source file: mills2.txt Date: Wed, 11 Oct 1995 14:29:05 -0700 From: "John H. Chalmers" From: mclaren Subject: Tuning & psychoacoustics - post 17 of 25 --- While Ohm's/Helmholtz's view of the ear as Fourier analyzer has staggered under the blows of psychoacoustic research, so has the Seebeck/Stumpf/Schouten model of the ear as a neural periodicity pitch detector. True, 50 years of research has unearthed many results which cannot be explained by the frequency-domain model or "place theory" of hearing... But the periodicity model of hearing has *also *shown many shortcomings. In particular, both models of the ear/brain system fail to explain or predict the important phenomenon of categorical perception. Neither model of hearing ex plains the existence or pitch of the Zwicker Tone, or Risset's and Shepherd's auditory paradoxes (sounds which when transposed upward by an octave, drop in perceived pitch; sounds which appear to rise or fall indefinitely in pitch yet whose fundamental frequency never changes; sounds which are heard as speeding up/slowing down constantly yet whose rate never changes). Moreover, if the structure of the human ear is responsible for the music we make and the tunings we use and the harmonies we prefer, how is it possible to explain the fact that different cultures make entirely different kinds of music? If the ear is either a Fourier analyzer or a time-based autocorrelator which responds most powerfully to either small-integer ratios played on instruments with integer harmonics (the Fourier analysis model of hearing) or fixed pitches played on instruments whose partials are matched to the tuning--for example, the Railsback stretch of the grand piano matched to the stretch of the partials of the piano strings--(this is the autocorrelation model of hearing in which tuning & timbral partials, even if stretched, will autocorrelate so as to yield uniform time-domain periodicities and thus a sense of definite pitch with fundamental)... If either of these models of hearing is accurate, why do the Javanese play inharmonic instruments using stretched octaves and non-just non-equal- tempered tunings? Are other cultures deranged? Are their ears physically different from ours? Musicologists of the 19th century dismissed the Javanese, the Balinese, and other non-western music with references to "the degree of aural development among races as well as individuals." The variability in Javanese and Balinese tunings was dismissed by De Lange and Snelleman in 1992 with the memorable phrase: "for those whose ears are insufficiently developed, the perfect fourth is not divided into two whole tones and a semitone, but rather as the sixth, eventh and eighth harmonic partials." [DeLange, Daniel and Snellman, J.F, "La Musique et les instruments de musique dans les Indes Orientales neerlandaises," in Lavignac, "Encylopedie de la musique et dictionnaire du COnservatoire: Histoire de la musique, premiere partie (Paris, 1922," Vol. 5, pg. 3148.] Such racism has become less fashionable over the last three quarters of a century, but much of the debate over psychoacoustics and tuning takes place in a cultural vacuum: only western music is considered, and psychoacoustic arguments for or against this or that tuning are often made only in the context of western equal temperament or just intonation tuning systems. However, such enthocentrism is slowly changing. "One of the revelations of modern psychoacoustic and etnomusicological reserach has been the extraordinary complexity of intonation as used by Western and non-Western musicians." [Perlman, Marc, "American Gamelan in the Garden of Eden: Intonation in a Cross-Cultural Encounter," Musical Quarterly, 1995, pg. 532] "There are...a number of musical cultures that apparently employ approximately equally tempered 5- and 7-interval scales (i.e., 240 and 171 cent step-sizes, respectively) in which the fourths and fifths are significantly mistuned form their natural values. Seven-interval scales are usually associated with Southeast Asian cultures (Malm, 1967). For example, Morton (1974) reports measurements (with a Stroboconn) of the tuning of a Thai xylophone that "varied only + or - 5 cents" from an equally tempered 7-interval tuning. (In ethnomusicological studies measurement variability, if reported at all, is generally reported without definition.) Haddon reported (1952) another example of a xylophone tuned in 171-cent steps from the Chopi tribe in Uganda. The 240-cent step-size, 5-interval scales are typically associated with the "gamelan" (tuned gongs and xylophone-type instruments) orchestras of Java and Bali (e., Kunst, 1949). However, mreasurements of gamelan tuning byHood (1966) and McPhee (1966) show e xtremely large variations, so much so that McPhee states: "Deviations in what i s considered the same scale are so large that one might with reason state that there are as many scales as there are gamelans." Another example of a 5-interval, 24--cent step tuning (measured by a stroboconn, "variations" of 15 cents) was reported by Wachsmann (1950) for a Ugandan harp. Other examples of equally tempered scales are often reported for pre-instrumental cultures... For example, Boiles (1969) reports measurements (with a Stroboconn, "+ or - 5 cents accuracy") of a South American Indian scale with equal intervals of 175 cents, which results in a progressive octave stretch. Ellis (1963), in extensive measurements in Australian aboriginal pre-instrumental cultures, reports pitch distirbutions that apparently follow arithmetic scales (i.e., equal separation in Hz). Thus there seems to be a propensity for scales that do not utilize perfect consonances and that are in many cases highly variable, in cultures that either are pre-instrumental or whose main instruments are of the xylophone type. Instruments of this type produce tones who partials are largely inharmonic (see Rossing, 1976) and whose pitches are often ambiguous (see de Boer, 1976)." [Burns, E. M. and Ward, W. D., "Intervals, Scales and Tuning," in The Psychology of Music, 1982, ed. Diana Deutsch, pg. 258] These empirical data would seem to indicate that of the three tunings (equal te mpered, just intonation, and non-just non-equal-tempered) non-just non-equal-tempered and equal temperament are most widely used by other cultures. This is a conclusion directly opposite to that implied by the idea of small whole numbers as uniquely preferred by the ear/brain system. The next post will examine in detail the third theory of hearing, first proposed by Fetis in 1843, and in later life espoused by Helhmoltz: namely, the view that the ear prefers a set of intervals determined by learning and culture. --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 12 Oct 1995 03:16 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id SAA00081; Wed, 11 Oct 1995 18:15:55 -0700 Date: Wed, 11 Oct 1995 18:15:55 -0700 Message-Id: <951012011313_71670.2576_HHB40-2@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu