Some considerations on the mechanism of directional hearing

ON THE MECHANISM OF

DIRECTIONAL HEARING

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAP AAN DE TECH-NISCHE HOGESCHOOL TE DELFT OP GEZAG VAN DE RECTOR MAGNIFICUS DR R. KRONlG, HOOG-LERAAR IN DE AFDELING DER TECHNISCHE NATUURKUNDE, VOOR EEN COMMISSIE UIT DE

SENAAT TE VERDEDIGEN OP WOENSDAG 6 JULI 1960 DES NAMIDDAGS-TE 4 UUR

door

NICO VALENTINUS FRANSSEN

ELECTROTECHNISCH INGENIEUR GEBOREN TE MAASTRICHT

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TECHNISCHE

HOGESCHOOL

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DIT PROEFSCHRIFf IS GOEDGEKEURD DOOR DE PROMOTOR Prof. Dr Ir J. L. VAN SOEST

Het in dit proefschrift beschreven onderzoek is in het Natuur-kundig Laboratorium der N.V. Philips' Gloeilampenfabrieken verricht. Voor de mij geboden gelegenheid tot dit onderzoek en voor de toestemming, de resultaten van dit onderzoek op deze wijze te publiceren, betuig ik de Directie mijn oprechte dank. Van de velen die op een of andere wijze een bijdrage tot het tot stand komen van dit proefschrift geleverd hebben, mag ik wel in het bijzonder Ir Vermeulen danken voor de talrijke besprekingen over dit onderwerp. Verder dank ik ook Drs Wansdronk voor de talrijke discussies.

Ook gaat mijn dank uit naar de velen die zich als proefpersoon bij de metingen beschikbaar gesteld hebben. Een speciaal dank-woord wil ik nog richten aan de Heer Ploos van Amstel, die mij zowel bij de metingen en de bouw der modellen als ook bij het corrigeren van het typewerk en de drukproeven op zo'n voor-treffelijke wijze heeft geassisteerd, aan de administratie van het Natuurkundig Laboratorium voor het typen van het manuscript en aan de tekenkamer van het lichtadvies-bureau voor het verzorgen van de illustraties.

Tenslotte wil ik de N.V. Uitgeversmaatschappij Centrex be-trekken in deze dankbetuigingen voor de wijze waarop dit proef-schrift is verzorgd.

1

Introduction

1

2 A review of theories about directional hearing .

4

3

On the concept of intensity

8

3.l. Introduction

8

3.2. Measurements 11

3.3. Discussion .

14

4

On the influence of the start of tones

21

4.l. Introduction

21

4.2. Observations

₂₂

4.3. Discussion .

26

5 On the mechanism of directional hearing .

28

5.l. Introduction

28

5.2. Description of tbe model .

29

5.3. Some calculations on tbe selectors

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5.4. Tbe determination of direction

39

5.5. Stereopbonic listening .

45

5.6. Discussion .

53

6

On spatial discrimination

55

6.l. Introduction

55

6.2. Measurements

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6.3. Tbe adaptation of tbe model to spatial discrimination .

59

6.4. Tbe projection in space .

62

7

On binaural frequency discrimination

64

7.l. Introduction

₆₄

7.2. Measurements

67

8 Selectivity magnification 8.l. Introduction

8.2. The electrical model

8.3. The binaural frequency analysis 8.4. The Meyer-Schodder curves .

8.5. The Huggins' phenomenon and its consequence . 8.6. Discussion .

9 The perception of pitch and timbre 9.l. Introduction

9.2. The behaviour of the model with respect of pitch and timbre. 9.3. The periodicity-formant diagram

9.4. Disctlssion . Summary Résumé Zusammenfassung Samenvatting References

73

73

76

80

82

87

89 92

92

95 100 104 106 108 110 112 114

colours, sounds, odours, tastes, heat, hardness, etc., I safely conclude that there are in the bodies, from which the diverse perceptions of the senses proceed, certain varieties corres-ponding to them, although, perhaps, not in reality like them; ... "

Descartes sixth meditation (translation by professor John Veitch).

INTRODUCTION

Man's sense of hearing contributes to a bigh degree to his contact with the world around him. When a person is speaking to us, vibrations in the air will reach our ears and they are coded by the hearing and nerve mecha-nism according to a certain system and will give rise to certain associa-tions in our brain. We recognize for instance the voice of the speaker or the words he has spoken, or we rem ark that he is standing at our left-hand side.

Now it appears that the hearing mechanism is of ten hardly incon-venienced by distorsions produced during the transmission of the vibra-tions through the air, although the wave form may sometimes be changed greatly. On the other hand, however, other distorsions, which change the wave form to a much smaller degree, have a large influence on perception. With these facts in view it is rather obvious that the instantaneous ampli-tudes of a vibration do not play an essential part in the coding by the hearing mechanism.

When hearing a tone, generated for example by an organ pipe, we receive a constant impression. Obviously our hearing sense reacts to the envelope of the vibration. However, taking a shorter organ pipe gives an-other tone, so the hearing mechanism does not perceive only the envelope, but also another property of the vibration: the time interval between the zero points, the frequency band or something like that.

"Listening tb a sine wave with a frequency of e.g. 2000 cps and modu-lated with a saw-tooth of e.g. 1 cps, we hear a sound corresponding in pitch to the original sine wave and with an increase and decrease in loud-ness corresponding to the modulation. If the periodicity of this saw-tooth is increased to 200 cps, however, we will perceive a sound with a pitch corresponding to the pitch of a sine wave of 200 cps, a constant loudness and a sharp timbre. Obviously the envelope now gives rise to a pitch perception. Changing the carrier frequency resuIts in a different timbre.

These examples indicate sufficiently that a variation of the presentation may result in a variation of the perception. However, the relation between presentation and perception is not at all clear. The experiments with the modulated sine wave showed, that a certain physical phenomenon can give rise to a completely different perception when tbis phenomenon is

2

-varied in an apparently not essential way. The envelope was perceived

first as a loudness and in the second case as a pitch; the carrier frequency first as a pitch, afterwards as a timbre. The question then arises, what

kind of mechanism can be imagined, wbich gives such different -

appa-rently not related - interpretations of one physical phenomenon.

The directional determination of sound is an important element of hearing. It is rather obvious that the directional hearing is possible be-cause we have two ears and that the direction is determined by the dif-ferences in the sound waves reaching the two ears. We may ask what properties of the sound waves are used for this and how they are trans-lated again in a direction impression. Investigations have shown that level as well as time differences play a part hereby. However, it does not appear necessary that both occur together to give a direction impression. Level or time differences hetween the ears can be introduced artificially, and the influence on the directional hearing of each of them can he deter-mined. Investigations have shown that level and time differences can op-pose each other and that the ultimate directional angle - at least for

small angles - is found by adding the impressions caused byeach

com-ponent separately. Obviously this directional hearing mechanism does not notice that a presentation is unnatural.

In 1933 Fletcher introduced stereophonic reproduction. He started from the idea of hanging a curtain covered with a large number of microphones in the recording hall. A curtain covered with the same num-ber of loudspeakers, each connected with the corresponding microphone might then be hung in the hall, where the sound was reproduced. In tbis way the sound waves in the recording hall might he reproduced exactly in the other room. Since this system is not very suitable for practical use, Fletcher simplified it to a combination of three microphones and three loudspeakers, placed in corresponding positions. Tbis experiment was very successful: transmission of sound, while retaining lts direction, was found to be quite possible. This re sult is rather surprising. For an approximation of the original conception by means of only three microphones and three loudspeakers is so primitiv:e that only a very poor result might be expected. The reason for a good transmission of direction in this way cannot he found then in the recording and reproducing system but probably in the properties of the hearing mechanism. The hearing mechanism is obviously able to combine sounds from various loudspeakers to one sound from a phantom source in an imaginary direction. The question can now be

posed, whether this ability of the hearing mechanism is related to the additivity of time and level differences.

The influence of reverberation on the appreciation of music and the intelligibility of speech is generally known. It is for example characteristic, that the reflections are not perceived separately. Obviously the directional hearing mechanism is blocked by the direct sound and again the question arises, how this phenomenon is related to normal directional hearing.

In this thesis we will study some problems of this kind. We will mainly confine ourselves to the binaural hearing phenomena and will try to relate various phenomena of directional hearing to each other and to explain these relations by means of an electrical hearing model, which reacts to sound rather like the hearing sense. This indicates already that this model is based mainly on the observed hearing phenomena and to a much smaller degree on physiological data. It is rather surprising that the general conception of this model nevertheles seems to be physiologi-cruly possible. However, we must always bear in mind that in any case this model is rather speculative.

In chapter 2 a survey is given on the theories of directional hearing and the related problems of stereophonic reproduction and reverberation.

In chapter 3 we will investigate the concept of intensity in binaural hearing.

In chapter 4 the influence of transients on the directional perception will be discussed. In chapter 5 a model for explaining directional hearing phenomena will be introduced, while chapter 6 will discuss front-back discrimination and projection in space. In chapter 7 the results are given of measurements concerning the influence of binaurally presented fre-quency differences. Chapter 8 extends the model in order to obtain a better agreement with these measurements. Since it seems that this latter model also gives some indications of an explanation about the perception of pitch and timbre, chapter 9 will discuss these possibilities.

CHAPTER 2

A REVIEW OF THEORIES ABOUT

DIRECTIONAL HEARING

Although it is possible to estimate the direction of a familiar sound with only one ear by reason of frequency-dependent diffraction of the sound by the head, the direction of a sound source is normally perceived by means of the two ears. Restricting ourselves to the latter case, we can conclude that there must be some difference, correlated with the direction of the sound, between the sounds, arriving at the two ears.

One of the flrst attempts to account for this, was based on the difference in the sound levels at the two ears [1] [2]. Owing to attenuation of the incident sound by the shadow of the head, the ear that is tumed away from the sound source will generally he acted upon by a lower sound pressure than the other ear. It will be c1ear that this attenuation is small if the wavelengths of the sounds are large compared with the dimensions of the human head.

For this reason Lord Rayleigh formulated a theory [S] in which the difference in phase of the sound waves at the two ears, due to a difference in distance from the two ears to the sound source, is held responsibie for the impression of direction. However, here is a difficulty similar to that arising in the case of level differences. Below a certain frequency the difference in level vanishes, so that direction cannot he determined from level differences; however beyond a certain frequency direction cannot be unambiguously determined according to the phase theory, because a given ph ase difference can then be correlated with any of several directions.

However, a combination of differences in phase and level gives an unambiguous impression of direction for any sound. The dimensions of the human head are responsible for the limitations of directional per-ception in virtue of both level and phase differences, and these limitations start to appear in both cases at about the same frequency. Because the differences in ph ase can give only an impression helow that frequency and the differences in level only above it, their combination makes it possible to determine direction efflciently throughout the frequency range . . However, some adherents of the phase theory, especially Bowlker(4],

have identified the phase angle with the angle of direction. This is clearly wrong, because tbe phase angles are different for sound waves from tbe same direction but of different frequency. On the otber hand, tbere exists a frequency-independent relation between direction and tbe time of arrival of isophasic parts of a sound wave at the two ears. Therefore it seems better to interpret phase differences as time differences.

Now, it is well-known that the direction of noises and pulses can be determined much more easily than -the direction of stationary tones. This supports tbe theory of time differences published by Von Homborstel and Wertheimer [SI, in wbich the time difference between the two sound waves at both ears is held responsible for the directional impression. According to Van Soest and Groot [6] these time differences are re

spon-sible only for the perception of the angle between the ear axis and tbe direction of tbe sound, while it is mainly the level difference that gives information about the elevation of tbe sound source.

Different values of tbe minimum perceptible value for the time

dif-ference are given in the literature. Von Homborstel and Wertheimer[51 give a value of 3 . 1 ()-5 sec .. W orking on the theory of Von Homborstel and Wertheimer, Wilska [7] discriminates 48 perceptible directions within tbe quadrant. On tbe other hand, in sirnilar investigations Van Soest and Groot [81 have found a minimum perceptible angle corresponding witb a time difference of 1 ()-6 sec.. According to Van Soest and Groot the difference between their results and those of Von Homborstel and Wert-heimer was due to the training of the observers.

The importance of the directional perception of sound waves for the appreciation of music has given rise to stereophonic music reproduction. For some time past the stereophonic long-playing record and the light-weight pick-up have provided this stereophonic reproduction in a con-venient form for the general public. Investigations have shown that it is not necessary to reproduce exactly the original sound waves, nor to use separate loudspeakers for each direction. The human hearing mechanism is able in certain circumstances to combine sirnilar sounds from various directions into one sound from one apparent direction irrespective of whether a real sound source is radiating from that direction. Hence the most simplified system, that could possibly be expected to give some in-formation about direction must use at least two loudspeakers, fed with two signals, differing in sound level or time of arrival.

De Boer [9) has investigated the influence of time and level differences on the apparent position of the sound image and found that each is capable, by itself, of giving a directional impression; bis experiments

6

-showed moreover that a deviation produced by a time difference can be compensated by a difference in sound level, that would have produ-ced the same deviation in the opposite sense.

Haas [10) investigated the influence of time differences, much larger than those occurring between the two human ears in natural listening. He found that up to time differences of about 50 milliseconds the delayed loudspeaker is not heard at all, but that with larger delays a distinct echo becomes audible. Meyer and Schodder [11] elaborated these experiments by making systematic measurements and their most notabIe result was that with a time delay of about 10 milliseconds the level of the delayed sound may he as much as 5 dB louder without being heard as a separate sound source.

When still more than two identical sound waves with sufficiently small mutual delays are striking the ears from different directions, they are not perceived separately, a fact well-known from the study of room acoustics, where the sound field is built up from many reflections. Such a sound has nevertheless a quite distinct character and many investiga-tors have searched for the criteria which determine its human appre-ciation.

Sabine [12), the founder of scientific room acoustics defined and mea-sured the reverberation time and was able to calculate it as a function of room volume and the quantity of absorbing materiaIs. Although tbis constitutes an important criterion for the appreciation of the quality of an auditorium, it became obvious that it was not a sufficient one and that other criteria were needed. Sommerfield and Gilford [lS) investi-gated irregularities in the reverberation curve; Bolt [14) defined the fre-quency irregularity and Furrer and Lauher [15) recommended the dif-fusion of the frequency characteristic as a useful tooI in the judgment of

. hall acoustics. Schröder [16), however, has shown, that in most cases these criteria only give the reverberation time. Meyer and hls co-workers [17) were the' first to look for a direct correlation between the quality of hall acoustics with the reflections occurring. These investigations are corroborated by the results Vermeulen [18) and Kleis [19) got with ambio-phony: artificial reflections, delayed by electronic means, are diffused in the hall with the aid of a large number of loudspeakers. The direct in-fluence of reflections on the subjective impression of room acoustics then can he shown.

Undoubtedly the appreciation of reverheration time and diffuseness of a hall has a novelty aspect; on the other hand, the optimum values of these quantities are dependent on the kind of sound: speech and

music require different reverberation times. This phenomenon cannot be disregarded as a mere novelty; an explanation for this must be found

in . the processes occurring in the hearing mechanism, when so many

reflections, differing only in time of arrival and sound level are perceived.

In all these instances, in directional hearing as weIl as in stereophonic reproduction, in the perception and appreciation of the acoustics of a hall as weIl as in ambiophony, the individual and the combined effects of time and level differences are obviously fundamental and worthy of study.

CHAPTER 3

ON THE CONCEPT OF INTENSITY

3.1. Infroduction

As we have seen in chapter 2, many investigators have firmly established the influence on directional hearing of both time and level differences between the sounds received by the two ears. When assuming that direc-tional hearing is a physiological perception, the question might be posed, what kind of mechanism can be imagined, which extracts the information about the direction from these parameters in a way analogous to the performance of the human hearing.

If only time differences were relevant, a mechanism might be possible, delaying the first sound, until the signais, supplied by the left and supplied by the right ear are completely coherent and measuring then the time delay, needed for that. If on the other hand only level differences were present, we might think in a similar way of a mechanism, attenuating the loudest signal, until the instantaneous amplitudes are equal. However, under normal circumstances, time differences and level differences occur together. It will be clear, that a combination of delay and attenuation is only suitable, when the signals from the two ears are identical in wave form, because only in that case can they be made completely equal by attenuation and delay. However, the attenuation depends on the ratio of the diameter of the human head to the wavelength and possibly -due to the influence of the concha's - it depends somewhat also on the elevation of the sound source. This means that for stationary complex tones the wave forms of the sounds at the left ear and the right ear are different. Wilska [201 has investigated this for such a complex tone and

has recorded the signals, presented by the two microphones of an artifi-cial head (fig. 1, facing p. 86). It is clear that on account of these diffe-rences in wave form, it will never be possible to equalize the signals from the two ears by delaying and attenuating one of them.

If the complex sounds were analysed into sinusoidal components, the phase and level differences could be evaluated for each component in the manner referred to above. Now, it is well-known that the basilar mem-brane performs a frequency analysis of the sound and thus the wave forms at corresponding parts of the basilar membrane might be more or

less sinusoidal. As Von Békésy [21] has shown, however, the separation

by this frequency analysis is rather poor and obviously insufficient to separate all the harmonies. Therefore it is improbable that a continual comparison of the instantaneous values of the two signals from the left and the right ear is the base for the determination of direction.

On the contrary the use of mean values of the intensities avoids the difficulties, caused by the inequality of the wave forms but as can easily be seen this method has some consequences in the domain of time

dif-ferences. A measurement of mean values implies necessarily an inte-gration time and an accurate evaluation of the time differences will be-come impossible. This contradicts the experience that time differences really influence the perception of direction. It can be concluded there-fore that determination of the intensities by measuring the mean values probably does not occur too.

