[Technical Field]
[0001] The present invention relates to a three-dimensional sound system, a recording device,
and a reproducing device.
[Background Art]
[0002] In the past, as a method for recording and reproducing a three-dimensional sound,
an ambisonics method has been known. In Non-patent Literature 1, it is explained that
the ambisonics is a method developed into a hierarchical structure from monophonic
to two-channel stereo, horizontal plane surround, and three-dimensional sound based
on the sound incident directional expression, and that the spherical harmonics are
introduced for expression and reproduction of the three-dimensional sound field. In
other words, the ambisonics is a method that an acoustic signal recorded by multichannel
microphones disposed in the sound recording space is hierarchically developed by the
spherical harmonics with respect to the incident direction of the wave front, and
three-dimensional sound reproduction is effected by multichannel loudspeakers disposed
in the sound reproduction space based on the spherical harmonics having been obtained.
[0003] In Patent Literature 1, as an example of the ambisonics method, there are disclosed
a sound field reproduction system and a sound collection method in an actual sound
field, the sound field reproduction system including a sound field reproduction device,
a reduced-scale model, a sound source, and a loudspeaker, the sound collection method
in an actual sound field being, in the format A out of the format A and Format B,
a method of using four pieces of the cardioid type microphones disposed at apexes
of a regular tetrahedron or a method of using a multichannel microphone disposed on
the spherical surface, and in the format B, a method of disposing one each of bidirectional
microphones for x-, y-, and z-axis directions and one piece of an omnidirectional
microphone in the vicinity of the center of the microphone unit, and so on.
[0004] Also, as a method other than the ambisonics method, in Non-patent Literature 2, there
is described a six-channel recording/reproducing system developed as a subjective
evaluation experiment tool for the sound. In Non-patent Literature 2, there are described
that this system is for reproducing a three-dimensional sound field in an experiment
in an experimental laboratory, six pieces of unidirectional microphones combined at
every 90 degrees are used for recording the sound in an actual sound field, six pieces
of loudspeakers are disposed in an anechoic room and reproducing the recording signal
of each direction as a reproduction system, and this system can be expanded to a general
audio recording/reproducing system.
[Citation List]
[Patent Literature]
[Non-patent Literature]
[Summary of Invention]
[Technical Problems]
[0007] With respect to the ambisonics method described in Non-patent Literature 1, there
was a problem that the three-dimensional sound system became complicated and large
in size because of the necessity that the plural microphones in the sound recording
space were increased in number and were disposed closely and the necessity that the
plural loudspeakers in the sound reproducing space were increased in number and were
disposed closely in reproducing the incident direction of the wave front highly precisely
for the sake of reproducing the three-dimensional sound based on the spherical harmonics.
Therefore, since increase of the number of piece of the microphone and the number
of piece of the loudspeaker involved increase of the calculation load of the spherical
harmonics, there was a problem in compatibility of recording and reproduction of the
three-dimensional sound with high realistic sensation and a three-dimensional sound
system that was simple and with less calculation load. Further, there is an auditory
and psychological research outcome that, in a high frequency region, the sensation
of the three-dimensional sound can be explained by parameters such as the interaural
time difference and the interaural level difference as well as the interaural envelope
time difference, and there was a possibility that highly precise reproduction of the
wave front requiring complication and enlargement of the conventional system was not
necessarily an only means in the viewpoint of recording and reproduction of the three-dimensional
sound with high realistic sensation.
[0008] On the other hand, with respect to the system described in Non-patent Literature
2, since the incident directions of the wave front orthogonal in the x-, y-, and z-axis
direction in a Cartesian coordinate system are configured by pairs of the microphone
or loudspeaker in three sets in total of opposing apexes across the center of the
regular octahedron and the incident direction of an optional wave front is expressed
by the vector sum thereof, by reproducing the recorded acoustic signal as it is, the
sound recording space can be reproduced stereophonically simply and with less calculation
load.
[0009] However, in the system described in Non-patent Literature 2, there was a problem
that a sound field different from an actual sound recording space was possibly reproduced
in expressing a sound field radiated from the sound sources of plural numbers of two
or more having high correlation disposed at different positions for the sake of expressing
the incident method of the wave front by pairs of the microphone or the loudspeaker
of three sets in total orthogonal in the space.
[0010] The present invention watched the problems described above, and its object is to
provide a three-dimensional sound system achieving recording and reproduction of a
three-dimensional sound with high realistic sensation simply and with less calculation
load.
[Solution to Problem]
[0011] Although the present invention includes plural systems solving the problems described
above, an example thereof is as follows.
[0012] A three-dimensional sound system of the present invention includes a recording unit
where twelve pieces of microphone are disposed three-dimensionally in a sound recording
space and a reproducing unit where twelve pieces of loudspeaker are disposed three-dimensionally
in a sound reproducing space, the reproducing unit reproduces the sound recording
space based on an acoustic signal recorded by the recording unit, a sound recording
polyhedron configured by connecting disposal points of the twelve pieces of microphone
and a sound reproducing polyhedron configured by connecting disposal points of the
twelve pieces of loudspeaker are of a generally same type, and the shape is a cuboctahedron.
[Advantageous Effects of Invention]
[0013] According to the present invention, since the sound recording polyhedron and the
sound reproducing polyhedron are of a generally same type, the geometric temporal
and spatial information of the sound recording polyhedron included in the recorded
acoustic signal can be reproduced in the sound reproducing polyhedron by reproducing
the acoustic signal as it is or by being subjected to a minor correction.
[0014] Also, according to the present invention, since the incident direction of the wave
front is configured by the pair of the microphone or the loudspeaker of six sets in
total at the apexes opposing each other across the center of the cuboctahedron and
the incident direction of an optional wave front is expressed by the vector sum thereof,
it is possible to express the wave front coming from two sound sources recognizable
by binaural hearing. Accordingly, recording and reproduction of a three-dimensional
sound with high realistic sensation can be achieved simply and with less calculation
load.
[0015] Problems, configurations, and effects other than those described above will be clarified
by explanation of embodiments described below.
[Brief Description of Drawings]
[0016]
[Fig. 1] Fig. 1 is a schematic configuration drawing showing a sound recording polyhedron
and a sound reproducing polyhedron of a three-dimensional sound system related to
the first embodiment and the relationship thereof.
[Fig. 2] Fig. 2 is a perspective view showing an example of a recording device related
to the first embodiment.
[Fig. 3] Fig. 3 is a schematic configuration drawing showing a sound reproducing polyhedron
related to the first embodiment and formed in a sound reproducing space having a rectangular
parallelepiped shape.
[Fig. 4] Fig. 4 is a schematic drawing showing a three-dimensional model related to
the first embodiment and corresponding to a cuboctahedron.
[Fig. 5] Fig. 5 is a schematic drawing showing revolution symmetry of the three-dimensional
sound system related to the first embodiment.
[Fig. 6] Fig. 6 is a schematic drawing showing a covariance matrix related to revolution
symmetry of a 24×24 matrix of the acoustic signal in a sound recording polyhedron
and a sound reproducing polyhedron of the three-dimensional sound system related to
the first embodiment.
[Fig. 7] Fig. 7 is a schematic configuration drawing showing a sound recording polyhedron
and a sound reproducing polyhedron of a three-dimensional sound system related to
the second embodiment and the relationship thereof.
[Fig. 8] Fig. 8 is a schematic drawing showing an expression of a large-scale sound
reproducing space by connection of sound reproducing polyhedrons in the three-dimensional
sound system related to the second embodiment.
[Fig. 9] Fig. 9 is a schematic configuration drawing showing a sound recording polyhedron
and a sound reproducing polyhedron of a three-dimensional sound system related to
the third embodiment and the relationship thereof.
[Fig. 10] Fig. 10 is a schematic configuration drawing showing a sound recording polyhedron
and a sound reproducing polyhedron of a three-dimensional sound system related to
the fourth embodiment and the relationship thereof.
[Fig. 11] Fig. 11 is a schematic configuration drawing showing a sound recording polyhedron
and a dual sound recording polyhedron as well as a sound reproducing polyhedron and
a dual sound reproducing polyhedron of a three-dimensional sound system related to
the fifth embodiment.
[Fig. 12] Fig. 12 is a schematic configuration drawing showing a sound recording polyhedron
and a dual sound recording polyhedron as well as a sound reproducing polyhedron and
a dual sound reproducing polyhedron of a three-dimensional sound system related to
the sixth embodiment.
[Fig. 13] Fig. 13 is a perspective view showing a recording device as a concrete example
of a recording unit of Fig. 12.
[Fig. 14] Fig. 14 is a perspective view showing a reproducing device as a concrete
example of a reproducing unit of Fig. 12.
[Fig. 15] Fig. 15 is a perspective view showing a sound reproducing polyhedron formed
in a sound reproducing space having a rectangular parallelepiped shape of the three-dimensional
sound system related to the sixth embodiment.
[Fig. 16] Fig. 16 is a schematic drawing showing a physical model in a two-dimensional
cross section of an acoustic space filled by a rhombic dodecahedron of the three-dimensional
sound system related to the sixth embodiment.
[Fig. 17] Fig. 17 is an image of an intrinsic mode showing an analysis result of a
two-dimensional acoustic space using the physical model of the acoustic space by the
three-dimensional sound system related to the sixth embodiment.
[Fig. 18] Fig. 18 is a schematic configuration drawing showing a sound recording polyhedron
and a sound reproducing polyhedron of a three-dimensional sound system related to
the seventh embodiment and the relationship thereof.
[Fig. 19] Fig. 19 is a perspective view showing a concrete example of a loudspeaker
enclosure that is a part of a reproducing device of the three-dimensional sound system
related to the seventh embodiment.
[Fig. 20] Fig. 20 is a configuration drawing showing a three-dimensional sound system
of a prior art by the ambisonics method.
[Fig. 21] Fig. 21 is a schematic configuration drawing showing a sound recording polyhedron
and a sound reproducing polyhedron of a three-dimensional sound system of a prior
art employing a regular octahedron as the sound recording polyhedron and the sound
reproducing polyhedron, and the relationship thereof.
[Description of Embodiments]
[0017] The present invention relates to a three-dimensional sound system executing recording
of a three-dimensional sound and reproduction of the three-dimensional sound based
on a recorded acoustic signal as well as a recording device and a reproduction device
used for the three-dimensional sound system.
[0018] In the present embodiment, an embodiment of a three-dimensional sound system related
to the present invention will be explained referring to the drawings. Also, in each
drawing, a same element will be marked with a same reference sign, and duplicated
explanation thereof will be omitted.
[0019] First, the first problem to be solved by the present invention will be explained
in detail using Fig. 20.
[0020] Fig. 20 shows a three-dimensional sound system of a prior art, the three-dimensional
sound system using the ambisonics method described in
[0021] Patent Literature 1.
[0022] As shown in the present drawing, first, a three-dimensional sound system of a prior
art hierarchically develops an acoustic signal 3 by a spherical harmonics with respect
to the incident direction of a wave front using an ambisonics encoder 4, the acoustic
signal 3 being recorded using multichannel microphones 2 disposed in a sound recording
space 1, and an acoustic signal 5 of the ambisonics method is obtained. Next, a reproducing
acoustic signal 8 is generated by an ambisonics decoder 7 so that the acoustic signal
3 recorded in the sound recording space 1 is reproduced in a sound reproducing space
6, and the acoustic signal 3 is reproduced by multichannel loudspeakers 9 disposed
in the sound reproducing space 6.
[0023] Since the incident direction of the wave front is expressed using the spherical harmonics
in the ambisonics method as described above, in reproducing the incident direction
of the wave front highly precisely, it is required that the plural microphones 2 in
the sound recording space 1 are increased in number and are disposed closely to record
the acoustic signal 3 and that the plural loudspeakers 9 in the sound reproducing
space 6 are also increased in number and are disposed closely. Therefore, the three-dimensional
sound system for recording and reproduction becomes complicated and large in size,
and the calculation load of the spherical harmonics in the ambisonics encoder 4 and
the ambisonics decoder 7 comes to increase. Accordingly, there was a problem in compatibility
of recording/reproduction of the three-dimensional sound with high realistic sensation
and a three-dimensional sound system that was simple and with less calculation load.
[0024] Next, the second problem to be solved by the present invention will be explained
in detail using Fig. 21.
[0025] Fig. 21 shows a three-dimensional sound system of a prior art, the three-dimensional
sound system using the method described in Non-patent Literature 2.
[0026] The three-dimensional sound system shown in the present drawing is configured of
a recording unit 10 where six pieces of the microphone 2 are disposed three-dimensionally
in the sound recording space 1 to effect recording and a reproducing unit 12 where
six pieces of the loudspeaker 9 are disposed three-dimensionally in the sound reproducing
space 6 to effect reproduction of the sound recording space 1 based on the acoustic
signal 3 recorded by the recording unit 10. A sound recording polyhedron 11 is configured
by connecting disposal points of six pieces of the microphone 2 which are the recording
unit 10. A sound reproducing polyhedron 13 is configured by connecting disposal points
of six pieces of the loudspeaker 9 which are the reproducing unit 12. Both of the
sound recording polyhedron 11 and the sound reproducing polyhedron 13 are of a generally
same type 52 with a regular octahedron.
[0027] According to the present method, the incident directions of the wave front orthogonal
in the X-axis, Y-axis, and Z-axis directions in the Cartesian coordinate system are
configured by pairs of the microphone 2 or the loudspeaker 9 which are in an opposing
relation 53 across the center of the regular octahedron, and the incident direction
of an optional wave front is expressed by the vector sum thereof. Thus, by reproducing
the recorded acoustic signal as it is, the sound recording space 1 can be cubically
reproduced simply and with less calculation load. On the other hand, when a sound
field radiated from plural sound sources of two pieces or more with high correlation
disposed at different positions was to be expressed, there was a problem that a sound
field different from the actual sound recording space 1 was possibly reproduced.
[0028] In view of these problems, the three-dimensional sound system disclosed in the present
description was created as shown in Fig. 1 explained later in detail as an embodiment
with a basic idea that the number of pieces of the microphone 2 configuring the recording
unit 10 in the sound recording space 1 was made twelve pieces or more, and the sound
recording polyhedron 11 which was geometric disposal and the sound reproducing polyhedron
13 which was geometric disposal of the loudspeaker 9 configuring the reproducing unit
12 in the sound reproducing space 6 were made to have a generally same type 15. Here,
the sound recording polyhedron 11 and the sound reproducing polyhedron 13 are made
to have the generally same type 15 with a polyhedron configured of apexes of twelve
pieces or more namely a cuboctahedron for example configured of apexes of twelve pieces
in order that the wave front coming from two sound sources recognizable by binaural
hearing can be expressed.
[0029] An embodiment will be hereinafter explained using the drawings.
[0030] Also, in the present description, "same type" means a graphical relation including
"congruence" and "similarity" in the mathematical meaning. Further, "generally same
type" means generally "same type". For example, with respect to two corresponding
apexes of two figures, in the polar coordinate (spherical coordinate) with the center
of the gravity of the figure being the origin point, even when the angle formed by
coordinate vectors of the two apexes in question may not be O (zero), two figures
fall into the category of "generally same type". Here, the angle formed by coordinate
vectors of the two apexes in question is preferably 15 degrees or less. Therefore,
when the angle formed by coordinate vectors of the two apexes in question is 15 degrees
or less, in the present description, two figures are to be included in the concept
of "generally same type".
[0031] Further, a term "generally congruent" used in embodiments described below also means
generally "congruent" in a similar manner to "generally same type" described above.
For example, with respect to two corresponding apexes of two figures, in the polar
coordinate (spherical coordinate) with the center of the gravity of the figure being
the origin point, even when the angle formed by coordinate vectors of the two apexes
in question may not be O (zero), two figures fall into the category of "generally
congruent". Here, the angle formed by coordinate vectors of the two apexes in question
is preferably 15 degrees or less. Therefore, when the angle formed by coordinate vectors
of the two apexes in question is 15 degrees or less, in the present description, two
figures are to be included in the concept of "generally congruent".
[First Embodiment]
[0032] Fig. 1 shows a three-dimensional sound system of the first embodiment.
[0033] As shown in the present drawing, the three-dimensional sound system is configured
of the recording unit 10 where twelve pieces of the microphone 2 are disposed three-dimensionally
in the sound recording space 1 to effect recording and the reproducing unit 12 where
twelve pieces of the loudspeaker 9 are disposed three-dimensionally in the sound reproducing
space 6 to effect reproduction of the sound recording space 1 based on the acoustic
signal 3 recorded by the recording unit 10. The sound recording polyhedron 11 is configured
by connecting disposal points of twelve pieces of the microphone 2 of the recording
unit 10. Also, the sound reproducing polyhedron 13 is configured by connecting disposal
points of twelve pieces of the loudspeaker 9 of the reproducing unit 12. Both of the
sound recording polyhedron 11 and the sound reproducing polyhedron 13 are of the generally
same type 52 to a cuboctahedron.
[0034] In the present embodiment, the recorded acoustic signal 3 includes temporal and spatial
geometric information of the sound recording polyhedron 11 related to realistic sensation.
Therefore, when the distortion and the like of the sound recording polyhedron 11 and
the sound reproducing polyhedron 13 are small, the recorded acoustic signal 3 can
be reproduced as it is. Also, when the distortion of the sound recording polyhedron
11 and the sound reproducing polyhedron 13 is large or when the difference in directivity
of the microphone 2 and the loudspeaker 9 is not negligible, by effecting minor correction
related thereto in reproduction, the three-dimensional sound of the sound recording
space 1 can be reproduced in the sound reproducing space 6 simply and with less calculation
load. Also, the incident direction of the wave front is configured by the pair of
the microphone 2 or the loudspeaker 9 of six sets in total at the apexes opposing
each other across the center of the cuboctahedron, and the incident direction of an
optional wave front is expressed by the vector sum thereof. Therefore, it is possible
to express the wave front coming from two sound sources recognizable by binaural hearing.
[0035] Fig. 2 shows a recording device as a concrete example of the recording unit 10 of
Fig. 1.
[0036] In Fig. 2, twelve pieces of the microphone 2 having sharp directivity are disposed
in a microphone holder 17, and each of the microphone 2 is disposed at the apex of
the cuboctahedron. The sound receiving section of the microphone 2 is disposed outward.
The microphone holder 17 is supported by a microphone stand 16. Thus, twelve pieces
of the microphone 2 are disposed radially so as to be of a generally same type with
a cuboctahedron, and incident of the wave front reaching the center of the polyhedron
can be recorded cubically.
[0037] Fig. 3 shows a sound reproducing polyhedron formed in a sound reproducing space having
a rectangular parallelepiped shape.
[0038] As shown in the present drawing, since an ordinary room (sound reproducing space)
such as a living room has a rectangular parallelepiped shape, recorded acoustic signal
is possibly reproduced by the sound reproducing polyhedron 13 that corresponds to
a rectangular parallelepiped shape. Even the shape corresponding to a rectangular
parallelepiped shape is referable to be of a generally same type with a cuboctahedron.
Since the cuboctahedron shown in Fig. 1 is a solid obtained by cutting off eight apexes
of a cube to the middle points of the sides, there is a feature that the sound reproducing
polyhedron 13 is configured easily in a room having a rectangular parallelepiped shape.
[0039] Fig. 4 shows a three-dimensional model corresponding to a cuboctahedron.
[0040] The present drawing shows a closest packed structure where twelve pieces of sound
elements 19 having a spherical shape are contactingly arrayed around a sound element
nucleus 18 that is a sound element having a spherical shape becoming a nucleus.
[0041] When energy is implanted to a certain point of a three-dimensional acoustic space,
a propagation phenomenon of acoustic energy caused by expansion and compression of
a medium occurs around the point. With respect to a minimum configuration element
for expressing such acoustic phenomenon, the sound element nucleus 18 having a spherical
shape is assumed as an implanting point of energy, and the sound element 19 having
similarly a spherical shape is assumed as a propagation object of acoustic energy.
Also, the three-dimensional acoustic space is assumed to be a homogenous field where
the sound element nucleus 18 and the sound elements 19 are closely packed.
[0042] Then, the sound element nucleus 18 and the sound elements 19 come to be disposed
as shown in the present drawing. In this case, the geometric structure configured
by connecting the centers of gravity of the surrounding sound elements 19 becomes
a cuboctahedron.
[0043] In the present embodiment, the three-dimensional sound system is configured thus
based on a cuboctahedron. Therefore, the three-dimensional sound system of the present
embodiment corresponds to a three-dimensional sound model based on a geometric thought.
[0044] Fig. 5 is a schematic drawing showing revolution symmetry of the three-dimensional
sound system related to the present embodiment.
[0045] In the present drawing, a cuboctahedron 20 includes rotation axes 21, 22, and 23
at the face of the regular triangle and the face and the apex of the square. The rotation
axes 21, 22, and 23 are representative examples of the axis. Here, when the positive
direction and the negative directions of the axis are considered, the rotation axis
21 is arranged by four pieces as those passing through the center of gravity of the
face of the regular triangle, the rotation axis 22 is arranged by three pieces as
those passing through the center of gravity of the face of the square, and the rotation
axis 23 is arranged by six pieces as those passing through the apex.
[0046] These rotation axes 21, 22, and 23 express the revolution symmetry axes in the sound
recording polyhedron and the sound reproducing polyhedron of the three-dimensional
sound system. In the three-dimensional sound system of the present embodiment, calculation
utilizing revolution symmetry of a cuboctahedron is possible.
[0047] The cuboctahedron has revolution symmetry transformation of 8 + 9 + 6 + 1 = 24 kinds
which are the total of 8 kinds of revolution (T
1, T
12, T
2, T
22, T
3, T
32, T
4, T
42) of every 120 degrees passing through the center of gravity of the face of the regular
triangle, 9 kinds of revolution (S
1, S
12, S
2, S
22, S
3, S
32, S
4, S
42) of every 90 degrees passing through the center of gravity of the face of the square,
6 kinds of revolution (V
1, V
2, V
3, V
4, V
5, V
6) of every 180 degrees passing through the apex, and the identity transformation I.
[0048] As an example of calculation utilizing this revolution symmetry transformation, three-dimensional
panning is cited first. Here, the present method using the revolution transformation
group is to be called a GBAP (Group Base Amplitude Panning) method.
[0049] The acoustic signal 3 recorded by the recording unit 10 of the cuboctahedron shown
in Fig. 2 is expressed by a following matrix (Expression (1)).
[Math. 1]

[0050] Here, each row corresponds to the acoustic signal 3 recorded by twelve pieces of
the microphone 2, the length n of the column corresponds to the time sample number,
and therefor the matrix X becomes a 12 × n matrix. Here, when one of the revolution
T
1 of every 120 degrees passing through the center of gravity of the face of the regular
triangle is performed to the matrix X, for example, the matrix comes to have such
shape that components of a row are substituted according to the revolution as expressed
by the following expression (2).
[Math. 2]

[0051] Therefore, according to the GBAP method, when an imaginary three-dimensional angle
ϕ [rad] and a maximum three-dimensional angle ϕ
0 = π/3 [rad] are determined based on the middle angle 60 degrees (= π/3 [rad]) of
rotation of 120 degrees, a gain w
I of the matrix X and a gain w
T1 of T
1(X) come to have a relation expressed by the following expression (3) according to
the sine law for example.

[0052] Alternately, a gain w
I of the matrix X and a gain w
T1 of T
1(X) become those having the relation expressed by the following expression (4) according
to the tangent law in a similar manner.

[0053] By either one of them, as natural expansion of the amplitude panning, various three-dimensional
panning by 24 kinds of revolution symmetry transformation can be achieved.
[0054] Next, as another example of calculation utilizing the revolution symmetry transformation,
a covariance matrix related to revolution symmetry of the recorded acoustic signal
3 will be cited.
[0055] Usually, the covariance matrix calculates covariance between the acoustic signals
3 recorded by respective microphones 2, and the result is used for analysis of the
sound recording space and correction of the sound reproducing space for example. However,
its meaning is statistic, and physical interpretation thereof is hard.
[0056] On the other hand, according to the three-dimensional sound system of the present
embodiment, geometric interpretation can be introduced to the value of the covariance
matrix by utilizing the revolution symmetry. That is to say, with respect to the matrix
X of 24 kinds of the acoustic signal 3 to which 24 kinds of the revolution symmetry
are performed, when covariance matrix calculation is executed after each of them is
transformed to a one-dimensional vector, a covariance matrix related to revolution
symmetry of the 24 × 24 matrix is obtained.
[0057] Fig. 6 shows a covariance matrix related to revolution symmetry of a 24 × 24 matrix
in a simplified manner.
[0058] As shown in the present drawing, each component of the matrix shows the variance
relation related to revolution symmetry transformation of 24 kinds of one kind of
identity transformation 24, 8 kinds of revolution 25 of every 120 degrees passing
through the center of gravity of the face of the regular triangle, 9 kinds of revolution
26 of every 90 degrees passing through the center of gravity of the face of the square,
6 kinds of revolution 27 of every 180 degrees passing through the apex. From the variance
relation, geometric interpretation related to revolution symmetry of 24 kinds×24 kinds
can be obtained.
[0059] Thus, even when the sound reproducing polyhedron 13 configured in the sound reproducing
space 6 is configured distortedly with respect to a cuboctahedron as shown in Fig.
3 or even when difference in directivity of the microphone 2 and the loudspeaker 9
is not negligible, for example, by subjecting the covariance matrix related to the
revolution symmetry obtained in the sound reproducing space 6 to geometric correction
so as to agree to the covariance matrix related to the revolution symmetry obtained
in the sound recording space 1, a sound field with high realistic sensation can be
reproduced.
[0060] Further, although explanation was given here with respect to revolution symmetry
transformation as the symmetric operation, according to the three-dimensional sound
system of the present embodiment, as shown in Fig. 5 for example, reflective symmetry
transformation can be utilized by a mirror symmetry plane 352 which is a plane including
the rotation axis 21 passing through the center of gravity of the regular triangle
and the rotation axis 22 passing through the center of gravity of the face of the
cube. Thus, reflection of sound can be expressed, and geometric interpretation with
respect to spatial sound reflection can be obtained by calculating the covariance
matrix with respect to reflective symmetry.
[Second Embodiment]
[0061] Fig. 7 shows a three-dimensional sound system of the second embodiment.
[0062] As shown in the present drawing, the three-dimensional sound system is configured
of the recording unit 10 where fourteen pieces of the microphone 2 are disposed three-dimensionally
in the sound recording space 1 to effect recording and the reproducing unit 12 where
fourteen pieces of the loudspeaker 9 are disposed three-dimensionally in the sound
reproducing space 6 to effect reproduction of the sound recording space 1 based on
the acoustic signal 3 recorded by the recording unit 10. The sound recording polyhedron
11 is configured by connecting disposal points of fourteen pieces of the microphone
2 of the recording unit 10. Also, the sound reproducing polyhedron 13 is configured
by connecting disposal points of fourteen pieces of the loudspeaker 9 of the reproducing
unit 12. Both of the sound recording polyhedron 11 and the sound reproducing polyhedron
13 are of a generally same type 28 with a rhombic dodecahedron.
[0063] In the present embodiment, the incident direction of the wave front is configured
by the pair of the microphone 2 or the loudspeaker 9 of seven sets in total at the
apexes opposing each other across the center of the rhombic dodecahedron, and the
incident direction of an optional wave front is expressed by the vector sum thereof.
Therefore, it is possible to provide an expressive power of the wave front of a case
another one set is added to six sets of the minimum configuration expressing the wave
front coming from two sound sources recognizable by binaural hearing.
[0064] Also, since a rhombic dodecahedron is a dual polyhedron of a cuboctahedron with the
center of gravity of the regular triangle and the face of the square of the cuboctahedron
being made new apexes, with respect to revolution symmetry of the rhombic dodecahedron
has 24 kinds of revolution symmetry transformation similarly to the cuboctahedron.
[0065] Further, a rhombic dodecahedron has a feature that single bodies thereof can pack
the three-dimensional space.
[0066] Fig. 8 shows a state that the three-dimensional space is packed by the rhombic dodecahedrons.
[0067] As shown in the present drawing, when the sound reproducing polyhedron 13 having
a generally same type with a rhombic dodecahedron is assumed in the sound reproducing
space 6, the sound reproducing space 6 can be filled without a gap by connecting 12
pieces of a sound reproducing polyhedron 113 to the periphery of the sound reproducing
polyhedron 13, the 12 pieces of a sound reproducing polyhedron 113 having been translated.
Thus, in reproducing a sound field when a listener physically or imaginarily moves
from the sound reproducing polyhedron 13 to the sound reproducing polyhedron 113 connected
to the periphery of the sound reproducing polyhedron 13, the polyhedrons can be connected
to each other smoothly, and therefore the sound reproducing space 6 having a large
scale can be reproduced.
[Third Embodiment]
[0068] Fig. 9 shows a three-dimensional sound system of the third embodiment.
[0069] As shown in the present drawing, the three-dimensional sound system is configured
of the recording unit 10 where twenty pieces of the microphone 2 are disposed three-dimensionally
in the sound recording space 1 to effect recording and the reproducing unit 12 where
twenty pieces of the loudspeaker 9 are disposed three-dimensionally in the sound reproducing
space 6 to effect reproduction of the sound recording space 1 based on the acoustic
signal 3 recorded by the recording unit 10. The sound recording polyhedron 11 is configured
by connecting disposal points of twenty pieces of the microphone 2 of the recording
unit 10. Also, the sound reproducing polyhedron 13 is configured by connecting disposal
points of twenty pieces of the loudspeaker 9 of the reproducing unit 12. Both of the
sound recording polyhedron 11 and the sound reproducing polyhedron 13 are of a generally
same type 29 with a regular dodecahedron.
[0070] In the present embodiment, the incident direction of the wave front is configured
by the pair of the microphone 2 or the loudspeaker 9 of 10 sets in total at the apexes
opposing each other across the center of the regular dodecahedron, the incident direction
of an optional wave front is expressed by the vector sum thereof, and therefore it
is possible to provide an expressive power of the wave front of a case four sets are
added further to six sets of the minimum configuration expressing the wave front coming
from two sound sources recognizable by binaural hearing.
[0071] With respect to revolution symmetry, the three-dimensional sound system of the present
invention has revolution symmetry transformation of 20 + 24 + 15 + 1 = 60 kinds which
are the total of 20 kinds of revolution of every 120 degrees passing through the apex,
24 kinds of revolution of every 72 degrees passing through the center of gravity of
the face of the regular pentagon, 15 kinds of revolution of every 180 degrees passing
through the middle point of the side, as well as the identity transformation I.
[0072] Therefore, compared to the first embodiment having 24 kinds of the revolution symmetry
transformation, the present embodiment having 60 kinds of the revolution symmetry
transformation enables expression of more sophisticated and complicated three-dimensional
sound by three-dimensional panning by the GBAP method as well as calculation of the
covariance matrix related to the revolution symmetry transformation and analysis thereof.
[Fourth Embodiment]
[0073] Fig. 10 shows a three-dimensional sound system of the fourth embodiment.
[0074] As shown in the present drawing, the three-dimensional sound system is configured
of the recording unit 10 where twelve pieces of the microphone 2 are disposed three-dimensionally
in the sound recording space 1 to effect recording and the reproducing unit 12 where
twelve pieces of the loudspeaker 9 are disposed three-dimensionally in the sound reproducing
space 6 to effect reproduction of the sound recording space 1 based on the acoustic
signal 3 recorded by the recording unit 10. The sound recording polyhedron 11 is configured
by connecting disposal points of twelve pieces of the microphone 2 of the recording
unit 10. Also, the sound reproducing polyhedron 13 is configured by connecting disposal
points of twelve pieces of the loudspeaker 9 of the reproducing unit 12. Both of the
sound recording polyhedron 11 and the sound reproducing polyhedron 13 are of a generally
same type 30 with a regular icosahedron.
[0075] In the present embodiment, the incident direction of the wave front is configured
by the pair of the microphone 2 or the loudspeaker 9 of six sets in total at the apexes
opposing each other across the center of the regular icosahedron, the incident direction
of an optional wave front is expressed by the vector sum thereof, and therefore it
is possible to provide an expressive power for expressing the wave front coming from
two sound sources recognizable by binaural hearing.
[0076] Also, since a regular icosahedron is a dual polyhedron of a regular dodecahedron
with the center of gravity of the regular pentagon being made new apexes, with respect
to revolution symmetry, the regular icosahedron has 60 kinds of revolution symmetry
transformation similarly to a regular icosahedron. Therefore, compared to the first
embodiment having 24 kinds of the revolution symmetry transformation, the present
embodiment achieves three-dimensional panning by more diversified GBAP method as well
as calculation of the covariance matrix related to the revolution symmetry transformation
and analysis thereof.
[Fifth Embodiment]
[0077] Fig. 11 shows a three-dimensional sound system of the fifth embodiment.
[0078] As shown in the present drawing, the three-dimensional sound system is configured
of the recording unit 10 where six pieces of the microphone 2 and eight pieces of
dual microphone 32 (the microphone of fourteen pieces in total) are disposed three-dimensionally
in the sound recording space 1 to effect recording and the reproducing unit 12 where
six pieces of the loudspeaker 9 and eight pieces of dual loudspeaker 35 (the loudspeaker
of fourteen pieces in total) are disposed three-dimensionally in the sound reproducing
space 6 to effect reproduction of the sound recording space 1.
[0079] The sound recording polyhedron 11 which is a regular octahedron is configured by
connecting disposal points of six pieces of the microphone 2 of the recording unit
10. With respect to disposal points of the dual microphone 32 disposed at a center
of gravity 31 of the face of the sound recording polyhedron 11 (including also a point
on a normal line passing through the center of gravity 31 in the face in question),
by connecting those contacting each other by a side, a dual sound recording polyhedron
39 which is a cube is configured.
[0080] The sound reproducing polyhedron 13 which is a regular octahedron is configured by
connecting disposal points of six pieces of the loudspeaker 9 of the reproducing unit
12. With respect to disposal points of the dual loudspeaker 35 disposed at a center
of gravity 34 of the face of the sound reproducing polyhedron 13 (including also a
point on a normal line passing through the center of gravity 34 in the face in question),
by connecting those contacting each other by a side, a dual sound reproducing polyhedron
36 which is a cube is configured. The sound recording polyhedron 11 and the sound
reproducing polyhedron 13 are of a generally same type 14. Also, the dual sound recording
polyhedron 33 and the dual sound reproducing polyhedron 36 are of the generally same
type 14.
[0081] In other words, followings are applicable.
[0082] The sound recording polyhedron 11 configured by connecting the disposal points of
six pieces of the microphone 2 and the sound reproducing polyhedron 13 configured
by connecting the disposal points of six pieces of the loudspeaker 9 are of the generally
same type 14 with each other whose shape is a regular octahedron. Also, the dual sound
recording polyhedron 33 configured by connecting the disposal points of eight pieces
of the dual microphone 32 and the dual sound reproducing polyhedron 36 configured
by connecting the disposal points of eight pieces of the dual loudspeaker 35 are of
the generally same type with each other whose shape is a cube. The cube in question
is in a duality relation with a regular octahedron which is in a relation of a generally
same type with the regular octahedron in question.
[0083] Here, a dual polyhedron which is a polyhedron (the dual sound recording polyhedron
33) in a duality relation with a certain polyhedron (the sound recording polyhedron
11 for example) means a polyhedron formed by that, in a certain polyhedron, the center
of gravity of a face is made a new apex, the centers of gravity of the faces contacting
each other by a side are connected by a side, and a polygon obtained by connecting
the centers of gravity of the faces contacting each other at an apex is made a face.
[0084] The sound recording polyhedron 11 and the dual sound recording polyhedron 33 contact
each other by the sides. Also, the sound reproducing polyhedron 13 and the dual sound
reproducing polyhedron 36 contact each other by the sides.
[0085] In the three-dimensional sound system shown in the present drawing, the sound recording
space 1 and the sound reproducing space 6 are configured by a regular octahedron and
a cube that is a dual polyhedron of the regular octahedron. Therefore, the incident
direction of the wave front is configured by the pairs of the microphone or the loudspeaker
of seven sets in total of three sets of the apexes opposing each other across the
center of the octahedron and four sets of the apexes opposing each other across the
center of the cube, and the incident direction of an optional wave front is expressed
by the vector sum thereof. Accordingly, it is possible to provide an expressive power
of the wave front of a case one set is added further to six sets of the minimum configuration
expressing the wave front coming from two sound sources recognizable by binaural hearing.
[0086] Also, by employing a polyhedron in a duality relation as a reference, it is enabled
to effect recording and reproduction in such manner that the duality relation underlying
an acoustic phenomenon, namely the duality of elasticity accompanying compression
and expansion of a medium and inertia accompanying motion of a medium in an acoustic
phenomenon, can be physically interpreted.
[Sixth Embodiment]
[0087] Fig. 12 shows a three-dimensional sound system of the sixth embodiment.
[0088] As shown in the present drawing, the three-dimensional sound system is configured
of the recording unit 10 where twenty-six pieces of the microphone 2 are disposed
three-dimensionally in the sound recording space 1 to effect recording and the reproducing
unit 12 where twenty-six pieces of the loudspeaker 9 are disposed three-dimensionally
in the sound reproducing space 6 to effect reproduction of the sound recording space
1.
[0089] The sound recording polyhedron 11 which is a cuboctahedron is configured by connecting
disposal points of twelve pieces of the microphone 2 of the recording unit 10. With
respect to disposal points of the dual microphone 32 disposed at a center of gravity
31 of the face of the sound recording polyhedron 11 (including also a point on a normal
line passing through the center of gravity 31 in the face in question), by connecting
those contacting each other by a side, the dual sound recording polyhedron 33 which
is a dual polyhedron of a cuboctahedron is configured.
[0090] The sound reproducing polyhedron 13 is configured by connecting disposal points of
fourteen pieces of the loudspeaker 9 of the reproducing unit 12. With respect to disposal
points of the dual loudspeaker 35 disposed at the center of gravity 34 of the face
of the sound reproducing polyhedron 13 (including also a point on a normal line passing
through the center of gravity 34 in the face in question), by connecting those contacting
each other by a side, the dual sound reproducing polyhedron 36 is configured. The
sound recording polyhedron 11 and the sound reproducing polyhedron 13 are of a generally
same type 37. Also, the dual sound recording polyhedron 33 and the dual sound reproducing
polyhedron 36 are of the generally same type 14.
[0091] Also, the rhombic dodecahedron shown in the present drawing is a spherical rhombic
dodecahedron where its apexes are disposed on a spherical surface 38 having same radii
from the acoustic center.
[0092] Fig. 13 shows a recording device as a concrete example of the recording unit 10 of
Fig. 12.
[0093] In Fig. 13, twelve pieces of the microphone 2 having sharp directivity are arranged
in the microphone holder 17, and each of the microphone 2 is disposed at the apex
of the cuboctahedron. The sound receiving section of the microphone 2 is disposed
outward. The microphone holder 17 is supported by the microphone stand 16.
[0094] Also, fourteen pieces of the dual microphone 32 having sharp directivity are arranged
in the microphone holder 17, and each of the dual microphone 32 is disposed at the
apex of the rhombic dodecahedron. The sound receiving section of the dual microphone
32 is disposed outward. The microphone holder 17 is supported by the microphone stand
16.
[0095] Thus, incident of the wave front coming to the center of the polyhedron can be recorded
in such manner that the duality underlying an acoustic phenomenon can be physically
interpreted.
[0096] Also, for the use of evaluation and the like of the absolute sound pressure of the
sound field to be recorded, an omnidirectional microphone 39 may be arranged at the
acoustic center. Thus, since it is enabled to pick up the absolute sound pressure
by the omnidirectional microphone 39 and to evaluate the physical relation between
arrival of the wave front and the absolute sound pressure by the acoustic signal 3
recorded by the sound recording polyhedron 11 and the dual sound recording polyhedron
33 in the surrounding shown in Fig. 12, the recording device can be utilized for noise
control measures, designing, and the like for example where evaluation of the absolute
sound pressure of the sound field is required.
[0097] Fig. 14 shows a reproducing device as a concrete example of the reproducing unit
12 of Fig. 12.
[0098] In Fig. 14, in a loudspeaker stand 40, twelve pieces of the loudspeaker 9 are disposed
so as to be of a generally same type with a cuboctahedron, and fourteen pieces of
the dual loudspeaker 35 are disposed so as to be of a generally same type with a rhombic
dodecahedron.
[0099] Thus, by reproducing as it is the acoustic signal 3 recorded by the recording unit
10 of Fig. 3 or by reproducing the acoustic signal 3 while being subjected to an operation
by the GBAP method and the like, the three-dimensional sound of the sound recording
space 1 can be reproduced in the sound reproducing space 6 simply and with less calculation
load.
[0100] Fig. 15 shows a sound reproducing polyhedron formed in a sound reproducing space
having a rectangular parallelepiped shape.
[0101] As shown in the present drawing, since an ordinary room (sound reproducing space)
such as a living room has a rectangular parallelepiped shape, recorded acoustic signal
is possibly reproduced by the sound reproducing polyhedron 13 and the dual sound reproducing
polyhedron 36 which correspond to a rectangular parallelepiped shape. Even the shape
corresponding to a rectangular parallelepiped shape is referable to be of a generally
same type with a cuboctahedron and a rhombic dodecahedron. Since the cuboctahedron
is a solid obtained by cutting off eight apexes of a cube to the middle points of
the sides and the rhombic dodecahedron is of a generally same type with a solid obtained
by connecting the eight apexes and the centers of the gravity of the six faces of
a rectangular parallelepiped, there is a feature that the sound reproducing polyhedron
13 is configured easily in a room having a rectangular parallelepiped shape.
[0102] Also, with respect to distortion of the sound reproducing space 6 caused by that
the sound reproducing polyhedron 13 is configured in a room having a rectangular parallelepiped
shape, there is a method for example that the covariance matrix related to the revolution
symmetry as shown in Fig. 6 is calculated in the sound recording space 1 and the sound
reproducing space 6 respectively and the acoustic signal is subjected to correction
so that the both agree to each other.
[0103] Further, the three-dimensional sound system of the present embodiment also has a
feature of corresponding to a physical model of the three-dimensional sound based
on the duality relation between elasticity and inertia.
[0104] Fig. 16 shows a physical model expression in a two-dimensional cross section of an
acoustic space packed by a rhombic dodecahedron.
[0105] The present drawing shows a state that acoustic compliances 42 expressed as springs
extend from an elasticity center 41 in six directions out of twelve directions (also
including those not illustrated because of the two-dimensional cross section) in total.
Between the springs, acoustic inertances 43 expressed as inertia centers are disposed.
That is to say, a polyhedron connecting the elasticity center becomes a cuboctahedron
20, and a polyhedron having a face of the inertia center becomes a rhombic dodecahedron
152. Therefore, the cuboctahedron 20 and the rhombic dodecahedron 152 that is a dual
polyhedron of the cuboctahedron 20 are made to correspond to a physical model of the
three-dimensional sound.
[0106] Since the present model is a physical model, acoustic calculation is possible. For
the sake of simplification, description will made here limiting to two-dimensional
pulsation.
[0107] As shown in the present drawing, the coordinate system of the acoustic calculation
takes three axes of x
1, x
2, and x
3 rotated every 120 degrees.
[0108] First, with respect to a region V surrounded by a closed curved surface S of a cell
(hexagon in the case of two-dimension, and rhombic dodecahedron in the case of three-dimension)
packing the space, the law of conservation of mass is considered. At a certain temporal
point, a mass included in V is expressed by the following expression (5).

[0109] Here, δ is the diameter of the acoustic element, and ρ is the density of the air.
[0110] Therefore, the mass change per a unit volume is expressed by the following expression
(6).

[0111] This mass change is caused by that a sound wave passes through the surface S and
flows in to the region V. Now, a mass flowing out through an area element dS of the
surface S is considered. It is ρv
ndS per a unit volume. However, v
n is a component of the direction of the outward normal line with respect to the surface
S of the particle velocity v, and components of three axes in total are considered
in the two-dimensional model of Fig. 16. The total flow-out amount is expressed by
the following expression (7).
[Math. 7]

[0112] Here, with respect to the surface element of the regular hexagon, the following relational
expression (8) was used.
[Math. 8]

[0113] Therefore, from the expressions (6) and (7) above, the equation of continuity (9)
expressed as described below is obtained.
[Math. 9]

[0114] Next, an equation of motion will be considered. As shown in Fig. 16, the motion of
the acoustic inertance 43 that is the inertia center in each axis x
1, x
2, and x
3 is considered as one-dimension. Therefore, similarly to the case of the one-dimension,
the equation of motion is given by the following expression (10).
[Math. 10]

[0115] Also, for the purpose of numerical analysis, the equation of continuity (9) and the
equation of motion (10) above are discretized. With the elasticity center 41 being
made a sound pressure reference point and the acoustic inertance 43 that is the inertia
center being made a particle velocity reference point, variable names shown in Fig.
16 are given. The inclination of the particle velocity in the equation of continuity
(9) above is discretized as the following expression (11) by the Euler method.
[Math. 11]

[0116] When the expression (11) is substituted to the equation of continuity (9) above for
rearrangement, a discretized equation of continuity (12) below is obtained.
[Math. 12]

[0117] Also, the inclination of the sound pressure in the equation of motion (10) above
is discretized as the following expression (13).
[Math. 13]

[0118] When the expression (13) above is substituted to the equation of motion (10) above
for rearrangement, the following expression (14) is obtained with respect to the x
1 axis direction for example.
[Math. 14]

[0119] As a result, from the expression (12) above and the expression (14) above, a state
space equation (15) below is obtained.
[Math. 15]

[0120] The matrix of the first term of the expression above expresses the accumulation characteristic
of energy in the elasticity and inertia, and the matrix of the first term of the right-hand
side expresses connection of the elasticity and inertia element.
[0121] As an example of numerical analysis, a two-dimensional rectangular acoustic space
expressed by the following expression (16) is considered.
[Math. 16]

[0122] The boundary was assumed to be rigid (the particle velocity was zero), the expression
(15) above having been formulated was merged, and a state space equation of the object
was obtained. Also, the vertical direction and the horizontal direction were divided
into 25 respectively, and calculation was executed for 625 elements in total.
[0123] The eigenvalue analysis was executed with respect to the state space equation obtained
from the expression (15) above, and the eigenmode and the eigenfrequency of the acoustic
spaces obtained respectively were shown in Fig. 17.
[0124] In the present drawing, the white color shows the node of the sound pressure, the
black color shows the antinode of the sound pressure, and (1, 0) for example in the
drawing shows a natural oscillation where one piece of the node exists in the vertical
direction, and zero piece of the node exists in the vertical direction. Also, "Sim"
in the drawing shows the eigenfrequncy obtained by the present model, and "Exact"
shows an exact solution of the eigenfrequncy in a rectangular room of l
x × l
y. This exact solution is expressed by the following expression (17).
[Math. 17]

[0125] Here, both of n
x and n
y become 0, 1, 2, 3 ....
[0126] From this result, it is known that the analysis result and the exact solution by
the model agree to each other with the error of 2.3% at a maximum.
[0127] From the above, it was proved that acoustic analysis could be executed based on the
geometric configuration of the three-dimensional sound system related to the present
embodiment.
[Seventh Embodiment]
[0128] Fig. 18 shows a three-dimensional sound system of the seventh embodiment.
[0129] With respect to the three-dimensional sound system shown in the present drawing,
the sound recording space 1 and the sound reproducing space 3 are an identical space,
and the sound recording polyhedron 11 and the sound reproducing polyhedron 13 are
generally congruent 44 with each other. Therefore, the recording unit 10 and the reproducing
unit 12 are fused in the three-dimensional sound system, the acoustic signal obtained
by subjecting the acoustic signal 3 recorded by the recording unit 10 to an operation
45 such as the revolution operation, addition of echo, filtering of sound pressure
reduction and the like for example is reproduced by the reproducing unit 12, thereby
an interactive three-dimensional sound system can be configured, and a creative sound
field can be provided.
[0130] Fig. 19 shows a part of a reproducing device as a concrete example of the recording
unit 10 and the reproducing unit 12 of Fig. 18.
[0131] Fig. 19 shows a state that a loudspeaker enclosure 46 that is a part of the reproducing
device is disposed at an apex 252 of a room having a rectangular parallelepiped shape.
In the loudspeaker enclosure 46, the microphone 2 is arranged in the vicinity of a
loudspeaker unit 50 so that the sound recording polyhedron 11 and the sound reproducing
polyhedron 13 become generally congruent with each other.
[0132] The loudspeaker enclosure 46 has a triangular pyramid shape, and contacts a wall
A (47), a wall B (48), and a wall C (49).
[0133] Thus, it is possible to provide a three-dimensional sound system having a device
configuration of accommodating the recording unit and the reproducing unit compactly.
[0134] With respect to the low-frequency characteristic as a loudspeaker, a horn type may
be employed where opening sections 51 are arranged in the vicinity of three sides
configured by the wall A (47), the wall B (48), and the wall C (49), and a space is
utilized. Further, a low-frequency compensation circuit of a passive radiator type
also may be arranged.
[0135] Also, by arranging a light source in the space in question and making the opening
section 51 a passage of light, the three-dimensional sound system may also have a
function of indirect illumination. Thus, an interactive three-dimensional sound system
using the sound wave and light can be configured.
[List of Reference Signs]
[0136] 1: sound recording space, 2: microphone, 3: acoustic signal, 4: ambisonics encoder,
5: acoustic signal of ambisonics method, 6: sound reproducing space, 7: ambisonics
decoder, 8: reproducing acoustic signal, 9: loudspeaker, 10: recording unit, 11: sound
recording polyhedron, 12: reproducing unit, 13: sound reproducing polyhedron, 14,
15, 28, 29, 30, 37, 52: generally same type, 16: microphone stand, 17: microphone
holder, 18: sound element nucleus, 19: sound element, 20: cuboctahedron, 21, 22, 23:
rotation axis, 24: one kind of identity transformation, 25: eight kinds of revolution,
26: nine kinds of revolution, 27: six kinds of revolution, 31, 34: center of gravity,
32: dual microphone, 33: dual sound recording polyhedron, 35: dual loudspeaker, 36:
dual sound reproducing polyhedron, 38: spherical surface having same radii from acoustic
center, 39: omnidirectional microphone, 40: loudspeaker stand, 41: elasticity center,
42: acoustic compliance, 43: acoustic inertance, 44: generally congruent, 45: operation,
46: loudspeaker enclosure, 47: wall A, 48: wall B, 49: wall C, 50: loudspeaker unit,
51: opening section, 53: relation opposing across the center, 152: rhombic dodecahedron,
252: apex of room, 352: mirror symmetry plane