source file: mills2.txt Date: Thu, 12 Oct 1995 06:33:22 -0700 From: "John H. Chalmers" From: mclaren Subject: Tuning & psychoacoustics - post 18 of 25 --- So far little has been said about the third theory of hearing, first proposed by Fetis in 1841 and supported by Helmholtz and Ellis, as well as by vast amounts of psychoacoustic data from Ward, Dixon, Terhardt, et alii. Fetis ascribed musical intervals and msuical conventions to "education" rather than to "nature," mathematics, or the structure of the ear. Although few of the proponents of equal temperament or just intonation who quote him will admit it, Helmholtz echoed this sentiment when he wrote that the Western musical system "does not rest solely upon inalterable natural laws, but is also, at least partly, the result of esthetical principles, which have already changed, and will still further change, with the progressive development of humanity." [Helmholtz, Hermann, "On the Sensation of Tone," 2nd. Dover ed., 1863, pg. 235] As previously noted, after exhaustive study of the musics of many cultures, Alexander James Ellis concluded that "the Musical Scale is not one, not `natural,' nor even founded necessarily on the laws of the constitution of musical sound, so beautifully worked out by Helmholtz, but very diverse, very artificial, and very capricious." [Ellis, A. J., "On the Musical Scales Of Various Nations," Journal of the Royal Society of the Arts, Vol. 3, 1885, pg. 536] "The evidence presented thus far implies that musical-interval categories are learned rather than are the direct result of characteristics of the auditory system. This evidence includes: (1) the variability found in measured scales and intonation, even when possible contextual effects are taken into account; (2) the intrasubject variability, large intersubject variability, and consistent deviations from small-integer-ratio categories found in category-scaling and adjustment expeirments; (3) the absence of small-integer-ratio ssingularities in frequency-ratio-JND functions and absence of small-integer- ratio confusions in absolute-identification experiments; and (4) the relative inability ofmusically untrained subjects to perform musical interval identification or discrimination exeriments. [Burns, E.M., and Ward, W.D, "Intervals, Scales, and Tuning," in The Psychology of Music, ed. Diana Deutsch, 1982, pg. 261] Moreover "since stimulus uncertainty in `real world' perception is, in general, high, it might be expected that categorical preception of musical pitchwould be the normal situation. This conclusion is supported by the results of the various investigations of intonation in performance. Second, the lack of evidence for the existence of natural categories for musical intervals implies that individuals in a given culture learn the scales of their culture from experience, not because of any innate propensity of the auditory system for specific intervals." [Burns, E. M., and Ward., W.D., "Categorical Perception," Journ. Acoust. Soc. Am., Vol. 63, No. 2, February 1978, pg. 466.] "To the casual glance, the range and variability figures of Table III may suggest that the performers were not very proficient, which is not at all true. Even when tuning an instrument to the *same* pitch as a standard, the typical musician will show a standard deviation, in repeated settings, of about 10 cents (Corso, 1954)." [Ward, W.D., "Musical Perception," in "Foundations of Modern Auditory Theory," ed. J.V. Tobias, 1970, Vol. 1, pg. 418] Again, these psychoacoustic results provide equal support for all three major systems of tuning: equal-tempered, just intonation, and non-just non- equal-tempered, inasmuch as the evidence strongly suggests that once the ear learns to accept any given set of musical intervals they are quickly learned and categorized as "pure," "preferred," "natural," etc. --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 12 Oct 1995 15:58 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id GAA08250; Thu, 12 Oct 1995 06:58:00 -0700 Date: Thu, 12 Oct 1995 06:58:00 -0700 Message-Id: <00997C43D9CD945A.4CBC@ezh.nl> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu