Perceptual analysis of sound
Citation for published version (APA):Duifhuis, H. (1972). Perceptual analysis of sound. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR115512
DOI:
10.6100/IR115512
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PERCEPTUAL ANALYSIS
OF SOUND
PERCEPTUAL ANALYSIS
OF SOUND
PROEFSCHRIFT
TER VERKRIJGING V AN DE GRAAD V AN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL EINDHOVEN, TEN OVERSTAAN VANEEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE V AN DEKANEN,OP DINSDAG 29FEBRUARI 1972 TE 16.00UUR
IN HET OPENBAAR TE VERDEDIGEN
DOOR
HENDRIKUS DUIFHUIS
GEBOREN TE BARNEVELD
DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOR PROF. DR. J.F. SCHOUTEN.
Aan Franaien Aan mijn ouders
CONTENTS
Chapter 1 INTRODUCTION 7
1.1 Historical Introduction to Hearing Theory 7 1.2 Subjective Attributes and Physical Parameters of
Sound
1.3 Formulation of the Subject of Investigation Chapter 2 FREQUENCY ANALYSIS
10 . 12
13
2. 1 Introduction 13
2.2 Frequency and Pitch 13
2.3 Pure-Tone Masking 17
2.4 The Critical Band 21
2.5 Anatomical and Physiologic Data 22
2.6 Comparison of Data on Aural Frequency Selectivity 28 Chapter 3 TIME ANALYSIS
3.1 Introduction 3.2 Periodicity Pitch 3.3 Temporal Masking 3.4 Neurophysiologic Data 3.5 Sununary
Chapter 4 EXPERIMENTS ON PERIPHERAL FREQUENCY AND TIME ANALYSIS 31 31 33 40 41 45 46 4. 1 Introduction 4 6
4.2 Audibility of Harmonics in a Periodic Pulse 50 4.3 Time Effect on the Audibility of High Harmonics
in a reriodic Pulse 60
4.4 Audibility of Harmonics in Periodic 'White Noise' 71
4. 5 Discussion 82
Chapter 5 MASKING 5.1 Introduction
5.2 Conce~ts and Terminology
5.3 Backward Masking: Central or Peripheral?
85 85 85 89
Chapter 6 THE TRANSFER CHARACTERISTICS OF THE PERIPHERAL AUDITORY SYSTEM
6.1 Introduction 6.2 The Filter Model 6.3 The Firing Model 6.4 Results of the Model 6.5 Discussion
Appendix No. 1 Some Properties of a Non-Homogeneous Poisson Process
Appendix No. 2 Simulation Chapter 7 EPILOGUE Acknowledgments List of Symbols Author Index References Samenvatting Curriculum Vitae 98 98 99 104 119 130 132 136 149 153 154 158 162 176 178
Chapter 1 INTRODUCTION
1.1 HISTORICAL INTRODUCTION TO HEARING THEORYt
Ohm's application of the Fourier analysis to the hearing theory (Ohm, 18~3), was an important contribution to the development of modern psychoacoustics. Ohm's acoustical law states that the ear can analyse a complex sound into its spectral components.
Helmholtz (1863) endorsed Ohm's law and performed a number of experiments which this view. Helmholtz, however, was aware of the restriction that the frequency resQlving power of the ear is limited. This restriction was of little importance in the perception of musical sounds, of which the musical quality was defined as the perception produced by the first six partials of the complex sound. Within this
restriction, Ohm1s law was extended by Helmholtz's phase rule.
This rule states that the musical quality of a complex sound is determined by the amplitudes of the partials while their phases are irrelevant.
Helmholtz also suggested that the frequency analysis takes place in the cochlea in such a way that high frequencies are detected near the windows and low frequencies near the helicotrema. In 1869 he indicated a mechanism which it was possible to hold
projection.
for this frequency-to-place
t The great number of excellent reviews of the development of the hearing theory make it little attractive to add a new one. Therefore this introduction gives a short and incomplete review of points that are of relevance to the underlying work. For further information the reader is, in addition to referen ces in the text, referred to handbooks such as Wever, 1949; Fletcher, 1953; Littler, 1965; Zwicker and Feldtkeller, 1967; Harris, 1969; and Tobias, 1970.
1.1.
As early as 1843 Seebeck argued against the interpretation which Ohm, in support of his acoustical law, had given to Seebeck1s (1841) experimental results. He noticed that his results did not completely agree, especially not quantita-tively, to an analysis of the sound into Fourier components. He therefore judged it premature to assume that the subjec-tive components (percepts) into which the ear can analyse a complex sound, correspond to sinusoidal vibrations;
Rayleigh (1896), who was not so involved in the discussion that followed, noticed that apparently there were exceptions to the original extreme formulation of Ohm's law
(sec. 2.1). It was, for instance, well known that two spectral components which are close together are not perceived as separate tones, but as a beating complex. Further, citing Mayer (1876b), Rayleigh mentioned the masking effect. Mayer
(1876a,b) had observed that a spectral component could 'obliterate' another, and.that this phenomenon was stronger at the high-frequency side than at the low-frequency side of the more intense sound, the masker.
Another argument against the assumption of a highly selective frequency separation in the inner ear, as hypoth-esized by Helmholtz, has been supplied by Wien (1905). The sharply tuned resonant places in the cochlea are incompatible with the short decay time of auditory sensation.
In 1924 Fletcher drew attention to the case of the missing fundamental. Although this effect was originally attributed to non-linear distortion in the ear (Fletcher, 1924), Schouten (1938) pointed out that it was possible to explain it in terms of time analysis. Besides the part-tones in a complex sound, Schouten distinguished a complex-tone which he termed the residue (Schouten, 1938, 1940a,b,c). The part-tones correspond to the lower harmonics, in accordance with Ohm's law. The higher harmonics were perceived together as one subjective component, the residue. The residue had a sharp timbre, and it had approximately the pitch of the fundamental. The residue thus accounted for the phenomenon of the missing fundamental.
1.1.
In the subsequent period, particularly Licklider, Small, De Beer, Schouten, Ritsma, Cardozo, McClellan, and Bilsen
(further references in sec. 3.2) worked further in the
direction of subjective time analysis of sound in relation to pitch perception. In 1954 this led to the introduction of the concept 'periodicity pitch' as a pendant of 'place pitch'
(Licldider-, 1954).