At first sight there are no objections to the assumption that the deter-mination of intensity takes place by measuring only the peak values of the signals. It has been suggested by Mol [22] that the nerve cells of the

basilar membrane act as peak-value meters. It seems reasonable to suppose that these peaks can be used too for the perception of direction. Then the influence of the time differences remains preserved. For the time difference can he measured as the time interval between two cor-responding peaks, one from the left and one from the right ear.

However, it is a well-known effect of technical peak-value meters, that the indication of a certain peak has some after-effects and diminishes the chance for the next peak to be indicated. Figure 2 shows a simple peak-value meter and in figure 3 the peaks, which are discriminated in a certain case, have been marked. It is clear that the first peak of a signal always will be discriminated because a preceeding peak and therefore its af ter-effect is not present. If the idea about determination of peak values by the hearing mechanism is right, this means that the start of a signal must have a great influence on directional perception and that for sounds of short duration only the first peak may determine the direction,

Fig. 2. Simple circuit for indicating only the peaks of a signa!.

•

- 10

i

r

Fig. 3. The voltages E, U and V of figure 2 as a function of time.

The arrows indicate the peaks which will be discriminated.

because this first can mask the following peaks. If this last effect really occurs, it might be imagined that the signals supplied to the left and to the right ear can be different and nevertheless give a fusion up to one impression, because the difference cannot be recognized after the peak detection due to the masking effect of the first peak.

In general then, it can be said that the necessity of equal wave form of the two signals at the left and the right ear is an essential element for directional hearing by means of instantaneous amplitudes of the sound curves; the absence of any influence by time differences seems typ al for an eventual use of mean values, whereas a large influence of time

diffe-rences, combined with an unimportance of the wave form - at least

under certain circumstances as mentioned above - indicates the peak

values as elements responsible for directional perception.

We have tried to arrange our measurements in such a way that a judgment with regard to these altematives seems possible. As signals in this investigation we have used therefore the response of resonant circuits to step functions. In this way we have got signals with a high first peak followed by several smaller peaks (fig. 4).

Fig. 4. Step function and the response of a resonant circuit to tbis.

3.2. Measurements

The measurements were carried out with the arrangement shown in figure 5. A is a pulse generator, giving two rectangular pulses with a time interval 6.t between them, variabie from zero up to 1 millisecond. The pulse length was so large that the transients at the beginning and at the end of the pulses are heard as separate signais. Only the transients

Fig. 5. Circuit for measuring the influence of differences in level, time of arrival and resonant fre-quency on the location of a

phantom source by binaural

hearing. I A II L L R~

at the beginning were used in the measurements. Further L = 0.43 H, Cl = 0.1 /-lF and C2 can be varied from 0.1 up to 0.5/-lF. Rl and R2

are potentiometers calibrated in dB's. The value of Rs and R4 (6000 n)

takes care that the Q factor of the re sonant circuits is so low that only a few vibrations occur. The pitch cannot be discriminated then and the signals sound like clicks. The sounds presented to the two ears of an observer are independent o~ each other and their intensity can be con-trolled separately with aid of the potentiometers Rl and R2. The loudness was not fixed, but adjusted at will by the observers. In general the loud-ness stood at 40 to 50 dB. The resonant frequency of the circuit L - C2 could be varied with aid of the capacitance C2. Any time difference 6.t could be adjusted between the two sound pulses.

When the interaural time and level differences are zero and equal wave forms are presented to the two ears, a subject listening through headphones ob serves that the two signals are fused up to one sensation in the centre of the head. When a time difference or a level difference is adjusted between the two ears, this fusion is located to one side. A

1 2

-displacement of the sound image due to any level difference can be com-pensated by a time difference in the opposite sense. The latter effect has been investigated quantitatively. For the easy course of the measure-ments the interaural time difference was adjusted by the examiner; the observer controlled the level difference to experience a sensation of fusion in the centre of the head. This has been done for various interaural time differences. Each time difference was presented four times to sixteen observers. The mean values of the required level differences are given in table 1. The observation of this large influence by time differences on the directional perception seems to be sufficient for neglecting the possibility, that the directional hearing mechanism makes use of the mean values of the intensities.

Time Level diff. diff. m.sec. dB 0.00 0.2 0.19 2.6 0.37 4.1 0.56 6.0 0.74 9.6 0.93 11.8 St. deviation dB 2.1 2.6 3.0 3.2 3.6 4.3 TABLE 1

The relation between time and level difference for getting fusion in the middle.

As we have seen, a judgment, whether instantaneous values or peak values of the intensities are essential elements for the discrimination of direction depends on the behaviour of the hearing mechanism in the case of presenting unequally formed signais. Such signals can be ob-tained by varying the resonant frequency of the second circuit with aid of the capacitance C2. When listening to such a combination of non-identical signals, the observer can remark really a fusion of both signals up to one sensation, as we could expect for the case of peak detection but the sound image goes to one side and surprisingly this is not the side of the strongest fust peak. This shift of location, however, can be com-pensated by introducing an additional level difference of opposite sign with aid of the potentiometers Rl and R2. Then the fusion is located again in the centre of the head.

These investigations have been carried out with sixteen subjects; each subject participated four times. The relations between the ratio of the

CZ/CI Level diff.

-

dB 1.0 0.6 1.5 3.5 2.0 5.8 3.0 8.4 4.0 11.2 5.0 13.2 St. 20 log deviation Cz/CI dB

-2.2 0.0 2.4 3.5 2.3 6.0 2.6 9.5 3.1 12.0 3.0 14.0 TABLE 2

Tbe relation between

tbe ratio CdCI and tbe

additional level diffe

-rence for getting tbe fusion in tbe middle. capacitances

edel

and the additionallevel difference for obtaining the fusion again in the centre of the head are given in table 2. Obviously the difference in the levels adjusted by the potentiometers is approxi-mately equal to 20 log

edel.

A third measurement can be done now. When both the influence of interaural time difference on the directional perception as weIl as the influence of variation of the ratio

edel

can be compensated with addi-tional level differences, then time differences and capacitance differences will possibly compensate each other too for getting a fusion in the middle. This experiment has been done in a similar way as the other measurements have taken place. This fusion appears possible; the results have been given in table 3.

Time diff. C2/CI ID.sec. -0.00 0.95 0.19 1.32 0.37 1.64 0.56 2.08 0.74 2.77 0.93 3.58 St. deviation

-0.23 0.54 1.02 1.17 1.95 2.15

I

TABLE 3

Tbe relation between time difference and tbe ratio C2/CI

for getting tbe fusion in tbe middle.

The obvious unimportance of equal wave forms for achieving fusion indicates that the instantaneous amplitudes of the sound curves at the two ears do not play a direct roie in directional hearing. However, the

- 1 4

-fact seems rather surpnsmg that the determination of direction is no more controlled by the peak values directly.

In table 2 we have seen that the additional level difference is approxi-mately equal to the value of 20 log CdCl. This result can be checked by a combination of the values of table 1 and table 3. Obviously tbe results of table 2 have been confirmed, as can be seen in table 4.

Time _C2/Cl diff. m.sec. -0.00 0.95 0.19 1.32 0.37 1.64 0.56 2.08 0.74 2.77 0.93 3.58 3.3. Discussion 20 log CdCl

--0.5 2.4 4.3 6.4 8.9 11.2 Level diff. dB 0.2 2.6 4.1 6.0 9.6 11.8 TABLE 4

The comparison of the level difference and the value 20 log C2/Cl needed for compen-sation of equal time difference.

At first sight, it seems remarkable that the results obtained in table 4 agree in such a surprisingly accurate way with the results of table 2, be-cause the statistical analysis showed a large standard deviation in the results of all the measurements. However, for all measurements the same ob servers have been participated. Calculation sbows that the large value of the standard deviations is mainly caused by the different proper-ties of the observers.

Although in natural binaural hearing time differences and level diffe-rences occur together, it is possible to get a directional impression, that is due to time differences or level differences alone. A simple explanation for these facts can he found in the assumption that the deviations caused respectively by the level differences and the time differences must be added to find the total deviation caused by both occurring together. If 1jJ (,1/, ,1t) is the deviation angle, caused by a level difference ,11 and a time dliference 1:.t, we can describe this - at least for small angles -with the form

Compensation of time differences by means of level differences can he explained in this way, that the deviation, caused by the time difference and an equal deviation with the opposite sign, caused by the level dif-ference, have been added.

Fig. 6. Relation between differen-ces in level and time of arrival for achieving fusion in the centre. The single arrows indicate the standard deviations, the double arrows the individual variations of the observers.

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The results of the measurements, given in table 1, have been plotted in figure 6. The obtained values are marked with dots. Further the stan-dard deviation has been given as weU as the stanstan-dard deviation of the individual variations. The slope of the designed curve has a value of about 13 dBfm.sec .. This means that a shift of the sound image caused by a time difference of 1 millisecond or less can be compensated by a level difference in the opposite sense of 13 dB or a proportional part thereof.

In his thesis De Boer [231 has calculated the interaural time

differen-ces and the interaural level differendifferen-ces for speech as a function of the direction of the sound (fig. 7 and fig. 8). For small angles both the level and the time differences are proportional to the angle of incidence of the sound. Here we find for equal angles a ratio of 15 dBfm.sec .. As this agrees approximately with the value we found for compensation,

- 1 6 -0.9 m.sec

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60

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90 120 150 180 _~.~ deg~es(O} Fig. 7. Influence of the angle of incidence on the time differences between the ears (after K. de Boer).

in other words for equal shlits, this means that at normal directional hearing, time and level dliferences are equally important, at least in the case of short signals and small angles.

Similar measurements have been carried out by David, Guttman and Van Bergeyk [24_{1. Their experiments were performed to obtain curves}

describing the exchangeability of interaural time and level differences for fusion of clicks in the centre of the head, as a function of the sound level. They have found that the exchangeability depends in a rather heavy way on the sound level. This result can be explained by the assumption and measurements have shown that this assumption seems justified -that the speed of pulses, travelling along the nerves, is dependent on the intensity of the stimulus. Furthermore David observed that at a

presen-dB

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8 o JO 60 90 130 150 180 _ degrees IOJ

Fig. 8. Influence of the angle of incidence on the mean values of level differences between the ears for male speech (after K. de Boer).

tation of sounds without time or level differences the sound image did not appear in the centre of the head, but systematically deviated to one side. Our measurements did not show this result, since each observer adjusted the levels previously till middle impression was obtained and this adjustment was considered as the zero-dB point.

The second measurement has given arelation between the value of the ratio CdCl and the level difference. If A.l is the level difference, mea-sured in dB, this relation can be described with the form

Fig. 9. Relation between the ratio of the capacitances and the additio-nal level difference for achieving fusion in the centre. The single arrows indicate the standard devia-tions, the double arrows the indi-vidual variations of the observers. The dotted curve represents the function 20 log C2!Cl. dB

1

6 ~ 8

f)

1/

0 2

/

/ /

/ /

V

/1

V

IJ

V

/1

~

3 5 6

In figure 9 the results of this measurement are shown, including the line 20 log CdCl, and the two standard deviations as defined for figure 6. Let us confine ourselves to the case where the value of the ratio C2/Cl was 5. Compensation of the directional shift was obtained then for a level difference of 13.2 dB. The two signals have been recorded simul-taneously with aid of a double-be am oscillograph, as is shown in figure

10. A recording with aid of the same double-be am oscillograph of the acoustical signals, as transduced by the headphones on artificial ears do

- 1 8

-Fig. 10. Recording on a double-beam oscillograph of two signals which when presented binaurally were fused up to one impression in the centre.

Fig. 11. Recording on a double-beam oscillograph of the signals of figure 10 af ter conversion by headphones on artificial ears.

not reveal any essential differences between the electrical signals and the acoustical output of the headphones (fig. 11).

Obviously the fusion in the centre of the head corresponds approxi-mately with equal slopes at the beginning of the two signais. A simple calculation shows that the slopes at the beginning of the signals are pro-portional to I/Cl and I/C2 respectively. Equal slopes occur obviously for a level difference having the value 20 log C2/Cl. The fusion itself has oc-curred, as we had expected for the case of peak detection, independently of the question, whether the signals had an equal wave form. On the other hand, the fust peak does not seem to have the influence on the direc-tional impression, that we had intended for it. However, equal slopes can be easily converted into equal peaks by differentiation. In our opinion an explanation of directional hearing in terms of peak values looks simpier than one in terms of equal slopes. Especially in the case, that time differences have been added, it seems difficult to explain how they can be compensated by unequal slopes. Therefore we assume for the present, that a differentiation of the signals is carried out by the hearing mechanism and that in this way equal slopes have been converted into equal peaks. This assumption seems justified: various investigators have emphasized a differentiation in the hearing mechanism, although they do not agree on where exactly this takes place. Bauch [25] holds the middle ear responsible for the differentiation; other investigators [26] in the contrary the nerve cells at the basilar membrane. We have investi-gated the influence of a differentiation on signals with equal slope at the beginning. Figure 12 shows the signals of figure 10 af ter differentiation by means of an R -C netwerk with a time constant of 1: = 3 • 10-3 _{sec ..} The equal slopes have been converted into nearly equal peaks, even for this rather large value of the time constant.

Fig. 12. Recording on a double-beam oscillograph of the signals of figure 10 af ter differentiation by means of an R-C network with a time constant of 3· lQ---3 sec.

The third measurement has given arelation between the time diffe-rences and the ratio of the capacitances Cl and C2. Figure 13 shows these results and also the standard deviations as defined above. Tbis measurement is mainly of interest as a check on the results of the other measurements. Combination of the results of the investigation, where time differences and level differences had been used, with the latter, where the same time differences are combined with a variation of the ratio of the capacitances C2 and Cl, gives arelation between level diffe-rences at the one side and the value of this ratio at the other side. These results can be compared with the results of the direct measurement of tbis relation: the agreement of both measurements seems rather good, as can be seen in figure 14.

The observations described in this chapter seem to confirm rather

~/C,

f

Fig. 13. Relation between the time differences and the ratio of the capaci-tances for achieving fusion in the centre. The single arrows indicate the standard deviations, the double arrows the indi-vidual variations of the observers.

4 3

,V

₀

V

V

0.25

V

/

V

V

J

V

U.I> 0.75 lO ._ m$ec

20

-Fig. 14. Theoretical relation between the ratio of capacitances and the addi-tional level differences for achieving fusion in the centre, compared with the measurements of figure 9 and with the combined results of figure 6 and 13.

+

=

measurements of figure 9;

o

= combined results. 6 dB

r '

8 0

/

!

/~

.V+

/+

V

J 5 6

weIl the assumption, that peak values are used for the directional per-ception. This assumption seems furthermore to be supported by other physiological data about hearing. In the following chapters it will be shown that an elegant explanation for the general properties of directional hearing seems possible on the basis of peak detection.

At last it can be mentioned that an interesting fact could be remarked during the investigations described here. When the Q factor of the cir-cuits was enlarged, the duration of the signals thereby being lengthened, fusion did not occur in cases where the natural frequencies of the reso-nant circuits were different. Two different signals could be heard, one in the left ear and the other in the right ear. This possibly indicates that frequency analysis was occurring in the ears, and taking place before the direction of a sound was determined.

ON THE INFLUENCE OF THE START OF TONES

4.1. Introduction

In general the art of drawing is considered as a rather usual expression of human mind. On c10ser inspection, however, it is quite remarkable that we are able to recognize some lines and dots on a paper as repre-senting a house, a tree or a car [271. These lines and dots correspond to

significant points in the original object and with sudden transitions in the original image. The image received by the eyes may apparently he divided in transient lines and areas of constant or nearly constant visual properties. The most consequent application of this curious method of perception may he found in drawing caricatures; the essential elements of afigure, presented by the transient lines, are exaggerated in a grotesque way.

Normal hearing seems based on similar principles. As is well-known the timbres of musical instruments are defined not only by the frequency spectrum of stationary tones, but for a great part too by the start of the tones. The dislike of many organists for electrified consoles is based on the sense of no longer dominating the start of the tones. Another example of the influence of transients on the perception can be found in speech. The importance of consonants exceeds heavily that of vowels for the recognition of speech.

With these facts in view, it is not surprising that similar tbings seem to occur in the directional hearing mechimism. It is well-known for example that we are able to perceive the direction of a sound source in a reverberant room, although the direct sound is only a small part of the total sound energy striking our ears, and that the directions of the various reflections are not perceived consciously at all. This effect is known in the litterature as the precedence effect or the law of the fust wave front [281. It seems that the hearing mechanism is interested mainly

in new features of a sound and that new phenomena (the direct sound) are responsible for the determination of direction of the total sound energy. At fust sight it might be remarked that tbis effect limits the use of a directional hearing mechanism. On the other hand, however, there would he teleologically little sense in a directional hearing mechanism,

- 2 2

-by means of wbich all the reflections could be heard separately with their own directions, for then it would hardly he possible to distinguish the rea! sound source between a lot of phantom sources.

Analyzing sound with damped filters, e.g. a visible-speech appara-tus [291, we can observe that speech or music has a "running spectrum" of frequency bands, wbich remain constant or nearly constant during certain time intervals. Speech, then, may he roughly considered as built up from a number of successive tone pulses. Now it can be expected that the duration of each frequency band is increased by reflections. According to the law of the first wave front tbis increase does not give rise to a separate impression of direction, but accepts the direction of the direct sound. This makes it seem likely that the apparent direction of a single tone pul se is determined in a similar way by the fust sound of tbis tone pulse. In other words the law of the first wave front seems to imply that the direction of a tone pulse is determined by its start.

Tbis hypothesis seems to he confirmed by the investigations of Lach-mund [301, Perekalin [311, and Wilska [321, who emphasized that the di-rection of slowly swelling tones hardly can be determined, but that a distinct start of the tone must necessarily be present for getting the cor-rect dicor-rectional impression. It seems quite possible that at the moment of the start or the end of a tone the time difference between the two ears can be measured in a simple way by the hearing mechanism. There-fore the hypothesis seems rather obvious that the direction of the whole tone pulse is determined for the greater part at the moment of its start. Tbis agrees with the conception that human senses are interested mainly in new phenomena. Applying tbis to the hearing of tone pulses, we might conclude that the beginning as weIl as the end of a tone pulse are more important than the rest and that their influence on directional perception is great.

4.2. Observations

The considerations, unfolded in the introduction to this chapter are based on a speculative extrapolation of the law of the first wave front; it seems desirabie therefore to prove the validity of these considerations. We can imagine that the influence of the start of a tone on the location of such a tone can be studied easily by dividing the tone pulse eiectronically into two parts, one comprising the beginning and the end and the other the

Fig. 15. Circuit for dividing a sinusoidal tone pul se into transients and duration tone.

the law of the fust wave front it might be expected that the whole tone pulse would he heard as coming from the direction of its beginning. A difficulty in this consideration is the definition of a signal, representing the beginning and the end of a tone pulse. At first sight, however, it seems justified to use exponentially decreasing signals as start and end of the tone pulse; the remaining part, called the duration tone, is then defined as the difference between the original tone pulse and these ex-ponential signaIs, calIed the transients.

For a sinusoidal tone pulse the division can be realized with aid of a circuit shown in figure 15. The tone pulse is supplied to a resonance circuit tuned to the carrier frequency of the tone pulse; the voltage across the resonance circuit can be now considered as the duration tone.

Amplifi-Tone pulse

generator

Fig. 16. Circuit for obtaining transients and duration tone.

This apparatus can be adjusted more easily than the apparatus

- 2 4

-cation and subtraction of the duration tone from the original tone pulse gives the transients. For the measurements we actually used a somewhat different circuit, shown in figure 16, wbich was more convenient in ope-ration. A generator generated a tone pulse and its envelope. Both signals were supplied to resonance circuits, tuned to the carrier frequency of the tone pulse. The duration of the transients was about 20 to 40 milli-seconds, and the duration of the tone pulse could he varied between 0.25 and 4 seconds. Each signal was supplied to a loudspeaker, the two loud-speakers being arranged stereophonically (fig. 17).

Fig. 17. Arrangement of the loudspeakers for observing the influence of the transients of a tone on its location.

Listening to the signals in tbis arrangement it was observed that the whole tone pulse seemed to come from the loudspeaker where only the transients sounded, as we would expect from the law of the first wave front. Listening with aid of headphones instead of loudspeakers, however, the law of the first wave front seems to be no longer valid: both signals were heard separately, the one at the left ear and the other at the right ear. This is not caused merely by the use of headphones. For, if an arti-ficial head is put before the loudspeakers and its microphones are con-nected to headphones, an observer listening to the headphones will again

Fig. 18. Rectification of the transients and the duration tone for obtaining complex sounds.

.

~.

Fig. 19. Rectification and filtering of the transients and the du-ration tone for obtaining residue tones.

hear the sound as coming from the direction of the transients.

It is not necessary to confine ourselves to sine waves for observing these effects. It was ascertained that both signals can be rectified, as shown in figure 18, before being supplied to the loudspeakers. Moreover a small high-frequency band can be filtered out of these rectified signals (known as residue tones in the literature) as is shown iJi figure 19. Further-more it was found that it is even possible to intro duce a time difference between the start and the duration tone (fig. 20). This time difference can be increased to about 50 milliseconds before the direction of the duration tone can be distinguished separately.

--+---I~

I

Fig. 20. Introduction of a time dif-ference between the first transient and the duration tone.

- 2 6

-4.3. Discussion

When the angle between the loudspeakers seen by the ob server exceeded about 40 degrees, the direction of the duration tone could be distin-guished separately. The exact value of tbis limit depended on various factors e.g. frequency range, reverberation time of the room and the duration of the transients. Since this is the same result as in the case where headphones were used, tbis means that the circumstances are ob-viously similar in these two cases. In the latter case each ear receives only one signal. When loudspeakers are used, however, each ear receives two signals, one from the left-hand loudspeaker and one from the right-hand loudspeaker. For small angles between the loudspeakers the sound levels at the two ears produced byeach loudspeaker are nearly equal; when this angle is increased, however, the difference between the sound levels at the two ears increases too for each signal. Tbis means that we get a situation more or less equivalent to the case where headphones are used. The phenomena described here suggest that the apparent direction of the duration tone is not deterroined mainly by instantaneous values of time and level differences, but by a previously established directional impression, unless the new situation is sufficiently different from the fust to disturb the original impression. Obviously this behaviour implies a directional memory. Tbis assumption agrees very weIl with the con-ception that peak detection takes place in the hearing mechanism, since peak detection must also entail some sort of memory.

It may now be thought that the transition from the start of a tone to the duration tone does not cause such a new situation if the angle be-tween the loudspeakers is rather small and the transition is therefore not tÇ>o abrupt. If headphones are used on the other hand, there is an abrupt transition from the one ear to the other and so a new direction is observed. observed.

The irivestigations where a time difference was introduced between start and duration tone show that a directional impression is preserved for about 50 milliseconds af ter the end of a sound. However, the addition of the duration tone, although coming from another direction, can lengthen tbis time up to some seconds. In other words the duration tone reinforces the directional impression of the transient, whenever it does not give rise to a new directional impression, corresponding to its own direction. In chapter 5 we will try to explain this rather remarkable phenomenon by means of a model of the directional hearing mechanism.

com-Fig. 21. Complete circuit for mea-suring the influence of the transients of a tone on its location.

plete quantitative description of the phenomena described here. Exact measurements might he carried out with aid of the equipment shown in figure 21. The location of the transients in the head can be controlled

with the potentiometers Rl and Ra. The level dliference between the

two ears for the duration tone can be adjusted with the potentiometers

R2 and R4. The influence of frequency, location of the transients or the duration tone on the apparent location of the duration tone can be studied in this way.

However, such quantitative data were not necessary for our purposes. We have therefore confined ourselves to the general observations and considerations, given above.

CHAPTER 5

ON THE MECHANISM OF

DIRECTIONAL HEARING

S.l. Introduction

Although our knowledge of the method of binaural co-operation is rather poor, an explanation of binaural listening and binaural fusion on a physiological basis seems justified. In 1930 Von Békésy [88] attempted to explain binaural hearing phenomena with aid of a model. In this model the two ends of a line of nerve cells are connected with the ears. The volleys, coming from the ears have a finite propagation velocity in this line. The nerve cells can create two situations reacting on the left-ear signalor on the right-ear signa! respectively; thls depends on whether the left-ear signalor the right-ear signal comes fust. The place on thls line of nerve cells, where the change-over occurs, gives an indication of the direction of the sound.

Sayers and Cherry[ 84] have discussed the mechanism of binaural fusion as a form of statistical operation, based upon the brain's execution of running cross-correlation of the two ear signais. The discrimination of pitch is based on auto-correlation methods. Licklider[ 85] in hls triplex

theory, on the contrary, combines the directional hearing with pitch discrimination in one mechanism. The time pattems of the volleys from both ears are responsible for directional perception. The model of David[ 86] is based on a latency time of the neurons and the dependence of the velocity in the nerves as a function of stimulus intensity.

The problem of studying the hearing mechanism can be divided into two parts. Firstly the conception of a block diagram, based on hearing phenomena and more or less speculative. It 5uggests only the operations, which may take pi ace in the hearing mechanism, without considering the question of how these operations are carried out. The model of Sayers and Cherry is a typical example of thls. Secondly the study of the pheno-menology of the nerve system and the consideration of its possibilities for the conception of a directional hearing mechanism. The model described in this chapter is related to the model of Von Békésy. For the greater part it is based on hearing phenomena and therefore it be-longs to the first category of hearing models mentioned above.

5.2. Description of the model

The main object of this investigation was the conception of a model, that reacts to the direction of sound in the same way as man does. Tbis means that tbis model must be sensitive to time and level differences between the two ears and that it translates again those time and level differences into a directional impression. Further conditions are determined by the requirements that this model must be able to combine sounds of various correlated sources to one stereophonic impression and that it should react to reverberation as we do. Furthermore it may be required that the results of our investigations, described in chapter 3 and chapter 4, correspond to the behaviour of such a model in similar circumstances, i.e. the model must make use of peaks for the determination of the in-tensities, and the influence of the beginning of a tone pulse on its di-rectional impression must be great. It seems obvious that the performance of the model relates the various properties and particularities of the directional hearing to each other in one mechanism, and lastly it is necessary that the essential elements of such a model should not he in contradiction with physiological data of the hearing and nerve mecha-nism. It is instructive to accomplish the conception of such a model by electronic means as far as possible. In our opinion, however, it is not necessary to imitate the properties of the nerve system exactly, as David has done, when it is not known whether and how far these qualities contribute essentially to the directional hearing.

As is known, the basilar membrane analyses the sound in a Fourier-like way, but the separation of the frequency bands is rather poor. Accor-dingly it seems justified to neglect this analysis for the present (in chapter 7, 8 and 9 we shall come back to tbis frequency separation), and to consider the model as connected directly to the two ears.

The model contains two time-delay lines with a retardation of 2'1: sec., one connected with the left ear and one with the right ear. Both these lines are interconnected by a large number of selectors (fig. 22). These selectors have a remarkable property. They get both the left-ear and right-ear signal, but then transfer only one of them in dependence of time and level differences. This takes place in such a way, that the first-coming signal is transferred unless the level of the other signal exceeds the level of the fust by a certain amount, depending on the time differences between the signais. The place where the change-over occurs gives the indication of direction.

Fig. 22. Symmetrical model of the directional hearing mechanism. The left-ear or the right-ear is transferred. Tbe position of change-over from left-ear to

- 3 0

-right-ear signal indicates the di- fR

rection.

where such a change-over occurs when the left-ear and the right-ear signal are equal or nearly equal. Therefore it can be recommended to perform the selectors themselves unsymmetrical in the sense, that each selector receives the left-ear and the right-ear signal but can choose only between one of them or nothing under conditions which are otherwise as mentioned for the first model. Now the indication is given by the change-over from zero to e.g. the right-ear signal. Furthermore the per-formance of the model can be simplified by replacing the divided time delay of one line by one compressed time delay with the value of 2r sec., mounted between the right ear and the right-ear side of the selec-tors and by increasing the other time delay to a value of 4r sec. (fig. 23). The mutual time differences between both signals at each selector remain the same as in the fust model. However, as the time delay for the right-ear sound is compressed in one unit, all the right-right-ear signals, passing the selectors, have the same time pattem and the same form. This means that a simple subtraction mechanism between adjacent output terminals

Fig. 23. Unsymmetrical model of tbe directional hearing mecha-nism. ûnly tbe right-ear signal can be transferred. Tbe position of change-over from zero to right-ear signal indicates tbe di-rection.

Fig. 24. Unsymmetrical model of the directional hearing mecha-nism. By means of a subtracting mechanism the right-ear signal appears only at the output termi-nal corresponding to the perceived direction.

transfers a signa! only at the change-over (fig. 24). At fust sight it might he remarked that this unsymmetrical construction does not satisfy our sense of aesthetics. However, as will be shown in chapter 6, tbis un-symmetry has some advantages for spatia! hearing.

For a better understanding of the functioning of the model it is useful to give an electrical substitution of the selectors. This substitution has been shown in figure 25. Let us assume that the right-ear signa!f~ives first. This signal is rectified by the diode DRl and the result of this

detec-tion is amplified by the D.e. difference amplifier AR' The alternating voltage at the output of this amplifier is rectified again to a

D.e.

voltage on the capacitance CR1. Tbis

D.e.

voltage is transferred via an integrating

circuit RRoz-CR2 and the diodes DR3 and D' R3 to the resistances R Ll and

R' Ll respectively. The diode D_{L l} will be blocked by tbis voltage,. when

the left-ear signa! arrives now. The left-ear signal cannot re ach the diode