source file: mills2.txt Date: Thu, 28 Sep 1995 10:31:12 -0700 From: "John H. Chalmers" From: mclaren Subject: Tuning & Psychoacoustics - post 5 of 25 -- As mentioned in the previous post, the elements of the modern place theory of hearing are found in Helmholtz's 19th-century model of the ear. Thus it's worth taking some time to examine the implications of that model: "Helmholtz's hearing theory can be considered as an elaboration of three hypotheses. In general terms, the first one is: "Hypothesis I. The analysis of sound is accomplished in the inner ear by means of a large number of resonators tuned to different frequencies from low to high." ["Experiments On Tone Perception," Plomp, pg. 102, 1966] Helmholtz originally ascribed the "resonator" function to the arches of Corti but (as mentioned in the last post) when he put his ideas down in his book he changed his mind and proposed that the transverse fibres of the basilar membrane act as resonators. His arguments were: [1] In the cochlea of birds, no arches of Corti are found (Hasse, 1867); [2] the width of the basilar membrane varies from about 0.04 mm at its base up to 0.5 mm at the helicotrema (Hansen, 1863); [3] the membrane is much more tightly stretched transversely than longitudinally. "On the basis of these measurements, Helmholtz estimated the selectivity of the resonators, amounting to about 4% of the resonance frequency, with bandwidth proportional to logarithmic frequency. "Hypothesis II. A particular tone-pitch corresponds to each of the numerous nerve fibers in such a way that pitch decreases gradually from the basal to the apical end of the organ of Corti." ["Experiments On Tone Perception," Plomp, R., pg. 103, 1966] While Helmholtz's hypotheses explained some aspects of human hearing, it did not explain others. In particular, these hypotheses did not explain how combination tones or beats of mistuned consonances occur. Thus Helmholtz proposed a third hypothesis: "Hypothesis III. The sound transmission of the ear is characterized by nonlinear distortion." ["Experiments On Tone Perception," Plomp, R., pg. 103, 1966] By means of these 3 hypotheses Helmholtz was able to explain much of the experimental data available to him in 1863. Other aspects of human hearing remained unexplained. As Plomp points out, "The Achilles' heel of his conception was why periodic sound waves are always characterized by a pitch corresponding to the fundamental. ... Even so, Helmholtz's theory became widely accepted soon after its publication under the names of resonance theory and place theory." [Plomp, R., 1966, pg. 104] There were other problems with Helmholtz's theory. Whether in modern form as the "place" theory or in terms of Helmholtz's original conception, the pitch sensitivity of the human ear is significantly greater than the predictions made on the basis of the place theory. Moreover, if the ear is primarily a Fourier analyzer, why did it respond to the irregularly- spaced holes of Seebeck's siren (Seebeck, 1846) with a sensation of definite pitch not present in any of the Fourier components of the waveform generated when the siren rotated? Stumpf, one of the proponents of a competing theory of hearing, pointed out these flaws in the original place theory: "The view that fibres of 0.5 mm length should be tuned to low frequencies did not sound very credible and we may suppose that many agreed with Stumpf's statement: `It remains wonderful, however, that so small particles can resonate even on the lowest tones that we produce by strings of enormous size and by which we can bring into resonance only strings of the same size.'" [Plomp, 1966, pg. 107; see also Stumpf, C., "Tonpsychologie," Vol. 2, Verlag S. Hirzel, Leipzig, 1890, pg. 92] Plomp points out: "Some investigators tried to save the resonance hypothesis by supposing that the resonators must be sought in other structures of the cochlea: the hair cells (Baer, 1872; Hermann, 1894; Myers, 1904; Specht, 1926) or the tectorial membrane (Kishi, 1907; Shambaugh, 1907, 1909, 1911; Leiri, 1932). Others, however, rejected the resonance hypothesis entirely, proposing new hearing theories in which the frequency-analyzing power of the hearing organ was approached in quite a different way (Meyer, 1896, 1898, 1899, 1907; Ewald, 1899, 1903, Wrightson, 1918, and many others)." [Plomp, 1966, pp. 107-108] Because of the failure of Helmholtz's original hypothesis to explain many auditory phenomena, many researchers cast about during the period from the 1840s to the 1860s for another model of human hearing. Many researchers seized upon Seebeck's 1843 proposal as the answer. Namely, that "Tones give rise to synchronous nerve impulses whose rate determines pitch. Wundt tried to evade the difficulty that according to this hypothesis Bernstein's findings would suggest a pitch limit at about 1600 cps. He explained that not the total duration of the nerve impulses but the much shorter duration of their peaks might determine the highest pitch audible..." [Plomp, 1966, pg. 105] In favor of this competing hypothesis, called the periodicity theory of hearing, two pieces of early evidence were advanced by Seebeck, Wundt, Stumpf and others: "1. Binaural beats. Dove (1839) had pointed for the first time to the fact that stimulating the ears separately with tones of slightly different frequencies gives rise to slow "binaural beats." Usually, they were explained as resulting from bone conduction between the ears (Seebeck, 1846; Mach, 1875; Stumpf, 1890, p. 458; Schaefer, 1891). Thompson, who discovered the beats independently, found that they do not change over into a difference tone when the frequency difference is increased (1877, 1878, 1881). Therefore, he suggested that binaural beats are caused by interference in a higher centre of the auditory pathway." [Plomp, 1966, pg. 105] This latter was the first suggestion that the brain was directly involved in the processing of musical sounds. Previous theories, like Helmholtz's, assumed that the ear did all the processing required and that the auditory nerve simply acted as a conduit through which the preprocessed nerve impulses travelled. Wundt's and Stumpf's observations made it clear, however, that the brain was *part* of the auditory system which determined pitch, spectral content, etc.