source file: mills2.txt Date: Wed, 18 Oct 1995 08:09:28 -0700 From: "John H. Chalmers" From: mclaren Subject: Tuning & psychoacoustics - post 23 of 25 --- Psychoacoustics is an empirical science. Mathematical theories abound, but they are attempts to explain experimental evidence. There are no valid "a priori" theories of hearing. Psychoacoustics uses choice and adjustment methods, along with computer analysis of live performances. The first methods involve laboratory setting, while the second generally does not. Overall results from both settings tend to agree. Psychoacoustic researchers are prone to bias. The goal of scientific investigation is not to reduce or eliminate the prejudice of the investigator, but to reduce or eliminate its effect on the measured results. All of the psychoacoustic researchers cited so far have tuning preferences. Some of these researchers warp the presentation of results to favor a given tuning system, while others do not. Ohm (1843), Helmholtz (1863) and Pikler (1898) strongly favored just intonation tunings and the ear-as-Fourier-analyzer model. To explain away the empirical evidence that 19th-century composers and performers universally used equal tempered tunings, Helmholtz claimed that modern performers were incompetent and that "true" (i.e., just) intonation was a lost art, requiring superlative skill. To refute the empirical evidence that most people who listened to music seemed to like equal-tempered intervals, Helmholtz claimed that modern listeners had been brainwashed by equal temperament. In order to determine a listener's "true" preference among musical intervals, he contended, one needs must find an ear uncomtaminated by debased modern equal-tempered music. Since ears accustomed to pure just intonation and unsullied by equal temperament were not to be found in 19th century Europe, Helmholtz's hypothesis ran afoul of the first demand on any scientific hypothesis: namely, that it be testable. However, in the second edition of his book "On the Sensations of Tone," Helmholtz modified his original position and wrote that music "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] Helmholtz is thus a contradictory figure, on the one hand explaining away empirical evidence with various pieces of circular reasoning, and on the other hand openly suggesting that the third, or learned, model for hearing had a strong influence on the auditory system. Pikler and Ohm proved less open-minded, and they consistently bury results which conflict with just intonation as the "best" tuning. Seebeck (1843), Stumpf (1896) Schouten (1938), Boomsliter & Creel (1965), Plomp (1967) and Roederer (1973) are strongly biased toward the periodicity model of the ear. Of these, Seebeck, Schouten and Stumpf do not attempt to explain all pitch processing or auditory phenomena on the basis of the periodicity theory: they simply give their results and omit mention of data which would tend to contradict their conclusions. Plomp's approach deserves special mention. He argues tenaciously and at length against von Bekesy's place theory near the end of his magnum opus, Experiments In the Tone Sensation (1967). After describing a model of the ear's pitch and spectral-analysis functions as a set of 1/3-octave bandpass filters, Plomp goes on to state: "This model of the ear's frequency-analyzing mechanism must be considered as a simplified representation, since the ear does not containa limited number of fixed filters but is a continuous system of overlapping filters. Nevertheless, Figure 60 elegantly accounts for both the discrimination of the lower harmonics and the preservation of periodicity. The way in which these waveforms give rise in the ear to periodic nerve impulses, however, is still rather unknown." [Plomp, "Experiments In the Tone Sensation," pg. 128, 1967] Plomp mentions experiments by de Boer (1956), Schouten (1962), Ritsma and Engel (1964) and Licklider (1956, 1959, 1962)--all staunch advocates of the periodicity theory. Significantly, Plomp does not mention any of the experiments which tend to contradict the periodicity theory of hearing--in particular, Flanagan and Guttman's 1959 experiments and the removal of the fundamental from the Seebeck click series. These experiments *are *described by von Bekesy. By neglecting to cite the full range of experimental results, Plomp creates a false impression that all psychoacoustic data support the periodoicity theory. Moreover, he neglects to mention that the Fourier-analysis (or place) theory of hearing could equally well account for the fact that pitch is primarily determined by the lower harmonics of a sound, and that even when those lower harmonics are masked by noise the ear still detects a definite pitch. "Apart from the question of how a model spanning only two octaves can throw any light on the perception of a complex tone, we may ask how this observation can explain why the pitch of a complex tone is not altered when the lower harmonics are masked completely by noise... In that case, thecontribution fo the place corresonding to the fundamental is eliminated." [Plomp, "Experiments In the Tone Sensation," 1967, pg. 130] Oddly, Plomp neglects to mention the obvious place-theory explanation of this effect. This phenomenon is well known from the perception of definite pitch ascribed to bells: the ear operates as a Fourier analyzer and fits the partials of the bell into the higher members of a harmonic series, then assigns the bell a perceived pitch given by the assumed fundamental. If the ear's Fourier analysis can assign a nonexistant fundamental to a bell, why not to a strictly harnonic sound whose lower harmonics are masked by noise? Houtsma summarizes this explanation concisely: "De Boer (1956) reported pitch matches in which inharmonic complex tones comprising five or seven partials with uniform frequency spacing were aurally matched to periodic complex tones with a fundamental that differed systematically from the spectral spacing of the inharmonic sound. Schouten, Ritsma and Cardozo (1962) produced similar data for AM complexes (three partials)...and smoorenburg (1970) found essentially the same results using complexes consisting of only two tones. [Houstma, A.J.M., and Goldstein, J.L., "The Central Origin of the Pitch of Complex Tones: Evidence from Musical Interval Recognition," Journ. Acoust. Soc. Am., Vol 51, No. 2, 1971, pg. 525] Moreover, Plomp glosses over the most serious objection to the periodicity theory--namely, that because of the duration imposed on the impulses from nerve fibers in the inner ear, pitches above 1600 Hz should not be perceptible. "The physiological process which sets an upper limit to the frequency of impulses in each fiber is the refractory period. For a brief interval of approximately 1 msec after each impulse the nerve-fiber is not excitable and cannot transmit another impulse." [Boring, E. G. and A. Forbes, Hearing: Its Psychology and Physiology, 1983, 2nd ed., pg. 401] Plomp's response to these objections is worth noting: "The hypothesis that hte pitch of a tone is based on the period of the sound waves may be criticized ont eh ground that this periodicity is preserved up to 3000-4000 cps, whereas we are able to distinguish tones up to about 16000 cps. This discrepancy is one of the most serious arguments against periodicity pitch. It is obviated by Wever's assumption (Chapter 7) that the ear is provided with two ptich-detecting mechanisms: one, based on periodicity, for low frequency and one, based on place of maximal stimulation along the basilar membrane, for high frequencies. This conception is not very attractive, however." [Plomp, "Experiments In the Tone Sensation, 1967, pg. 130] This is a remarkable statement. Plomp saves the periodicity model of pitch by dragging in another model of ear/brain function, then criticizing his own conclusion! Plomp never explains why the idea of multiple auditory pitch detection mechansisms is "not very attractive." Moreover, his arguments for the periodicity theory lose much of their power because he's forced to appeal to the very theory he's arguing against (the place theory) in order to save the periodicity theory for notes with high fundamentals. In several cases where both the periodicty and place theories offer equal explanatory power, Plomp consistently comes down on the side of the periodicity theory. Consider the following example: "Upon presenting tone intervals with the same freuqnecy ratios to the ear, for instance the mistuned interval 200 + 601 cps, the same phenomena were observed as with (von Bekesy's) model. This corresondence was considered by von Bekesy as an affirmation that in both cases the same mehcanism is involved. In his opinion, it seems clear that the periodicity of the nerve impulses does not play an important part in the production of beats. Although this reasoning appears rather attractive, I prefer an alternative explanation of the beats which is based on the assumption that pitch is related to the periodicity of nerve impulses." [Plomp, "Experiments In the Tone Sensation," 1967, pg. 125] Perhaps even the most diligent researchers become confused when attempting to explain away their own biases. At least Plomp admits his prejudice: "In the writer's opinion, this explanation of pitch perception in terms of periodicity is more satifactory than those based on the palce principle. If the pitch of complex tones is derived from periodicity, it is difficult to see why this should not be the case for simple tones, too." [Plomp, "Experiments In the Tone Sensation," 1967, pg. 129] Aside from the fact that many of his objections to the place theory are easily answered, and that he neglects to point out some of the most serious problems with the periodicity theory, Plomp is reasonably straightforward about his leanings toward the periodicity theory. Boomsliter & Creel, in "The Long Pattern Hypothesis in Music," Journ. Mus. Theory, 1965, are not so forthcoming. They are strongly prejudiced toward just intonation, and their article does not cite results which tend to contradict either periodicity or JI tunings (viz., combination tones, the universal preference for stretched intervals, etc.) and they explicitly attempt to derive all of the ear's functions from the periodicity theory. For example, there's no mention of the body of psychoacoustic evidence for a universal preference for stretched intervals, and Boomsliter and Creel explain away their own data showing a general preference for just intervals on their "search organ" singificantly larger than those predicted by the just intonation theory of small whole numbers. The same is true of Roederer in his book's section on the physical makeup of the ear/brain system: there is a great deal of discussion of neurons and neural firing pattern, none at all on the processing of medullar and higher brain areas nor any detailed discussion of von Bekesy's experiments, the physical action of the organ of Corti, etc. However to his credit Roederer does cite extensively the results of Ward, Corso, Terhardt, Sundberg and Lindqvist for the unviersal preference of stretched invtervals. Thus Roederer, like Helmholtz, is a contradictory figure--deliberately overemphaszing some of the evidence, while remaining open-minded about other contradictory results. Fetis (1943), Ellis (1885) Corso (1954), Ward (1970), Burns (1970), Hood (1975) and Erickson (1983) are all strongly biased toward the ear-as-controlled-by-learned-preference model of hearing. Terhardt and Ward/Burns tend to bury evidence which does not favor their view by dumping a superflux of additional results on top of the relevant data; this has the same effect as squirelling the relevant data away in a bibliograhy at the back of the article, but it achieves the same end by opposite means. Fetis, Hood, Ellis, tend to stress the multiplicity of results and musical cultures, rather than concentrating on empirical data from specific experiments. Von Bekesy demonstrates a bias toward the place theory but his bias does not appear to affect his willingness to bring forward contradictory results. In particular, he cites both the periodicity and place theories as worthy of additional investigation in his 1966 article "Hearing Theories and Complex Sounds," Journal of the Acoustic Society of America. Terhardt & Zick, Kameoka & Kuriyaga, Pierce, Mathews, Green, Wessel, Risset and Sundberg do not exhibit a bias toward any specific theory of hearing. These authors all cite competing hypotheses and suggest lines of further experimental inquiry into all 3 ear/brain models. Throughout this article the intent has been to present psychoacoustics data as clearly as possible. In many cases this meant extracting experimental results from layers of refutation or from citations buried in bibliographies because this or that psychoacoustician preferred not to bring the inconventient result out into the body of the text, where it might raise embarassing questions. In other cases, viz., Risset or von Bekesy or Pierce, extensive direct quotes of secondary sources were used because these sources offered the most detailed survey of the evidence. Thus the casual reader must be wary of Roederer, Helmholtz, Plomp and other sources widely cited because of the covert (sometimes overt) bias toward this or that tuning or theory or hearing. As mentioned at the outset, acousticians have fared far worse than psychoacoustics researchers in this regard. Backus (1969), like von Bekesy, is biased toward just intonation--but unlike von Bekesy he neglects to mention any of the psychoacoustic experiments which cast doubt on either just intonation as the ideal tuning system or the place theory as the sole explanation of hearing. In the chapter ""Intervals, Scales, Tuning, and Temperament," Backus lavishes 3 pages on just intonation and 2 pages on Pythagorean intonation but only 1 page on equal temperament. No tunings are mentioned other than Pythagorean, meantone, just intonation and equal temperament: there is, for example, no reference to pelog, slendro, the Indian srutis, or any other non-European tuning.. Moreover, Backus buries or is not aware of many psychoucstic data which contradict his view of the ear as simple Fourier analyzer. In part (as mentioned earlier) this is because Backus had the bad luck to publish his book "The Science of Musical Acoustics" just before computers introduced an immense unpheaval into acoustic and auditory research. In part the problem appears to be overt prejudice against acoustic results which do not favor just intonation. As mentioned earlier, texts by Rossing and Hall supersede the acoustics in Backus and the psychoacoustics (where Backus refers to them at all) are incorrect as well as out of date. Thus Backus' entire text should be ignored. Benade (1975) cannot excuse his lapses on the basis of bad timing. In the period 1970-1974 much of the data cited throughout this series of posts was already well known; Benade chooses not only to ignore it, but actually to argue with a number of independently-confirmed results, particularly the universal preference for stretched musical intervals and the accumulated evidence for the periodicity theory. For example: "Experiments by Paul Boomsliter and Warren Creel give us very important information on what a musician actually does about tuning. My discussion in this capter is strongly influenced by these data, although I do not completely accept their published interpretatiojn. Paul C. Boomsliter and Warren Creel, "The Long Pattern Hypothesis in harmony and hearing," J. Mus. Theory, Vol. 5, No. 2, 1961, pp. 2-30, and Paul C. Boomsliter and Warren Creel, "Extended Reference: AN Unrecognized Dynamic in Melody," J. Mus. Theory, vol. 7, No. 2, 1963: pp. 2-22. " [Benade, A., "Fundamentals of Musical Acoustics, 1975, pg. 303] In short, Benade agrees with Boomsliter and Creel's claim for "small- integer-ratio" detectors in the ear, but rejects the evidence they provide for the periodicity theory of hearing. Benade's commentary is notable because [1] it is hidden away in a footnote and [2] it ignores the fact that a wealth of additional evidence supports the periodicity theory of hearing--evidence which cannot be easily explained by the place theory, which Benade espouses. Again: "Everywhere in our experiments we have found indications that our nervous system processes complex sounds coming to it by seeking out whetever subsets of almost harmonically related components it can find." [Benade, A., "Fundamentals of Musical Acoustics," 1975, pg. 68] This statement is as deceptive as it is true. The accuracy of Benade's claim depends on experiments he chooses to perform: and by failing to perform auditory experiments which would cast doubt on the place theory of hearing, Benade creates the impression that no such doubt exists. As has been seen throughout this article, there is ample evidence both to support and contradict the place theory of hearing (and to support and contradict the other two models of hearing as well). By omitting mention of any of this additional evidence, Benade creates a profoundly misleading impression in the unwary reader. The implication of Benade's statement is that all psychoacoustic experiments support the place theory of hearing--entirely untrue, as we have seen. Again: "The situation with tones having harmonic partials is much more straightforward. We have already learned that pitch-matchings between usccessive and superposed tones are in agreement the tones consist of a few strong partials." [Benade, A., "Fundamentals of Musical Acoustics," 1975, pg. 302] The psychoacoustic data do not support this claim. On the contrary: every psychoacoustic experiment since the 1830s shows a distinct and measurable difference betwen intervals heard as "perfect" when played successively and when played simultaneously, with a strong tendency for successive tones to be played wider than simultaneous tones, and a consistent tendency for both categories of tones to be played wider than small-integer ratios. Clearly in this case Benade is unware of (or has chosen to ignore) 150 years of psychouacoustic data. For these reasons Benade's text is unreliable insofar as it bears on psychoacoustics. Some of Benade's acoustic results remain valid, others have been disproven--particularly Benade's discussion of oscillation patterns in woodwinds and his theory of regimes of oscillation for brass instruments. On balance the entire text should be ignored in favor of more detailed and far more accurate treatments by Rossing, Fletcher, Askill and Lord Rayleigh. Rossing and Fletcher's "The Physics of Musical Instruments," and Askill's "The Physics of Musical Sound" remain excellent surveys of the state of the art in musical acoustics. As mentioned, however, little information on psychoacoustics can be gleaned from these texts because psychoacoustics is not their concern. These texts do not cite appreciable amounts of psychoacoustic data and should not be quoted to support this or that tuning or theory of hearing. "Musical Acoustics: An Introduction," by Donald Hall, 1980, contains an accurate precis of acoustics of piano strings, metallohpohnes and woodwinds, as well as good survey of brass instruments, et alii. Hall is strongly biased toward just intonation and he buries or calls into question psychoacoustic data which do not accord with his prejudices. The acoustic portion of Hall's text is impeccable and worth reading, while the section of the book which bears on tuning systems and psychocoustics is incomplete, outdated, full of errors of omission, and should be ignored. The single best overall survey of psychoacoustic experiments peformed up to the 1960s is Plomp's 1966 text "Experiments In the Tone Sensation." It contains an exhaustive bibliography unmatched anywhere else, and constantly uses extensive direct quotes from the original sources. Plomp exhibits a constant and strong bias toward the periodicity theory; however, he readily admits his prejudice. He is also conscientious in pointing out behaviours of the human ear which are not well explained. Georg von Bekesy is biased toward the place theory; not surprising, inasmuch as his work put the place (Fourier) theory of hearing on a firm foundation. He cites both the periodicity and place theories as deserving further study, however, and (like Plomp) also cites results which contradict all three models of the ear/brain system. "Experiments in Hearing," New York: Robert E. Krieger, 1960 and republished in 1980, is the single best source of references for the place theory of hearing. Harvey Fletcher's "Speech and Hearing in Communication," 1953, is dated but unlike Backus and Benade it is not rendered worthless by overt bias. Better texts now exist (Sundberg, Rossing, Pierce, Terhardt & Zick) but the results Fletcher cites tend to be accurate. Diana Deutsch's 1982 "The Psychology of Music" summarizes key psychoacoustic results by many of reserachers who made the original findings. Most of the contributors are biased toward one or another tuning and the reader must take care to separate experimental results from the conclusions drawn by the various authors. As has been seen, the conclusions of various researchers are on occasion mere opinions, unsupported by the facts. The data cited in Deutsch's compilation are extensive and accurate, although the bibliogpraphies for each section prove distinctly selective. "Psychological Acoustics," edited by E.D. Herbert, is a collection of the original papers in psychocoustics from the 1870s to the 1970s. This is the only text which amasses all the original results in the original authors' own words. Much of the material is now dated, however, and therefore provides an incomplete picture of the ear/brain system. "Auditory Scene Analysis," by Albert S. Bregman, 1990, is a disappointment. It is vague on crucial points and does not cite enough psychoacoustic references. While Bregman does not exhibit major biases toward any specific tuning system, he appears to gloss over many difficult areas of psychoacoustics; viz., the contradictory evidence for various theories of hearing, unexplained ear/brain phenomena, the role of musical illusions in the auditory path, etc. On the whole Bregman's text is useful as a quick overview but should not be cited as a primary source. The next and last post of this series will discuss the higher-level ineraction of tuning, timbre and structural tonality as considered by Rothenberg, Keislar, Douthett and as examined in the work of Pierce, Risset, Sethares, Carlos, et al. --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 18 Oct 1995 18:02 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id JAA13167; Wed, 18 Oct 1995 09:01:51 -0700 Date: Wed, 18 Oct 1995 09:01:51 -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