<s>
Tuning	O
two	O
tones	O
to	O
a	O
unison	B-Protocol
will	O
present	O
a	O
peculiar	O
effect	O
:	O
when	O
the	O
two	O
tones	O
are	O
close	O
in	O
pitch	O
but	O
not	O
identical	O
,	O
the	O
difference	O
in	O
frequency	O
generates	O
the	O
beating	B-Application
.	O
</s>
<s>
As	O
the	O
two	O
tones	O
gradually	O
approach	O
unison	B-Protocol
,	O
the	O
beating	B-Application
slows	O
down	O
and	O
may	O
become	O
so	O
slow	O
as	O
to	O
be	O
imperceptible	O
.	O
</s>
<s>
As	O
the	O
two	O
tones	O
get	O
further	O
apart	O
,	O
their	O
beat	B-Application
frequency	I-Application
starts	O
to	O
approach	O
the	O
range	O
of	O
human	O
pitch	O
perception	O
,	O
the	O
beating	B-Application
starts	O
to	O
sound	O
like	O
a	O
note	O
,	O
and	O
a	O
combination	O
tone	O
is	O
produced	O
.	O
</s>
<s>
This	O
combination	O
tone	O
can	O
also	O
be	O
referred	O
to	O
as	O
a	O
missing	B-Application
fundamental	I-Application
,	O
as	O
the	O
beat	B-Application
frequency	I-Application
of	O
any	O
two	O
tones	O
is	O
equivalent	O
to	O
the	O
frequency	O
of	O
their	O
implied	O
fundamental	O
frequency	O
.	O
</s>
<s>
This	O
phenomenon	O
is	O
best	O
known	O
in	O
acoustics	O
or	O
music	O
,	O
though	O
it	O
can	O
be	O
found	O
in	O
any	O
linear	O
system	O
:	O
"	O
According	O
to	O
the	O
law	O
of	O
superposition	O
,	O
two	O
tones	O
sounding	O
simultaneously	O
are	O
superimposed	O
in	O
a	O
very	O
simple	O
way	O
:	O
one	O
adds	O
their	O
amplitudes	B-Application
"	O
.	O
</s>
<s>
Consider	O
two	O
sine	O
waves	O
of	O
unit	O
amplitude	B-Application
:	O
</s>
<s>
Instead	O
,	O
it	O
is	O
perceived	O
as	O
a	O
periodic	O
variation	O
in	O
the	O
amplitude	B-Application
of	O
the	O
first	O
term	O
in	O
the	O
expression	O
above	O
.	O
</s>
<s>
that	O
its	O
amplitude	B-Application
is	O
modulated	O
.	O
</s>
<s>
However	O
,	O
because	O
the	O
human	O
ear	O
is	O
not	O
sensitive	O
to	O
the	O
phase	O
of	O
a	O
sound	O
,	O
only	O
its	O
amplitude	B-Application
or	O
intensity	O
,	O
only	O
the	O
magnitude	O
of	O
the	O
envelope	O
is	O
heard	O
.	O
</s>
<s>
Therefore	O
,	O
subjectively	O
,	O
the	O
frequency	O
of	O
the	O
envelope	O
seems	O
to	O
have	O
twice	O
the	O
frequency	O
of	O
the	O
modulating	O
cosine	O
,	O
which	O
means	O
the	O
audible	O
beat	B-Application
frequency	I-Application
is	O
:	O
</s>
<s>
Beating	B-Application
can	O
also	O
be	O
heard	O
between	O
notes	O
that	O
are	O
near	O
to	O
,	O
but	O
not	O
exactly	O
,	O
a	O
harmonic	B-Library
interval	O
,	O
due	O
to	O
some	O
harmonic	B-Library
of	O
the	O
first	O
note	O
beating	B-Application
with	O
a	O
harmonic	B-Library
of	O
the	O
second	O
note	O
.	O
</s>
<s>
For	O
example	O
,	O
in	O
the	O
case	O
of	O
perfect	O
fifth	O
,	O
the	O
third	O
harmonic	B-Library
(	O
i.e.	O
</s>
<s>
second	O
overtone	O
)	O
of	O
the	O
bass	O
note	O
beats	O
with	O
the	O
second	O
harmonic	B-Library
(	O
first	O
overtone	O
)	O
of	O
the	O
other	O
note	O
.	O
</s>
<s>
As	O
well	O
as	O
with	O
out-of	O
tune	O
notes	O
,	O
this	O
can	O
also	O
happen	O
with	O
some	O
correctly	O
tuned	O
equal	O
temperament	O
intervals	O
,	O
because	O
of	O
the	O
differences	O
between	O
them	O
and	O
the	O
corresponding	O
just	O
intonation	O
intervals	O
:	O
see	O
Harmonic	B-Library
series	O
(	O
music	O
)	O
#Harmonics	O
and	O
tuning	O
.	O
</s>
<s>
A	O
binaural	O
beat	O
is	O
an	O
auditory	B-Application
illusion	I-Application
perceived	O
when	O
two	O
different	O
pure-tone	O
sine	O
waves	O
,	O
both	O
with	O
frequencies	O
lower	O
than	O
1500Hz	O
,	O
with	O
less	O
than	O
a	O
40Hz	O
difference	O
between	O
them	O
,	O
are	O
presented	O
to	O
a	O
listener	O
dichotically	O
(	O
one	O
through	O
each	O
ear	O
)	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
a	O
530Hz	O
pure	O
tone	O
is	O
presented	O
to	O
a	O
subject	O
's	O
right	O
ear	O
,	O
while	O
a	O
520Hz	O
pure	O
tone	O
is	O
presented	O
to	O
the	O
subject	O
's	O
left	O
ear	O
,	O
the	O
listener	O
will	O
perceive	O
the	O
auditory	B-Application
illusion	I-Application
of	O
a	O
third	O
tone	O
,	O
in	O
addition	O
to	O
the	O
two	O
pure-tones	O
presented	O
to	O
each	O
ear	O
.	O
</s>
<s>
Binaural-beat	O
perception	O
originates	O
in	O
the	O
inferior	O
colliculus	O
of	O
the	O
midbrain	O
and	O
the	O
superior	O
olivary	O
complex	O
of	O
the	O
brainstem	O
,	O
where	O
auditory	B-Algorithm
signals	I-Algorithm
from	O
each	O
ear	O
are	O
integrated	O
and	O
precipitate	O
electrical	B-Algorithm
impulses	I-Algorithm
along	O
neural	B-General_Concept
pathways	I-General_Concept
through	O
the	O
reticular	O
formation	O
up	O
the	O
midbrain	O
to	O
the	O
thalamus	O
,	O
auditory	O
cortex	O
,	O
and	O
other	O
cortical	O
regions	O
.	O
</s>
<s>
Musicians	O
commonly	O
use	O
interference	B-Application
beats	I-Application
objectively	O
to	O
check	O
tuning	O
at	O
the	O
unison	B-Protocol
,	O
perfect	O
fifth	O
,	O
or	O
other	O
simple	O
harmonic	B-Library
intervals	O
.	O
</s>
<s>
The	O
composer	B-Application
Alvin	O
Lucier	O
has	O
written	O
many	O
pieces	O
that	O
feature	O
interference	B-Application
beats	I-Application
as	O
their	O
main	O
focus	O
.	O
</s>
<s>
Italian	O
composer	B-Application
Giacinto	O
Scelsi	O
,	O
whose	O
style	O
is	O
grounded	O
on	O
microtonal	O
oscillations	O
of	O
unisons	B-Protocol
,	O
extensively	O
explored	O
the	O
textural	O
effects	O
of	O
interference	B-Application
beats	I-Application
,	O
particularly	O
in	O
his	O
late	O
works	O
such	O
as	O
the	O
violin	O
solos	O
Xnoybis	O
(	O
1964	O
)	O
and	O
L'âme	O
ailée	O
/	O
L'âme	O
ouverte	O
(	O
1973	O
)	O
,	O
which	O
feature	O
them	O
prominently	O
(	O
Scelsi	O
treated	O
and	O
notated	O
each	O
string	O
of	O
the	O
instrument	O
as	O
a	O
separate	O
part	O
,	O
so	O
that	O
his	O
violin	O
solos	O
are	O
effectively	O
quartets	O
of	O
one-strings	O
,	O
where	O
different	O
strings	O
of	O
the	O
violin	O
may	O
be	O
simultaneously	O
playing	O
the	O
same	O
note	O
with	O
microtonal	O
shifts	O
,	O
so	O
that	O
the	O
interference	O
patterns	O
are	O
generated	O
)	O
.	O
</s>
<s>
Composer	B-Application
Phill	O
Niblock	O
's	O
music	O
is	O
entirely	O
based	O
on	O
beating	B-Application
caused	O
by	O
microtonal	O
differences	O
.	O
</s>
<s>
Computer	O
engineer	O
Toso	O
Pankovski	O
invented	O
a	O
method	O
based	O
on	O
auditory	O
interference	B-Application
beating	I-Application
to	O
screen	O
participants	O
in	O
online	O
auditory	O
studies	O
for	O
headphones	B-Device
and	O
dichotic	O
context	O
(	O
whether	O
the	O
stereo	O
channels	O
are	O
mixed	O
or	O
completely	O
separated	O
)	O
.	O
</s>