--perhaps *the* crucial part (as subsequent late-20th-century "pattern transformation" hypotheses of hearing have stressed). The second piece of evidence supporting the Seebeck/Stumpf/Wundt periodicty theory was: "2. Direct stimulation of the auditory nerve. The sensational conclusion that the cochlea is not essential for obtaining an auditory sensation was drawn independently by Fano and Massini (1891) and by Ewald (1892). They based their opinion on the positive reactions on sound by pigeons with removed hearing organs. The conclusion was severely crticized by Matte (1894), Bernstein (1895), Strehl (1895), and Kuttner (1896), and defended by Ewald (1895) and Wundt (1895)" [Plomp, 1966, pg. 106] Plomp points out that although this second competing hearing theory could explain interruption tones and beats of mistuned consonances much better than Helmholtz's theory did, its influence was small, perhaps because Wundt did not work the theory out in nearly as much detail as did Helmholtz in the 2nd edition of "On The Sensation of Tone." The whole later development of physiological acoustics can be regarded as an elaboration of these two competing and contradictory hypotheses, along with Fetis' 1843 learned- response theory of hearing. Like Seebeck's and Stumpf's periodcity theory--which was largely ignored until Schouten in 1935 performed a convincing series of experiments which clearly demonstrated the inadequacy of the place theory of hearing--Fetis' 1843 theory of learned response was likewise ignored for many years. Starting in the 1950s, Ward, Burns, Corso, Licklider, and others performed a series of experiments which cast profound doubt on many aspects of both the periodicity and place theory and strongly supported Fetis' 1843 hypothesis. Recently, the auditory artifacts produced by cochlear implants have provided strong evidence against the periodicity theory: "If we believe the extreme position that at low frequencies information is carried purely by the temporal pattern of nerve impulses, then periodic electrical stimulation should produce faithful auditory sensations and good discrimination of frequencies. The results of electrical stimulation have on the whole been disappointing for such a prediction. In only a few cases to electrical stimuli seem to produce clear tonal sensations. A typical report is that tones sound like "comb and paper" (e.g., Fourcin et al., 1979). [Pickles, James. O., "An Introduction to the Physiology of Hearing," Academic Press, 2nd ed., 1988, pg. 316] On the other hand, the place theory also conflicts with experiment: "In a quasi-linear spectral analyzer such as the cochlea the physical limits of frequency resolution are limited by the duration of the stimulus, as a result of spectral splatter: stimulus duration x spectral line width = 1. (..) Temporal theories are not so limited... (..) On the hypothesis that place and not temporal cues are used, we can calculate a lower limit for the frequency difference limen as a function of the length of the stimulus. Moore (1973) showed that below 5 khz frequency discrimination for short stimulus was up to an order of magnitude better than expected on a place basis. " Pickles, James. O., "An Introduction to the Physiology of Hearing," Academic Press, 2nd ed., 1988, pg. 273] As a result, "At the moment pattern hypotheses are dominant..." Pickles, James. O., "An Introduction to the Physiology of Hearing," Academic Press, 2nd ed., 1988, pg. 273] The phenomenon of forward and backward masking also directly contradicts the place theory. In forward masking, a masking tone precedes the test tone by a small time period--in backward masking, the masking tone occurs *after* the test tone. If Fourier analysis is occurring mechanically in the ear, it's difficult to explain how a second tone appearing *after* the test tone can interfere with the Fourier analysis. And in any case, the fact that masking occurs is a fundamental problem for Fourier models of hearing. "Masking is an example of limitations of the auditory system's ability to analyze individual frequency composnents in a complex sound. If the ear were a perfect frequency analyzer, then one sound would never mask the detecability of another sound. Instead, simultaneously presented sounds would be independently processed, and the perpcetion of one would not affect the perception of others. Masking demnstrates that this ideal state does not exist. Whenever masking occurs, frequency analysis fails. When the presence of a sound of a particular frequency makes it difficult or impossible to hear another sound of a different frequency, the ear has failed to analyze and detect the individual frequency components of the complex sound created by simultaneous presentation of the two sounds." [Gulick, W. Lawrence and George A. Geschneider and Robert D. Frisina, "Hearing: Physiological Acoustics, Neural Coding, and Psychoacoustics," Oxford University Press, 1988, pg. 300] As a result of these pervasive problems with both the place and periodicity theories of hearing, Fetis' model of the ear/brain system as a feedback path controlled primarily by software (viz., learned response) has now gained great currency. in part because of the inadequacy of current evidence In part this is also probably due to increasing use of computers and software in the congitive sciences and their consequent popularity as a conceptual model for neural systems. (As will be seen in a future post, a researcher's tools exert a potent influence on the mental models he forms.) If accurate, the "pattern transformation" model of hearing implies that many different tuning systems and musical syntaxes are appropriate. According to this theory of hearing, no particular complex of overtones has a privleged status in the ear, and no specific musical tuning is implied as superior on the basis of the structure of the ear. Because of the importance of this question for tuning and music, the next post will examine detailed evidence for and against the periodicity and place models of pitch perception. --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 29 Sep 1995 07:12 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id WAA06397; Thu, 28 Sep 1995 22:12:35 -0700 Date: Thu, 28 Sep 1995 22:12:35 -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