source file: mills2.txt Date: Fri, 29 Sep 1995 09:24:03 -0700 From: "John H. Chalmers" From: mclaren Subject: Tuning & Psychoacoustics - Post 6 of 25 --- MYTH: THE OPERATION OF THE EAR CAN BE EXPLAINED AS THAT OF A FOURIER ANALYZER, WITH SOME SLIGHT MODIFICATIONS. FACT: Today there are 3 competing models which explain how the ear/brain system operates, and some experimental data supports each hypothesis and contradicts the others. Each theory has enjoyed proponents for more than 100 years, primarily because many aspects of the ear's behaviour cannot be explained by means of Fourier analysis. --- During the late 19th and early 20th century, rapid advances in technology allowed scientists to subject both the place theory and the periodicity theory of hearing to ever-more-sophisticated tests. "On the basis of these different methods, the fact is now well established that the stimulated region of the basilar membrane shifts for decreasing frequency from the basal to the apical end." [Plomp, 1966, pg. 108; see also Cioco, 1934; Crow et al, 1934, Oda, 1938; Stevens et al., 1935; Walzl and Bordley, 1942; Schuknecht, 1960; Kemp, 1935, 1936, Smith, 1947, Smith and Wever, 1949; Davis et al. 1953; Culler, 1935, Culler et al. 1937, 1943; and particularly von Bekesy, 1944, 1955, 1957.] von Bekesy constructed a large and simplified physical replica of the cochlea which used the tactile sense of the arm to stimulate the organ of Corti and the auditory pathway. He proved that even in the case of a very broad maximum of the pattern of vibration, only a small section was felt subjectively to vibrate. This lent strong suport to the view that the place of maximal stimulation along the basilar membrane corresponds to pitch. (That is, to Helmholtz's theory, with a good deal of updating; Helmholtz's idea of "resonators" had to be abandoned, and many of the details of his theory modified, to explain experimental results, as we've seen.) While von Bekesy's experiments provided strong confirmation for some of the place theory's prediction, they contradicted other aspects of the place theory. There remained unresolved, for instance, the question of how to account for the ear's extraordinary sensitivity to tuning differences of individual partials and of the fundamental frequency of the sound wave itself. WIth only 3000 hair cells each spaced 9 microns apart, this was difficult to explain. Known pitch discrimination would demand sensitivity to stimulation on the basilar membrane measured in fractions of a micron, even though the measured width of the travelling wave on the basilar membrane is many times that width. (This objection was originally raised to Helmholtz's now-obsolete hypotheses of the 1860s, and it still bedevils advocates of the modern place theory.) Moreover, if pitch sensitivity were due solely to the hairs lining the basilar membrane, and not to neural processing, there would have to be far more hairs than the known 3000 inner hair cells (electron microscopy has shown that the remaining 12,000 outer hair cells serve an ancillary function, rather than a direct freqency-detection role. This is also supported by data from the action potentials of the two classes of stereocilia as obtained by microelectrodes.) "The two types of coupling can therefore be associated with the different roles of the two types of hair cell in cochlear function, inner hair cells detecting the movement of the [basilar] membrane, and the outer hair cells helping to generate it." [Pickles, James O., "An Introduction to the Physiology of Hearing," Academic Press, 1988, 2nd ed., pp. 158-159] It is also difficult to explain pitch perception of sounds with low but missing fundamentals: "Suppose high harmonics generate the low pitch. They wil be relatively closely spaced and will not be resolved by the auditory stytem. Recognition of the psectral pattern will not therefore be possible, but hte harmonics wil eb able to interact in the nervous system to produce periodically varying activity. Temporal theories are therefore supported." [Pickles, James O., "An Introduction to the Physiology of Hearing," Academic Press, 1988, pg. 273] However, Pickles points out that "This is again an area which is controversial, and over the years opinions have swayed in favour of one hypothesis or the other." (I.e., periodicity or place theory.) Both theories suffer from the limits imposed mathematically by their proposed mechanisms of action, which are in each case different from those observewd: "The lower limit for the place principle is believed to be about 150 Hz becuase the excitation pattern on the basilar membrane does not change with frequencies