<s>
A	O
Shepard	B-Application
tone	I-Application
,	O
named	O
after	O
Roger	O
Shepard	O
,	O
is	O
a	O
sound	O
consisting	O
of	O
a	O
superposition	O
of	O
sine	O
waves	O
separated	O
by	O
octaves	B-Language
.	O
</s>
<s>
When	O
played	O
with	O
the	O
bass	O
pitch	O
of	O
the	O
tone	O
moving	O
upward	O
or	O
downward	O
,	O
it	O
is	O
referred	O
to	O
as	O
the	O
Shepard	B-Application
scale	I-Application
.	O
</s>
<s>
This	O
creates	O
the	O
auditory	B-Application
illusion	I-Application
of	O
a	O
tone	O
that	O
seems	O
to	O
continually	O
ascend	O
or	O
descend	O
in	O
pitch	O
,	O
yet	O
which	O
ultimately	O
gets	O
no	O
higher	O
or	O
lower	O
.	O
</s>
<s>
Each	O
square	O
in	O
Figure	O
1	O
indicates	O
a	O
tone	O
,	O
with	O
any	O
set	O
of	O
squares	O
in	O
vertical	O
alignment	O
together	O
making	O
one	O
Shepard	B-Application
tone	I-Application
.	O
</s>
<s>
The	O
color	O
of	O
each	O
square	O
indicates	O
the	O
loudness	B-Algorithm
of	O
the	O
note	O
,	O
with	O
purple	O
being	O
the	O
quietest	O
and	O
green	O
the	O
loudest	O
.	O
</s>
<s>
Overlapping	O
notes	O
that	O
play	O
at	O
the	O
same	O
time	O
are	O
exactly	O
one	O
octave	B-Language
apart	O
,	O
and	O
each	O
scale	O
fades	O
in	O
and	O
fades	O
out	O
so	O
that	O
hearing	O
the	O
beginning	O
or	O
end	O
of	O
any	O
given	O
scale	O
is	O
impossible	O
.	O
</s>
<s>
As	O
a	O
conceptual	O
example	O
of	O
an	O
ascending	O
Shepard	B-Application
scale	I-Application
,	O
the	O
first	O
tone	O
could	O
be	O
an	O
almost	O
inaudible	O
C4	O
(	O
middle	O
C	O
)	O
and	O
a	O
loud	O
C5	O
(	O
an	O
octave	B-Language
higher	O
)	O
.	O
</s>
<s>
The	O
two	O
frequencies	O
would	O
be	O
equally	O
loud	O
at	O
the	O
middle	O
of	O
the	O
octave	B-Language
(	O
F4	O
and	O
F5	O
)	O
,	O
and	O
the	O
twelfth	O
tone	O
would	O
be	O
a	O
loud	O
B4	O
and	O
an	O
almost	O
inaudible	O
B5	O
with	O
the	O
addition	O
of	O
an	O
almost	O
inaudible	O
B3	O
.	O
</s>
<s>
(	O
In	O
other	O
words	O
,	O
each	O
tone	O
consists	O
of	O
two	O
sine	O
waves	O
with	O
frequencies	O
separated	O
by	O
octaves	B-Language
;	O
the	O
intensity	O
of	O
each	O
is	O
e.g.	O
</s>
<s>
The	O
scale	O
as	O
described	O
,	O
with	O
discrete	O
steps	O
between	O
each	O
tone	O
,	O
is	O
known	O
as	O
the	O
discrete	O
Shepard	B-Application
scale	I-Application
.	O
</s>
<s>
Jean-Claude	O
Risset	O
subsequently	O
created	O
a	O
version	O
of	O
the	O
scale	O
where	O
the	O
tones	O
glide	O
continuously	O
,	O
and	O
it	O
is	O
appropriately	O
called	O
the	O
continuous	B-Application
Risset	I-Application
scale	I-Application
or	O
Shepard	O
–	O
Risset	O
glissando	O
.	O
</s>
<s>
A	O
sequentially	O
played	O
pair	O
of	O
Shepard	B-Application
tones	I-Application
separated	O
by	O
an	O
interval	O
of	O
a	O
tritone	O
(	O
half	O
an	O
octave	B-Language
)	O
produces	O
the	O
tritone	O
paradox	O
.	O
</s>
<s>
Pedro	O
Patricio	O
observed	O
in	O
2012	O
that	O
,	O
by	O
using	O
a	O
Shepard	B-Application
tone	I-Application
as	O
a	O
sound	O
source	O
and	O
applying	O
it	O
to	O
a	O
melody	O
,	O
he	O
could	O
reproduce	O
the	O
illusion	O
of	O
a	O
continuously	O
ascending	O
or	O
descending	O
movement	O
characteristic	O
of	O
the	O
Shepard	B-Application
Scale	I-Application
.	O
</s>
<s>
Regardless	O
of	O
the	O
tempo	O
and	O
the	O
envelope	O
of	O
the	O
notes	O
,	O
the	O
auditory	B-Application
illusion	I-Application
is	O
effectively	O
maintained	O
.	O
</s>
<s>
The	O
uncertainty	O
of	O
the	O
scale	O
the	O
Shepard	B-Application
tones	I-Application
pertain	O
allows	O
composers	O
to	O
experiment	O
with	O
deceiving	O
and	O
disconcerting	O
melodies	O
.	O
</s>
<s>
James	O
Tenney	O
's	O
For	O
Ann	O
(	O
rising	O
)	O
consists	O
entirely	O
of	O
a	O
Shepard	B-Application
tone	I-Application
glissando	O
with	O
gradual	O
modulations	O
.	O
</s>
<s>
A	O
section	O
near	O
the	O
end	O
of	O
Karlheinz	O
Stockhausen	O
's	O
Hymnen	O
incorporates	O
multiple	O
descending	O
Shepard	B-Application
tone	I-Application
glissandos	O
.	O
</s>
<s>
The	O
ending	O
of	O
The	B-Application
Beatles	I-Application
 '	O
"	O
I	O
Am	O
the	O
Walrus	O
"	O
incorporates	O
a	O
Shepard	B-Application
tone	I-Application
with	O
a	O
chord	O
progression	O
built	O
on	O
ascending	O
and	O
descending	O
lines	O
in	O
the	O
bass	O
and	O
strings	O
that	O
line	O
up	O
to	O
create	O
the	O
auditory	B-Application
illusion	I-Application
.	O
</s>
<s>
The	O
ending	O
of	O
Pink	O
Floyd	O
's	O
"	O
Echoes	O
"	O
from	O
their	O
1971	O
album	O
Meddle	O
features	O
an	O
ascending	O
Shepard	B-Application
tone	I-Application
created	O
using	O
a	O
feedback	O
technique	O
involving	O
two	O
tape	O
recorders	O
sharing	O
a	O
single	O
tape	O
,	O
with	O
one	O
set	O
to	O
play	O
and	O
the	O
other	O
to	O
record	O
.	O
</s>
<s>
Queen	O
's	O
1976	O
album	O
A	O
Day	O
at	O
the	O
Races	O
opens	O
and	O
closes	O
with	O
a	O
Shepard	B-Application
tone	I-Application
.	O
</s>
<s>
In	O
his	O
1979	O
book	O
Gödel	O
,	O
Escher	O
,	O
Bach	O
:	O
An	O
Eternal	O
Golden	O
Braid	O
,	O
Douglas	O
Hofstadter	O
explained	O
how	O
Shepard	B-Application
scales	I-Application
could	O
be	O
used	O
on	O
the	O
Canon	O
a	O
2	O
,	O
per	O
tonos	O
in	O
Bach	O
's	O
Musical	O
Offering	O
(	O
called	O
the	O
Endlessly	O
Rising	O
Canon	O
by	O
Hofstadter	O
)	O
for	O
making	O
the	O
modulation	O
end	O
in	O
the	O
same	O
pitch	O
instead	O
of	O
an	O
octave	B-Language
higher	O
.	O
</s>
<s>
In	O
1995	O
,	O
Ira	O
Braus	O
argued	O
that	O
the	O
final	O
sequence	O
of	O
Franz	O
Liszt	O
's	O
1885	O
piano	O
piece	O
Bagatelle	O
sans	O
tonalité	O
could	O
be	O
continued	O
to	O
produce	O
a	O
Shepard	B-Application
scale	I-Application
using	O
Hofstadter	O
's	O
technique	O
.	O
</s>
<s>
In	O
a	O
1967	O
AT&T	O
film	O
by	O
Shepard	O
and	O
E	O
.	O
E	O
.	O
Zajac	O
,	O
a	O
Shepard	B-Application
tone	I-Application
accompanies	O
the	O
ascent	O
of	O
an	O
analogous	O
Penrose	O
stair	O
.	O
</s>
<s>
In	O
the	O
video	O
game	O
Super	B-Application
Mario	I-Application
64	I-Application
(	O
1996	O
)	O
for	O
the	O
Nintendo	B-Operating_System
64	I-Operating_System
console	O
,	O
a	O
piece	O
that	O
plays	O
when	O
the	O
player	O
tries	O
to	O
climb	O
the	O
neverending	O
stairs	O
located	O
in	O
the	O
penultimate	O
room	O
of	O
Peach	O
's	O
Castle	O
incorporates	O
a	O
slightly	O
modified	O
Shepard	B-Application
scale	I-Application
played	O
in	O
the	O
background	O
.	O
</s>
<s>
This	O
auditory	B-Application
illusion	I-Application
complements	O
the	O
spatial	O
loop	O
effect	O
,	O
seemingly	O
giving	O
the	O
impression	O
that	O
the	O
stairs	O
never	O
end	O
.	O
</s>
<s>
Black	O
Emperor	O
's	O
"	O
The	O
Dead	O
Flag	O
Blues	O
"	O
from	O
their	O
1997	O
album	O
F♯	O
A♯	O
∞	O
,	O
a	O
section	O
mainly	O
consisting	O
of	O
slide	O
guitar	O
is	O
briefly	O
looped	O
into	O
itself	O
to	O
create	O
a	O
downward	O
Shepard	B-Application
tone	I-Application
.	O
</s>
<s>
Austrian	O
composer	O
Georg	O
Friedrich	O
Haas	O
incorporates	O
Shepard	B-Application
tones	I-Application
at	O
various	O
points	O
in	O
his	O
orchestral	O
piece	O
in	O
vain	O
(	O
2000/02	O
)	O
.	O
</s>
<s>
Christopher	O
Nolan	O
said	O
in	O
an	O
interview	O
that	O
the	O
soundtrack	O
of	O
his	O
film	O
The	O
Prestige	O
(	O
composed	O
by	O
David	O
Julyan	O
)	O
explores	O
the	O
potential	O
of	O
Shepard	B-Application
tones	I-Application
as	O
a	O
fundamental	O
basis	O
for	O
compositions	O
.	O
</s>
<s>
In	O
Stephin	O
Merritt	O
's	O
2007	O
song	O
"	O
Man	O
of	O
a	O
Million	O
Faces	O
"	O
,	O
composed	O
for	O
NPR	O
's	O
"	O
Project	O
Song	O
"	O
,	O
the	O
Shepard	B-Application
tone	I-Application
is	O
a	O
key	O
aspect	O
.	O
</s>
<s>
In	O
the	O
2008	O
film	O
The	O
Dark	O
Knight	O
and	O
its	O
2012	O
followup	O
The	O
Dark	O
Knight	O
Rises	O
,	O
a	O
Shepard	B-Application
tone	I-Application
was	O
used	O
to	O
create	O
the	O
sound	O
of	O
the	O
Batpod	O
,	O
a	O
motorcycle	O
that	O
the	O
filmmakers	O
did	O
not	O
want	O
to	O
change	O
gear	O
and	O
tone	O
abruptly	O
but	O
to	O
accelerate	O
constantly	O
.	O
</s>
<s>
In	O
the	O
2017	O
film	O
Dunkirk	O
,	O
a	O
Shepard	B-Application
tone	I-Application
is	O
used	O
to	O
create	O
the	O
illusion	O
of	O
an	O
ever	O
increasing	O
moment	O
of	O
intensity	O
across	O
intertwined	O
storylines	O
.	O
</s>
<s>
In	O
Lucrecia	O
Martel	O
's	O
feature	O
film	O
Zama	O
(	O
2017	O
)	O
,	O
there	O
is	O
extensive	O
use	O
of	O
the	O
Shepard	B-Application
tone	I-Application
creating	O
a	O
"	O
loud	O
and	O
shreechy	O
soundscape	O
,	O
in	O
order	O
to	O
achieve	O
closeness	O
to	O
the	O
viewer	O
"	O
,	O
according	O
to	O
the	O
director	O
.	O
</s>
<s>
The	O
2018	O
track	O
"	O
Always	O
Ascending	O
"	O
by	O
Franz	O
Ferdinand	O
from	O
the	O
album	O
of	O
the	O
same	O
name	O
features	O
a	O
rising	O
Shepard	B-Application
tone	I-Application
throughout	O
the	O
song	O
.	O
</s>
<s>
In	O
Sumio	O
Kobayashi	O
's	O
piano	O
work	O
"	O
Unreal	O
Rain	O
"	O
,	O
the	O
Shepard	B-Application
tone	I-Application
is	O
entirely	O
used	O
.	O
</s>