In 1928 Bekesy provided the first direct evidence of frequency separation in the cochlea along the cochlear partition (Bekesy, 1960). The frequency resolving power, however, appeared to be considerably lower than the value foreseen by Helmholtz, a value that would fit in with the results of psychoacoustical measurements such as of the just noticeable difference (jnd) in frequency. In this scope it should be noted that the amplitudes of elevations of the cochlear partition are extremely small, viz. of the order of' magnitude of 50 nm at 100 dB SPL. In order to obtain
observable elevations, Bekesy (1943) had to supply high intensity stimuli, viz. 120-160 dB SPL. At this level the influence of non-linear distortion could considerably affect the frequency resolving power. The low value found by Bekesy led to the postulation of neural inhibiting mechanisms that would account for a sharpening of the cochlear frequency selectivity (e.g., Bekesy, 1960, Ch. 13) .. During the last few years new techniques have made possible measurements at lower intensities (Johnstone et aZ., 1970; Rhode, 1971). A tentative interpretation is that the recent results show a greater cochlear frequency selectivity (at all events when measured at low intensities) than would be expected from linear extra-polation from Bekesy's data. Thus, the more recent findings do not underline the necessity of a sharpening mechanism.
Since Galambos and Davis (1943) recorded activity from fibres in the auditory nervous system, many neuro-physiologic experiments have 'provided data about discharge patterns in auditory nerve fibres in response to acoustic stimuli. A certain tonotopy of fibres as well as representa-tion of time structure of the stimulating wave-form in the spike pattern are observed. The question whether the
frequen-1.1. 1. 2.
cy coding of fibres, or the time representation in spike patterns is relevant to the perception of pitch is still unanswered and remains a point of further investigation (see, e.g., Whitfield, 1970; Hind et aZ., 1970). This question is not a new one. Schouten (1940b) made that
Helmholtz's place theory in fact consisted of two assump-tions, viz. the place theory of the (frequency) analysing mechanism and the place theory of the transmitting mechanism. The former, predicting a frequency analysis (with a limited resolving power) along the cochlear partition, has been confirmed sufficiently by experimental data. The latter, stat.ing that excitation at one place at the cochlear _parti-tion corresponds with one pitch, is still subject to discus-sion, as mentioned above. Where the term place theory is used henceforth, it is in the latter , the one-place-one-pitch theory. The place theory assumes that information from the cochlear partition to the higher neural centres is transmitted by the identity of a fibre and its spike rate. Its. alternative, the periodicity (time} theory, states that in addition to the spike rate the temporal organization of the spikes is relevant to pitch perception. The periodicity theory therefore enables more than one pitch to arise from a single place at the cochlear partition. It appears that a number of experimental results can be described easily in terms of a place theory, whereas others seem to fit only in a periodicity theory. Therefore, sometimes the suggestion is advanced that both mechanisms play a part (e.g., Zwicker· and Zwislocki, in the discussion on Schouten, 1970).
1.2 SUBJECTIVE ATTRIBUTES AND PHYSICAL PARAMETERS OF SOUND In the preceding section the subjective attribute pitch was introduced in relation to hearing theory. Pitch is one of the subjective attributes of sound. Others are timbre, loudness, duration and direction. However, in many of the complex sounds reaching us in daily life (e.g., speech) we are hardly aware of these attributes, unless special atten-tion is paid to them.
1. 2.
Subjective attributes are only partly related directly to the physical parameters of sound, viz. a spatial pressure fluctuation as a function of time. A proper mathematical transformation of these parameters in e.g. frequency and phase often leads to simplification of the signal descrip-tion. It must be realized, however, that these parameters · are not new, but alternative parameters.
At this point the term frequency deserves some closer attention. Kneser (1948) (see also Nordmark, 1968, 1970) pointed out that, depending on the method of measurement, in fact two different frequencies can be defined. The first,
phase frequency~ is determined by measuring the period
between two points of equal phase calculating its recip-rocal. The measurement of one period provides accurate determination of this value. The second, group f~quency,
is the tuning frequency of the resonator that responds
maximally. The latter determination requires an analysis time that is inversely proportional to the bandwidth of the
resonator, and its accuracy cannot be better than the limita-tion given by the uncertainty relalimita-tion. As Stewart (1931) and, later, Gabor (1946, 1947) pointed out, frequency and time, as related by the Fourier transformation, are subject -to the uncertainty-relation~~· ~t ~ 1. The product
-~f • ~t ls minimal for the normal distribution function, an
ei~enfunction of the Fourier transformation. In the given
relation Af and ~t are defined as 211T times the r.m.s. deviation of the mean frequency and of the mean time respec-tively. Rise time and decay time of the response of a filter are related to its bandwidth according to the uncertainty relation. In auditory theory, frequency is mostly used in the meaning of group frequency as defined above. Phase frequency can be a useful concept the description of pitch discrimination for tones of short duration where the uncertainty product can reach a value as low as 0.05 (Cardozo, ·1962). An alternative interpretation of this find is that the
bandwidth effective in pitch discrimination of short tonal signals is much narrower than the r.m.s. value defined above.
1. 3.
1.3 FORMULATION OF THE SUBJECT OF INVESTIGATION
The present work will be concentrated mainly on the role of the peripheral part in the auditory system. The subjective analysis in frequency and time, related to some aspects of pitch perception, is the subject of the main experiments, treated in Ch.4. These experiments are concerned with the audibility of harmonics in periodic pulses and periodic
'white noise', and show the limitation of the ear's frequency resolving power. They provide an estimate of the selectivity of the ear. Ch.S deals with masking, and especially with the behaviour of masking as a function of time, such as occurs in forward and backward masking. These phenomena are related to results of Ch.4. Ch.6 describes theoretically the transfer characteristics of the peripheral part of the auditory system. A new hypothesis describing the behaviour of the auditory recaptor cell is presented.
In .. Chapters 2 and 3 further attention is paid to literature data on frequency and time analysis in hearing, referring to psychoacoustical as well as to (neuro)physiologio experiments.
2.1 INTRODUCTION
Chapter 2 FREQUENCY ANALYSIS
According to Ohm's (1843) law, subjective frequency anal-ysis is a separation of a complex sound into its Fourier components, as follows from his defenition of tone (p.518): "Es mi.issen die zur Bildung eines Tones von der Swingungs-menge m erforderlichen Eindri.icke in Intervallen von der Liinge 1/m hinter einander hergehen und in jeden dieser Inter-valle fortdaurend die Form a• sin~(mt + ~) entweder ganz rein in sich tragen, oder diese Form muss wenigstens als ein reeller Bestandtheil aus jenen Eindrllcken abgeschie~en werden konnen". To this formulation he adds that for such a tone a and ~ ought to be constant.
Realizing that a Fourier analysis requires in fact an infinitely long time interval, it becomes clear that with subjective frequency analysis one should ri;ither think of a short-time Fourier analysis. The latter can be represented by a bank of band-pass filters, characterized by tuning frequen-cies and bandwidths. Assuming that such a representation is adequate, it is of importance to know the characteristics of the band-pass filters, and where these properties are to be located in the auditory system.
2.2 FREQUENCY AND PITCH 2.2.a Pitch scaling
The notion that musical tones can be arranged on a musical scale goes back to the time of the ancient Greek philosophers. The discovery of the relation between length ratios of a vibrating string and pitch intervals in the sounds which it produces, is ascribed to Pythagoras (see Bekesy and
Rosenblith, 1948). This finding made possible the (objective) 13
2. 2. a.
description of musical intervals with mathematical ratios (e.g., by Ptolemy).
In 1912 Revesz suggested that pitch should be considered to have two aspects: a unidirectional tone-height and a cyclical chroma (e.g., Revesz, 1946)t . Two frequencies an octave apart thus had a different tone-height but equal chroma. In a
training experiment on perception of absolute pitch, Brady (1970) suggests a similar differentiation. Revesz' s :assump-tion that a subjective octave equals a physical octave is not correct. The subjective octave turns out to be slightly larger than the physical octave, particularly for frequencies above 1kHz (Ward, 1970).
A systematic investigation of the rel~tion between the subjective attribute pitch and the frequency of a sinusoidal sound stimulus has been performed by Stevens et a~. (1937). In their experiment, subjects were asked to set frequencies of a pair of stimuli so that the second was 'twice as high' in pitch as the first. A monotone relation was found between the frequency of a stimulus, expressed in Hz, and the pitch subjectively attributed to this signal, expressed in mel. In a subsequent experiment (Stevens and Volkmann, 1940) the task of the subject was to adjust the third of three tones so that the 'interval' between second and third was equal to that between the first and the second. The relation between frequency (Hz) and pitch (mel) as found in this experiment is shown in Fig. 2.1. It appeared that the results depend strongly on the procedure used, and that individual differ-ences were far from negligible (Ward, 1954).
There appears to exist a slight influence of the intensity on the pitch of a pure tone, as was reported by Stevens (1935). His data, results of one subject, show a pitch shift of two semitones at 150 Hz (downward) and at 1.8 kHz (upward)
t The original terms were "Tonhohe" and "Tonqualidit", trans-lated to "pitch-quality" and "octave-quality" by H.J. Watt (The Psychology of Sound, Cambridge, 1917). The terms given above were used by Ward (1970).
2. 2. a. 2. 2 .b. <11 .J Ill _22~--~~++--,_--r-r+,_~r, % I) 1-~~r-_,~~+---t-~r-r+~--+---t-~~--~ .10 100 200 - 1000 zooo 4000 10000 FREQUENCY
Fig. 2.1. Pitch of a pure-tone, scaled in subjective units, as a function of frequency (from Stevens and Volkmann, 1940, by permission of the American Joumal of Psychology).
when the level is increased from 40 to 90 dB SPL. In a recent review paper, Ward (1970) concludes that the change of pitch with intensity is generally somewhat less than mentioned above, and that, e.g., in music the effect is usually neglig-ible.
2.2.b. Difference limen
The difference limen of frequency, DL
1
,
of two alternating pure tones, subjectively determined as a jnd in pitch, is a measure of the frequency resolving power of the ear. From the classical measurements of Shower and Biddulph (1931) it ap-peared that below 1 kHz the DLf is approximately constant( "' 2 Hz), whereas above 1 kHz the relative DLf ( = DLrf f) is cGnstant (0.2 to 0.4%; see Fig. 2.2). Later experiments showed a similar picture, although under conditions slightly lower values have been reported (DL
1
1t "' 0.1%,Konig, 1957). Henning (1966) showed that the effect of in-tensity on DL plays an important part particularly at high
2.2.b. 2. 2. c.
~·
.
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• - HARAIS f'IX£0 AMP\.tTUO£ SIGNAl.$
a-W£V€R a W£011~~
it-W. H } RMQOM AMPL ITUO£ ttGfrfAt.-1
V ... f-a. THIS STUDY
Fig. 2.2. Relation between relative DLf and frequency
obtained in experiments in which fixed- and random-amplitude signals were used (from Henning, 1966, by permission of the Journal of the Acoustical Society of America).
frequencies. Therefore he eliminated the intensity effect using random amplitude signals. For frequencies below 5 kHz the behaviour of DLf as a function of f shows a clear simi-larity with former results. Above 5 kHz, however, DLf in-creases sharply, as is shown in Fig. 2.2.
2.2.c. Complex sounds
For signals consisting of more frequency components, the relation between pitch and frequency is less obvious (e.g., Fletcher, 1934). Generally, a complex signal is perceived as one complex, with a definite timbre, a loudness and a
1 complex 1 pitch. Listening more analytically, 'one is often able to discern part-tones in the complex signal, which individually show characteristics of a pure tone in accord-ance with Ohm's law. Besides these part-tones the residue is often perceptible as a complex-tone (Seebeck, 1841; Ohm, 1843; Helmholtz, 1863; Schouten,1940b; Plomp, 1964b). The extent to which the ear is able to discern part-tones in a complex signal provides another indication about the ear's frequency resolving power.
2.2.d. 2. 3. 2.2.d. In our experiments, to be treated in Chapter 4, the pitch-frequency relation is of importance with regard to the identification of harmonics in a complex sound. The DL! and the 'ability to discern individual harmonics in a complex sound are of relevance to the discussion on the frequency selectivity of the ear.
2.3. PURE-TONE MASKING
Masking has been defined as:"(1) The p:r>ooess by which the threshold of audibility for one sound is raised by the pres~ ence of another (masking) sound. (2) The amount by which the threshold of audibility of a sound is raised by the presence of another (masking) sound. The unit customarily used is the decibel" (American Standards Association, 1960).
Masking is affected by a number of physical parameters. With respect to time, sim)Jltaneous and non-simultan_eous masking must be distinguished. The treatment of non-simultan-eous masking is postponed to Sec. 3.3 and in further detail to Ch. 5.
Wegel and Lane (1924) were the first to examine simultan-eous masking of pure tones extensively. They determined the threshold of audibility of a masked tone with adjustable frequency in the presence of a masker at fixed frequency and intensity. As beats occur at small frequency separations, in later experiments often a narrow band of noise was used for one of the two sounds (e.g., Egan and Hake, 1950; Zwicker, 1954; Chistovich, 1957; Greenwood, 1961a). However, Bos and De Boer (1966) showed that for narrow band maskers the masking results are again strongly affected by intensity fluctuations that are inherent to this type of stimulus.
In 1959 Small gave a survey of pure-tone masking results, in addition to data from an experiment in which the masker level was adjusted at constant masked tone level (Fig. 2.3). It appears that the masking of a pure tone drops sharply at its low-frequency side (80 to 240 dB/oct at pure-tone masking and 55 to 190 dB/oct at narrow band masking, Small, 1959). At the high-frequency side the slope is commonly less steep,
2. 3.
Fig. 2.3. Masker SPL(Lm) necessary for the signal to be just detectable as a function of the frequency of the masker (fm), for two indicated signal levels. The parameter is signal fre-quency, cuzves from left to right representing the results for 0.4, 0.8, 1.6, 3.2, and 6.4 kHz. Vertical bars show the 95% confidence interval of data points. Circled data points indicate those conditions for which some listeners were unable to mask the signal even with the highest levels used (from Small, 1959, by permission of the Journal of the Acoustical Society of America).
dependent on the level of the masker (Zwicker, 1958) as is indicated in
Originally, and Lane (1924) indicated the possibility that pure-tone masking could be brought about by mutual in-fluence of waveforms at the cochlear partition. This point of view became questionable when Bekesy (1943) showed poor fre-quency selectivity of the cochlear partition. The sharpening mechanism, which was already required for a reasonable accurate place-pitch theory, however, might also account for 1B
2. 3.
i
LrFig. 2.4. Means of narrow-band masking curves. The noise band is centred at 1.2 kHz. Parameter is the SPL of the noise band (from Zwicker, 1958, by permission of Acustica).
the sharpness of the tone masking curves. Thus, pure-tone masking, though apparently not being attributable to mechanical cochlear interaction, might still be attributed to interaction of excitation patterns at a peripheral stage. Bekesy (1963) pointed out that two different modes of inter-action of excitation patterns are conceivable. The first is the summation of excitation patterns of masker and masked tone. The masking criterion will then be determined by the magnitude of the local secondary maximum in the excitation pattern. The second mode is given by the consideration that
the excitation by the masked tone is decreased by the excitation of the masker, so that the effective excitation pattern is the result of a subtraction. Although both modes will hardly demonstrate a difference at the masking thresh-old, at partial masking they predict, within the place theory, a pitch shift of the suppressed tone in opposite directions. Summation of excitation patterns produces a pitch shift towards the masker, subtraction gives a pitch shift away from the masker. Psychophysically measured pitch shifts do not provide un unambiguous decision in favour of either pr>inciple (see, e.g., Terhardt and Fastl, 1971). We
2. 3.
want to stress the fact that at a cochlear level
interfere. Therefore, cochlear interaction is not a super-position of (energy) excitation patterns resulting in a stationary excitation. The superposition of momentary values of excitation generally results in an excitation with a non-stationary envelope (cf. also Bos and De Boer, 1966).
From neurophysiologic data Hind et a~. (1967, 1970) intro-duced a new experimental definition of masking. They exam-ined the response of single fibres from the nerve of the squirrel monkey to stimuli of two low-frequency tones. It was found that the
pattern showed time synchronization (Sec. 3.4) either (1) only to the first tone, or {2) only to the second tone, or (3) in a varying degree to both. Further they stated that if
discharges in response to this stimulus are to
one tone, the synchronized response is identical with that which results when the appropriate tone alone is sounded. The authors suggested that under these circumstances the other tone is masked. This hypothesis differs from the idea that a masking tone causes a maximum rate of
in a nerve fibre, thus preventi~g other sounds to send infor-mation along the same channel. Although the present defini-tion gives a reasonable descripdefini-tion of in a
fibre in the periodicity theory, for the moment the question remains how this definition can be extended to cover the behaviour of an ensemble of fibres.
The masking definition of Hind et aZ. can be considered
the periodicity theory counterpart of a of
interaction of (cochlear) excitation patterns. As for the
effective excitation pattern this seems to be
most closely related to the second mode of interaction trea~
ted above. The difference is that with masking no pitch shift is to be expected on the bais of a top shift in the excitation pattern. However, a shift might be brought about by the influence of the masker on the time pattern of the suppressed tone.
2. 4.
2.4 THE CRITICAL BAND
In 1940 Fletcher introduced the term critical band (CB) for the effective width of a noise band which masks a tone having the same power and lying within that noise band. At present values found by Fletcher are called 'critical ratio', in accordance with the suggestion of Zwicker et al.
(1957). The term critical band is used for more direct
mea-surements of the bandwidth at which subjective responses change rather abrubtly (e.g., Greenwood, 1961a). Between critical band and critical ratio (CR) there exists a s relation: CB = 2.5 x CR. In Fig. 2.5 the magnitude of the critical band is shown as a function of its centr~ frequen-cy (from Zwicker et al., 1957).
2000 1000 500
~200
...
a: 11!100"'
...
...
~ ~..
..
50 20 10 ~ DiffERENCE LIME"{by frequency modutahOI'lt
I 50 100 200 500 1000 2000 5000 10000 FREQUENCY I" C'ICLES PER SECCND
Fig. 2.5. Critical band and critical ratio as a function of centre frequency, The CB curve is based on the results of four kinds of experiments (from Zwicker et aZ., 1957, by permission of the Journal of the Acoustical Society of America).
2:4. 2. 5.
There are several classes of experiments the results of which give a measure of the CB. First, there is the effect of phase on frequency components that lie within a CB. This was measured by Zwicker (1952) in an experiment in which the auditory sensitivity to amplitude and frequency modulated sinusoidal stimuli was determined. Modulation thresholds for AM and FM stimuli are comparable when related to the ampli- · tudes of the side bands if these fall outside the CB centred around the carrier. For lower modulation frequencies the difference between AM and FM thresholds becomes prominent. Goldstein (1967) obtained similar results when comparing modulation thresholds of AM and QFM signals (A QFM signal is obtained by shifting the phase of the carrier of an AM signal over 90°).
Another class of measurements of the CB treats the loud-ness of noise (or other complex sound) as a function of band-width at a constant energy contents (e.g., Zwicker and
Feldtkeller, 1955; Zwicker et
at.,
1957). As the bandwidth exceeds the CB, the loudness increases with the bandwidth, whereas within the CB the l·oudness remains constant.Greenwood (1961a) derived the CB from a masking experiment in which a sinusoid was masked by a band of noise with vari-able bandwidth and intensity. His results fit in with those obtained by Zwicker et al. (1957) for sensation levels below some 60 dB. Above this level Greenwood's pass-band shrinks to a smaller width. De Beer (1962) and Bos and De Boer (1966) indicated tnat the effect of intensity fluctuation, which occurs in this type of stimulus for narrow noise bands, can lead to an exceptionally small value of the CB. They suggest that the discrepancy between the CB and
CR
value is attrib- · utable to this effect.The CB has shown its usefulnes in calculting the loudness of complex sounds (e.g., Zwicker, 1958; Zwicker and Scharf, 1965).
2.5 ANATOMICAL AND PHYSIOLOGIC DATA
2. 5.
obtained from experiments with laboratory animals, the hearing organ of which is assumed to function more or less similarly to the human hearing organ.
The first step in the aural processing of sound is the conversion of air vibration into a membrane displacement at the tympanic membrane. The ossicles transfer this vibration to the oval window in the inner ear (Fig. 2.6). The transfer function of auricle, auditory canal, eardrum, and middle ear can be considered that of a broadband filter with a charac-teristic which, for frequencies above some 0.5 kHz, roughly approximates the threshold of audibility curve (Bekesy, 1960;
M~ller, 1963; Zwislocki, 1965).
2
Fig.2.6. Schematic longitudinal section of the peripheral ear. 1, auricle; 2, auditory canal; 3, eardrum; 4, middle ear; 5, ossicles (hammer, anvil, stapes); 6, unrolled cochlea; 7, oval window; 8, cochlear partition; 9, round window; 10, Eustachian tube; 11, balancing organ. a(t), acoustic stimulus; on the cochlear partition th• responding waveform is sketched. High-frequency stimuli excite the cochlear partition near the win-dows, low-frequency stimuli at the apex.
Bekesy (1928) was the first to observe travelling waves along the cochlear partition, wnich were produced by acous-tical stimulation. The waves result from the interaction between cochlear partition (basilar membrane, Reissner mem-brane, and organ of Corti) with the surrounding liquid (perilymph). The travelling waves, affected by dispersion and resonance along the cochlear partition, produce a fre-quency separation in the inner ear (Bekesy, 1943) as had already been hypothesized by Helmholtz. High frequencies produce maximum stimulation of the cochlear partition near
2. 5.
the oval window, low frequencies near the apex. The distri-bution of places of maximum excitation as a function of signal frequency is approximately logarithmic for frequencies above 0.5 kHz and linear below this value (Bekesy, 1960). It is noted that this finding associates with the psychoacous-tical CB, which corresponds with a constant length interval along the cochlear partition (Greenwood, 1961b). The fre-quency resolution at the cochlear partition appeared to be rather poor. Measurements by Bekesy of resonance curves as well as decay time of a response to a tone burst provide an estimate of Q of about 2. Therefore, Bekesy assumed the pres-ence of a sharpening mechanism which was required for the place theory of pitch perception and which also explained, e.g., the small DLf and the sharp masking slopes of pure-tone masking curves.
The application of a new measuring procedure, the
Mossbauer technique, enabled measurements to be made of the motion of the cochlear partition at levels considerably lower than required for Bekesy1s direct optical observations (Johnstone and Boyle, 1967; Johnstone and Taylor, 1970; Johnstone et aZ., 1970; Rhode and Geisler, 1970; Rhode, 1971). Although this method has produced but a restricted set of data up to now, the results point in the direction of such a sharp frequency resolution at the cochlear partition that the necessity of an efficient sharpening mechanism,,as mentioned before, seems hardly any longer present. Sharpening through inhibition by neural feed-back is improbable as was pointed out by Spoendlin (1970). His anatomical results, supported by physiologic and pshychoacoustical findings, only leave open the possibility of feed-forward interaction:
At the level of the auditory nerve (nervus VIII) high frequency selectivity is demonstrated in the tuning curve of single auditory nerve fibres (e.g., Katsuki, 1961; Kiang, 1965). The tuning curve depicts the level of a sinusoidal stimulus at which the spike rate shows a just noticeable increment with regard to spontaneous rate, as a function of the stimulus frequency ( . 2.7). The freq~ency for which the threshold of a fibre is minimal, is teufued the
charac-2. 5.
..
..
! 0 -60 3 -eo..
"'
.. ..
"'
f -100 .2 .5 I 5 ~ W 50 100FREQUENCY OF TONE 9URSTS IN KC
Fig. 2.7. Tuning curves of single auditory nerve fibres in the cat (from Kiang,l965, by permission of the publisher).
teristic frequency (CF) or best frequency of that fibre. Simmons and Linehan (1968) showed that the tuning curve is a reasonable constant measure of the frequency selectivity of a fibre. As regards shape and slope magnitudes, tuning curves correspond with pure-tone masking curves (Small, 1959;
Chistovich, 1971).
Spoendlin (1970) has found that the greater part of audi-tory nerve fibre endings stem radially from single inner hair cells. Therefore, with measurements in the auditory nerve, the probability of innervating an inner hair cell is relativ-ely high. This suggests that activity measured in primary auditory nerve fibres stems from stimulation at a restricted area from the cochlear partition. This idea was also advanced by Goblick and Pfeiffer (1969) when discussing the neural responses to combination-click stimuli, and by Rose et aZ. (1969) in the discussion of fibre responses to stimuli consisting of two tones. In the auditory nerve the fibres are slightly tonotopically organized. The relation between the CF of the fibre and the electrode position shows some system (e.g., , 1965).
A schematic representation of the afferent and efferent 25
2. 5.
acoustical neural pathway is given in Fig. 2.8. In Fig. 2.9 are shown the auditory projection areas of the cerebral cortex (from Neff, 1961t). It would support the place theo-rists (of pitch perception) if a clear tonotopic organization could be shown to exist from primary auditory neurons up to the auditory cortex. Indeed, tonotopy has been found at several levels in the auditory pathway (Rose et a~., 1960; Woolsey, 1960, 1961; Tunturi, 1960; Hind et a~., 1960; Evans, 1968; Aitkin et a~., 1970). The original findings of Woolsey and Walzl in 1942 and Tunturi in 1952 led to the conclusion that there existed a projection of the cochlea on to the cortex. At present there are serious objections to this view (Evans, 1968). The former experiments were carried out under deep anaesthesia. Later experiments both under reduced and without anaesthesia indicated that the frequency representation in the auditory cortex is less cate-gorical. Behavioural studies of Neff et al. (see, e.g., Neff, 1960, 1961, 1968) showed that after bilateral ablation of those areas of the cerebral cortex that receive projection from the GM (regions AI, AII, Ep, and I-T; Fig. 2.9), a cat is able to learn to respond to changes in frequency. This finding undermined the notion that the tonotopic organization of the auditory cortex is the only cue serving for the fre-quency analysis. Gersuni (1971) pointed out that the differ-ence in duration of stimulus in either physiologic or behav-ioural experiments (approx. 10 ms vs 1 s) might be responsible for this fact. The cortical tonotopic organization would in that view mainly be utilized for sounds of short duration.
Under normal hearing conditions the tonotopic organization does not seem to improve towards higher levels of the auditory pathway. Galambos (1960) reported cells in the auditory
t The map presented in Fig. 2.9 was based upon earlier electro-physiologic and anatomical studies. Evoked response studies provided new and more complex maps (e.g. Woolsey, 1960). It is to be expected that in the next few years new maps of the audi tory cortex will be produced defined in terms of gross and microelectrode recordings and anatomical experiments (Neff, 1971).
f
--cJ,
'
I I I I.P:
' I / I ; I~o~
~-~c
I --~.,.. .... 'i)
WG I N LL 2. 5.fig. 2.8. Afferent (left)and efferent (right) connections of the auditory pathway. Connections not firmly established anatomically are shown by dashed lines.
DCN, dorsal cochlear nucleus; VCN, ventral cochlear nucleus;
Cb, cerebellum; AO, accessory olive; SO, lateral olivary
nucleus; T, nucleus of the trapezoid body; BN, brainstem motor nuclei; NLL, nuclei of the lateral lemniscus; IC, inferior
colliculus; MG, medial geniculate body; C, cortex (from Whitfield, 1967, by permission of the publisher).
b
fig. 2.9. (a) Auditory projection areas of the cerebral cortex.
AI,II, auditory areas I , I I ; Ep, posterior ectosylvian area;
I-T, insular-temporal cortex; SII, somatic area II; SS,
supra-sylvian gyrus.
(b) Diagram illustrating projection of medial geniculate body (GM) upon different areas of auditory cortex (from Neff, 1961,
2. 5. 2. 6.
TABLE 2.I (after Galambos)
properties of a number of cells from the cortex.
The table shows the percentage of units from the examined population, indicated in parentheses, the responded to the stimuli mentioned.
localisation of cell
units responds AI Ep
% (out of) % (out of)
to some acoust. stim 82 ( 9 6) 60 (68)
in more than 50% of
the trials 62 (96) 31 (68)
to pure tones 70 (88) 44 (61)
broad band stimuli 10 ( 62) 74 (27)
to single click 26 (99) 8 (52)
to noise 66 (41) 20 (59)
cortex that did not respond.to pure tone stimulation. In Table 2.I some of his results from single unit responses in a cat are given. Cells not responding to pure tone stimula-tion have not been observed in the primary auditory nerve. Therefore, the suggestion is advanced that already at a
rather low neural level further handling of information takes place, probably to elaborate an efficient transport of in·-formation.
Finally, we must remark that the demonstration of tono-topy, as found with sinusoidal stimulation, does not provide crucial evidence of either place or periodicity theory, since in the case of a sinusoid, frequency and period are
related. And although a tonotopy would be of help for the of the place theory, data showing no tonotopy are no direct evidence against this theory.
2.6 COMPARISON OF DATA ON AURAL FREQUENCY SELECTIVITY In the preceding sections a number of psychoacoustical and
2. 6.
(peripheral) frequency-resolving power of the ear. The simi-in the results of different experiments advance the suggestion that a common mechanism underlies the different phenomena.
Zwicker et al. (1957) showed the relation between CB and DL
1
,
the latter determined as the just noticeable range offrequency modulation. For their data one has.: CB = 30 x DLf (Fig. 2.5). Other values of DLf (e.g., . 2.2) require a higher value of the proportionality constant (approx. 60). For frequencies above 5 kHz, however, this relation does not cover Henning's data (1966).
Zwicker et al. pointed out also that the CB is related to the mel scale. Within the accuracy of this scale the number of mels per CB is constant and equals approximately 150. Each CB corresponds also to between 1 and 1.5 mm along the human cochlear partition, and innervates approximately 1300 primary auditory neurons (e.g., Greenwood, 1961b; Zwislocki, 1965; Scharf, 1970).
Plomp (1964b} and Plomp and Mimpen (1968) showed a relation between the number of harmonics that can be per-ceived separately .in a complex sound, and the CB. Harmonics of equal amplitude were perceived separately when their mutual distance was at least one CB.
In 1894, Mayer published the results of experiments on the consonance of two tones, generated by tuning forks. The frequency interval required for tonal consonance shows with-in the frequency region from 0.4 to 1 kHz a good correspon-dence (especially the series of ect Mm.S) with the CB. More recently, Plomp and Levelt (1962, 1965) confirmed the relation between. appreciation of tonal consonance and the CB.
Goldstein (1967) has assumed that the auditory analysing filter may be approximated by a trapezoidally shaped band-pass filter, thus bringing CB (band-pass-band) and filter slopes as expected from pure-tone masking and tuning curves in one picture. At present (e.g., Zwicker, 1971; Chistovich, 1971), assumptions converge to the notion that CB and pure-tone masking as well as tuning curve are related to different
2.6.
characteristics of the same cochlear filter (see Ch. 4). The slopes of this filter reflect both the slopes of the tuning curve and the pure-tone masking curve (cf. Fig. 2.3,
2.4 and . 2.7). The filter slopes increase with the centre frequency. Therefore the relative bandwidth"of .the filters is not exactly constant, but it decreases with in-creasing centre frequency. This means that the postulated cochlear filter is sharper than would be expected on the basis of results of direct observations of cochlear movement by Bekesy (1960) as well as by Johnstone et al. (1970), as was pointed out by Evans and Wilson (1971) (see also Evans, 1970a,b, and Evans et al., 1970). The results of Rhode's experiment, however, thus far seem to be in better agreement with a highly selective cochlear filter.
3.1 INTRODUCTION
Chapter 3
TIME ANALYSIS
In auditory analysis two main categories are to be
dis-tinguished~ both of which may be entitled time analysis. The
first is the analysis of temporal order, in which time inter-vals are perceived. The other covers the phenomena based on the detection of characteristics from the time pattern of the
(cochlear filtered) stimulus~ which characteristics give rise to perception of, for instance, pitch or direction.
In the auditory system we are dealing with a cochlear fre-quency separation (Ch. 2), which results in stimulation of the auditory receptor cell by a modified stimulus. Because the frequency separation always precedes a time analysis of an auditory stimulus, the time analysis can only partly be considered a pendant of frequency analysis. In man, the cochlear frequency separation is active in the frequency region of about 20 Hz to 20 kHz. At slower fluctuations the perception of time becomes more prominent.
The auditory receptor cells transform the stimulating waveforms into spike signals and can be considered analogue-to-digital converters. A current question is Whether the re-lation between the times at which are generated and the time pattern of the stimulating waveform does not only provide information on the functioning of the receptor cell, but is also of relevance to the theory of pitch perception.
The alternative to the place theory of pitch perception and especially to its importance to auditory frequency analy-sis, is an analysis of the cochlear stimulating waveform in the time domain, as proposed in the periodicity theory. Several authors have pointed out the possibility that a correlation process occurs in the nervous system (e.g.,
3.1.
The possibilities of a digital correlator are determined by the stochastic properties of the digital signal, the sample
in~erval (bandwidth), and the characteristic times that play
a part in the coincidence process among which the time avail-able for the correlation. The quality of a correlator may be inferred from the output signal-to-noise ratio (SNR).
Generally, the output SNR increases monotone with the input_ SNR, with the correlation time and with the sampling fre-quency f (Peek, 1967). In the nervous system the SNR
repre-a
sents the ratio between responding (synchronized) activity and spontaneous activity, is related to the latency of the auditory system, and the sampling frequency or bandwidth is related to internal jitter.
Despit~ the noisy character of the neural spike patterns,
the possibility of giving a accurate
descrip-tion of pitch with a correlation seems
available. Siebert (1970) calculated, under some further conditions, that optimal use of neural time informa-tion would lead to a very low DL
1. Adaption of correlation
time T
0 and jitter might increase this prediction to a reasonable value (Ch. 6).
In the next section (sec. 3.2) attention is paid to periodicity . In this phenomenon time intervals of approx. 0.2 ms to 10 ms play a part. Both monaural and binau-ral periodicity pitch are mentioned. In the present study no attention is paid to binaural directional hearing. The role of temporal structures in the stimulus material is elu-cidated further with neurophys literature data in Sec.
3.4. In Ch. 6, where a description is given of the
process of the auditory receptor cell, we will go further in-to the of the time stucture in the spike_pattern in auditory nerve fibres and its relevance to
processing.
auditory The of temporal order, in which time i.ntervals of the order of 50 ms and over play a part, falls beyond the scope of this study. But some attention will be to a typical transition region, viz. that where two differ~
3.1. 3. 2. a.
order is no perceptible, while, on the other hand, the succession is slow enough to enable each of the components to be distinguished. Such signals affect each other's audi-bility. Particularly, if one of the is much stronger than the other, the latter will be masked. In that case the separately presented signals are not perceived simultaneously, and i t would be possible to speak of too scanty a time
resolving power (Sec~ 3.3, Ch. 4, Ch. 5).
3. 2 PERIODI.CITY PITCH t
3.2.a Stimuli consisting of relatively few harmonlcs
The ascertainment of the relation between the period of a periodic signal and its pitch dates from before 1843, the year in which Ohm formulated his acoustical law.
The perception of combination tones dates back to the eighteenth century (see, e.g., Plomp's review, 1965), as does the suggestion to relate the difference tone to the beat period. In 1700 Saveur (cited by Smith, 1749) mentioned that beats faster than 6 per second were no longer percep-tible as such, but that they render a consonance less agree-able. Smith (1749) found that this boundary lay at a higher value, but he confirmed the transition to another phenomenon. He suggested also that the beat tone, arising at higher beat frequencies, was related to the beat frequency. Further exam-ination by e.g., Young (1800) and Konig (1876) has made this hypothesis more explicit.
In the second half of the nineteenth century the 'periodi-1 view met with much opposition from the influential Helmholtz (Sec. 1.1). The difference tone as well as the perception of the other part-tones that were not accompanied by spectral components. was attributed to non-linear distor-tion, which was supposed to occur at the tympanic membrane (Helmholtz, 1869}. Since a stimulus consisting·of a single
t Recent reviews related to this topic were presented by: Ritsma (1970), Schouten (1970), and Small (1970).
3.2.a.
sinuoid does not provide discrimination between frequency and periodicity contemplation, convincing arguments in favour of either of the theories always stem from experiments with complex stimuli, i.e., stimuli consisting of more than one spectral component. In Ch. 1 was mentioned the conflict between Ohm (18q3, 1844) and Seebeck (1841, 1843, 1844a,b). Seebeck's objection against Ohm's law concentrated on the following points. First, he judged it premature to assume that the components into which the ear can analyse a complex sound, were sinusoidal vibrations. Further, he ascertained from his observations that, if a periodic signal is imagined decomposed into its Fourier components, the high harmonics in the Fourier series amplify the fundamental in loudness, apparently on the basis of their common period which corres-ponds with the fundamental. A hundred years later on the grounds of his observations on periodic pulse-shaped signals, Schouten (1940a) discriminated between the fundamental, which is discernable as a pure part-tone, and the residue, which has the pitch of the fundamental, but deviates from it by its sharp timbre (see also Ch. 1). After demonstration of the first effect of pitch shift (Schouten, 1940c) it was evident that the pitch the residue was neither determined exactly by the period of the signal envelope, nor by the difference tone, although in the harmonic residue these quantities coincide.
Subsequent work fitting into this context comprises the experiment of Mathes and Miller (1947) on the pitch of (amplitude) modulated signals. Licklider (1956) in a masking experiment showed that a residue and a pure-tone having equal pitch arise from different spectral regions, and therefore can be masked selectively by different maskers.
In 1956, De Boer demonstrated that five spectral compo-nents were sufficient to give rise to a residue tone. He confirmed the existence of the first effect of pitch shift and, moreover, showed a deviation from it, which was called the second effect of pitch shift.
Ritsma (1962, 1963) indicated the existence region of the three-component residue. Roughly it is bounded by the values
3. 2. C!·
f ~ 5 kHz, g ~ 60 Hz and n ~ 20. The first and second effects were verified for this complex, and, in accordance with De Boer's hypothesis, the first effect was attributed to the temporal fine-structure of the stimulus (Schouten et al., 1962).
Meanwhile, the smallest residue, viz. that of two spectral components, has been examined by Smoorenburg (1970a,b, 1971a), Sutton and Williams (1970), and Houtsma and Goldstein
(1970a,b). Smoorenburg, and Sutton and Williams, examined the effect of pitch shift (first and second effects) for complexes with a difference frequency of 200 Hz. Fir higher values of n (approx. n ~ 5) the pitch shift is significantly greater than expected on the basis of the fine-structure of the stimulus (which explains the first effect only). Thus a distinct second effect is demonstrated. Smoorenburg attributes the second effect of
nation tones.
shift to the influence of
combi-The relevance of the time structure for the residue tone was supported by an in which subjects were asked to match the pitch of QFM signals. The matched values
corresponded with the based on the temporal
fine-structure of the stimulus (Ritsma and Engel, 1964). Repeti-tion of the experiment by other experimenters and with other subjects did not confirm results (Wightman and Smoorenburg, 1971). But possibly we must here take into account the no-ticeable differences that occur between the .responses of
different subjects to complex sounds (Smoorenburg,
1970b).
Ritsma ( 1967) the contributions of different
bands from the spectrum of a stimulus to the residue pitch, He concluded that, if information concerning pitch is available over a wider area of the cochlear partition, the ear uses only iformation from a restricted band out of that area. This band, which is within the existence of the tonal residue, lies
at the region with a (tuning) frequency of 3 to
5 times the fundamental frequency and is termed the dominant frequency region, or more precisely, the dominant frequency ratio.
3. 2. a. 3.2.b.
The dominance principle shows that the residue is most readily perceptible, if it is produced by spectral components that can easily be perceived separately. At n
=
3 to 5, har-monics are more than one CB apart. These low harhar-monics are rather well separated in the cochlear. Therefore, the time pattern which they constitute in the acoustic stimulus will not be represented clearly in the cochlea. It is, therefore, unlikely that the temporal fine structure of the stimulus is represented at a low neural level (nervus VIII). If it is assumed that at a higher neural level in the auditory path-way a proper correlation process takes place between activity of fibres that innervate different places in the organ of Corti, then the perception of the residue at low harmonics can be explained within the framework of the periodicity theory. This correlation process must involve the construction of the least common multiple of the periods of the available har-monics.For the construction of the fundamental out of higher harmonics, one has, as an alternative for the construction of the least common multiple of the periods of the harmonics, the possibility of generating the greatest common divisor of the harmonic frequencies (Schouten et aZ., 1962; Schroeder, 1968).
In fact, Walliser (1969) uses this alternative in his extended place theory of pitch perception. He assumes that the listener on account of his experience with sounds containing many har-monics (speech, music), is capable of reconstructing the fun-damental from the high harmonics. The latter are detected according to the place theory. At the end of this section
(3.2.d) we will return to this point.
After the treatment of stimuli with a decreasing number of spectral components, a number of experiments with broad band stimuli deserve our attention.
3.2.b Broad band stimuli
Miller and Taylor (1948) described the pitch of periodically gated uncorrelated white noise. In this signal consecutive noise pulses contained arbitrary independent time structures.
3. 2 .b.
For a duty cycle t (Fig. 3.1) between 0.1 T and 0.6 T subjects were able to match with reasonable accuracy a pure tone to the repition rate in 40 per cent of the trials, if this rate was below 250 Hz. Similar results were obtained by Small (1955). In the two experiments great differences between the subjects' performances were demonstrated.
~1
0 D
0
t
T
timeFig. 3.1. Envelope of a periodi-cally gated signal with period T and duty cycle t.
Fig. 3. 2. Envelope of a pulse-train together with the same pulse-train which is delayed over a time T.
Pitch effects occuring when some pulse-traint (pulse period T) together with a similar pulse-train but delayed over a timeT, is presented have been investigated by Thurlow and Small (1955), Thurlow (1957, 1958), Small and McClellan
(1962, 1963) and McClellan and Small (1968, 1965a,b, 1966, 1967) (see Fig. 3.2). In the case ofT F T/2, a pitch corre-spending with the delay T was perceptible in addition to the
< T/2, then p
1
=
1/T was dominant; T) was mostly perceived. In the were narrow-band filtered clicks. fundamental ( "'1/T). If Tif T > T/2, then p
2
=
1/(T first experiments the pulsesLater is was demonstrated that with uncorrelated noise pulses
t Pulse is used here in a broad sense, covering all signals for which the duty cycle (envelope) is sm&l with respect to the pulse period.
3. 2. b. 3.2.c.
the 1 delay-pitch 1 was not perceptible, at least much fainter
when the delayed nois.e pulses were correlated to the non-delayed. It was also perceived that an ambivalent pitch shift occurred if the polarity of the delayed pulse-train was
reversed.
Experiments with sound, e.g., noise, and its repetition, delayed overT, gave also rise to the perception of a complex-tone (Fourcin, 1965; Bilsen, 1966, 1967b, 1970; Bilsen and Ritsma, 1967, 1969, 1970). The pitch of this repet tone corresponds to 1/c. Here too, phase reversal of the delayed sound gives an ambivalent pitch, one slightly above the other
below 1/T.
3.2.c Binaural effects
The binaural repetition pitch, perceived by Huggins in 1953, was described by Licklider (1956, 1959). White noise was sent through an all-pass network with a strong shift around
600 Hz. If input and output of the network are presented to the two ears, the heard a faint but unmistakable pitch of approx. 600 Hz. Licklider (1959) verified that this pitch was perceptible in the case of proper phase transitions at frequencies up to 1 kHz.
Fourcin (1970) perceived that a periodicity pitch appears if at least two independent noise sources stimulate the two ears with different interaural delays. If the delays are 0 for the first source and T for the second source, a pitch corre-sponding to aT is perceived. If either of the signals is reversed in phase, the pitch becomes 1/T. Phase reversal in the two channels to one ear gives again rise to a pitch of ac. In this connection, Fourcin remarks that the pitch is best perceived if T varies slightly. (This is commonly expe-rienced when to the periodicity pitch; but also when tracing part-tones in complex signals one is aided by varying the tone traced.)
Further binaural pitch phenomena are described by Houtsma and Goldstein .(1970a,b). They claim that a tone the pitch of the fundamental can be perceived if for instance the
3. 2. c. 3. 2. d.
4th harmonic is presented to one ear and the 5th to the other. point out that this effect indicates that the pitch of the residue is not generated peripherally but centrally. The assumpt:lon in this form is opposed by the fact that in many cases the pitch of the monaural residue is much more pro-nounced than in the binaural situation.
3.2.d Discussion
In Sec. 3.2.a the possibilities of constructing the period-icity pitch as either the least common multiple of periods of high harmonics (periodicity theory) or as the greatest common divisor of the harmonic frequencies (place theory) were men-tioned (e.g., Schouten et al., 1962).
The two theories describe equally well the first and second effects of pitch shift if the role of combination tones of the type (2ft- fhYis taken into account (Smoorenburg, 1970a,b). The pitch shift occurring in experiments with sound plus delayed sound when the phase of the delayed sound is reversed (monaural as well as binaural effects), can be inter-preted in terms of periodicity theory. Thurlow's (1963) argu-ment against this view, stating that polarity reversal of pulse train A or B (filtered at 1 kHz) produced different intervals and therefore gave rise to different pitches in the periodicity theory, which was not observed, is not a closely-reasoned one, because it passes by the ambiguity of the pitch shift as well as the cochlear_ filtering process. Cochlear filtering accomplishes responses at the cochlear partition the rise and decay times of which depend on the place on the partition. Reversal of polarity of one of the two signals produces reversal of the polarity of its cochlear response. This means that the interval T (Fig. 3.2) changes, but because of the greater number of peaks in the cochlear response it can change by +AT as well as by -~T, thus resulting in an ambiguity (cf. Flanagan and Guttman, 1960a, b). The alter-ation AT must equal half a period of the centre-frequency of
t The higher of the two partials is denoted by fh' the other
by
