Introduction to Acoustics

Concert Hall Acoustics Based on Subjective Preference Theory 10.1 Theory of Subjective Preference for the Sound Field 359
room under investigation:
x2 = log � �
∆t1/[∆t1]p , (10.11)
x3 = log � �
Tsub/ [Tsub] p , (10.12)
x4 = IACC . (10.13)
Scale values of preference have been formulated approximately
in terms of the 3/2 powers of the normalized
objective parameters, expressed in the logarithm for the
parameters, x1, x2 and x3. Thus, scale values are not
greatly changed in the neighborhood of the most preferred
conditions, but decrease rapidly outside of this
range. The remarkable fact is that the spatial binaural
parameter x4 is expressed in terms of the 3/2 powers
of its real values, indicating a greater contribution than
those of the temporal parameters.
Limitation of Theory
Since experiments were conducted to find the optimal
conditions, this theory holds in the range of preferred
conditions obtained by the test. In order to demonstrate
the independence of the four orthogonal factors, under
the conditions of fixed ∆t1 and Tsub around the preferred
conditions, scale values of subjective preference
calculated by (10.8) fortheLL with (10.10) andthe
IACC with (10.13) with constants listed in Table 10.2
are shown in Fig. 10.8. Agreement between the calcu-
Scale value of preference
1
0.5
0
–0.5
–1
–1.5
74
IACC
0.39
0.72
0.98
77 80 83
Listening level (dBA)
Fig. 10.8 Scale values of subjective preference for the
sound field with music motif A as a function of the listening
level and as a parameter of the IACC [10.13]. Solid line:
calculated values based on (10.8) together with (10.9) taking
the two factors (10.10) and(10.13) into consideration;
Dashed line: measured values
Table 10.3 Hemispheric specializations determined by
analyses of AEP (SVR), EEG and MEG 1
Factors AEP (SVR) EEG, ratio of MEG, ACF
changed A(P1 − N1) ACF τe values τe value
of α-waves of α-wave
Temporal
∆t1 L>R L>R L>R
(speech) 2 (music) (speech)
Tsub – L>R –
(music)
Spatial
LL R>L – –
(speech)
IACC R>L R>L –
(vowel /a/) (music) 3
R>L
(band noise)
1 See also [10.44] for a review of these investigations
2 The sound source used in experiments is indicated in the
bracket
3 Flow of α-wave (EEG) from the right hemisphere to the left
hemisphere for music stimuli when changing the IACC was
observed by |φ(τ)|max between α-waves recorded at different
electrodes [10.45]
lated and observed values are satisfactory [10.13]. Even
though both LL and the IACC are spatial factors, which
are associated with the right cerebral hemisphere (Table
10.3), these are quite independent of each other. The
same is true for the temporal factors of ∆t1 and Tsub associated
with the left hemisphere. Of course, the spatial
factor and the temporal factor are highly independent.
Example of Calculating the Sound Quality
at Each Seat
As a typical example, we shall discuss the quality of the
sound field at each seating position in a concert hall with
a shape similar to that of Symphony Hall in Boston. Suppose
that a single source is located at the center, 1.2m
above the stage floor. Receiving points at a height of
1.1 m above the floor level correspond to the ear positions.
Reflections with their amplitudes, delay times,
and directions of arrival at the listeners are taken into
account using the image method. Contour lines of the
total scale value of preference calculated for music motif
B are shown in Fig. 10.9. Results shown in Fig. 10.9b
demonstrate the effects of the reflection from the sidewalls
adjusted to the stage, which produce decreasing
values of the IACC for the audience area. Thus the preference
value at each seat is increased compared with that
Part C 10.1