(3-1) Method of acoustical estimation
of an auditorium
(3-1-1) Spatial discrimination for sound field
The next paper is on angle discrimination.
It is taken from a few papers and figures are copied from them.
A rectangular pulse of 0.05ms was
generated every one second in the anechoic chamber of our lab. A tested person
was on a rotary chair and asked when he felt that coming direction was changed Seven
center angles were chosen from 0 degree to 180 degrees at every 30degrees to
start with. The chair was rotated clockwise and anticlockwise. The median plane
was 0 degree and the loud speaker was rotated at 1.2 meters away from a tested
person. It is shown in Fig.12.
Eight boy students were tested twice for
each and its average was obtained. The results in Fig.22 are for the clockwise
and anticlockwise. Threshold angle of discrimination for monaural hearing is
given for each center angle in Fig.22 (i), and that for binaural hearing in Fig.22
It is very interesting that the
binaural hearing shows much more sensitive. The cross talk between both ears is
possible to explain it.
The monaural discrimination
threshold is supposed to be given by the change of head-related transfer
function (HRTF). Namely, it was caused by the cross-correlation function
between the HRTF at the center angle and the discriminated angle.
HRTF was measured at the eardrum
of a dummy head at a different incident angle with the rectangular pulse of
0.05ms. The directivity of the HRTF at 30 degrees and 150 degrees is shown in
Fig.14 as examples after it was deconvolved or normalized with the one at the
front incidence. They are shown for the time domain in the left and the
frequency domain in the right.
The transient response of our hearing
system, usually written by R(t), was measured at the front. If R(t) is
convolved with the directivity at an incident angle, the transient response of
our hearing system of the angle is obtained. When directivity is expressed in
the time domain being deconvolved with the front one, it can be clearer to
understand its feature and it is the information enough for the direction.
As the angle discrimination was
caused by the directivity of HRTF, the maximum value of the cross correlation
function Υ12(Ρjbetween the
directivity at a center angle fP(t) and the one at the angle when it was
felt changed, f2 (t)was discussed. It
was normalized by the autocorrelation of f1(t),Σ1(0)and f2(t), Σ2(0)as shown in
the following equation,
whereΣ1(0) is obtained atΡ0 in the next
equation, and the same for
The maximum cross correlation for
each center angle is shown in Fig.15 for clockwise with and counter clockwise with X. It deviates
The result in Fig.15 was obtained
from the experiment in the horizontal level. It is evident that the
discrimination is strongly depending on the directivity of the HRTF. If the directivity of a dummy head
for a different angle is obtained and the space is divided with angles where
cross correlation is 0.98, the spatial discrimination angle will be found.
sound field information on the impulse response is separated in the angle and
then the transient response of hearing system modified to the angle is
convolved to it. The acoustic information is smoothed and easier to discuss
(3-1-2) Visual sound field
It is not enough to have the information
only in the time domain for the evaluation of an auditorium. It must be
discussed with the spatial information. Here is a try to do so which is called
the visual sound field.
of a boundary accompanies edge waves and they give time and spatial
information. When we discuss auditorium acoustics, a sound field must be well
explained to be with. It is tried to see a sound field in the stereoscopic
expression. Using the parallax, an impulse response of a sound field is
observed in the space.
examples of boundary reflection with edge waves are given in Fig.6.
a large and small plane panel, a convex panel, concaved panel and a panel with
reflection coefficient. Amplitude is expressed in the logarithmic scale. A
positive wave is expressed with and a negative with .
fields of a rectangular room of 100x60x150cm3 are shown in Fig.3.
The first reflections, the ones up to the third reflections and the ones up to
the fifth reflections are given. Not only spectular reflections but also edge
waves come out.
example is a sound field of a scale model auditorium whose reflections are up
to the second. There are two pairs for two receiving points.
Here, not only
many specular reflections but also a lot of edge waves are expressed.
It was shown only
for an impulse response of a sound field. It must be convolved with the
transient response of hearing system in the discrimination space.
actual concert hall has complex boundaries. For the sound field calculation, it
must be efficiently abbreviated. Here in Fig.5 is a preparation example of
Boston Symphony Hall for the first reflection calculation.
(3-1-3) Summary for the method of acoustical
estimation of an auditorium
(1) Calculation of the impulse response of
an auditorium to see it in the time domain and spatially
(2) Convolution of the transient response
in a discrimination angle with the directivity-modified HRTF: The space must be
0.98 on the cross correlation.
(3) Integration of its absolute value in
the time window for loudness: 40ms is a temporary time window.
(4) The loudness in each
discrimination angle is calculated every 40ms.
This loudness of reflections is expressed
in the time sequence through the auditorium space.
(5) Using visual sound
field to see the reflections in loudness, its change can be observed from one
seat to another. Reputation of each seat is referred to the visual sound field.
When I got a
sabbatical year in 1985 to 1986, I visited world famous concert halls for
acoustical measurements. The purpose was to find good guidance for a concert
hall design. Firstly the sound fields are simulated and expressed in visual
sound fields, and they are compared with their reputations.
The concert halls I visited for the purpose
were as follows:
Stadt Casino (Switzerland)A
Boston symphony Hall(USA)A
Tanglewood Music Shed (USA),
Teatro Colon (Argentine)