A practical evaluation method of auditory source width in concert halls

This paper investigates how to measure the degree of interaural cross correlation (ICC) as a physical measure of auditory source width (ASW), the just noticeable difference (jnd) of ASW and the estimation equation of ASW in degree for a music motif as a practical evaluation method of ASW in concert halls. Some physical measurements and psychological experiments show the following results. (1) ICC measured without Aweighting using a dummy head without ear simulators agree with spatial impression measured by Barron and Marshall which corresponds to ASW. It is termed DICC, in distinction from IACC measured with A-weighting. (2) Weber's law is applicable to the

Auditory source width (ASW) is one of two characteristics that compose broadening of a sound image.1)The lateral energy fraction Lf,2) and the degree of interaural cross correlation (ICC) are wellknown as physical measures for ASW.The criteria2) and the measurement method3) of Lf have been discussed for its practical use.As a result, Lf is already put to practical use.But, any knowledge necessary for practical use of ICC has not yet been clarified except that ICC has a negative correlation with ASW.
The interaural cross correlation function ƒÓ1r("") is generally defined as: ( where p1(t) and pr(t) are the input signals to the left and right ears, respectively and described as follows.
(3) †Present address: AV & C Research Laboratory, Matsushita Communication Industrial Co., Ltd., Saedo, Tsuzuki, Yokohama, 224 Japan where s(t) is a source signal, r(t) is a room impulse response, h(t) is a head-related impulse response and an asterisk indicates convolution.
As shown in Eqs. ( 1), ( 2) and (3), ICC depends not only on a room impulse response r(t), but also on a source signal s(t) and a head-related impulse response h(t).Therefore, it is impossible to discuss the usefulness of a single number physical measure without limiting source signals, so long as all cues for perception of ASW do not become clear, though one of authors is investigating the estimation method of ASW for any source signal.4)At present, however, even for a limited source signal, there is no practically useful physical measure and criterion based on ICC to evaluate ASW for acoustical designs of concert halls.Most of present data is obtained for narrow band source signals such as 1/1 and 1/3 oct.band noises.5,6) In this paper ASW for a music motif is discussed, since this is the appropriate signal for a concert hall.The following three topics relevant to the practical acoustical design of concert halls are investigated: (1) the measuring method of ICC as a physical measure which is the most useful for ASW for a music motif, (2) the just noticeable difference (jnd) of ASW for a music motif, and (3) the absolute value of ASW in degree for a music motif as functions of ICC and the sound pressure level.However, there are a limitless number of possible music samples.Therefore, which music motif should be selected as a standard one is an important problem to make the results more general.In this paper, Mozart's Symphony No.41 "Jupiter" is used as a standard music motif, since it is an orchestra music composed of various musical instruments and it was used in Barrow and Marshall's experiment from which 1,2) was derived.its 1/3 oct.band spectrum is shown in Fig. 4. Figure 5 shows the amplitudes of the head-related transfer functions (HRTF) from a sound source placed in the front to the left ear of the KEMAR dummy head.The HRTF of the dummy head with artificial ear simulators has a significant resonance caused by the ear simulator around 2.5 kHz (Fig. 5 3).

JUST NOTICEABLE DIFFERENCE OF DEGREE OF INTERAURAL CROSS CORRELATION AS A PHYSICAL MEASURE
FOR ASW An earlier study on just noticeable difference (jnd) of the degree of interaural cross correlation used various noises as source signals.10)But now, ASW for music motif cannot be estimated from the data for noises.In this paper, jnd of DICC as a physical measure for ASW of a music motif is measured as a criterion for practical acoustical design.

Method
The psychological experiment was performed by the constant method, using the paired comparison method between the reference sound field with a fixed DICC and the comparison sound fields with different DICC.

Music motif
The motif used in this experiment was a 6 s section from bar 94 of the 4th movement of Mozart's Symphony No.41 "Jupiter", which was the beginning part of the same motif as used by Barron and Marshal1.2) each series alternatively and separately.Each subject was tested individually, while seated, with his head fixed in a darkened anechoic chamber.The task of the subject was to judge which ASW was wider.

Subject
Eight male students with normal hearing sensitivity acted as subjects for the experiment.(4) where K is Weber's ratio, DICC is a reference field and ADICC is jnd.The ratios for all reference fields can be considered to be almost constant in the range from 0.2 to 0.3.Consequently, Weber's law is applicable to the perception of ASW at least in the region of DICC between 0.5 and 0.9.

FUNCTION OF DEGREE OF INTERAURAL CROSS CORRELATION AND BINAURAL SPL
In most past studies, ASW was only evaluated relatively, namely as "which was wider or narrower?"Absolute values of ASW (angle in degree) seem to be more useful for practical design.Only Keet11) has measured ASW in absolute degrees of angle.But in his measurement, the degree of cross correlation between signals radiated from two loudspeakers was used as a physical measure, in place of the degree of interaural cross correlation between input signals to the left and right ears.The purpose of this measurement is to obtain an equation and a chart for estimation of the absolute values of ASW in degree as variables of DICC and the binaural summation of sound pressure level (BSPL).12)

Method
Two kinds of psychological experiments (A and B) were performed in a darkened anechoic chamber.In Experiment A, the relative values of ASW were obtained and in Experiment B, the absolute values of ASW were measured in degree.

Music motif
The motif used in both experiments was a 6 s section from bar 94 of the 4th movement of Mozart's "Jupiter" Symphony (No.41) , which was the same motif as that used in the experiment on jnd.( where L1 and Lr are the sound pressure levels at the left and right ears, respectively.

Procedure
In Experiment A, a paired comparison test was carried out separately for each BSPL.For each BSPL, the test had 30 pairs of stimuli including reversals.As before, the interval between two stimuli was 1 s.All pairs of stimuli were arranged in random order and separated by an interval of 5 s.Each subject was tested individually and 20 times for each BSPL, while seated, with head fixed.The task of the subject was to judge which ASW is wider.
In Experiment B, eight of 24 stimuli were used to shorten the necessary time of experiment.Their DICC were 0.4 and 0.9 and their BSPL were 50, 60, 70 and 80 dBA.The subject's task was to adjust the position of the shining LED at the both horizontal ends of a sound image which he perceived.The angle in degree between two shining LED was regarded as the absolute value of ASW.The presentation of each stimulus was repeated every 1 s interval until the subject finished his task.The presentation order of different stimuli was random.The interval between different stimuli was 10 s.Each subject was tested individually and 20 times for each stimulus, while seated, with head fixed.4.1.5Subjects Five and seven male students with normal hearing sensitivity acted as subjects for Experiments A and B, respectively.Five males acted as subjects for both experiments.Figure 12 is the chart for evaluation of ASW obtained from Eq. ( 6), that is, the equal ASW contours for various DICC and BSPL.

CONCLUSIONS
For putting the degree of interaural cross correlation (ICC) to practical use as a single number physical measure for evaluation of auditory source width (ASW) in concert halls, the measuring method of ICC, the just noticeable difference (jnd) of ASW and absolute values of ASW (angle in degree) were investigated, using Mozart's Symphony No.41 "Jupiter" as a standard source signal .The results of physical measurements and psychological experiments lead to the conclusions that:

Fig. 4 1Fig. 5
Fig.4 1/3 oct.band spectrum of a music motif used as a source signal in measurements.

Fig. 8 Fig. 9
Fig. 8 Psychological scale of ASW as a function of DICC and as a parameter of BSPL.

Fig. 10
Fig. 10 Absolute value of ASW as a function of DICC and as a parameter of BSPL.

Fig
Fig. 11 Relation between perceived ASW and estimated ASW.

Figure
Figure 11 shows the relation betwen the perceived e

Table 1
jnd of DICC and Weber's ratio with regard to ASW.