<s>
Virtual	B-Application
pitch	I-Application
is	O
the	O
pitch	O
of	O
a	O
complex	O
tone	O
(	O
a	O
physical	O
vibration	O
that	O
can	O
be	O
decomposed	O
into	O
partials	O
or	O
pure	O
tone	O
components	O
)	O
.	O
</s>
<s>
Virtual	B-Application
pitch	I-Application
corresponds	O
approximately	O
to	O
the	O
fundamental	O
of	O
a	O
harmonic	O
series	O
that	O
is	O
recognized	O
among	O
the	O
audible	O
partials	O
.	O
</s>
<s>
A	O
virtual	B-Application
pitch	I-Application
may	O
be	O
perceived	O
even	O
if	O
the	O
perceived	O
pattern	O
is	O
incomplete	O
(	O
in	O
particular	O
,	O
if	O
the	O
fundamental	O
is	O
missing	O
)	O
or	O
mistuned	O
.	O
</s>
<s>
In	O
that	O
respect	O
,	O
virtual	B-Application
pitch	I-Application
perception	O
is	O
similar	O
to	O
other	O
forms	O
of	O
pattern	O
recognition	O
.	O
</s>
<s>
Virtual	B-Application
pitch	I-Application
is	O
contrasted	O
to	O
spectral	O
pitch	O
,	O
which	O
is	O
the	O
pitch	O
of	O
a	O
pure	O
tone	O
or	O
spectral	O
component	O
.	O
</s>
<s>
Virtual	B-Application
pitch	I-Application
is	O
called	O
"	O
virtual	O
"	O
because	O
there	O
is	O
no	O
acoustical	O
correlate	O
at	O
the	O
frequency	O
corresponding	O
to	O
the	O
pitch	O
:	O
even	O
when	O
a	O
virtual	B-Application
pitch	I-Application
corresponds	O
to	O
a	O
physically	O
present	O
fundamental	O
(	O
or	O
first	O
harmonic	O
)	O
,	O
as	O
it	O
often	O
does	O
in	O
everyday	O
harmonic	O
complex	O
tones	O
,	O
the	O
exact	O
virtual	B-Application
pitch	I-Application
depends	O
on	O
the	O
exact	O
frequencies	O
of	O
higher	O
harmonics	O
and	O
is	O
almost	O
independent	O
of	O
the	O
exact	O
frequency	O
of	O
the	O
fundamental	O
.	O
</s>
<s>
Virtual	B-Application
pitch	I-Application
is	O
an	O
experimentally	O
established	O
phenomenon	O
in	O
humans	O
that	O
can	O
be	O
mathematically	O
described	O
.	O
</s>
<s>
In	O
its	O
basic	O
form	O
,	O
given	O
a	O
series	O
of	O
pure	O
tones	O
whose	O
frequencies	O
correspond	O
to	O
a	O
harmonic	O
series	O
,	O
one	O
will	O
hear	O
a	O
virtual	B-Application
pitch	I-Application
near	O
the	O
fundamental	O
frequency	O
,	O
even	O
if	O
there	O
is	O
no	O
pure	O
tone	O
at	O
that	O
frequency	O
.	O
</s>
<s>
The	O
perceptual	O
salience	O
(	O
clarity	O
,	O
probability	O
of	O
noticing	O
)	O
of	O
the	O
virtual	B-Application
pitch	I-Application
depends	O
on	O
how	O
closely	O
the	O
audible	O
partials	O
match	O
lower	O
harmonics	O
above	O
the	O
virtual	B-Application
pitch	I-Application
.	O
</s>
<s>
In	O
Terhardt	O
's	O
pitch	O
algorithm	O
,	O
virtual	B-Application
pitches	I-Application
are	O
predicted	O
by	O
looking	O
for	O
subharmonic	O
coincidences	O
between	O
audible	O
partials	O
in	O
a	O
complex	O
tone	O
-	O
in	O
other	O
words	O
,	O
by	O
looking	O
for	O
missing	B-Application
fundamentals	I-Application
.	O
</s>
<s>
Virtual	B-Application
pitch	I-Application
can	O
be	O
visualized	O
in	O
the	O
time	O
domain	O
by	O
adding	O
together	O
sine	O
waves	O
corresponding	O
to	O
harmonics	O
of	O
a	O
given	O
fundamental	O
and	O
deleting	O
the	O
fundamental	O
.	O
</s>
<s>
However	O
,	O
in	O
Terhardt	O
's	O
theory	O
the	O
virtual	B-Application
pitch	I-Application
does	O
not	O
depend	O
on	O
this	O
period	O
.	O
</s>
<s>
measurements	O
of	O
the	O
gradual	O
shift	O
of	O
the	O
virtual	B-Application
pitch	I-Application
of	O
a	O
complex	O
tone	O
with	O
a	O
missing	B-Application
fundamental	I-Application
when	O
the	O
partials	O
were	O
gradually	O
shifted	O
.	O
</s>
<s>
On	O
this	O
basis	O
,	O
Terhardt	O
proposed	O
that	O
spectral	O
pitches	O
-	O
which	O
are	O
what	O
the	O
listener	O
experiences	O
when	O
hearing	O
out	O
partials	O
(	O
as	O
opposed	O
to	O
the	O
physical	O
partials	O
themselves	O
)	O
-	O
are	O
the	O
only	O
information	O
available	O
to	O
the	O
brain	O
for	O
the	O
purpose	O
of	O
extracting	O
virtual	B-Application
pitches	I-Application
.	O
</s>
