INDIVIDUAL SUBJECTIVE PREFERENCE OF LISTENERS TO VOCAL MUSIC SOURCES IN RELATION TO THE SUBSEQUENT REVERBERATION TIME OF SOUND FIELDS
Kirishima International Concert Hall,
The purpose of this study is to evaluate individual differences and intraindividual changes of subjective preference of simulated sound field judged by listeners in changing subsequent reverberation time Ts„b using a vocal source. A great deal of effort has been made studying subjective preferences by using music or speech. Subjective preference tests were conducted by changing Ts„b, which is one of the four orthogonal-objective parameters of sound field.
It is well known that subjective preference evaluation of sound fields is accompanied by individual differences [1, 2]. Using results from subjective preference tests in relation to. orthogonal parameters of sound fields, each listener can select his or her optimum seat in a given concert hall . Psychological evaluations in relation to preference of sound fields have been considered by their global results as an average of many subjects and also for each subject [4, 5]. In order to clarify individual differences in subjective preference, intra-individual changes should be investigated. The variations of preference evaluations caused by aging, seasons, time (morning, evening or night), a certain period of time during the repetition of psychological tests, and so on, are considered. As a typical example, a person's hearing level may be affected by aging. In this study, the variation of preference evaluations during the repetition of psychological tests is applied to intra-individual changes.
In a previous study on intra-individual changes in SPL by using a music source , it was found that subjects with large a values (see later for the definition of a) have smaller intra-individual changes than subjects with small ones, and the range of the variation of preferable SPL is small.
Subjective preference evaluations for intra-individual changes are identified by two factors from subjective preference curves obtained from paired-comparison tests as well as their global case and individual differences. One factor is the value at the most preferred parameter, which coincides with the peak of the preference curves. The other is the sharpness of the curve, a, which is an index of the degree of preference; see equation (3). For a unit variation of a parameter, the scale value for a certain subject with a large a value changes more rapidly than that of other subjects with a small a. Procedures for obtaining these parameters are described in the next section.
For vocal music, which is one of the main components of performances in opera houses, this study evaluates listener's individual differences and intra-individual changes in subjective preference to various simulated sound fields. Subjective preference tests were conducted by changing subsequent reverberation time, TS„b, which is one of the four orthogonal parameters that describe subjective preference to sound fields. The value of TS„b is defined by the decay rate of the sound pressure level after arrival of the first reflection until -60 dB. For calculating scale values of tests, a simple method of calculating individual subjective preference was adopted .
2. EXPERIMENTAL METHOD
2.1. CHARACTERISTICS OF A SOUND SOURCE
The sound source used was an initial 6-0 s piece of a solo performance of a soprano single ("O mio babbino caro" from "Gianni Schicchi" composed by G. Puccini) recorded in an anechoic chamber. Values of ce, which is the effective duration of the normalized autocorrelation function (ACF), O(i), of a short-time moving ACF or running ACF (2T = 2-0 s with the interval of 100 ms)  for the initial 6-0 s part of the source reproduced in the listening semi-anechoic chamber, were calculated. The waveform and values of running r'. are indicated in Figures 1(a) and (b) respectively. The short-time moving ACF was calculated in order to obtain the minimum of its running ie, which represents the most rapid movement of music, activating the left cerebral hemisphere . As indicated in Figure 1(c), the running ie is practically obtained by calculating the decay rate extrapolated in the range from 0 dB, at the origin, to - 5 dB. The 2-0 s duration corresponds to the psychological present  and the minimum duration of signals corresponds to response to any subjective attributes. The most preferred Ts„b averaged for a number of listeners can be calculated by using the equation 
[Tsub] p =23(ôe)min.
where (ôe)min is the minimum value of ôe for the source music. The calculation of global preferable subsequent reverberation time [Ts„b] p is about 0-53 s, which is shorter than usual music sources but longer than that of speech signals.
2.2. PSYCHOLOGICAL EXPERIMENT
Paired-comparison tests were conducted in a semi-anechoic room (see Figure 2). With [Ts„b] p taken to be about 0-53s as mentioned above, the subsequent reverberation time Ts„b of the sound field was changed from 0-1 to 1-6 s (see Table 1). The conditions of the other orthogonal parameters were fixed as indicated in Table 1. The initial time-delay gap between the direct sound and the first reflection, At,, was fixed at 14 ms near to the most preferred value [Atl] p (1 - log 10A) (Te)min -_ 16 ms. The IACC is near to unity because the two loudspeakers were set in front of the subjects. The total amplitude of reflections A is kept constant at 2-0. The duration of each stimulus presented to subjects was 6-0 s. The time interval between the two stimuli in a pair was 1-0 s and between each pair lasted 4-0 s.
Figure 2. Experimental set-up of subjective preference tests controlling both the initial time delay gap between the direct sound and the first reflection, dtl, and the subsequent reverberation time, Tsdb.
There are 10
2.3. CALCULATION OF THE SCALE VALUE
used the subjective responses from each subject to calculate the scale values
of preference for each sound field. The procedure for calculating scale values
of preference is outlined in Table 2. The scores for each presented pair are
obtained by giving scores of + 1 and 0 corresponding to positive and negative
/ Si-Sj / Poor = Sj-Si >0 , if Yi=0, =0 if Yi=0
The value of ë corresponds to the average error of the scale value. This should be small enough: for example, less than 10%. The value of Yi represents the score for each alternative judgment.
Another observation is that, when the poorness number is K, satisfying the condition expressed by upper part of equation (6), then the percentage of violations d is defined by
d= 2K/ N(N-1) x 100
3.1. INDIVIDUAL DIFFERENCES AND GLOBAL CASE
The measured results of the scale values of preference as the function of the Tsub for each subject and its global case are indicated in Figure 3. In this figure, different symbols represent the results from each subject, and the bold line represents the averaged value as the global result.
As the sharpness of the curves are found to be different for each side of the preference curves' peaks, two values of a for both sides of the peak are considered as as for Tub < [ Tub] p, m and al for Tsub > [Tsub] p,m in equation (3). The range of most preferred values of subsequent reverberation time [Tsub]p,m obtained for all subjects in the tests was between 0-55 and 122 s. The largest value of as was 2-02 (subject B) and the smallest one was 0-97 (subject F). On the other hand, the largest value of a, was 1104 (subject G) and the smallest one was 1-69 (subject C). The values of a, are always greater than those of as, for all subjects tested without exception. The experimental measurements of [Tsub ] p,m, as, and al for each subject as well as global results are listed in Table 3. The goodness of fit of this model for each subject, expressed using A, in equation (5) representing the poorness of the model for each subject, gives zero except for 0-04 for subject B. The values of din equation (7) were also zero for all subjects except for 0- 1 for subject B. These small values indicate that a consistent model is achieved for this test. Individual difference is found in log([Tsub]p,m / [Tsub]p) (p < 0-05) and as (p < 0-01) by use of analysis of variance (ANOVA), as shown in Table 4. The method of ANOVA is referred to in Appendix II. For example, subject B (as = 2-02 and a, = 7-09) and subject G (as = 1-87 and a, = 1104) show a sharper preference curve than subject D (as = 1-38 and al = 327) and subject F (as = 0-97 and al = 2-12). In the global results obtained in the tests, [Tsub]p,m was -0.78 s, and values of as and al were 1-53, and 524 respectively. This means that for Tsub greater than the most preferred value, preference curves are sharper than those for Tsub less than the most preferred value.
3.2. INTRA-INDIVIDUAL CHANGES
measured results of intra-individual changes of subjective preference for each
subject (A-H) are indicated in Figure 4. In this figure, different symbols
represent the results in every four series of tests performed over three or
four days. Each peak value of the preference curves is shifted to the origin
without losing any information, because a scale value is a relative and a
linear scale. For example,
There are only two curves of both subjects C and H, because the other three sets could not be obtained. The measured results of log([Tsub]p,m / [Tsub]p), as, and cc, for each set are indicated in Figure 5. Subjects with large a values, like subjects B and G, have small intra-individual changes with respect to values of log([Tsub]p,m1 / [Tsub1p),ás. Standard deviations of these factors obtained from each set of tests are listed in Table 5. The values of subjects C and H, with only two sets, are not listed. Subject B (0033) and subject G (0035) have the two smallest standard deviations of all subjects, and subject D (0163) and subject F (0-168) have larger standard deviations. In relation to those of ás and ál, subject B (ás: 0-16; ál: 1-84) and subject G (ás: 026; ál: 1-68) have smaller standard deviations as well as the values of log([Tsub]p,m/[Tsub]p). On the other hand, subject D (ás: 0-61; ál: 321) and subject F (ás: 0-55; ál: 3-67) have larger standard deviations.
Values of both as and al of subjects B and G were greater than those of
the other subjects and have almost the constant values, and these values of
subjects D and
TABLE 5 ,Fig.6
The results of log([Tsub]p,m l [Tsub]p), the values of as, and oc, in every four series for each subject are indicated in Figure 4. On both sides of the peaks, for subjects who have larger a, such as subjects B and G, the standard deviations of log([Tsub]p,m/[Tsub1p) for each set are small. On the other hand, for subjects who have smaller a, such as subjects D and F, the preferable Tsub values are larger: 0-163 and 0-168 respectively.
Relationship between the standard deviations of log([Tsub] p,m/[Tsub] p), as and a, values for each subject (except subjects C and H) are plotted in Figure 6. Subjects with large a values, such as subject B or subject G, have smaller intra-individual changes, so that the standard deviations of preferable T,.b is small. On the other hand, subjects with small a values such as subjects D and F show minor preferences as T,.b changed. This result is similar to that of previous results for SPL .
The value of [Tsub]p calculated by using equation (1) with (ôe)min (= 23 ms) is 0-53 s. For the global subjects, the value of [Tsub]p,m obtained by the tests was 0-78 s, longer than the calculated value.
Subjects with large a values indicate smaller intra-individual changes, so the standard deviation of log([Tsub] p,m/[Tsub] p) is small. On the other hand, subjects with small a values without sharp curves show minor preference as Tsub changed. The averaged value of preferred Tsub for vocal sources was 0.78 s, which is greater than the value (0-53 s) calculated by equation (1). Individual differences are observed in values of log([Tsub]p.m/[Tsub]p) and ás but not in value of ál.
The authors wish to thank Mrs. Mikiyo Setoguchi as a soprano singer for her cooperation in recording source signals. This work is supported by the Ministry of Education, Grant-in-Aid for Scientific Research (C), 9838022, 1998.
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13. L. L. THURSTONE 1927 Pschological Review 34, 273-286. A law of comparative judgment.
For calculating the scale values of preference, a simple method  was used as an approximation for case V of Thurstone's law of comparative judgment . It must be noted that the estimated scale value obtained by this method is smaller than the result estimated by the case V of Thurstone's law, though high correlation coefficient (r = 0-99) was found between the scale values obtained from both methods. The results of two recent psychological tests , including this test with five sound fields show that the correlation ratio becomes about 1-26. This ratio may be mainly changed by the number of sound fields and individual differences.
In this article, the one-way analysis of variance (ANOVA) is adopted in order to evaluate individual differences in relation to the values of factors, log([Tsub]p,m1[Tsub]p), as and a, as shown in Table 4. Its definitions and usage are briefly described here. By use of the ANOVA, significance tests of individual differences are conducted for the each factor which is categorized by each subject as levels.
At first, two hypotheses are set as follows. As the null hypothesis, each group, categorized by each subject, is considered to be sampled from one population. In this hypothesis, an individual difference is reserved. As the alternative hypothesis, each group is considered to be sampled from different populations. In this case, the null hypothesis is rejected and alternative hypothesis is adopted. Hence individual difference is accepted.
The values of F-ratio, F, are given as ratios of between-individuals variance and residual variance, calculated by the following equations:
Here the values of SA and SE are given as a square-sum due to between-individuals variation and residual sum of squares respectively. The values of dfA and dfE are degrees of freedom of between-individuals variation and residual respectively. The F-ratio is a statistical value representing the difference among groups. If the null hypothesis is correct, the expected value of the F-ratio approaches unity, and the individual difference is reserved. If the F-ratio is greater than unity, it is considered that individual differences exists for the factor. Judgments of the tests are estimated by comparison between the F-ratio of samples and the Fp-ratio Fp. The value of Fp can be obtained from the well known F-distribution with dfA, dfE and a significant level as a probability, p. If the F-ratio is smaller than the Fp value, difference among subjects and judgement for significant difference are reserved. If the value of F is greater than that of Fp, difference among subjects can be obtained. In this case, the null hypothesis is rejected and the alternative hypothesis is adopted. The value of p that the F is greater than Fp, is obtained as an upper-sided probability of the F-distribution. Values of p smaller than 0-05 and 0-01 indicate significant differences of each factors among subjects with their probability of 5 and 1 %, respectively.