Presentedat AuD,o the 82nd Convention 1987 March

Presentedat AuD,o the 82nd Convention 1987 March
Preprint 2466 (H-6)
Unified theory of microphone systems for stereophonic
sound recording
M.Williams
tnstitut National d'Audiovisuel
Ecole Louis Lumi_re
Paris, France
/
Presentedat
the 82nd Convention
1987 March 10-13
London
AuD,o
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AN AUDIO ENGINEERINGSOCIETY PREPRINT
UNIFIED
THEORY
STEREOPHONIC
OF MICROPHONE
SYSTEHS
for
SOUND RECORDING
Abstract:
None
of
the
present
microphone
systems
used
for
stereophonic
sound
recording
(X/Y,
A/B-ORTF-NOS,
etc)
can
be considered
as universal
or
rarely
even
optimum.
This
paper
shows
how
these
different
systems
are
in
fact
part
of a much
larger
continuous
field,
where
"recording
angle"
(in
the
horizontal
plane
and
for
various
elevations)
and
"geometric
distortion"
of the
sound
field
are
related
to
angle
and
distance
between
microphones.
The
limits
of our
choice
in
this
continuous
field
are
shown
to be determined
by an unacceptable
ratio
of direct
to reverberant
sound.
Introduction:
In
the
field
of monophonic
sound
recording,
the
sound
engineer
has
considerable
freedom
to choose
the microphone
position
according
to
the
sound
quality
desired.
The
relationship
between
the distance
of
the
microphone
from
the
sound
source,
its frequency
response
curve,
and
the
amount
of "presence"
required
is easily
appreciated;
and
the
different
microphone
directional
characteristics
available,
enable
the
ratio
of direct
to indirect
sound
to be easily
optimized.
This
unfortunately
is not
the
case
in stereophonic
sound
recording.
The
number
of different
microphone
systems
available
for
stereophonic
sound
recording
is very
limited
and
almost
without
exception
these
systems
have
fixed
characteristics.
Each
system
has
been
developed
to be "optimum"
in a given
set
of circumstances;
however,
as recording
conditions
are
infinitely
variable,
this
optimum
is rarely
achieved.
Microphone
position
is generally
a compromise
between
a good
coherent
stereophonic
image
and
the
required
ratio
of direct
to
reverberant
sound.
Many
attempts
have
been
made
to compare
different
stereophonic
microphone
systems
in a given
recording
situation,
however,
the
fact
that
each
system
has
a unique
combination
of characteristics
renders
this
operation
almost
futile.
My
aim
in presenting
this
paper
is to try and
clarify
the
different
characteristics
of
a
given
microphone
system
and
show
how
these
characteristics
vary
from
one
System
to another.
It
will
then
become
clear
that
there
is
an infinitely
larger
choice
of systems
available,
forming
in
fact
a
continuous
field
of
choice.
It
is
therefore
possible
for
the
sound
engineer
to choose
within
this
field
the
characteristics
unique
to his
particular
recording
situation.
(i)
Derivation
In 1966,
between
apparent
configuration
necessary
from
one
generated
of
Recording
Angle(l):
H. Mertens(2)
published
Intensity
Differenoe(dI)
reproduction
(Fig.
to give
the
loudspeaker
sound
source
1)
angle
- that
information
and/or
Time
of
30'
in
is the
minimum
impression
that
or the
other.
to produce
this
giving
the
Difference(dr)
relationship
for
the
normal
values
of dl
the
reproduced
Mertens
used
information.
an
listening
and/or
dt
sound
is
coming
an
artificially
In October
1984,
G. Slmonsen(3)
published
a new set
of
psycho-acoustic
data
using
natural
sound
sources
_voice
and
maracas),
Intensity
Difference
and/or
Time
Difference
information
was
given
for
the
apparent
angles
of reproduction
of 10'_
20'
and
30'.
The
results
obtained
by Mertens
and
by Simonsen
are
given
in Fig.
2.
To help
in
computer
analysis
of these
results,
[ have
used
a convenient
po[ynome
to interpolate
between
the data
established
by Simonsen.
The
graphical
representation
shows
an
apparent
statistical
spread
of
psychoaooustica[
information,
but
this
is symbolic
only.
No detailed
statistical
analysis
is at present
available
for
a large
number
of
subjects.
The
data
for
dl/dt
at 30'
reproduction
angle
established
by
Simonsen
differs
slightly
from
that
obtained
by Mertens
probably
due
to the
use of natural
sound
sources.
The
intensity
and
time
difference
for a spaced
pair
of
high
quality
cardioid
microphones
can be calculated
as a function
of sound
source
position
and
various
distances
and
angles
between
the
microphones.
This
purely
physical
information,
together
with
the
psychoacoustic
limits
of the
stereophonic
listening
situation,
enabJes
a usable
angle
for
coherent
stereophonic
recording
(Recording
Angle)
to
be
determined.
The
relationship
between
)ntensity
Difference,
sound
source
position,
and
angle
between
microphones
for a coincident
pair
of
cardioid
microphones
is given
in
Figure
3.
The
psycho-acoustic
limits
of the
listening
situation
(15db
Intensity
Difference
for
30'
data
established
by Simonsen)
are also
indicated
on Figure
3.
We can
use
this
information
to
determine
the
Recording
Angle
of
any
given
coincident
pair.
We
must
look
for
the
intersection
between
the
variation
of Intensity
Difference
for
different
sound
source
positions
and
the
15 db
Intensity
Difference
necessary
to produce
an
apparent
angle
of
reproduction
of
30'.
For
example,
if
we
consider
a
coincident
pair
of
cardioid
microphones
with
120'
between
the
microphones,
we obtain
intersection
when
the
sound
source
is at about
70'.
The
limit
to the
Recording
Angle
is therefore
at 70'
on
the
right
side
of the
axis
of the
pair
and
70'
on the
left
side
the
total
Recording
Angle
is therefore
140'.
For
an angle
of 90'
between
the
microphones
the
half
recording
angle
is about
90'
(the
total
Recording
Ang[e
being
i80').
Using
between
a
spaced
time
pair
of
difference
omnidirectional
and
sound
microphones
the
source
position
relationship
can
also
be
determined
as a function
of
different
spacing
between
the
microphones
(Fig.
4).
The
Recording
Angle
can
also
be
determined
from
the
intersection
between
the
physical
and
the
psychoacoustica!
information
(the
same
way
as in Fig
_).
For
example,
with
50cms
between
omnis
the
total
Recording
Angle
Is about
lO0'.
Combining
microphones
Difference
these
two
functions
one
obtains
a whole
and
Time
Difference
as
for
a
spaced
pair
of
series
of
curves,
with
a function
of sound
source
spacing,
and
angle
between
microphones.
A
few
different
microphone
spacings
(12cm,
I7cm,
22cm
illustrated
in
Figs.
5,6,7
and
8.
This
time,
Differences
and/or
Time
Differences
are
indicated
for
of reproduction.
cardioid
Intensity
position,
examples
using
and
30om)
are
both
Intensity
apparent
angles
Figs.
5 to 8
are
used
to determine
the Recording
Angle
of
a
spaced
pair
of
cardioid
microphones
for
different
distances
and
angles
between
microphones
(using
the data
established
by Simonsen
for
the
apparent
angle
of reproduction
of 30').
For
instance,
in Fig.
6 one
can
see
that
with
spacing
of i7cm
and
an angle
of ilO'
between
the
microphones,
the
half
recording
angle
is about
50'
(total
recording
angle
of lO0').
However,
the
same
recording
angle
can
obtained
with
i2cm
130'(Fig.
5),
22cm
90'(Fig.
7),
30om
55'(Fig.
8) etc.
A series
of equivalents
can
be established
for
other
recording
angles
and
the
various
values
of spacing
and
angle
between
microphones
produce
the
graphical
representation
shown
in Fig.
9.
A whole
series
of
combinations
of
distance
and
angle
are
possible
for
a
given
reoordfng
angle.
For
instance,
for
a total
recording
angle
of 80',
the
roi towing
combinations
are
possible
:
i2cm
160',
i7cm
146',
22cm
125',
30om
90'
(NOS),
40om
50'
and
50om
20'.
For
adjacent
"equivalents"
the difference
in subjective
quality
is quite
difficult
to determine.
However,
if extreme
equivalents
(17om
135'
as against
40om
50')
are
compared,
the
listener
can
begin
to feel
the subjective
contribution
of Time
Difference
as against
intensity
Difference.
The
final
choice
of a particular
equivalent
is of course
a
personal
one
and
long
may
it
remain
so!
One
can
deduce
from
Fig.9
that
the
Recording
Angle
can
be
varied
by
keeping
one
of
the
axes
constant
and
varying
the
other,
or
by
gradually
varying
both.
This
situation
is somewhat
similar
to
the
zoom
tens
of a ts[evision
or film
camera.
For
instance,
starting
with
loom
60'
and
gradually
changing
to 50om
180',
one
"zooms"
from
a total
recording
angle
of 180'
(wide
angle
lens)
to a Recording
Angle
of
40'
(narrow
angle
lens).
It
is common
practice
in recording
a symphony
orchestra
to
place
an
additional
stereophonic
pair
we[ [ behind
ithe main
recording
microphone
pair
in
order
to
"open
up the
sound".
It
is
obvious
that
the
Recording
Angle
of this
additional
pair
must
be carefully
determined
so
as
not
to mix
up the
main
stereophonic
image
or create
a
double
image.
For
instance
if a iTcm
110'
pair
is used
(total
recording
angle
of 100')
in its normal
position
in front
of the
orchestra
and
another
pair
is
placed
G metres
further
away,
it
must
cover
a
Recording
Angle
of
only
60'
(from
Fig.
9 the
values
of spacing
and
mic
angle
can
be determined
for
a Recording
Angle
of 60'),
i.e.
35om
130',
40cm
ilO"
or AScm
90'.
Conclusion
at
the
ratio
:
in a given
situation,
the
microphone
optimum
distance
from
the
sound
source
to
of
direct
to
indirect
sound.
The
values
angle
can
then
be
possible.
We
must
different
combinations
chosen
now
of
to repr, oduce
the
look
at
the
angular
angle
and
distance
pair
can
produce
the
of
spacing
be
p_aced
desired
and
mic
beet
stereophonic
image
distortion
produced
by
between
the
microphones.
(Il)
Angular
Distortion
Each
combination
of
angle
and
of
distance
between
microphones
introduces
a certain
amount
of angular
distortion.
Already
recording
angles
of more
than
60'
produce
expansion
of the
sound
image
whilst
recording
angles
less
than
60'
produce
compression
of the
sound
image.
Added
to this,
angular
distribution
within
this
recording
angle
is in
itself
non
linear.
If
we take as an example
the "NOS"
(30cm 90"-Fig
8/,
we can see from
the
intersections
between
the
physical
and
the
psycho-acoustical
information
that:
i)
the
curve
representing
an apparent
angle
of
reproduction
of
10'intersects
with
the 30cm
90'
curve
at dt=O. iSmS
and
dl=O. i4.
These
values
are
produced
when
the
sound
source
position
is
il'
in relation
to the axis
of the microphone
pair.
ii)
for
with
an apparent
the
30em
angle
of reproduction
90'
curve
is at dt=O.32mS
source
position
is 22'
in relation
to
iii)for
an apparent
angle
of reproduction
and
d]=0.45.
The
sound
source
position
axis
of
the
microphone
pair
(39*
recording
angle).
(These
values
are
represented
graphically
If
the
this
one
considers
pair
can
and
be
a
sound
source
at
halfway
of
20',
the
and
d]=0.26.
intersection
The
sound
the
axis
of the
pair.
of 30 °, we obtain
dt=O.56mS
is 39'
in relation
to the
is,
of
course,
the
half
in
Fig.
between
10).
the
the extreme
limit
of the
Recording
Angle
taken
as about
the
maximum
"deviation"
centre
axis
of
(i.e.
at S0%),
from
a
linear
reproduction
that
will
be produced
by a given
microphone
pair.
I
propose
to
take
this
value
of "deviation"
as characteristic
of
the
geometrical
distortion
produced
by a given
microphone
pair
and
to ca]]
it "Standard
Deviation".
In the example
illustrated
above
("N.O.S."),
the
50_
position
is at about
20'
to the
axis
of the
pair.
With
linear
reproduction,
this
sound
source
should
normally
be reproduced
at 15"
to the centre
of the standard
listening
situation.
However
"Standard
Deviation"
is
about
4"
so the
sound
source
in
question
will
be
reproduced
in
Fig. lO.
posible
for
Values
of
distance
ars
at a position
of about
19'
to the
listening
axis,
as seen
This
value
of deviation
is near
to the
minimum
that
is
any combination
of distance
and angle
between
microphones.
"Standard
Deviation"
for
other
combinations
of
angle
and
given
in
Fig. ii.
]t is interesting
to note
that
systems
using
a balanced
combination
of
Intensity
Difference
and
of Time
Difference
in general
produce
]ess
angular
distortion
than
systems
using
a predominance
of one
or
the
other
- a predominance
of Time
Difference
being
most
prone
to
angular
distortion
(up to 10'
Standard
Deviation)
(111)
Directivity
Although
produce
second
results
Patterns
and
Frequency
Response.
I have
used
microphones
with
cardioid
directivity
patterns
to
Intensity'Difference
information
to
illustrate
the
first
and
sections
of
this
paper,
it
is
obvious
that
equally
valid
can
be obtained
using
almost
any
directivity
pattern,
However,
each
directivity
with
respect
to
the
"on
the
regularity
of the
range,
pattern
has
its
own associated
axis"
frequency
response
of
the
directivity
pattern
throughout
difficulties
microphone
and
the
frequency
i)
Theoretically
perfect
omnidirectional
microphones
(i.e.
small
diaphragms)
can
of course
only
be used
on the
time
axis
with
associated
high
value
of angular
distortion
(Standard
Deviation
being
about
10').
However,
if we are
prepared
to use
only
2/3
of
the
available
reproduction
base
for
the
main
sound
sources,
the
angular
distortion
is not
quite
as high.
The
excellent
frequency
response
of omnis
at
low frequencies
is an obvious
attraction
in
using
this
system.
ii)
Hypooardioid
(wide
angle
oardioid)
microphones
offer
an
interesting
compromise
between
low
frequency
response
and
reasonable
angular
distortion.
Using
combinations
of time
and
Intensity
Difference,
we
can
see
that
values
of
Standard
Deviation
at various
Recording
Angles
(Fig.
12),
are
considerably
lower
than
with
Time
Difference
only
systems.
Low
frequency
response
is much
better
than
with
cardioid
mice
even
though
not
as
good
as with
omnis.
It is unfortunate
that
no small
dtapragm
hypocardioJd
microphones
ara
at present
commercially
available.
iii)
The
direc%_vity
patterns
of small
diaphragm
cardioid
microphones
are
very
near
to the
theoretical
value
up until
about
120'
to the
main
axis,and
within
the major
part
of the
frequency
spectrum
(200Hz
8kHz).
It
is
worth
noting
that
the
majority
of
microphone
systems
for
stereophonic
sound
recording
use
cardioid
directivity
patterns
(X/Y,
A/B
- ORTF,
NOS,
etc.)
However,
low
frequency
response
is not
very
satisfactory
and
this
has
led many
recording
engineers
to look
for other
systems
with
better
low
frequency
response.
Larger
diaphragms
can
of
course
improve
somewhat
the
response
in the
iow frequencies,
at
the
expense
unfortunately,
of
good
cardioid
directivtty
at
the
higher
frequencies.
iv)
Hypercardiold
dfreotlvity
stereophonic
response
with
Unfortunately,
hyperoardioid
maintained
on
the
side
behind
.
Low
frequency
with
cardioids.
can
produce
totally
adequate
very
low angula_
distortion
(Pig.13).
direotivity
patterns
are
rarely
weli
of the
microphones
and
even
Jess
so
response
is of course
even
worse
than
v)
(lV)
Coincident
bi-d'irectional
microphones
at
90'
have
been
used
for
some
time
(since
the
BJumlein
patent
in 1934)
for
stereophonic
recording.
However,
spaced
bi-directional
microphones
at various
angles
between
microphones
can
produce
some
very
useful
results
(Fig.
14).
It must
be noted
that
intensity
Difference
information
is
in
opposition
to Time
Difference
information
behind
the
microphone
pair.
This
zone
of more
er Jess
compensated
stereo
can
in fact
be used
to produce
some
interesting
effects
(as
with
any
other
directivity
patterns
working
in compensation).
Angular
becoming
image
in
distortion
negative;
the
middle
Ratio
Direct
The
ratio
recording
combinations
of
to
is
very
corresponding
of the
sound
Reverberant
Iow,
to
base.
Standard
squeezing
Deviation
of
the
even
sound
Sound
of
direct
to reverberant
sound
situation
and
become
a limiting
of distance
and angle
between
can
vary
within
factor
in
using
microphones.
a
given
certain
When
one
]istens
to a sound
souce
at an angle
greater
than
about
65'
to the axis
of a single
cardioid
microphone,
it is posible
to detect
a
decrease
in
direct
sound
with
relation
to
the
fixed
leve!
of
reverberant
sound.
This
limit
of 65'
is of course
subjective
and
small
variations
wil]
be found
with
different
subjects.
(The
response
of
the
cardioid
at 85'
is about
-3db)
0 °
'<._j )
)
\
/_O °
/
This
same
limit
of
65'
can
also
we
consider
a pair
of coincident
angle
of
60'
between
the
axis
obtain
a Recording,Angle
of
about
be
of
applied
to
microphones
the
cardioids,
+/ilO'.
a microphone
pair.
with,
for
example,
we should
normally
If
an
[
However,
to
the
if
cardioid
we
consider
axis,
we
the
have
direct
a usable
Therefore,
from
95'
to
110'
we will
ratio
of
direct
to
reverberant
sound
the
the
sound
source
is
receding.
to
reverberant
Recording
sound
Angle
of
begin
to hear
and
therefore
limit
only
a decrease
have
the
at
95'.
65'
in
impression
the
In
order
distance
to
and
avoid
angle
this
difficulty
so that
:Angle
Recording
For
when
a coincident
the
angle
pair
between
of
the
B/2
= 40,
Recording
The
ratio
of
have
passed
applies
to
microphones:
direct
We
the
can
plot
this
lower
limits
relationship
of distance
The same
situation
microphone
pair
is
Suppose
we
have
+ 65'
=
for
B=
occurs,
greater
180'
angle
this
105'
BO'
is
< Angle
across
and angle
mice
about
+/-
becomes
+
is
degrees.
100
between
2
fulfilled
degrees.
unacceptable
mice
after
we
also
between
+ 65'
the
bottom
of
Fig.
11
for various
microphone
microphones
of
65'
This
same
relationship
what
the
distance
is
in reverse,
when
a certain
limit.
between
combinations
relationship
about
BO
is
sound
but
than
choose
between
2
Angle
limit.
no matter
Angle
must
angle
reverberant
this
Recording
spaced
pairs,
Recording
<
microphones,
microphones(B)
B/2
Angle
to
we
the
angle
to
obtain
pairs.
between
the
:
:(H- For
a
about
coincident
+/45'
unacceptable
of
the
sound
ratio
base
pair
in
of
and
of
cardioid
relation
direct
covers
to
the
to
microphones,
axis
of
reverberant
majority
of
the
the
sound
the
Recording
Angle
pair.
Therefore,an
occurs
Recording
in
the
Angle.
centre
is
To
avoid
this problem
one has to accept
that
the angle
b_ween
the
microphones
must
not
be
more
than
130
-degrees---C2x65
degrees),
no matter
what
distance
there
is between
microphones.
This
"no
go"
area
is also
indicated
by shading
above
an angle
of
i30'in
Fig. ii.
The
same
analysis
can
be applied
to Hypocardioids,
Hypercardioids
Figure
of Eight
microphones.
The
critical
point
is stil)
-3db
can
see
in f_gs.12,
13 and
14 the
resulting
shaded
areas
that
our
choice
of distance
and
angle
between
microphones.
and
and
we
limit
ConQlusion:
in
choosing
a combination
of distance
and
angle
for
a
given
Recording
Angle,
we must
in general
observe
two
conditions:
(i)
choose
a
combination
of distance
and
angle
with
a
reasonable
minimum
angular
distortion.
(ii)
avoid
the
shaded
areas
where
reverberation
"creeps"
into
the
recording
angle.
However,
an_ular
distortion
can
have
some
useful
applications.
It is
also
possible
to
use
the
"reverberation
effect"
in
special
circumstances
(increase
in reverberation
giving
an impression
cf
the
source
receding).
(iV)
Variation
of
Recording
Angle
-lth
EievatiQn.
We
now
have
a reasonably
complete
picture
of the
characteristics
cf
various
microphone
systems
in the
horizontal
plane.
It is of course
usual
to
place
the
sound
source(s)
as near
as
possible
to
this
horizontal
plane.
However,
in certain
circumstances
it is sometimes
necessary
sound
sources
well
away
from
this
horizontal
plane.
When
sound
effects
and
environmental
sound,
the
sounds
may
come
any
direction,
and
of course
reverberation
almost
completely
the
microphone
pair.
to record
recording
from
almost
surrounds
It
is
therefore
necessary
to
have
a
good
idea
of
characteristics
of a given
microphone
pair
vary
at various
and
perhaps
to choose
certain
combinations
of distance
and
control
to a certain
extent
what
happens
above,
below
and
microphones.
every
aspect
of
However,
these
it is beyond
variations.
the
scope
of
this
paper
how
the
elevations
angle
to
behind
the
to
study
The
Recording
Angle
is,
of
course,
the
first
stereophonic
characteristic
that
is of interest
to us.
Figs.15,
16,
17 and
18 show
the
variation
of Recording
Angle
using
cadioid
microphones
for various
values
of
elevation,
Recording
Angle
in the
hoetzontal
plane
being
kept
constant,
whilst
various
combinations
of angle
and
distance
are
tried.
The
amount
of information
to be shown
on this
type
of graph
ts
very
difficult
to represent
without
loosing
sight
of the wood
for
the
trees!
So
I have
kept
the
number
of
steps
in
the
changing
parameters
to a minimum.
What
deductions
can
we
make
from
Our
appreciation
of
the
ratio
becomes
a lftt[e
more
difficult
between
two
types
of reproduction
As
with
direct
sound
sources,
reproduction,
i.e.
the
coherent
of
the
original
sound
source
(between
the
two
loudspeakers),
concentrated
at the
extremities
the
right
loudspeaker).
these
elevation
characteristics?
of
to
direct
to
reverberant
sound
now
describe.
We can
now
distinguish
of indiret
sound
or
reverberation.
we have
both
coherent
and
non
coherent
reproduction
produces
a virtual
image
within
the
reproducing
sound
base
whilst
non
coherent
reproduction
is
of the
sound
base
(on the
left
and/or
Therefore,
depending
on
the
variation
of
recording
angle
with
elevation,
we can
have
Gore
or less
coherent
reverberation,
i.e.
more
or
less
reverberation
reproduced
between
the
loudspeakers.
We can
say
in
general
that
if the
quantity
and
quality
of
reverberation
is
acceptable,
then
it
can
be
reproduced
between
the
loudspeakers
(coherent)
to good
advantage.
This
means
that
we must
choose
a system
with
as much
angle
between
the
microphones
as possible.
However,
the
more
it becomes
a negative
factor,
the
more
we must
try
to "push
it to
each
side"
to leave
the
main
sound
sources
as free
as
possible.
In
this
case
the
system
must
have
an angle
between
the
microphones
as
small
as possible.
Our
appreciation
of
becomes
the
appreciation
coherent
We
are
engineer.
choice
therefore
now
of
sound
now
within
the
individual
choice
of
the
subjective
decision
which
will
determine
coherent
and
non
coherent
indirect
sound
sound
the
and
direct
indirect
completely
1%
is
his
direct
to
the
the
ratio
of the
distance
and
of direct
ratio
of
plus
non
angle
for
a
to
reverberant
direct
coherent
indirect
given
recording
angle.
However
the
situation
is slightly
different
if we are
concerned
by
a
specific
event
in environmental
sound,
or sound
sources
distributed
over
a large surface
in relation
to the microphones.
We must
remain
within
the
front
sector
of elevation
as here
the
recording
angle
varies
very
much
less
than
behind
the microphones.
This
means
that
a
change
in the direction
of the microphone
pair
in the vertical
plane
has
very
little
effect
on the
reproduced
sound
image.
A good
example
of
this is in recording
an opera
using
only one pair of
microphones,
where
the
position
adopted
is above
the orchestra
and
directed
towards
the
stage.
The
re¢ordin
E angle
presented
to
the orchestra
will
be
approximately
the
same
as
that
covering
the
stage.
As
to
the
desirability
of one
microphone
pair
for orchestra
and
stage,
that
is
another
matter
and
again
depends
on one's
personal
preference.
lO
(V)
Pratical
application
to
stereophonic
9ound
recording.
The
sound
recording
engineer
now
has
control
over
the
majority
of
characteristics
of a microphone
pair.
The
order
in which
he chooses
consider
each
characteristic
in
a specific
recording
situation
again
suggest
(l)
(ii)
a
a
matter
possible
However
1
would
_ike
to
Deviation:
have
to decide
within
certain
limits
on
the
amount
of
distortion
that
we can accept.
In most cases
we
are
for
a
minimum
of standard
deviation.
]n
which
case,
to
the
appropriate
graph
(appropriate
to
the
used)
will
give
us the unique
combination
of distance
between
the microphones.
Distribution
The
ratio
of
of Reverberation:
coherent
to non
predetermined
(v)
preference.
Microphone
position:
Choice
of directivity
is perhaps
the
most
important
factor
in the
whole
process.
Frequency
response
in
the
bass
frequencies
is
almost
completly
dependent
on
this
choice.
Once
microphone
directivity
has
been
determined,
the
desired
ratio
of direct
to
reverberant
sound
will
dictate
the
position
of
the
microphone.
Little
attention
to Recording
Angle
is necessary
at this
stage,
however
nothing
prevents
adjustment
of the
recording
angle
at
the
same
time
Recording
Angle:
The
position
of the
microphone
obviously
determines
the
Recording
Angle
- it is simply
a matter
of measuring
the angle
presented
by
the
sound
sources
plus
any margin
one
wishes
to leave
on
each
side.
(iii)Standard
We
now
angular
looking
reference
directivity
and
angle
(iv;
of personnel
approach.
the
to
is
by
the
coherent
preceeding
reverberation
is
of
course
considerations.
Compromise,
Preferences,
or Preconceived
Ideas:
The next
stage
is one of compromise.
Modification
of Just one of
these
characteristics
will
produce
a corresponding
shift
in
the
others.
Also,
any
preferences
or preconceived
ideas
can
dictate
the
choice
of one
of these
characteristics
to the
detriment
of
the
others,
or
simp|y
change
the
Il
order
of
priority.
(VI)
Here
Notes
are
on
the
comparison
characteristics
stereophonic
X/Y
the
sound
of
Stereophonic
of
the
Microphone
fixed
systems
at
Systems.
present
- Coincident
cardtoids
at 90 degrees.
....
Recording
Angle
is +/- 90 degrees
(180
degrees
....
Standard
Deviation
is about
6 degrees
....
Recording
Angle
constant
(+/-90';
up
to
90'
gradually
reducing
to +/20'
at 180'
elevation.
Coincident
....
....
....
used
Figure
of Eights
Recording
Angle
is
Standard
Deviation
Four
equal
sectors
at 90 degrees.
+/- 45 degrees
(90
is about
5 degrees
of stereo
pick
up
degrees
in
all;
elevation,
in
ail)
A/B
(ORTF)Cardioids
at 17cms
and
ilo degrees.
--Recording
Angle
is +/50 degrees
(i00
degrees
in al))
--Standard
Deviation
is about
5 degrees
--Recording
Angle
diminishing
gradual
ly to +/20'
at the
back
of the
pair
(180'
elevation).
A/B
(NO£)
-------
Omnis
at
-------
- Cardioids
at 30cms
and
90 degrees,
Recording
Angle
is +/- 40 degrees
(80 degrees
Standard
Deviation
is less
than
_ degrees
Recording
Angle
diminishing
gradual
ly to +/back
of the
pair.
50cms
(for
example)
Recording
Angle
is
Standard
Deviation
Recording
Angle
is
in
15'
*/50 degrees
(lO0 degrees
is about
8 degrees
constant
at all elevations
I
think
the differences
between
these
themselves
without
even
considering
the
There
are
so many
characteristics
that
to
another
that
no useful
information
comparaison.
However,
contribution
subjective
for
recording:
all)
at
in
individual
systems
different
frequency
are
different
from
can
be
determined
it
is now
possible
to construct
an experiment
to
of
Time
Difference
and
Intensity
Difference
quality
of a stereophonic
sound
recording.
It is obvious
that
directivtty
and
Recording
any
comparison
between
microphone
pairs,
and
the
total
quantity
of reverberation
do
other.
Combinations
of distance
and
angle
standard
deviation
remains
constant.
12
the
al[)
spear
for
reponses.
one
system
by
direct
study
to
the
the
Angle
must
be the
same
in
so that
microphone
position
not
change
from
one
to
the
can
also
be chosen
so that
For
example,
a coincident
pair
of
cardiold
microphones
at
an angle
of
90
degrees
can
be compared
to
a pair
of
spaced
cardioids
at
20cms
and
an
angle
of
30
degrees.
The
recording
angle
is
+/90
degrees,
Standard
Deviat'{on
is
6
degreees
and
the
limit
to
.,.acceptable
reverberation
is Just
at the
limit
of Recording
Angle.
Evolution
of
Recording
Angle
with
elevation
is very
similar
for
both
pairs.
]f smaller
recording
angles
are
compared
with
37cms/30
degrees.
Deviation
is about
5.7 degrees,
with
elevation
is not
quite
the
I
have
chosen
something!
IF
extreme
values,
desired
then
lOcms/130
degrees
can
be
R.A.
is +/50 degrees
and
Standard
however
variation
of Recording
Angle
same.
extreme
values
to give
the
maximum
chance
you
have
been
able
to detect
a difference
less
extreme
values
are
much
easier
to set
cf
with
up.
hearing
these
However,
! think
the best
chance
of understanding
this
highly
complex
subject
will
come
from
collaboration
between
sound
recording
engineers
and
psychoacoustical
experts
working
in the
universities.
There
are
three
aspects
of
%his work
that I think
important
and
need
to
be
studied.
i)
The
work
done
by Simonsen
needs
to be expanded
in a
number
of
respects.
Intensity
Difference
and
Time
Difference
information
were
studied
only
in the
positive
sector.
This
information
needs
to
be
developed
in
the
compensated
sectors
were
Intensity
Difference
information
is
tn
opposition
to
Time
Difference
information.
It
would
aisc
be interesting
to have
intermediate
values
of apparent
angles
of reproduction
at say
5' intervals.
It
is
also
important
to
confirm
these
results
with
detailed
statistical
analysis
of a large
number
of subjects.
] would
like
to
stress
two
important
aspects
of Simonsen's
worR.
One
is
the
use
of natural
sound
sources.
The
other
is the
way
in which
the
standard
stereophonic
sound
recording
system
was
used
for
all
measurements.
ii)
Anybody
who
has worked
in this
field
knows
that
perception
of
Intensity
Difference
information
is different
to
perception
of
Time
Difference
information.
It would
be interesting
to know
if
these
psychoacoustical
characteristics
vary
throughout
the
frequency
range.
This
might
solve
some
of the
problems
concerning
dispersion
of the
sound
image.
iii)
The
function
of _roup
propogation
time
aS
effects
still
cause
considerable
confusion.
system
in
use
is there
any
contradiction
factors?
This
also
could
explain
certain
instability
in the
sound
image.
13
against
purely
phase
In the
stereophonic
between
these
two
dispersion
problems
or
Postscript
The
calculation
impossible
the
theoretical
of
all
these
characteristics
without
the
help
of
a computer.
basis
of
this
work
or
continue
If
would
be
absolutely
you
wish
to
reproduce
its
development
in
the
light
of
new measureme.
Nts,
I have
included
at
the
end
of
this
paper,
the
programme
1 used
to calculate
the
main
characteristics.
I am
a
sound
recording
engineer
not
a computer
programmer,
so I ask
you
to
make
allowances
for
what
ts neither
the
nearest
nor
the
most
efficient
of programmes.
performance
or
For
this
presentation
reason
any
suggestions
would
be welcome.
that
might
improve
its
This
paper
presents
the
theoretical
basis
on whtch
the
unified
theory
of microphone
systems
for
stereophonic
sound
recording
was
developed.
The
calculation
of the purely
physical
characteristics
of a microphone
pair
would
be of little
interest,
if it were
not
for
the
interaction
with
psychoacoustical
measurements
carried
out
at
the
Acoustical
Laboratory,
Lyngby
in Denmark.
Experimental
verification
and
"in
the
field"
recording
has
been
carried
out
not
only
by myself
as
a
sound
engineer,
but
also
by my colleagues
and
students
at
the
/NST/TUT
NATIONAL
D'AUDIOViSUEL,
the ECOLE
NATIONALE
de PHOTO
et CINEMA
(ECOLE
'LOUIS
LUMIERE)
in Paris,
and
at RADIO
MONTECARLO
in Monaco.
References:
(1)
Section
I
of this
paper
(Derivation
of the Recording
Angle
in
horizontal
plane)
is an update
of the
paper
[ presented
to
A.E.S.
in March
1984
in Paris
entitled
"The
Stereophonic
Zoom".
(2)
H.Mertens,
(3)
G.Slmonsen,
Revue
du
Master's
Son,
[966.
Thesis,
October
1984,
Lyngby,
Denmark.
Michael
January
14
Uilliams
1987
the
the
###_##################a########M#Md###1#####M#d###################l########
#
#
UNIFIED
THEORY
OF MICROPHONE
SYSTEMS
FOR STEREOPHONIC
SOUND
RECORDING
#
by Michael Willtams
#
(A.E.S.
March
07)
#
######_################fi#################################################_#
#
#
RECORDING
ANGLE
AND ANGULAR
NON-LINEARITY
#
IN THE HORIZONTAL
PLANE AND IN ELEVATION.
#
#
Developed
on an ATARI
1040
using
GFA Basic
(no
110196)
#
################################f#######f#k#f###################f###f#f####
wi# MAINPROGRAM
# MAINPROGRAM
# MA1NPROGRAM
# MAINPROGRAM
# MAINPROGRAM
f###################N##fi#################################fi#f###############
Gosub
Initialization
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ltlew
2,"
RECORDING
ANGLE AND STANDARD
DEVIATION
IN THE HORIZONTAL
PLANE
;osub
Horizontal.recording.angle
'itlew
2,"
VARIATION
OF RECORDING
ANGLE AS A FUNCTION
OF ELEVATION
"
;osub
Elevation,recording.angle
:nd
################################################################fi##########
# subroutines
## subroutines
## subroutines
## subroutines
## subroutines
f###############f###########fi#f###M###i####f###fi###M########fffi############
'rocedure
Directtvitycode
Fullw
2
Clearw
2
Deftext
1,0,0,13
Print"
- GOEFICIENTS
FOR MICROPHONE
DIRECTIVITY
-"
Print
Print"
- Hypocardioid
microphones
.....
2"
Print
"
- Card#cid
microphones
.........
1"
Print"
Hypercardtoid
microphones
--- 0.5"
Print "
~ Figure of eight microphones
-- O"
Print
Print "
You can modify
these ooeficients
if you"
Print"
require
intermediate
directivlty
patterns."
Print
Print
"
What
is the directivity
coefictent
of"
Input"
the microphones
you wish
to use
?
--> ",F
Clearw
2
{eturn
15
#
#
#
#
#
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#
#
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#
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"
#
' ##1####N########i###################N#######1i#l#d###i##########il##tN'##_##
Procedure
Horizontal.recording.angle
N####MWN###K**#NNN**N****_*MN##***###N#*M#i#**f#**##NM##N_##M#iNM##N*****
*
VARIATION
OF
RECORDING
ANGLE AND ANGULAR
IN THE HORIZONTAL
PLANE
NON-LINEARITY
,
*
,
#
#NM*_k*##N####**##**####N**##_*#N_N##NeN*#n#i*#**#N*_M##*_#N**NN*#N**#*#_
N
*
*
..................
First
Step
......................
Calculation
of
distance
between
microphones
given
the recording
angle
and the angle
between
microphones
"RA"
= Recording
Angle
"B" = Angle
between
microphones
"D" = Distance
between
microphones
"U" = Indite
for
apparent
angle
of reproduction
*
*
*
*
*
*
*
M
*
*
#
,
N*NN#_##***N*N*_**#N_*_**NN*N*_**#N**N###***N*N*******_*N*****#_#***_*#*#
Gosub
Axesi
For Rat=90
To 20 Step
-lO
X2=O
B%=O
For
B_=O
To 180
XI=X2
! ****************.**************************
Preceeding
graph
Y1=¥2
! ******N****N*_**_#***N**_N*****N***_N*_*
coordinates
memorized
A=Ra%
E%=O
! *******************#**************************
Horizontal
plane
Gosub
Intensity
W=30
! ***********
Selection
code
for
30 degree
psychoacoustlcal
curve
Gosub
Psychotime
Goeub
Distance
X2=D
! ************************************************
New
graph
y2=B%
! *************_***********N***********_****XNN*
coordinBtes
If
D>50
Or D<O Then!"D"is
outside
the upper
or lower
limit
of the Xaxts
Goto
Jumpl
! so avoid
return
scan
by going
to next
coordinate
Endif
If
Yl=lSO
Then
! *MM*N**.
Avoid
return
scan
by going
to next
coordinate
Goto
Jumpl
Endif
*
*
*
................
Second
Step
......................
Calculation
of non-]tnearity
of microphone
pair
determination
of "standard
deviation"
and
***********_#**#N***#****#**M***M***N****#*#***#*N**MXXMXN*#XX_NK#**#
_=20
! t****_****
Se_ection
code
for 20 degree
psuchoaooustical
curve
Gosub
Inte_cept
Ac2a=Ac2b
! ***************************
Previous
value
of Ac2
memorized
Ac2b=A-(Ra%,O.G666)
! ,,#,,*****,
Difference
w.r.t,
linear
reproduction
*=lO
! ,_********
Selection
code
for 10 degree
psyohoacoustlcal
curve
Gosub
Intercept
Acta=Acib
! ***************************
Previous
_alue
of Aci memoTized
Acib=A-(Ra%*0.3333)
! *****N*****
Difference
w.r.t,
linear
reproduction
Gosub
[nterpolatLon
Gosub
Standard.deviation
Jumpl:
Next
B%
Next
Rat
Hardcopy
Clearw
2
Return
16
*
*
*
###########M#MHM###NM############dMM#########1#MM#M#NM#M#d##N##t###########
Procedure
Elevation.
recording.angle
####_N_#N##M#####N##N##MMM_#NMN###_N###MN#NJmM##MN#N######_#########_###_
VARIATION
N
M
OF
RECORDING
ANGLE
AS A FONCTION
OF ELEVATION
Calculation
of
distance
between
microphones
given
the
recording
angle
and the angle
between
microphones
"RA"
: Recording
Angle
"B"
= Angle
between
microphones
"D"
= Distance
between
microphones
"W"
= Indice
for apparent
angle
of reproduction
For Rat:90
To 30 Step
-15
Gosub
Axes2
X2=O
For B%=20
To 180 Step 20
A=Ra%
E%=O
Gosub
Intensity
W=30
Gosub
Psychotime
Goeub
Distance
If D>50
Or D<O
ThenI"D"is
outside
Goto Jump3
Endif
Gosub
Elevation
! *N*.****N_**.*_
Jump3:
Next
B%
the
This
upper
is
or
where
lower
the
limit
real
·
Calculation
- 'A" =
"B"
=
"E" =
"F"
=
*
N
#
of
the
work
Hardcopy
! _**MN*W*_N_#_**_M*.N.*#._N.*_MM*_*_
Copy
screen
Ciearw
2
Next
Rat
Return
, ###########_################fi################_#########################M###
· #M#################################fi#fi####################1################
Procedure
Intensity
.
#
is
to
of Intensity
Difference
between
two microphones
sound sourceposition
angle
between
the axis
of the microphones
elevation
angleof
sound
source
directivity
indice
(see
initial
input
conditions)
#
Xaxis
done
!
printer
.
w
#
Local
L,R,X,Y,Z
V=Pi/igo
X=A*V
Y=(B%/2).V
Z=E_*V
L=F+Sin(X).Stn(Y)+Cos(X)*Cos(Y)MCos(Z)
R=F+Sin(X)NSLn(-Y)+Cos(X)*Cos(-Y)*Cos(Z)
DI=I-(R/L)
Return
17
·
######H###########d#d#Ni###########d#d###d####################MdEII#####N##
Procedure
Psychotime
#
N
.................
Psychoaooustical
N
Time
N
..........
"W"
f
U=30
Dt=-i.
Difference
expressed
for
is
curves
various
as
a
apparent
identification
code
.......................
function
of
angles
to
of
select
the
d
Intensity
Difference
reproduction
LO,
20
or
-
*
............
30
deEree
curve
*
Then
Vg_Di^3+l._13_Di'2-1.F26_Di+l.i2
Endif
]f
W=20
Then
Dt=-i.O79.Di^3-i.65wDi-2+O.
Goto
iOl*Di+0.439
Finish
Endif
If
W=iO
Then
Dt=-22.858,D_^3+8.857.Di^2-O.336.Di+0.2
Goto
Endlf
Finish
Finish:
Return
'
#################################################################t$########
Procedure
!
'
'
*
_
'
.
Time
Calculation
"D"
of
time
= distance
difference
between
"A"
=
source
sound
between
microphones
two
microphones
*
.
position
T=(D_Sin(A.O.O1745_3))/_
Return
, ###########################################################################
Procedure
Distance
#
Calculation
the
value
of
of
distance
time
between
difference
two
and
microphones
sound
source
Eiven
position
N
D=(34#Dt)/Sin(A*O.Oi7_533)
Return
18
'
####N######d#1#####################d#########1############################l
Procedure
Intercept
##N#_####d####N#i_##_#_###_####_#####W###_#1###NN#N###_####Nm_###*_fiN#fi##
.
Calculation
#
curve
#
physical
N
aniie
of
for
30
the
curve
and
intersection
degrees
between
apparent
(intensity
the
and
calculated
*
t
"K"
angle
time
of
m
and
for
between
precision
psychoacoustioal
reproduction
difference)
distance
=
the
of
the
the
the
#
given
#
microphones
#
.
#
Iccp
#NWNW###W#_MW#NN##WRWW#WWWWWWNNWM_N_W_###W##W##W##WMW_##W#WM#############
A=O
gms
De
!
Add
_##t##W#M*##N#WW#WN##MWWWMW_#W_#A#N#WW#mW#_WWMW#WWWNWMWW#WW
Gosub
Intensity
Gosub
Goeub
Psychotime
Time
Exit
If
step
lnt(Dt#1OOOO+O.5)=[nt(T#10000+0.5)
K=(((-1.12.A)/((Dt-T)-i.12))-A)*0.5
Loop
Return
'
Test
A,K
!
*#,,
Calculation
of
automatic
step
#############################################1#############################
Procedure
Interpolation
#M#NN##N##N##_N#N#WW#NNNN#N#N#N#N#A_#NNNWN##N_#NN#_#WKNNWWNN#NNNWNNNM###
#
f
W
of
#
Calculation
#
#
values
AlO
"K"
=
curve
and A20,
amp{#rude
*
"L"
=
assymetrie
*
"G"
=
precision
Sgn(Aclb)<>Sgn(Ac2b)
Dev=O
passin
and
of
8
R.A.,
sinus
of
of
sinus
through
origin,
to within
function
intercept
one
degree.
function
*
#
#
determination
in
loop
#
Then
Endif
L=l.iSAT.Atn(1.732*(Acib-Ac2b)/(Aclb+Ac2b))
K=Acib/(Ra%eSin(1.O_7_O.86_L))
Return
,
#######################################fi###################################
Procedure
Standard.deviation
#NW##WWNW#WN#_NiNN#W#WN_WN_W#WN#M#_#WN#N*_##_N_WNNMWWW#WMNW_#N#NNN_WNN###
#
#
"
........
....
CALCULATION
Deviation
.........
*
i.e.
#
of
a
of
from
a
Value
of
sound
source
the
from
#
DF
an
"STANDARD
assymetrical
linear
at
axis
of
Beginning3:
Z]=O.5-(Q/PI)
Zc=KNSln(O+L#Sin(Q))
[nt(Zl#lOOO)={nt(ZcNlO00)
Goto
_ndif
(k=O,{=O)
from
situated
O=O
G=i
[f
sinus
function
deviation
the
DEV{AT[ON"
Then
Jumpa
19
hail
the
linear
the
pair
........
function
....
*
#
.........
reproduction
recording
angle
#
If
Sgn(ZJ-Zc)=+l
Then
Add Q,G
Goto
Beginning3
Endlf
Sub q,G
Olv
G, lO
Goto
Beginning3
Jump4:
Dev=((Q-i.ST1)_lSO/Pi)/6
Devi=Dev2
! .....#.d..M..N,N_*WW"""""""""
Previous
value
of
"Der"
memorized
Gosub
Plot
If YI=O
Or Y2=180
Then
Goto Jumps
! NN*WW..W**....
Otherwise
a false
deviation
will
be
Endlf
! MMM.WWWN.**MW*
plotted
on the return
scan
If
lnt(Devl)=lnt(Dev2)
Then
! wNM**wMM.M*MMM*Mw.**,
do not print
deviation
Goto Jumps
Endif
If Int(Devl)<[nt(Dev2)
Then
! N..W...#*...
the deviation
is now
increasing
U=48+Int(Dev2)
Goto
Jump5
Endlf
u=Ag+lnt(Devl)
! ...W_N**W_
"U"
is ASCIi
value
of deviation
(whole
number)
JumpS:
Deftext
i,l,O,S
! ***w.**_*w._*..ff
Size
of print
for
"standard
Deviation"
Text
Xof+X1.Xcf-2,Yof-Y1.Ycf+2,
l,Chr$(U)
! x..*
Print
"Standard
Deviation"
JumpS:
Return
' ####l##############d###d##################1##############################_#
Procedure
ELevation
Angle
and
Distance
having
been
determined
Recording
Angle
in the Horizontal
Plane,
of Reoording
Angle
can
be determined
as
Elevation
(Angle
and
Distance
remaining
"E" = angle
of elevation
of sound
·
.
·
for
a given
the variation
a fonction
of
constant)
source
E=O
For
E%=O To
180
If XI<O Then
Goto Jump2
EndLf
_=30
Gosub
Intercept
Step
! do
If
Xl=O
Or Y1=180
Goto
Jump2
Endif
Gosub
Plot
1
not
try
Then
I
analysing
supress
compensated
return
Jump2:
Next
E_
Return
2O
scan
stereo
*
*
.
' ################################################l#####1N###################
Procedure
Axesl
Xof=S5
!*#######*##.*###_K*
X AXIS
OFFSET
in
pixels
Xcf:ll.3
!*..**x.*..w....****
X CONVERSION
FACTOR
(degrees
Yof=325
!.*..*x*.**#.*..*#..
Y AXIS
OFFSET
in
pixels
Ycf=l.75
!....*M.W*.M**MK*WMW
Y CONVERSION
FACTOR
(degrees
Gosub
Xaxisl
Gosub
Xscalel
Gosub
Yaxisi
Gosub
Yscalel
Return
...........................................................................
to
pixels)
to
pixels)
. rocedure
Axes2
Xof=55
!*M**W_..*M***._*W*.
X AXIS
OFFSET
in
pixels
Xcf=6.3
!*.N*N**MW**._W*W*W*
X CONVERSION
FACTOR
(degrees
Yof=325
!..**_.M**ww_w_**_**
Y AXIS
OFFSET
in pixels
Ycf=l.7
!**N*M*M**_**.*****_
Y CONVERSION
FACTOR
(degrees
to
Gosub
Xaxis2
Gosub
Xscale2
Gosub
Yaxis2
Gosub
Yscale2
Return
t ...........................................................................
Procedure
Xaxisl
Fo_
X=O To SO Step 5
Line
Xof+X*Xcf,Yof+S,Xof+XMXof,Yof-180*Yof
Next
X
Line
Xof-l,Yof-i,Xof-i,Yof-18OmYcf
Return
y ...........................................................................
Procedure
Xaxis2
For
X=O
To 90 Step
lO
Line
Xof+X_Xcf,Yof+S,Xof+X*Xcf,Yof-igO*Ycf
Next
X
Line
Xof-l,Yof-i.
Xof-l. Yof-180*Ycf
Return
...........................................................................
Procedure
Xscalel
Deftext
1,16,0,8
Text
Xof-4,Yof+18,-67,"O
5"
Text Xof+lO2, Yof+lg,-477,"lO
15 20 25 30 35 40 45 50"
Text
Xof,358,-550,"--DISTANCE
BETWEEN
MICROPHONES
(cms)---"
Return
, ...........................................................................
Procedure
Xscale2
Deftext
1,16,0,8
Text
Xof-4,Yof+ig,-i6,"O"
Text
Xof+lO.Xcf-12,Yof+lS,-(80NXcf+24),"lO
Text
Xof+30,358.-SO0,"
........
HALF
Return
21
20
RECORDING
30 40
ANGLE
50 60 70 80
........
"
90"
to
pixels)
pixels)
!
...........................................................................
Procedure
Yaxisl
For
Y=O To 180 Step
10
Line
Xof-5,Yof-Y.Ycf,Xof+SOMXcf,Yof-Y"Ycf
Next
Y
Line
Xof-l,Yof-l,×of+5OwXcf,Yof-I
Return
t ...........................................................................
Procedure
Yax s2
For
Y=O To 180 Step
10
Line
Xef-S.Yof-Y,Ycf.
Xof+90*×of.
Yof-Y"Ycf
Next
Y
Line
Xof-l,Yof-l,Xof+9OwXcf,Yof-1
Return
...........................................................................
Procedure
Yscalel
Deftext
1,16,0,13
Text
Xpf-23iYof+5,19."Ox"
Text
Xof-30,Yof-20_Ycf+5,27,"20x"
Text
Xof-30
yof-40.Ycf+S,27,"40x"
Text
Xof-30,Yof-GO*Ycf+5,27,"60x"
Text
Xof-30
yof-80_Ycf+S,27,"80x"
Text
Xof-38, yof-lOO.Ycf+5,35,"100x"
Text
Xef-38¥ef-i20#Ycf+S,35,"120x"
Te_t
Xof-38
yof-l_O.Ycf+5,35,"140x"
Text
Xof-38
yof-[60_Ycf+5,35,"lSOx"
Text
Xof-38
yof-iSO*Ycf+5,35,"lSOx"
Deftext
1,16,900,8
Text
[O,Yof,325,"ANGLE
BETWEEN
MICROPHONES
-"
Return
t ...........................................................................
Procedure
Ysca|e2
Deftext
1,16,0,13
Text
Xof-23,Yof+5,19,"Ox"
Text
Xof-30, Yof-20#Ycf+5,27,"20x"
Text
Xof-30, Yof-40_Ycf+5,27,"40x"
Text
Xof-30, Yof-60_Ycf+5,27,"60x"
Text
Xof-30,Yof-80.Ycf+5,27t"80x"
Text
×of-38,Yef-lOO.Ycf+5,35,"iOOx"
Text
Xof-38,Yof-120*Ycf+S,35,"120x"
Text
Xof-38,Yof-140.Ycf+5,35,"140x"
Text
Xof-38,Yof-160.Ycf+5,35,"lSOx"
Text
Xof-38, Yof-180.Ycf+5,35,"iSOx"
Deftext
1,16,900,8
Text
10,¥of,310,"--ELEVATION
ANGLE
---"
Return
, ##4#######################################t################################
Procedure
Plot
! .**_x_
Line
Xof+Xi.Xcf,Yof-YI.Ycf,Xof+X2*Xof,Yof-Y2"Ycf
Line
Xof+X1.Xcf,Yof-Y1.Ycf-l,Xof+X2.Xcf,Yof-Y2*Ycf'l
Return
, #########################################m_################################
22
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