source file: mills2.txt Date: Tue, 17 Oct 1995 08:40:51 -0700 From: "John H. Chalmers" From: mclaren Subject: Tuning & psychoacoustics - post 22 of 25 --- In the course of this series of posts much experimental evidence has been reviewed. Forum subscribers open-minded enough to have read the original references now understand the degree of contradiction and complexity which attends the human auditory system. As we've seen, the evidence offered by psychoacoustic research is not simple and straightforward. Some results conflict, and others support none of the three accepted models of human hearing. There is, however, a preponderance of evidence to support a number of basic conclusions about the ear/brain system: The fact that different aspects of the ear/brain's sound processing function are evoked by different experiments opens up the likelihood that at least 3 different ear/brain systems operate to process sound. Wever (1964) was the first to suggest that more than one mechanism exists to process sound; von Bekesy strongly implies this conclusion in his 1966 paper. Plomp (1967) strongly disagrees, but gives no basis for his objection. Pickles (1989) points out that "the best support for [this] view is the rather negative one that the evidence in favour of either of the other two [place and periodicity] theories is not conclusive, and this may be a function of the quality of the evidence available, rather than of the acutal operation of the auditory system." [Pickles, James O., "An Introduction to the Phsyiology of Hearing," Academic Press, 2nd ed., 1988, pg. 277] The leading candidates for different mechanisms for detecting pitch and processing sounds, they are: [1] the Fourier analyzer action of the basilar membrane; [2] the encoding of pitch and spectral content by repetition rate of neurons firing along the auditory nerve; [3] the combination of received neural impulses in medullar and higher brain areas and the consequent active feedback pathway between the Sylvian fissure, the superior medial nucleus, and the different classes of neurons in the primary, secondary and third- and fourth-order nerve fibers of the auditory nerve. What does this imply? First, the role of learning and the possible conflict twixt periodicity and Fourier analysis makes it clear that "the pitch of musical sounds is not directly proportional to the logarithm of the frequency and is probably complexly conditioned." [Corso, J.F. "Scale Position and Performed Musical Octaves," Journal of Psychology, Vol. 37, 1954] This renders suspect tuning theories which ascribe absolute and invariant qualities to this or that scale degree or interval. Instead, pitch and intervallic quality appear to be storngly influenced by musical context, as well as by the overtone content of the intervals. This conclusion would tend to support all three tunings equally, depending on musical context, and learning: just intonation, equal temperament, and non-just non-equal-tempered tunings are all equally supported by the brain's learned sound processing capacities. With instruments using strictly harmonic spectra, this conclusion weakly supports the use of just intonation tuning--weakly, because of the important role of learned response in the ear/brain system. For instruments which do not use strictly harmonis spsectra, non-just non- equal-tempered systems are weakly supported: this conclusion does not support use of equal temperament except insofar as education and acculturation can sufficiently indoctrinate listeners into accepting that tuning. Second, from Plomp and Levelt's and Kameoka and Kuriyagawa's work it is clear that the roughness or sharpness of musical intervals is largely determined by proximity of individual overtones with the critical band for that frequency range. It is also clear from Mathews', Pierce's, Geary's, Sethares' and Dashow's work that timbres can be matched to tunings using digital technology so as to precisely control the degree of audible roughness or smoothness within the intervals of the scale. However, it is less clear from the psychoacoustic evidence that audible roughness and sharpness of musical intervals equates with "consonance" and "dissonance," much less with the more sophisticated quality of "concordance" and "discordance" put forward by Easley Blackwood. Much of the music-theory literature on consonance and dissonance merely redefines those terms to favor the author's chosen list of references. By redefining consonance as "beats," just intonation emerges as the preferred tuning; by redefining consonance as "roughness," the periodicity theory is favored with the proviso that the partials of the overtones be warped to fit the tuning (so that all the partials share sub- and super-multiples of the same periodicity); and if consonance is redefined as "learned preference," or "experimental results of interval preference," non-just non-equal-tempered tuning emerges as the "best" tuning based on the empirical evidence of preference for stretched non-just non-equal-tempered intervals. A good example of this process can be found in the following quote from Plomp: "In conclusion, Helmholtz's theory, stating that the degree of dissonance is determined by the roughness of rapid beats, is confirmed. It appears that maximal and minimal roughness are related to critical bandwidth..." [Plomp, "Experiments on the Tone Sensation," 1967, pg. 58] By discussing only harmonic tones and by defining dissonance as "the roughness of rapid beats," just intonation emerges as the de facto winner. A different set of assumptions produces an entirely different conclusion. For example, Risset's composition Inharmonique is based on inharmonic tones which also exhibit a lack of "roughness of rapid beats." Thus Risset's harmonic practices would appear to be equally acceptable according to Plomp's definitions, yet Risset's composition does not employ small-integer ratios--but the compositions still exhibits marked examples of dissonance and consonance. Moreover, musical intervals are often not heard as isolated units: "there is considerable evidence that melodies are perceived as *gestalts * or patterns, rather than as a seuccession of individual intervals, and that interval magnitude is only a small factor in the total percept." [Burns., E.M., and Ward, W.D., "Intervals, Scales and Tuning," in "The Psychology of Music," ed. Diana Deutsch, 1982, pg. 264] As Plomp points out, "A clear relationship exists between these data, justifying the conclusion that consonance is closely related to the absence of (rapid) beats, as in Helmholtz's theory. The critical-bandwidth curve fits the data rather well." [Plomp, "Experiments In the Tone Sensation," 1967, pg. 58] Thus, while the psychoacoustic evidence on "roughness" and "smoothness" of musical intervals is clear, the musical imlications are less striaghtforward. As von Bekesy points out, "...linearity can be assumed of the mechanical part of the [auditory] stimulation; but from a physiological point of view, the question of linearity in the nervous system is still open to speculation." [von Bekesy, G., "Hearing Theories and Complex Sounds," Journ. Acoust. Soc. Am., Vol. 35, No. 4, 1963, pg. 588] Although "beats" are castigated by one group of theorists and used as the justification for one set of tuning theories, strong evidence exists that a beat rate of 6 to 7 Hz adds to the perceived musicality of a performance. This is true of both non-Western and Western music: "Even a cursory acquaintance with the sound of a Balinese gamelan uncovers some puzzling aspects of musical timbre. The beating complex that is the result of all the beats produced in the gamelan, and especially dependent upon the beats of paired metallophones, resembles in its effect the quality of a string, woodwind or brass section in a Western orchestra. (...) It appears that some type of pulsation at rates between 6 and 7 times per second -- and slightly irregular -- is musically desirable, both in Bali and in the West, that the effects of beats and the effects of vibrato are similar so far as the quality of richness is concerned, and that the unfiication of hte sound (section sound) can be accomlished with either technique." [Erickson, R., "Timbre and the Tuning of the Balinese Gamelan," Soundings, 1984, pg. 100] In fact the argument for this or that tuning according to beat rate is not supported by the psychoacoustic data, except insofar as the data strongly support a universal preference for low-level beats in the 6-7 Hz region. The ability of the ear to extract individual components from complex sounds, however, argues strongly in favor of just intonation. JI tunings are the only tunings which accord with the ear's Fourier analysis mechanism. It is, however, clear that Fourier analysis is only one method used by the ear to process sounds, and in many situations it is the least important system. Both Plomp & Levelt's and Kameoka and Kuriyagawa's findings strongly support all three general kinds of tunings, provided that the overtones of the individual partials of the notes are matched to the scale as suggested by Sethares, Risset, Pierce and McLaren. We've seen from Shepard's and Risset's auditory illusions and from Wessel's streaming phenomenon that all 3 ear/brain systems of pitch processing interact; sometimes they conflict. This provides opportunities for composition using digital media, and tends to support non-just non-equal- tempered tunings (albeit weakly). At first glance, the surprising and universal human preference for stretched intervals, including a stretched octave of between 1210 and 1215 cents on average, strongly favors non-just non-equal-tempered scales. However Terhardt has brought forth convincing evidence that much of this effect is due to learning: and in that case, since any musical tuning can be learned, all three tunings are supported by this body of evidence to the degree that acculturation is involved. The wide variability of interval size in live concerts by expert performers tends to support this concludion; however Terhardt's findings in comparing stretched, compressed and equal-tempered tunings found a differential preference for all three types of tunings--depending on context. This evidence gives superiority to either equal-tempered, stretched or compressed tunings, depending on whether harmony or melody predominates. The body of psychoacoustic evidence as a whole clearly shows a difference between the size of preferred melodic and harmonic intervals called by the same name; this also provides strong evidence for categorical perception of musical intervals, which in turn tends to vitiate the superiority of any given tuning. If, once learned, an interval can be recogtnized even though significantly altered in size, then many different tunings should prove equally musical and effective provided that Rothenberg's properiety criteria are observed. The experiments also show a clear dichotomy between the preferred size of vertical intervals and sequential intervals. Both preferred interval sizes as measured in adjustment tests are significantly larger than small-integer ratios predicted by conventional Western theory, but the sequential intervals heard as "true thirds," "true fifths," "true octaves," etc. are even wider than the already winder-than-just vertical intervals. This body of data strongly supports the use of non-just non-equal-tempered tunings, inasmuch as the psychoacoustic data support neither a preference for tempered nor just intervals. Lastly, the limitations on the applicability of the Fourier transform do not argue against just intoantion or for any other tuning, since the FFT is entirely appropriate for strictly harmonic sounds; however an awareness of the limitations of the FFT as a tool for explaining and analyzing musical sounds serves as a warning against generalizing the results of this or that psychoacoustic experiment beyond its proper range. Thus the data is mixed and, as promised, there exists considerable psychoacoustic evidence to support each major type of tuning, as well as a significant body of findings which tend to *refute * the arguments for each particular tuning. To date, the psychoacoustic data amassed by various researchers has been considered as though it were a perfect array of unbiased results. However, all the major psychoacoustic researchers have exhibited strong biases toward this or that particular tuning philosophy. In some cases this muiscal bias had little effect on the conclusions they chose to draw from their data; in other cases, these researchers deliberately buried or ignored results which did not conform to their tuning prejudices. The next post will examine in detail the biases of each major reseracher, and the degree to which it warped his conclusions. --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 17 Oct 1995 18:17 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id JAA08685; Tue, 17 Oct 1995 09:16:38 -0700 Date: Tue, 17 Oct 1995 09:16:38 -0700 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu