source file: mills2.txt Date: Sun, 1 Oct 1995 09:31:39 -0700 From: "John H. Chalmers" From: mclaren Subject: Tuning & Psychoacoustics - post 8 of 25 --- As xenharmonists, it's of some interest to us exactly how the ear/brain system works. If the human ear favors one tuning system over another, we want to know about it. Alas, the evidence is far from clear, and there are problems with all three hypotheses of ear/brain function. Concerning the place and periodicity hypotheses of hearing, "On current evidence, it is not possible to decide betwene the temporal and place theories of frequency distribution. (..) In any case the best support for the eclectic [pattern recognition] view is the rather negative one that the evidence in favour of either of the other two theories is not conclusive, and this may be a function of the quality of evidence available, rather than of the actual operation of the auditory system." [Pickles, James O., "An Introduction to the Physiology of Hearing," Academic Press, 2nd ed., 1988, pg. 277] Risset summarizes the evidence for and problems with all 3 proposed ear/brain mechanisms in his 1978 IRCAM report: "Numerological theories of consonance suffer difficulties. Because of the ear's tolerance, intervals corresponding to 3:2 (a simple ratio) and 300,001/200,000 (a complex ratio) are not discriminated. Also psychophysiological evidence indicates that numerical ratios should not be taken for granted. The subjective octave corresponds to a frequency ratio a little larger than 2, and is reliably different for different individuals (Ward, 1954; Sundberg and Lindqvist, 1973); this effect is increased by sleep-deprivation (Elfner, 1964). There are also physical theories of consonance. Helmholtz (1877) links the degree of dissonance to the audibility of beats between the the partials of the tones. This theory is hardly tenable, because the pattern of beats, for a given interval, depends very much on the placement of the interval within the audible frequency range. Recent observations (Plomp, 1966) suggest an improved physical explanation of consonance: listeners find that the dissonance of a pair of pure tones is maximum when the tones are about a quarter of a critical bandwidth apart; the tones are judged consonant when they are more than one critical bandwidth apart. Based on this premise, Pierce (1966, also in von Foerster and Beuachamp, 1969, pp. 129-132) has used tones made up on non-harmonic partials, so taht the ratios of fundamnetal leading to consonance are not the conventional ones: Kameoka et al. (1969). have developed an involved method to calculate the magnitude of disonance... "Whereas the explanation put forth by Plomp can be useful to evalutate the "smoothnesss" or "roughness" of a combination of tones, it is certainly insufficient to account for musical consonance. In a laboratory study, Van de Geer et al., (1962) found that intervals judged the most consonant by laymen do not correspondent to the ones usually term consonant. This result is elaborated by recent work by Fuda and Wessel (1977). The term consonance seems ambiguous, since it refers at the same time ot an elemental level, where "smoothness" and "roughness" are revaluated, and to a higher esthetic level, where consonance can be functional in a given style. The two levels are related in a culture- bound fashion. In music, one does not judge only the consonance of isolated tones: as Cazden (1945) states, "context is the determining factor. (...) the resoution of intervals does not have a natural basis; it is a common response acquired by all individuals within a culture area (cf. also Lundin, 1947)." Musical consonance is relative to a musical style ( Guernesey, 1928); ninth chords, dissonant in Mozart's music, are treated as consonant by Debussy (Chailley, 1951; Cazden, 1962, 1968, 1972). The cultural and contextual aspects of musical consonance are so important that, despite nativists' claims to the contrary, purely mathematical and/or physical explanations can only be part of the story. cf. Costere, 1962)." [Risset, J-C., "Musical Acoustics," Rapports IRCAM, 1978 pp. 7-8] In short, all 3 hypotheses of hearing explain different aspects of the ear/brain system. Depending on the acoustic stimulus, different systems appear to operate to process sound. This is most powerfully evidenced by Sethares, W., "Local Consonance and the Interaction between Timbre and Tuning," JASA, vol. 94 No. 3, 1993, pp. 1218-1219, Slaymaker, J., "Inharmonic Tones," JASA 1970, and Roads, C. "An Interview with Max Mathews," Computer Music Journal, 1980. In the latter, Mathews points out: "Our initial experiments were aimed at finding out what properties of normal harmonic music carried over to music that was made with stretched overtones. We found some things carried over and some things did not. The sense of "key" carried over better than we expected. ROADS: So you can actually detect "keys" in sequences of completely inharmonic sounds. MATHEWS: That's right. You play two samples and a person can reliably say whether they're in the same or a different key. Other properties do not carry over. The sense of finality in a traditional cadence does not carry over. A person who hears a cadence with unstretched tones says, "That sounds very final to me." When he hears the same cadence played with stretched tones, he'll say "That doesn't sound especially final." But we have been able to make other inharmonic materials which do convey a sense of cadence. (...) ROADS: If we can detect "keys" and some form of finality within a cadence or progressions within inharmonic tones, then some of the theories of harmony in the past must not have been as cogent as some of their proponents have thought them to be. MATHEWS: Our results are contradictory. We loked at two theories. One was the Rameau theory of the fundamental bass, and the other was the Helmholtz and Plomp theory of the consonance and dissonance of overtones. The destruction of the cadence would support the Rameau theory and the persistence of the sense of key would support the Helmholtz and Plomp theory. So we have one result which supports one theory and one which supports the other, with the overall conclusion that the world a more complicated place than we had perhaps hoped it was. We will have to dig deeper before we can say which is causing the various perceptions we find meaningful to music" [Roads. C, "An Interview With Max Mathews, Comp. Mus. Journ., Vol 4 No. 4, 1980, pp. 21-22] MYTH: PITCH PERCEPTION IS SIMPLE, AND CONSONANCE, DISSONANCE AND HARMONY CAN BE EXPLAINED BY EITHER RAMEAU'S OR HELMHOLTZ'S MODELS FACT: Musical phenomena are a complex interaction of at least 3 ear/brain mechanisms for recognizing and assigned pitch, and each ear/brain system can conflict with the other 2, leading to paradoxical results, auditory illusions and a great deal of learned behaviour on the part of the listener as to what "consonance," "dissonance," and even what "pitch" is. This latter will prompt the usual screams of protest from those into whose brainpans little information about modern psychoacoustics has dripped; thus it is important to make clear that even something as purportedly "elementary" and "innate" as the pitch sense displays extremely complex behaviour. The next post will examine the meaning(s) of the term "pitch," the psychophysical factors which influence its perception, and the implications for tuning & music. --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 1 Oct 1995 20:53 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id LAA27839; Sun, 1 Oct 1995 11:52:54 -0700 Date: Sun, 1 Oct 1995 11:52:54 -0700 Message-Id: <199510011852.AA24025@net4you.co.at> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu