Results of the analysis of variance for the scale value SR indicate that both factors the IACC and WIACC contribute to SR independently (p < 0.01), so that

where coefficients α ≈ −1.64 and β ≈ 2.44 are obtained by regressions of the scale values with 10 subjects as shown in Fig. 7.5. This holds under the condition of τIACC = 0. Obviously, as shown in Fig. 7.6, the calculated scale values by Equation (7.4) and measured scale values are in good agreement (r = 0.97, p < 0.01).

Fig. 7.5 Scale values of apparent source width (ASW) for the 1/3-octave band-pass noises with 95% reliability as a function of (a) the IACC and (b) the WIACC. The regression curves are expressed by Equation (7.4) with α = 1.64 and β = 2.44

For each individual listener, the scale value can be calculated by Equation (7.4) in a similar manner. Coefficients α and β in the equation for each listener are obtained by the multiple regression analysis and are indicated in Table 7.1. Figure 7.7 shows the relationship between the measured scale values and the calculated scale values with the constants for each of 10 subjects. The different symbols indicate the scale values of different subjects. The correlation coefficient between the measured and calculated S(ASW) is 0.91 (p < 0.01).

7.2.2 Apparent Width of Multiband Noise

Keet (1968) showed that the apparent source width ASW of sounds depends on the amplitude of coherence between signals fed to the two loudspeakers and their listening level LL. On the basis of our central auditory signal processing model, however, source width may be described in terms of spatial factors extracted from the interaural correlation function IACF (Sato and Ando, 2002). It is assumed that this depends most directly on WIACC, rather than on the spectrum of the source signal per se, and also as well on the interaural correlation magnitude IACC and

Fig. 7.6 Relationship between the measured scale values of apparent source width (ASW) and the scale values of ASW calculated by Equation (7.4) with α = 1.64 and β = 2.44. Correlation coefficient r = 0.97 (p < 0.01)

Table 7.1 Coefficients α and β in Equation (7.4) for calculating ASW of each individual and the correlation coefficient between the measured and calculated scale values of the ASW

binaural listening level LL. It has been reported that even if the IACC is constant, the ASW increases as low-frequency components increase (Morimoto and Maekawa, 1988; Hidaka et al., 1995). The fact that wider source widths are perceived for sound sources with predominately low-frequency components might have a correlate in the behavior of WIACC.

This study examines the apparent source widths of complex noise signals, which consist of several band-pass noises whose center passband frequencies are the harmonics of a fundamental frequency. The question here is whether pitches associated

Fig. 7.7 Relationship between the measured individual scale values of apparent source width (ASW) and the scale values of ASW calculated by Equation (7.4) with each individual value of α and β as listed in Table 7.1, r = 0.90 (p < 0.01). Different symbols indicate data obtained by different individual subjects

with the fundamental frequencies of these noise complexes in some way influence or predict the apparent source widths ASWs of these sounds (Sato and Ando, 2002). Scale values of the ASW for these complex noise signals are compared with those of comparable noise signals with single passbands.

Single band-pass noises with center frequencies of 200, 400, and 800 Hz and multiband complex noises with center fundamental frequencies of 200, 400, and 800 Hz were used as source signals. Each complex noise stimulus consisted of three passbands, and the center frequencies of the lowest passbands were fixed at 1,600 Hz. When the fundamental frequency (F0) was 200 Hz, the three passbands were 1,600, 1,800, and 2,000 Hz. Similarly, for F0 = 400 Hz these were 1,600, 2,000, 2,400 Hz, and for F0 = 800 they were 1,600, 2,400, 3,200 Hz. The amplitudes of all passbands were adjusted to be the same by measuring Φ(0). Bandwidths of the noise passbands in all signals were 80 Hz with a cutoff slope of 2,068 dB/octave.

A single frontal loudspeaker for direct sound (ξ = 0◦) and two symmetrical loudspeakers (ξ = ±54◦) that added reflections were used simulate different source widths in an anechoic chamber (Section 2.3). To produce incoherent sound signals, time delays of reflections t1 and t2 were fixed at 20 and 40 ms, respectively. To reconfirm the effects of listening level LL on apparent source width ASW, the sound pressure level at the listener’s head position was also changed from 70 to 75 dB. The values of the IACC of all sound fields were adjusted to 0.90 ± 0.01 by controlling the identical amplitude of the reflections (A1 = A2). The IACF was measured with two 1/2-in. condenser-type microphones, placed at the ear entrances of a dummy head. The output from the microphones was passed through an A-weighting network and was digitized at a sampling frequency of 44.1 kHz.

Paired-comparisons tests (PCT) using 12 sound fields (6 × 2) were performed on five subjects with normal hearing ability in order to obtain scale values for perceived source width ASW. Subjects were seated in an anechoic chamber and asked to judge which of the two paired stimuli they perceived to be wider. The duration of each sound stimulus was 3 s, the rise and fall times were 50 ms, and the silent interval between stimuli was 1 s. Each stimulus pair was separated by an interval of 4 s and the pairs were presented in random order. Twenty-five responses (five subjects × five repeats) to each stimulus were obtained. Scale values of ASWs were obtained by applying the law of comparative judgment. The relationship between the scale values of source widths ASWs and WIACCs of the source signals is shown in Fig. 7.8. There are significant differences between the scale values of apparent widths of noises with single and multiple passbands (p < 0.01) even when they evoke the same pitch. However, the change in the factor WIACC explains these differences. The results of the analysis of variance for scale values S for apparent source width ASW revealed that the explanatory factors WIACC and LL are significant (p < 0.01) and independent, so that

Fig. 7.8 Average scale values of apparent source width (ASW) as a function of interaural correlation magnitude (IACC) WIACC and as a parameter of listening level (LL). •, band-pass noise, LL = 75 dB; , band-pass noise, LL = 70 dB; , complex noise, LL = 75 dB; , complex noise; LL = 70 dB. The regression curve is expressed by Equation (7.5) with a = 2.40 and b = 0.005

where a and b are coefficients. The powers, 1/2 and 3/2 for the terms of WIACC and LL in Equation (7.5), respectively, were determined to obtain the best correlation between the scale values measured and its calculated value. The curves in Fig. 7.9 confirm the scale values calculated using Equation (7.5) with the coefficient values a ≈ 2.40 and b ≈ 0.005 that were obtained. The correlation coefficient between measured and calculated scale values was 0.97 (p < 0.01).

Fig. 7.9 Relationship between the measured scale values of ASW and the scale values of ASW calculated by Equation (7.5) with a = 2.40 and b = 0.005. Correlation coefficient r = 0.97 (p < 0.01)

It is noteworthy that the above-mentioned scale value of ASW for 1/3-octave band-pass noise is expressed in terms of the 1/2 power of WIACC and that the coefficient for WIACC (β ≈ 2.44) is close to that of this study. The factor WIACC is determined by the frequency component of the source signal, thus the pitch or the fundamental frequency represented by the temporal factor τ 1 is not necessary to describe or predict apparent source width. Results of ANOVA for scale values of ASW indicated that the explanatory factor LL is also significant (p < 0.01). The scale values of ASW increase with an increase in binaural listening level LL, similar to Keet (1968).

Individual differences may be also expressed by the weighting coefficients in Equation (7.5), which are obtained by multiple regression analysis. For each individual, Fig. 7.10 shows the relationship between measured scale values of ASW and those calculated from Equation (7.5) using coefficients a and b (Table 7.2). The different symbols correspond to the different subjects. The correlation coefficient between the measured and the calculated scale values is 0.90 (p < 0.01).

Because the weighting coefficients of (WIACC)1/2 in Equations (7.4) and (7.5) are apparently similar, one can construct a common formula

S = SR = f (IACC) + f (WIACC) + f (LL) ≈ α(IACC)3/2 + β(WIACC)1/2 + γ (LL)3/2 (7.6)

where α ≈ −1.64, β ≈ 2.42, γ ≈ 0.005. It is worth noting that units of scale value of subjective preference even in different subjects and using different source signals appeared to be almost constant (Section 3.3).