source file: mills2.txt Date: Sat, 30 Sep 1995 09:09:50 -0700 From: "John H. Chalmers" From: mclaren Subject: Tuning & Psychoacoustics - post 7 of 25 --- We've seen that three competing theories of pitch perception have tried to explain the ear-brain system since the middle of the 1840s. No one model accounts for all the ear's behaviour, and some evidence contradicts each hypothesis. "Protagonists of both place and time theories point out how small the detectable limits are when translated into the terms of the other theory. Temporal [i.e., periodicity] theorists point out that a frequency discrimination limen of 3 Hz at 1 Khz corresponds to a shift in the pattern of excitation on the basilar membrane of 18 microns, or the width of 2 hair cells. Place theorists point out the that the same limen corresponds to a time discrimination of 3 microseconds, as against some 1000 microseconds for the width of a nerve action potential, and a variability of some hundreds in its intiation. (..) There are several lines of evidence for and against these two theories, none of which is conclusive." [Pickles, James O., "An Introduction to the Physiology of Hearing," Academic Press, 2nd. ed., 1988, pp. 271-272.] At this point it's instructive to step back and recall that all cultures are conceptually limited by their experience. The Cargo Cult of the South Seas Islands during WW II arose because the islanders fitted B-17s into their experience as godlike birds from a supernatural realm. In the same way, the most sophisticated means of frequency analysis available to Helmholtz was a set of tuned glass resonators. By putting his ear to these globes, he could hear a particular resonant frequency amplified out of a complex harmonic timbre. So it was natural for Helmholz to model the ear/brain system as a set of millions of tuned resonators. As technology advanced during the late 19th and early 20th century, high-precision machine tools became available. So it was natural for von Bekesy & others to model the ear/brain system as a precision machine for performing mechanical Fourier transforms of complex harmonic sounds. [For more details on these hypotheses, see: Helmholtz, "On the Senations of Tone," 1863; Plomp, R. "The ear as a frequency analyzer," JASA, 1964, vol. 36, pp. 1628-1636; Boomsliter & Creel, "The Long Pattern Hypothesis of Pitch and Harmony," Journ. Mus. Theory, Vol. 5, 1961, p. 1-12; von Bekesy, G. "Concerning the Fundamental Component of Periodic Pulse Patterns and Modulated Vibrations Observed on the Cohlaer Model with nerve Supply, JASA, Vol. 33, 1961, ppg. 888-896; von Bekesy, "Three Experiments Concerned with Pitch Perception," JASA, Vol. 35, pp. 602-606, 1963; von Bekesy, G. "Hearing Theories and Complex Sounds," JASA, Vol. 35, pp. 588-601, 1963; Licklider, J.C. R. : "Periodicity Pitch and Related Auditory Process Models," Intern. Audiol. Vol. 1, pp. 11-36, 1962.] Then in the 1940s and 1950s computers became available, and with them software. So it became natural for modern researchers to model the ear/brain system as a combination of hardware and software, with software performing the crucial functions of pitch detection, perception of consonance, dissonance, etc. Thus we now see papers like: Goldstein, J.R. "An optimum processor theory for the central formation of the pitch of complex tones," JASA, 1973, Vol. 54, pp. 1496-1616; Wightman, F. I. "The pattern- transformation model of pitch," JASA, 1973, vol. 54, pp. 407-416. So what do we have? Quite possibly, a series of cargo cults. The ear/brain system is viewed by each era in terms of the most convenient available paradigms, regardless of whether those paradigms are actually appropriate. In an interview with Curtis Roads, Max Mathews summarized all 3 theories of hearing with typical elegance and pith: "In a book first published in 1863, Helmholtz proposed that dissonance arises from unpleasant beats between partials whose drequencies are too close together. [4] The octave is the most consonant of intervals because all of the partials of the upper coincide in frequency with partials of the lower tone. (...) Rameau had another view of harmony. [6] He observed that in a major triad all frequencies present are integer multiples of a basse fundamentale or fundamental bass which, in the root position of the chord (C, E, G) lies two octaves below the root of the chord. (...) But, one might hold that musical harmony is merely a matter of brainwashing; that we accept combinations of tones that we have been taught are correct, and reject those that we have been taught are incorrect. We have some experimental evidence that bears on this." [Mathews, M. and Pierce, J.R. "Harmony and Non-Harmonic Partials," Rapports IRCAM, 1980, pp. 3 -5] The above passage describes clearly the 3 different competing hypotheses of hearing still competing even today: namely, [1] that the ear is a frequency-domain Fourier analyzer; [2] that the ear is a time-domain autocorrelator; [3] that the ear/brain system uses a learned neural net system of pitch/interval recognition and consonance/dissonance classificiation. The contradictory results of experiments on pitch sensation lead to the conclusion that some aspects of all of these 3 models of human hearing bear some relation to the ear/brain system's actual operation. However, because some of the experimental results are contradicted by each of these 3 models of hearings, it is inescapably clear that under various circumstances one or more of these ear/brain hearing systems becomes dominant, and in some cases (particularly in the case of auditory illusions) all 3 of the ear/brain systems can clash and yield conflicting results. These 3 separate hypothetical mechanisms for processing both vertical and horizontal (sequential) pitch are: [1] a frequency-based or Fourier analysis system; [2] a time-based or autocorrelative system; [3] ear/brain "wetware" that includes a strong learned component, and which is capable of actively filtering out auditory information, creating illusory auditory information, and transforming some or all of the information conveyed from the basilar membrane and the hair cells to the auditory nerve, and from there into the Sylvian fissure, the superior medial olive and the geniculate nucleus--all areas in the brain responsible for dealing with aspects of auditory perception. This last point is important, because it is now known that musicians and non-musicians use different brain centers when hearing the same music. Musicians show glucose metabolism primarily in the left brain when listening to music, while non-musicians show glucose metabolism both brain hemispheres. These PET scan results offer strong confirmation of the third model of hearing-- what Mathews and Pierce call the "brainwashing" hypothesis, the model of hearing as molded by learned response (first put forward by Fetis and Alexander J. Ellis in the middle of the 19th century). While the Fourier analysis model of the ear/brain and the autocorrelative (or periodicity pitch) model have been extensively documented, what about experiments documenting the "wetware" component of the ear/brain system? Auditory illusions provide strong evidence for this hypothesis of the ear/brain system: Shepard, R. N., "Circularity in judgments of relative pitch," JASA, 1964, vol. 36, pp. 2346-2353; McAdams, S. and Bregman, A. "Hearing Musical Streams," Computer Music Journal, 1979, Vol. 3, pp. 26-44; Locke, S. and Kellar, L., "Categorical percpetion in a non-linguistic mode," Cortex, Vol. 9, 1973, pp. 355-369; Cohen, A. "Inferred sets of pitches in melodic perception," In R. Shepard, Cognitive structure of musical pitch," symposium presented at the meeting of the Western Psychological Association, San Francisco, CA, April 1978; Burns, E. M. and Word, W. I., "Categorical perception--phenoneon or eiphenomenon: Evidence from experiments int ehperception of melodic musical intervals," JASA, 1978, vol. 63, pp. 456-468; Blcehner, M.J. "Musical Skill and categorical perception of harmonic mode," Status Report on Speech Perception, SR-51/52. New Maven, Connecticut, Haskins Laboratories, 1977, pp. 139-174; Balzano, G. J., "Musical versus psychoacoustical variables and their influence on the perception of musical intervals," Bulletin of the Council for Research in Music Education, 1981; Bachem, A. "Tone Height and tone Chroma as two different pitch qualities," Acta psychogica, 1950, vol. 7, pp. 80-88; Moreno, E., "Expanded Tunings in Contemporary Music: Theoretical Innovations and Practical Applications," Vol. 30, Studies in the History and Interpretation of Music, The Edwin Meller Press, Lewiston: 1992; Moreno, E. "The Existence of Unexplored Dimensions of Pitch: Expanded Chroma," Proc. ICMA, 1992, pp. 404-405; Pierce, J.R. "Attaining Consonance in Arbitrary Scales," JASA, 1966, pg. 249; Butler, J. W. and Daston, P. G., "Music Consonance as Musical Preference: A Cross-Cultural Sutdy," Journ. of Gen. Spcyh.., 1968, vol. 79, pp. 129-142; Hutchinson, W. and Knopoff, L., "The Acoustic Component of Western Consonance," Interface, Vol. 7, 1978,, pp. 1-29; Watkins, A. J., "Perceptual Aspects of synthesized approximations to Melody," JASA, Vol. 78 No. 4, 1985, pp. 1177-1186; Pikler, A. G., Mels and Musical Intervals," Journ. Mus. Theory, Vol. 10, 1966, pp. 288-298; Risset, J-C., "Musical Acoustics," Rapports IRCAM 1978, pp. 7-8. Why are these 3 models of ear/brain function important to musicians in the real world? They're of crucial concern to microtonalists because if the place theory is right, then just intonation is the ideal tuning. If the periodicity theory is the correct description of how the ear hears, then many tunings are acceptable provided that the interval between the fundamental and the first partial, and twix each subsequent pair of partials, is larger than the critical band at that frequency. As Pickles points out, the periodicity theory does *not* offer support for conventional Western musical practice: "It might be thought that the pleasant consonance of simple musical intervals depends on the simple relations between their periods, resulting in synchronous nerve firing. However, once it is realized that most musical notes are rich in overtones, and that consonance might depend on a lack of beats between the harmonics, the argument cannot be used to support the importance of time information." [Pickles, James O., "An Introduction To the Physiology of Hearing," Academic Press, 2nd ed., 1988, pg. 274] On the other hand, if Fetis/Ward/Burns' "pattern recognition" hypothesis of the ear as a pliable active feedback system molded by learned response is the true picture of human hearing, then *any* type of tuning is acceptable. After a while, the listeners will become acculturated and learn to accept *any* arbitrary interval as "consonant" or "dissonant." And what if elements of all three models are at work in the ear/brain system? In that case, the implications for musical tuning are more complex--a situation which will be considered in the next post. --mclaren & Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 1 Oct 1995 02:44 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id RAA20743; Sat, 30 Sep 1995 17:43:51 -0700 Date: Sat, 30 Sep 1995 17:43:51 -0700 Message-Id: <9510010034.AA17220@us2rmc.zko.dec.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu