattern differently from native Californians. And when the effect was demonstrated to audiences in other countries and theywere asked to indicate their judgments with a show of hands, audiences appeared to differ from each other in what theyheard.
So on the basis of these observations, Deutsch (1991) compared two groups of subjects. Those in the first group hadgrown up in California, and those in the second group had grown up in the south of England. These two groups tended to differ in how they heard the tritone paradox: Frequently when a Californian subject heard a pattern as ascending, a subject from thesouth of England heard the identical pattern as descending, and vice versa.
In another study, Deutsch, North, and Ray, 1990, obtained a significant correspondence between the pitch range of aperson's speaking voice and how he or she perceived this pattern. This study provided a further indication that speech patternsinfluence the the way the tritone paradox is heard.
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Other studies have uncovered regional differences within the United States and Canada in the perception of the tritoneparadox (Ragozzine and Deutsch, 1994; Treptoe, 1997, Giangrande, 1998, Dawe, Platt and Walsh 1998; Chalikia, 1999, 2000. Because there are regional dialects within the United States, it seems that speech patterns are likely to lie at the root of thesedifferences also. It even appears that the way a person hears the tritone paradox is related, not only to the geographical regionin which he or she grew up, but also to the regions in which his or her parents grew up (Ragozzine and Deutsch, 1994;Deutsch, 1996; Deutsch, Henthorn, and Dolson, 2000). So it seems that the speech to which we were exposed as children influence the way we hear the tritone paradox as adults. In addition, people who have spent considerable time in more thanone geographical region sometimes produce mixed results. For example, their plots may have two peaks, reflecting theirexposure to different languages or dialects.
The signals for a full experiment on Deutsch's Tritone Paradox are published in the compact disc 'Musical Illusions andParadoxes.'
Tritone paradox example
References:
Deutsch, D. A musical paradox. Music Perception, 1986, 3, 275-280. [PDF Document]
Deutsch, D. An auditory paradox. Journal of the Acoustical Society of America, 1986, 80, s93. [Web Link]
Deutsch, D., Kuyper, W. L. and Fisher, Y. The tritone paradox: Its presence and form of distribution in a general population.Music Perception, 1987, 5, 79-92. [PDF Document]
Deutsch, D. The tritone paradox: Effects of spectral variables. Perception & Psychophysics, 1987, 41, 563-575.[PDF Document]
Deutsch, D., North, T. and Ray, L. The tritone paradox: Correlate with the listener's vocal range for speech. Music Perception,1990, 7, 371-384. [PDF Document]
Deutsch, D. The tritone paradox: An influence of language on music perception. Music Perception, 1991, 8, 335-347.[PDF Document]
5/14/08 10:18 PMDiana Deutsch - Deutsch's Musical Illusions / Tritone paradox
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Deutsch, D. Paradoxes of musical pitch. Scientific American, 1992, 267, 88-95. [PDF Document]
Deutsch, D. Some new pitch paradoxes and their implications. In Auditory Processing of Complex Sounds. PhilosphicalTransactions of the Royal Society, Series B, 1992, 336, 391-397. [PDF Document]
Deutsch, D. The tritone paradox: Implications for the representation and communication of In M. R. Jones and S. Holleran(Eds.). Cognitive bases of musical communication, 1992, American Psychological Association Monog, 115-138.
Ragozzine, F., & Deutsch, D. A regional difference within the United States in perception of the tritone paradox. Journal of theAcoustical Society of America, 1993, 94, 1860. [Web Link]
Ragozzine, F. and Deutsch, D. A regional difference in perception of the tritone paradox within the United States. MusicPerception, 1994, 12, 213-225. [PDF Document]
Deutsch, D. The tritone paradox: Some further geographical correlates. Music Perception, 1994, 12, 125-136. [PDF Document]
Deutsch, D. Mothers and their children hear a musical illusion in strikingly similar ways. Journal of the Acoustical Society ofAmerica, 1996, 99, 2482. [Web Link] [Laylanguage version]
Deutsch, D. The tritone paradox: A link between music and speech. Current Directions in Psychological Science, 1997, 174-180. [PDF Document]
Deutsch, D. The tritone paradox: A link between music and speech. Invited paper. Workshop on Language and MusicProcessing, 1997, Marseilles
Giangrande, J. The tritone paradox: Effects of pitch class and position of the spectral envelope. Music Perception, 1998, 13,253-264.
Dawe, L. A., Platt, J. R. and Welsh, E. Spectral-motion after-effects and the tritone paradox among Canadian subjects.Perception and Psychophysics, 1998, 60, 209-220.
Deutsch, D., Henthorn T. and Dolson, M. Speech patterns heard early in life influence later perception of the tritone paradox.Music Perception, 2004, 21, 357-372. [PDF Document]
Deutsch, D. Mothers and their offspring perceive the tritone paradox in closely similar ways. Archives of Acoustics, 2007, 32, 3-14. [PDF Document]
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