lower than this limit. Some investigators think that the temporal principle codes ptich for the very low frequencies and supplements the place principle over the midrange frequencies. The upper frequency limit of the applicability of the temporal principle is uncertain. Some investigators put this limit as low as 300 to 400 hz, and others put it as high as 4000 to 5000 Hz." [Gulick, W. Lawrence, George A. Geschneider and Robert D. Frisina, "Hearing: Phsyiological Acoustics, Neural Coding, and Psychoacoustics," Oxford University Press, 1989, pg. 261] Equally troubling for advocates of the place theory is the fact when sine tones are used, the ear displays a completely different consonance/ dissonance curve than that produced by complex tones--instead of a series of peaks and troughs, a smooth shifted-bell-curve-like response is seen for sine tones. The Ohm/Helmholtz Fourier theory of hearing fails to explain this result. Moreover, von Bekesy found that contrary to Helmholtz's presumption, "it appeared that combination tones are not due to nonlinear vibration of [the timpanic] membrane. Furthermore he discovered that the introduction of a negative or positive static pressure into the external meatus changed the loudness of difference tones. This would imply that these tones are produced in the middle ear." [Plomp, 1966, pg. 111] "However Wever et al, 1941, conducted experiments which contradicted von Bekesy's findings just mentioned. ... Further investigations...suggested that the main source of combination tones must be sought in the sensory processes, where the microphonic potential is evoked, and not in the mechanical part of the inner ear (Wever and Lawrence, 1954)" [ Plomp, 1966, pg. 111] In addition, the experiments of von Bekesy, who did more than any other researcher to put the place theory of hearing on a modern scientific basis, were also open to considerable doubt. " Von Bekesy's observations have been questioned on two grounds. Visual observations mean that the vibration amplitude had to tbe at least of the order of the wavelength of light, and the high intensities (130 dB SPL) necesssary make extrapolation to a more physiological range unjustified. Secondly, his measurements were performed on cadavers. It is now known that not only does the experimental animal have to be alive, but the cochlea has to be in extremely good phisological condition, to show a satisfactory mechanical response." [Pickles, James O., "An Introduction to the Physiology of Hearing," Academic Press, 1988, end ed., pg. 40] In short, investigations began to suggest that many important auditory phenomena could only be explained by the software, not the hardware, of the ear/brain system-- that is, by the brain itself. "[For] the phenomenon...once called "periodicity pitch" [there are] alternative explanations... known as "pattern" theories. They suppose that the auditory system, by recognizing that the tones sounded are the upper harmonics of a low tones, supplies the missing fundamental that would have generated them. This is again an area which is controversial, and over the years opinions have swayed in favor of one hypothesis or the other." [Pickles, James O., "An Introduction to the Physiology of Hearing," Academic Press, 1988, 2nd. ed., 1988, pg. 273] Clearly by the 1980s much of the support for the place theory of hearing had crumbled. In 1984 Pierce writes: "Helmholtz accomplished a great deal despite the limitations of the technology available to him. Yet he reached false conclusions. He believed the perception of musical pitch depends on the presence of the fundamental frequency. This is not true for low keys on the piano keyboard, or for orchestra chimes, or for bells. HIs other false conclusion was that the relative phases of sinusoidal components do not affect the timbre of a sound." ["The Science of Musical Sound," Pierce, J.R. , 1992, pg. 185; see also "Tone Segregation by Phase: On the Phase Sensitivity of the single ear," Kubovy and Jordan, JASA, Vol. 66, No. 1, 1979, pp. 100-106] Still, the place hypothesis accounts very convincingly for at least a few characteristics of the ear/brain system: it explains how the ear can resolve complex sounds into separate pitches, explains the function and structure of some of the mechanical components of the inner ear, it explains elegantly the near-logarithmic nature of pitch, and it explains why very close tones are heard as being identical in pitch. On the other hand, the place theory does *not* explain why stretched intervals significantly larger than those predicted by the small whole number ratios (or numerological, essentially Kabalistic) theory of consonance are universally preferred to so-called "pure" intervals (which in psychoacoustic tests are consistently heard as "flat" or "too narrow"). Nor does the modern place theory explain combination tones, (as mentioned above), or the fact that two inharmonic-series tones matched to an inharmonic- series scale sound strongly consonant (Risset, 1978, 1984, 1985; Sethares, 1992; Geary, 1980; Pierce, 1966; Carlos, 1987; Plomp and Levelt, 1965, Kameoka and Kuriyagawa, 1969); nor does the place theory explain (or predict) modern auditory illusions-- Shephard's tones, Risset's tone containing ten 1180-cent intervals which when transposed UP an octave DROPS in audible pitch by a perceived 20 cents, etc. All of these phenomena *can* be explained by the periodicity theory of hearing as emergent properties of an autocorrelation system. However, the periodicity theory itself has a number of problems. It does not explain the universal human preference for stretched octaves, fifths and thirds, a preference found in the earliest experiments performed on measured intervals and in all double-blind psychoacoustic tests performed for 150 years since; the periodicity theory of hearing cannot account for the fact that pitches very close together create a "chorus" effect instead of massive dissonance. By contrast, the broad region of general stimulation of the basilar membrane around the much narrow region of maximal stimulation--one of the hallmarks of the place theory--explains this effect simply and clearly. The phenomenon of combination tones is poorly explained by *both* competing hypotheses. As Plomp points out, "This problem applies both to place pitch and periodicity pitch. If pitch is based on the place of maximal vibration, it is essential for hearing a combination tone that the corresonding place of the basilar membrane is stimulated. Then the question may be asked of how this can be accomplished by sensory processes of hair cells at a distant place of the cochlea. The ascertainment of Six (1956) that cochlear microphonics correponding to combinationg tones have their maximum at the same place as the primary tones, contradicts this possibility. If, on the other hand, pitch is based on the periodicity of nerve impulses, the problem arises how impulses that are synchronous with the frequency of combination tones can be initiated when the waveform of cochlear michrophonics is flattened (the common form of distortion)" [Plomp, 1966, pg. 121] Summing up, James Pickles points out that "Frequency difference limens are very much smaller than cirtical bands. Two mechanisms are possible. For instance, the subject may detect shifts in the place of excitation in the cochlea. This is called the "place theory." Or he may used temporal information. We know that the firing int he auditory nerve is phase-locked to the stimulus waveform up to about 5 khz. In this theory, called the "temporal" [or "periodicity] theory, the subject discriminates the two tones by using the tme interval between the neural firings. It is not clear which of the two mechanisms is used. Indeed the controversy has been active for more than 100 years, and the fact that it is not yet settled shows that we still do not have adequate evidence. Auditory physiolgoists divide into three groups, namely those that think only temporal information is used, those that think only place information is used, and an eclectic group, who suppose that temporal information is used at low frequencies, and only place information at high." [Pickles, James O., "An Introduction To the Physiology of Hearing," Academic Press, 2nd ed., 1988, pg. 271] The implications for musical tuning are mixed. Because no clear evidence has emerged in favor of any of the three major theories of hearing, no single tuning can be considered to "privileged" or uniquely suited to the human ear. On the other hand, because of the mixed results from pscyhoacoustic experiments, the data examined so far would tend to support the use of any of the major categories of musical tuning: namely, just intonation, equal temperament, or non-just non- equal-tempered scales. The next post will discuss several modern experiments which provide evidence for the third "pattern recognition" hypothesis of hearing, and the implications of all 3 of these hypothetical auditory mechanisms for music & tuning. --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 29 Sep 1995 19:07 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA23266; Fri, 29 Sep 1995 10:07:19 -0700 Date: Fri, 29 Sep 1995 10:07:19 -0700 Message-Id: <9509291007.aa21406@cyber.cyber.net> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu