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Pythagoras and Pierrot: An Approach to Schoenberg's Use of Numerology in the Constructionof 'Pierrot lunaire'Author(s): Colin C. SterneReviewed work(s):Source: Perspectives of New Music, Vol. 21, No. 1/2 (Autumn, 1982 - Summer, 1983), pp. 506-534Published by: Perspectives of New Music
Stable URL: http://www.jstor.org/stable/832890 .Accessed: 22/09/2012 04:28
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PYTHAGORAS AND
PIERROT
an
approach
to
Schoenberg's
use of
numerology
in
the
construction f
Pierrot
unaire'
Colin
C.
Sterne
"It
s not
uperstition,
t
s
belief."'
hus did Arnold
choenberg
defend
he
mportance
e
attached
othe
power
f
numerology
nd to ts
influencen his ife.
isfear
f
he
number
hirteenscommon
nowledge.
So, too,
s the
way
n
which hat umber
arked
isbirth
September
3,
1874)
anddeath
Friday,
uly
3, 1951,
t
ge
76).
Schoenberg
s
said o
have bservedhe
lagging
f
his reative
nergyuring
he
ompositional
process
t
measures
whose
numbers
ere
thirteenr
its
multiples,
circumstancehat eportedlyedto hisnumberingfmeasuresnhis
manuscripts
s
12, 12a,
14. We
are
told
hat
ven he
hoice f
name
forhis
son,
Lawrence
dam,
was made
only
fter
oland,
he
name
originally
ntended
orhim
and
an
anagram
f
hisfather'sirst
ame),
wasfoundobe
numerologically
nfavorable.
choenberg's
lmost
atho-
logical
ear
fthenumber hirteen
roduced
orebodings
f his
death,
and,
ne
suspects,
ay
venhave
ontributed
o
bringing
t
bout.
Nor has the number
ymbolism
f
Schoenberg's
ierrot
unaire
beencompletelyverlooked.thas beennoted hat orhisOpus 21
Schoenberg
hose
21 ofAlbert
iraud's
ifty
oems
s texts
translated
from renchnto
German
y
Otto
rich
Hartleben),iving
he
work
he
complete
itle
reimal ieben
Gedichteus ALBERT
GIRAUDs
ierrot
lunaire,
nd
beginning
o
compose
it in the
thirdmonth f
a
year
containing
he
ymbolic
igits
1 in
reverse
rder,
912.
In
spite
f ll
this,
urprisingly
ittlettentionas been
focused
n the
part
hat he
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507
numbers
and
7
play
s structural
eterminantsithin he
work-
something
choenberg's
itle
bviouslyuggests.2
Pierrotunaire
s indeed
governed
y
numbers,
ot
by
the
crisp,
bright
umbers
f
mathematics,
ut
by
the
more
shadowy,
moonlit
numbers
f
numerology.
ome
knowledge
f basic
numerological
procedure
s
essential,
hen,
efore
pproaching
he
music.3
The
numerologist
s convinced
hat umbers
nd
number elation-
ships overnhe niversendthat hewell-beingf n individualepends
upon
his
being
n
ccord
with
osmic
ibrations.e traces isbelief
ack
to
ntiquity-to
he
gyptians,
ebrews,haldeans, hoenicians,hinese,
and
Hindus--but
t
s
Pythagoras
owhom e
gives
redit or
stablishing
the
system
n theWest.As to the
power
f numbers
n
individuals,
person's
name nd birthdatere
the
two
reas
where he
nfluence
f
numbers
s
most
trongly
elt. o determinehe everal
umber
ibrations
in
person's
ame,
he
etters
f
he
lphabet
re
numbered
onsecutively
from
through
6. In all
aspects
f
numerology,
owever,
ouble-digit
numbersrereduced osingle-digitumbersy dding hedigits. he
tenthetter
f he
lphabet,
,
or
xample,
s not
numbered
0,
but . The
following
hart
ill
emonstratehe
procedure.
1
2
3
4 5 6
7
8 9
A B
C
D E F
G H
I
J
(K)
L
M N
O
P
Q
R
S T U (V) W X Y Z
Note hat wo
etters,
and
V,
are
parenthesized.
hey
re
the11th
and
22nd
letters
f he
lphabet
espectively,
nd
they
etain
hose
alues.
Exceptions
othe
eneral
ule,
1
and
22
are
never
educedn
raditional
numerology
nd
are
referred
oas
master
umbers.
The
application
f
the
chart
may
be
demonstrated
y
using
Schoenberg's
ame:
ARNOLD
SCHOENBERG
195634
1386552597
(=28
=
10=)1 +(=
51=)6
=
7
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508
The
process
s that f
ssigning
ach letternthe
name tsnumber
value,
rriving
t
two
ums,
ne
for
he
first ame
nd one for he
ast,
reducing
hose
ums
by
dding
igits,
nd
arriving
t the
inal
um,
-
the
basicnumber
alue
or
choenberg's
ame.
Expression
umber"s
the
numerological
erm.
ut
here re
additional
umberso be
derived
from
person's
name.
Here
is
a
list
of
those
pertaining
o
Arnold
Schoenberg:4
First
ame LastName Total
Basic
number
expression)
1
+
6
=
7
Consonants
quiescent
elf)
3
+
8
=
11
Vowels
soul
urge)
7
+
7
=
5
Firstnitial
cornerstone)
1
=
1
Total
numberf
etters
name ycle)
6
+
1
=
7
The
procedure
or
rriving
t thebirth atenumbers not
ertinent
to thematter
mmediately
t
hand.
Nor re thenumbers
ssociated
ith
the
planets,
ith
olors,
with
ems,
tc.Butnumbersre also associated
with
he
notes
f he
cale.
The
traditional
rocedure,
ne
geared
o the
diatonic
cale,
was
obviously
f ittlese to
Schoenberg.
is
modification,
to
be
substantiated
resently
romts
pplication
n
Pierrot,
esultsn
the
following
etof
number
alues
or
he
hromaticcale:
C
C#
D
D#
E F
F#
G
G#
A A
B
1 2 3
7
5
6
7
8
9
1 11
3
Itwillbe seen that
choenberg's
rocedure
f
assigning
umber
values o caledegreesssimilarothat sedfor he lphabet. ,the enth
note
n the
hromatic
cale,
s
reduced
o
become
1,
and
B,
the
welfth
note,
ecomes
.
A#.
s
expected,
s not
educed,
ut etainstsmaster
number,
1.
Totally
nexpected,
owever,
s the
ssigning
f7 to
D4,
the ourth
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509
note.
choenberg's
erivation
f7 for hat ote
s not ifficulto
discover:
D#
s not
only
he
fourth
ote n a chromaticcale
built n
C,
but
he
sixteenths well.And
16=6+1=
7.
But
hat
an
Schoenberg's
eason
be?
The most
ogical
xplanation
as
to
do withhatateful
umber,
3.
In
reduction,
3=4.
And
Schoenberg
eems
determined
o
avoid
13,
even
in
ts eduction.
n
additionalactor
ay
e that
#
s
E
b
has
particular
significance
or he
omposer:
s Es
in
German
t
s his
ignature
ote,
representing
he
nitialf his astname.
To
give
his
mportant
ote 4
valuewouldbe unthinkable.
There
willbe occasion o returnoD*-Eb
and
Schoenberg's
usical
ignatureater.)
wo dditionalonuses
esult
from
he
banishmentf
4 from hecanon:
1)
the
scale is
thusmade
consistent
ith he
lphabet,
oth
having
total umber
alue f
9,
and
(2)
the
calecontains
double
ortion
f
choenberg's
avorite
umbers,
1,
3,
and 7.
In
the
title
f
Pierrot
choenberg
ndicateshe
mportance
n
the
work f
wo
numbers,
and
7.
The
importance
f heir
roduct,
1,
is
also implied,ndalthough1 does indeed ssume ome mportancen
Pierrot,
t
must e
rememberedhat
umerologically
1
=3.
It
has been
pointed
ut,
or
xample,
hat he
pus
number f
Pierrot,
1,
is
reversed
in
he ast
wo
igits
f he
year
f
ts
omposition,
912. But his
s
not
he
point.
heterm
retrograde"
s not
part
f he
numerologist's
ocabulary.
Ratherre 12
and 21
related ecause
both re
3 values.
On the
other
hand,
he
umof
and
7
is
important
n
Pierrot.
he
additionf
numbers
is,
fter
ll,
n
essential
art
f
numerology:
+3= 10=
1.
Numerologists
often oint ut, hough,hat numberrrived t byreduction ever
completely
oses its
original
mprint.
1
arrived t
through
0,
for
example,
till
etainshe
vibrationsf
10. This factwill
igure
o
some
extentn
the
nalysis
f
Pierrot.
There
re,
hen,
hree
umbershat
ssume
primary
mportance
n
Pierrot:
, 7,
and
1.
Numbers
1
and 10
lurk
n
he
background,
aking
their
resence
elt,
utnot
eing
ut
o use
except
s 3
and 1.
Two
other umbers
igure
n
Pierrot
hat re
not
ingled
ut
n
the
title
f the
work:
he
master
umbers,
1
and 22.
There re
several
reasonsfor heir ppearance. he firstfthesehas to do with heir
numerological
ignificance.
t
must e
kept
n
mind hat
, 7,
and
1
are
not
merely
umberso
numerologists.
hey
re
not
ven
lucky"
umbers.
Rather
re
they owerful
orces or
ood
or
evil,
xerting
heir
nfluence
on the niverse
nd
profoundly
ffecting
he ives
f
ndividuals.r
at east
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510
they
ere hat
or
Arnold
choenberg.
ere re
meanings
or
,
7,
and
1
that
re
generallygreed
pon
bynumerologists:
3
-
artist,
he ealm
f
rtistic
xpression
7 -
priest,
he ealm f
pirituality
1
-
creator,
nnovator,
ioneer,
he
ealm
f
invention,
f nnovation
The
three umbers
ay
e seen as
appropriate
o Arnold choen-
berg.
But more
mportant,hey
re
particularlyppropriate
o
Pierrot
lunaire,
here
he rt-artist
elationship
nd the
piritualspect
ofthat
relationship
s
a
primary
heme.
11
and
22 have hese
meanings:
11
-
idealist,
isionary,
reamer,
he ealm
f
rtistic
inspiration
22
-
practical
dealist,
ne
whouses his
power
o benefit
mankind
Again,
he
ppropriateness
f
hese
umbers
o
the
ubject
matterf
Pierrotsapparent.hestronglavorf11 and22 throughouthefinal
section
f
Mondestrunken,"
hefirst
ong
n
Pierrot,
uggests
choen-
berg's
iew f
he
Poet-Pierrot-Schoenberg
igure
escribed
here.5
Number
1
is
also
important
ecause
t
figuresmong
Schoen-
berg's
wn
namenumbers.
nd
inally,
t
s of ome
nterestonote
hatt
is associated
with omeone
else who
figures
n
Schoenberg's
work:
Pierrot
imself,
hose
otal
amenumber
s
11,
whose
nitial
umber
s
7,
andwhose
name
ontains
letters.
The 3X7 poemsofAlbert iraudwhich hoenbergelected or
Pierrot
re each
thirteen
ines
ong.
However,
he
poetic
orm,
hat
f
he
rondeau,
aves
he
omposer
rom
ver
having
o come
to
grips
with
3,
since ines
ne and
two
of
each
poem
are
repeated
s
lines
even nd
eight,
nd
ine ne s
repeatedgain
s
line
hirteen.heresult
s
only
0
(= 1)
different
ines
n
each
poem.
choenberg's
omposition,
is
Opus
21
(=3),
was
composed
n
1912
=3),
when
he
omposer
as
37
years
old
=
10=
1).
He commenced
ork n
the
omposition
n
Tuesdayday
3
of he
week),
March
month
)
12
(=3),
and
he had
completed
0 of
the 1 songsbyMay 0. Hedelayedompletinghework, owever,ntil
he
could
omplete
he
emaining
ong
n
Tuesdayday
),
Julymonth
)
9--the
numbers
f
he wo
ates,
2 and
9,
adding
p
to
21
(=3).6
In
his
otherwise
erman
itle,
choenberg
etains
he rench
Pierrot
unaire"--
with letters
neach
word.
ive
nstrumentalists
nd
a reciter
re called
-
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511
for o
perform
he
work,
nd
they,
lus
conductor,
orm
group
f7.
With he hree
pecified
lternate
nstruments
piccolo,
ass
clarinet,
nd
viola),
his umber
ecomes
7+3=-10=1.
A
most
mpressiveisplay
f
Pierrot
umberss
presented
n
the
1914
edition's
itle
age,
theformatfwhichmust
ertainly
avebeen
overseen
y
he
omposer.
he numberf ettersnd ofwords n ach of
its ines
s
used
to
produce
he
ignificant
umbersf he
omposition:
words
letters
per
ine
per
ine
3
DER
ERSTEN
NTERPRETIN 20=2
3
FRAU
LBERTINE
EHME 18=9
3
INHERZLICHERREUNDSCHAFT
24=6
17=8-
=22
3 DREIMALIEBEN EDICHTE 21=3
3
AUSALBERT
IRAUDS
16=7
2
PIERROT
UNAIRE 14=5
5
(DEUTSCH
ON
OTTO ERICH
ARTLEBEN)
28=1 =16=
7
16=7
-
31
FOr
ine
prechstimme
19=1
7
=
16=
Klavier,
l6te
auch
Piccolo),
larinette
auch
Bass- 41
=5
6
7
Klarinette),eige auchBratsche)
nd
Violoncell
40=4
10=1
-
=11
1
(MELODRAMEN)
10=1
1
=
4von
3
2
ARNOLD
CHONBERG
15=6
10=1
Op.
21
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512
Even he
ndividual
oems
f
Pierrot
hare,
or
hemost
art,
n
this
number
lay
withwords
nd
letters,
nd one factorn the
composer's
choices from
Hartleben's
ifty
ranslations
ould seem to have been
whetherr
not heir
umbersittedisown
cheme. he text f Monde-
strunken,"
he irst
f
he
ongs,
its
xtremely
ell:
words
letters
per ine per ine
7
Den
Wein,
en
manmit
ugen
rinkt,
27=9
7
GiesstNachts er
Mond
n
Wogen
nieder,
32=5
4]7
Und ineSpringflutberschwemmt 29=11
3J
Den stillen orizont. 18=9
16=
34=7
7
4] Geloste,chauerlichnd Oss, 25=7
5 Durchschwimmen
hne
Zahl
die Fluten
31= 4
7 Den
Wein,
en
man
mit
ugen
rinkt,
27=9
7 GiesstNachts erMond n
Wogen
nieder.
32=5
25= 7
61
Der
Dichter,
endie Andacht
reibt,
29=1
1
6
257
Berauscht
ich n dem
heilgen
ranke,
31=
4
5 Gen Himmel endetrverzCckt 25=7
8
Das
Haupt
nd aumelnd
augt
nd
schlorft
r
37=
1
7 Den
Wein,
en
manmit
ugen
rinkt.
27=9
32=5
19=10=1
"Mondestrunken"ill lso serve o demonstratehemusical
ro-
cedure of
Arnold
choenberg.
he three tanzasof Giraud's
poem
impose
n
the
piece
ts verall
esign
f
hree
musical
ections,
he lose
of
ach section
eing
marked
y
ritard.
ection
is
14
(=5)
measures
in
ength.
ection
Ialso consists f14
(=5)
measures,
nd Section
II
s
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513
11
(=11)
measures
n
length.
he total
ength
f the
piece
is 39
(=12=3)
measures,
ut ts
numerological
ength
s
5+5+11 =21=3.
The
nfluence
f
he
ive
umbers,,3,
7,
11,
and
22,
is
felt,
owever,
ot
only
n he otal
ength
f
he
piece
nd
n he
engths
f ts
hree
ections,
but
nthe
ength
f
very
ne
of
ts
omponent
hrases
s
well.
he
time
span
of ach
phrase
and
each
rest)
s
measured
n
units
f
ighth
otes,
sixteenth
otes,
r,
ess
frequently,
uarter
otes.
choenberg's
hoice f
the
unit
f
measure
eems o
depend
n the
predominantctivity
ithin
phrase.
At times he
activity
f
the ines
oncurrent
ith
phrase
will
determinets
unit
f
measure.
Within
ach
phrase
ach
note
will
have
pitch
umber
alue,
nd
the
um
f
hese
alues,
n
ppropriate
eduction,
ill e the
itch
umber
value
f
he
phrase
s
opposed
o
ts
ime
pan
value.
Two additional
etsof
number alues re
generated
y
he
music.
The firstf
hese erives
rom
he
measurement
fdistances etweenhe
individual
itches
f
phrase. pplied
o
chords,
he
measurement
s
that
of he istanceetweenachof hepitch omponentsf he hord. hese
intervallic
alues re
normally
easured
n emitones.he
second
et s
a
simplequantitativeumbering
f the
pitches
hat
go
to
make
up
a
particular
egment
f line.
To sum
up,
there
re
four lements
n the
closed
number-system
used
by
choenberg
n
Pierrot:
1. Pitch
values,
derived rom he
numbers
s
assigned
by
Schoenberg
o
the
welve
otes f he
hromaticcale
2. Time panvalues, erived rommeasuringhe engthf
musical
tatement
or
rest)
n
eighth
otes,
ixteenth
otes,
or
quarter
otes
3. Intervallic
alues,
derived
rom
measuring
he
distances
between
itches,
n
either
melodic ine
or
a chord
formation,
he unitof
measurement
ormally
eing
the
semitone
4.
Quantitative
itch
alues,
erived rom
ounting
he
number
of
pitches
hat
o
tomake
p
a
particular
usical tatement
The
process
will e clarified
y ctuallypplying
t o
Schoenberg's
music. score f
Mondestrunken,"
ontaining
numerologicalnalysis,
formsn
integral
art
f he
present
rticle.n
pursuit
f
larity,
nly
lurs
and
phrase
markings
ave een
retained ith he
notes f ach
part,
uch
markings
s those
f
dynamics
nd
tempo
having
een
eliminated.
he
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514
part
or he
reciter as been
beamed n
order o make
phrases
more
apparent,
nd
Schoenberg's
ote
tem
ancellations
n
that
art
have
been
removed.
Number
alues or
he ime
pan
of
each
phrase
ave
been
placed
below
he
staff,
hosefor
pitches
ave
been
placed
above,
with
otals
circled or
mphasis.
n xtended
hrases,
articularly
hose f
he
eciter,
subtotals
f maller
nits
ave een
alculated
here
hey
re
ppropriate.
Each
ubtotal
s
marked
ith
semicircle.
inal otals ave een omputed
fromhem
nd circled.7
"Mondestrunken"
egins
ith
quasi-ostinato
igurelayed y
iolin
and
piano.
he violin
igure
s one of
3
notes.
ach of he wo
pitches
n
the
figure,
#
nd
D#,
has
a
pitch
alue
f
7,
and
3X7=21 =3.
The
3
eighth
otes f he
igure,
ith heir
nitial
ighth
est
= 1),
are
repeated
four
imes,
hereby
ccupying
time
pan
of
16=7
eighth
otes. he
range
f he
igureD#-F#)
s
3 semitones.
Meanwhile,
he
piano
s
playing
figure
f7
notes
preceded
y
singleixteenthest 1).Thepitchalue f hese otes s 9+5+1 +3+
1
1+2+8=39= 12=3. The four
epetitions
f he
igureccupy
time
span
of
16=7
eighth
otes. he
range
f
he
igure,
"#-g"'#,
measured
in
emitones,
s
19=
10=
1.
Alternatively,
he
nterval
#-G#
f
onsidered
withinn
octave,
epresents
distance f
7
semitones.
he
unreduced
sum of
the
pitches
s
39-the
same
figure
s
the
total
number
f
measures
n
"Mondestrunken."
nd
its ntervallic
alue,
measured
n
semitones,
s4+4+2+4+9+6=29= 11. But
n
his
articular
nstance,
an interestinglternativeeasurementanbemadewith heunit f he
whole one:
Go
to E=2 whole
ones,
to C=2 whole
ones,
to
D= 1
whole
one,
nd
D
to
Bb=2
whole ones.
With he
umthus ar
t
7,
a
switch
s then
made o
the
econd f he
wo
vailable
hole one
cales,
and
the final
C#
to
G=3 wholetones.
The
result s 7+3=10=1.
Accepting
his ivision
f
he
notes nto +2 leads
o nother
evelation.
The
pitch
alue f he
irstive otes s 9+5+1+3+11
=29=
11,
and
that f
he
inal wo
notes
s
2+8=
10.
11
+10=21.
Before
he
iolinnd
piano igures
re
concluded,
he lute
akes
n
entry
ollowing
restwith time
pan
of 10
(=1)
eighths.
is line
occupies
time
pan
of
10
(=1) eighths,
nd the
pitch
alue fhisfive
notes s 1+11+1+7+1=21=3.
The intervallicalue of his
phrase
(measured
n
emitones)
s
14=5,
a subtotal
hich,
hen dded othe
value fhis econd
phrase,
esults
n 12= 3.
-
8/18/2019 Pythagoras and Pierrot
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515
The reciter
elays
or time
pan
of7
eighths
efore
ntering
ith
phrase
whose ime
pan
s 21
(=3)
eighths.
ts
itch
alue s
11 +4= 15
=6,
but
hat f
he
following
hrase
s
22+6=28=10=1,
the
otal
f
the
wo
hrases
eing
+1
-7.
The intervallicalue
f
he
irst
hrase
s
34=7,
while
hat
f the
econd
phrase
s
49=13=4.
7+4=
11.
The
second
phrase,
ncidentally,
ince
it
begins
with
hree
ixteenth
otes
following
sixteenth
est,
must ave ts ime
pan
measurement
ade
n
sixteenths.
hat alue s
39 12= 3.
The
quantitative
itch
alues
n
Section of
Mondestrunken"re
as
follows;
Flute
5+(13=)4+(14=)5+(16=)7=21
=3
Violin
(12=)3+(28=)1
+
1
+
11
=
16=7
Reciter
(31=)4
Piano
(28=)1 +(19=)1
+9+(34=)7+(12=)3+(14=)5=26=8
The
part
or he
recitern
Section
contains 1
pitches,
figure
which t first
eems
disappointing.
n
measure
,
however,
choenberg
takes
n
unusual ction: e
insertsn
eighth
estbetween
he
yllables
"Spring"
nd
"flut." his
aesura
not
nly
roduces
n
unexpecteditch
value
f
22 at that
oint,
ut
lso divides he
ine
nto 1
pitches
lus
10
pitches. and1 arethus he wo uantitativealues.
The
total
uantitative
alue
or
he
ections 22. The
total or
ection
II
s
also
22,
andthat
or
ection
II
s 11.
22+22+11
=55=10=
1.
Both he
flute nd
the
reciter
egin
nd
end their
hrases
t the
beginning
f
Mondestrunken"
n
the
noteA
(=
1)
and
pivot
round
hat
pitch.
f
more nterest
s the
very
irst
oteof the
piece-the
piano's
opening
#
That
note
marks he
beginning
f
ach of he
hree
ections
of he
ong.
tsnumber
alue s
9,
and t
functions
hus.
G#
s,
however,
not nlyheninthhromaticote, utnote 1 as well-a fittingeynote,
then,
o
the
ong
nd to
the
ntire
omposition.
The
procedure
o be
observedn
"Mondestrunken",
s it
ontinues
to
unfold,
s the
procedure
or
hewhole
of
Arnold
choenberg's
Pierrot
lunaire.
, 3,
7, 11,
and
22
retain heir
ontrol
hroughout
he
omposition.
What s
fascinating,
owever,
s
therich
variety
f
pproaches
to
those
key
-
8/18/2019 Pythagoras and Pierrot
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516
numbers.
art
I,
hat
ourney
nto
he
ark
ight
f he
oul,
ummons
p,
as
might
e
expected,
requentppearances
f 13. The malevolence
f
that umber
s
felt
nly
riefly,
owever,
efore
t
s
swiftly
ransformed
into
omething
ess inister.
xamples
rethe
pening
iano
notes fNo.
8
(5+8),
the
first
wo
notes
f
the
recitern
No. 9
(8+5),
thefirst
wo
string
hords
f
No.
10
(8 +5),
the
irst
wo
notes f he ecitern
No. 12
(5+8),
andthe irst
wo
notes
f he eciter
n
No.
13
(6+ 7).
As befitshe oetry,here remore elicitousppearancesfnumber
5
(freedom,
hange,
ccording
o
numerology)
n
Part
ll.
Two of
them
(5+5=10=1)
in the
pianopart
re
the
ast nstrumental
ounds
f he
piece.
They
re
preceded y
ne of
Schoenberg's
usical
ignatures,
n
this nstance
multi-layered
ne
A,
S,
AS,
and
A.
SCHoenBErG)
layed
by
he
piano
nd
occurring
n
measure 8
(=
10=
1)
of
he
inal
ong.
But
ertainlyy
now
he
point
as
been
made:number
ymbolism
plays
crucial
ole
n he
rganization
f
his
xtraordinary
omposition,
role
hat
choenberg
as carefulo
point
ut
n
the
itle,
nd one that
cannot e ignoredn ny horoughtudyf hework's tructure.
Finally,
n
pite
f he act hat
he
itle f
Pierrot
unaires
the
ingle
instancef ts
omposerndicating
isuse
of
numerology
n
he
tructuring
of
work,
he
procedure
s not
t
all
peculiar
o that
omposition.
sed
systematically
t leastas
early
s
the
Chamber
ymphony,
pus
9,
numerology
ontinued
o be used
by
choenberg
s a structuralevice
n
hismusic ntil
he
ery
ndof
his ife.
hroughout
he
eriod choenberg
remained
oyal
o
thenumbers sed
n
Pierrot
unaire:
, 3, 7,
11,
and
22. Butwithstonishingersatilityhismeagerroupessumes nnumer-
able roles
in
constantly
aried
ettings
nd
with
n
ever
changing
supporting
ast.
That
heir
ontribution
o
Schoenberg's
usichas
gone
unnoticed
s
most
nfortunate.
verlooking
he
revailing
umber
uphony
in a
work
uchas
Erwartung,
or
xample,
as led
to frustrationn
the
part
f hose ritics hose
iligent
earch asbeen or
more onventional
system
f
rder.
Perhaps
most
stonishing
f
all,
even
Schoenberg's
welve-tone
musicretains his
ndispensable
econd
ayer
f
numerological
rder.
The row
may ropose
he
equence
nwhich
itches
re to be used na
particular
omposition,
ut
rhythms,hrase
engths,
adence
points,
section
engths,
ote
epetitions,
hord
ormations,
ndrow
ranspositions
are
all
regulated,
ot
y
he
ow,
ut
y
he
numberalues
f
numerology.
Indeed,
n examination
f
choenberg's
ows hemselves
ill
eveal
hem
-
8/18/2019 Pythagoras and Pierrot
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517
to
be,
not
rbitraryrrangements
f
welve
otes,
ut he areful
ntegration
ofthe
number
alues
of
those notes.
t
follows, hen,
hat o
emphasize
he
numbers
f the
row
n
this ater
music,
s has been
done,
and to
ignore
the
mystical
igures
f
numerology
s
to
project seriously
istorted
mage
of
the
composer
and
his
work.
NOTES
(1)
Quoted
by
Walter
ubsamen
n
"Schoenberg
n
America,"
he Musical
Quarterly,ol.XXXVII,o.4, October, 951.
(2)
George
Perle,
or
nstance,
in
his rticlePierrot
unaire,"
ublished
n
The
Commonwealth
f
Music,edited
y
Gustave eese
and
Rose
Brandel,
he
Free
Press,
New
York,
965)
makes
he
tatement
hat
Schoenberg's
se
of
magic
numbers
as,
f
ourse,
o musical
ignificance.
ince ach of
he
poems
onsists f
hirteen
ines,
n
unlucky
umber,
erhaps
e
thought
t
well
to
organize
he whole
according
o two
ucky
umbers,
hree
nd
seven."
(3)
Much
ofthe
nformation
n
numerology
s
supplied
rom
our
Days
Are
Numbered
y
Florence
vylinn
ampbell,
M.A.,
The
Gateway,
erndale,
Pennsylvania,
931.
There
are
many
more
modern,
more
systematic
handbooks n
the
ubject,
ut his ather
uaint ublication,
classic
n ts
field,
eflects
umerology
s it
was
practiced
uring
hefirst
uarter
f he
century,
he
eriod
hen
choenberg
must
ave irst
ecome nterestedn t.
(4)
The
composer
sed
the
riginal
pelling
f
his
name,
Schonberg,"
uring
theperiod f he ompositionfPierrot.hechange o"Schoenberg" as
evidently
ade oon after is rrivaln he
Unites tates
n
1933.
The
name
numbers or
he
original pelling
re
presented
elow
for
omparison.
n
computing
he
xpression
umber,
aw
valueshavebeen
used ratherhan
reduced nes
in
order
ot o conceal he
mportant
otal,
1.
Arnold ranz
Walter
chonberg,
is
rarely
sedfull
ame,
as a
consonant
umber alue
of
13.
-
8/18/2019 Pythagoras and Pierrot
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518
ARNOLD SCHONBERG
195634 138652597
First
ame
Last
Name Total
Expression
28
(= 10)
+
46
(= 10)
=
74= 11
Quiescent
elf
3
+
8
=
11
Soul
urge
7
+
11
=
18=9
Cornerstone
=1
Name
ycle
6
+
9
=
15=6
(5)
That
choenberg
dentifiesith he
poet
s
stronglyuggested
y
he
music.
First
f
ll,
he
ello,
having
emainedmute
uring
he
first
wo
ections
f
"Mondestrunken,"
nters
ith n
impassioned
ong
at
the
first
ention
f
the
poet. olidly
rounded
y
3-note
pedal
10= 1),
and with heviolin
soaring irily
bove
t,
his
ine
s saturated
ith
1's
until
t
inally
omes
to
rest
with ive
izzicato
hords.
he four-notehord f
hefinal
ar,
played
twice,
onsists f
the
notes
C,
B
(H
in
German),
'
(read
as
Eb,
S in
German), -forming
he
ignature
.
SCH.
Recalling
hat educed umbers
still etainome of heir
riginal
lavor,
he
emptation
s
strong
o
assign
A
the
valueof
10
here,
herebyeading
he hord s
1+3+7+10=21--a
summation,
s it
were,
f
he
numbers
hat
ave
ontrolled
he
piece.
n he
analytical
core,
hat
emptation
as
been
yielded
o
on
the
final
hord,
chord
hat hen
as,
not
nly
pitch
alue
of
21,
but n intervallicalue
of
21 as well.
(6)
The dates
re from
Joseph
Rufer,
he
Works
f
Arnold
choenberg:
Catalogue fHisCompositions, ritings,ndPaintings,. Newlin,r., t.
Martin's
ress,
New
York,
962.
(7)
Neither
he ntervallicor
he
uantitative
umber alues
havebeen
ntered
in
the
nalytical
core.
To
havedone so
would
havebeen to
produce
n
indecipherableumble
fnumbers.
hen
too,
he
procedures
or
ounting
notes nd
measuring
ntervals
re,
fter
ll,
imple
nough
o
as to
hardly
call for
guidance.
This action
s not to
be
interpreted
s
an
attempt
o
minimizehe mportancef itherntervallicrquantitativealues.On the
contrary.
here re instances
n
Pierrot,
or
xample,
here he
ntervallic
value
would
eemto take
precedence
ver
he
pitch
alue. uch
a
situation
exists
n
he
passacaglia
heme fNo.
8,
where hehead
motivef
he
heme,
E-G-Eb,
has
a
pitch
alue
of 5+8+7=20=2.
Two
is not
significant
number
n
Pierrot.
he
intervallicalue of
the
same
motive,
owever,
s
3+4=7.
-
8/18/2019 Pythagoras and Pierrot
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Mondestrunken
a
numerological
analysis
SEcroM
ff
1
7
FLUTE
I
,,
=
(
,
>0
=0
7
7
7
-
-4
=
12t
VIOLIN
tI
in6
=
,
CELLO
1
5
11
9
1
1
5
9=
1
t
=
1
DEN
WEIN,
DEN
MAN
MIT
AIU.EN
TRINKT,
GIESST
RECITER
2
4
J
1
0
L
l2
I
12
--
--
x0=
9=
:
=
I
Uptb=
"==
-
8/18/2019 Pythagoras and Pierrot
16/30
9 1
3
8
7'=
=
10
f11
7 2
6
3
1
2
11
9
7
7
7
7 2
3 391 i
S3
11
7=
3
2 1
7
3
Cz
UND
EINE
SPRING-
FLUT
USER-
SCHWEMMT
DEN
.7
l
w
I
6
31=110=
9
2 3
3
9
1 i1
8
2 6 5'8=
f
=
13
=
(
98
2339 82
666663
-
8/18/2019 Pythagoras and Pierrot
17/30
3
7513112
159
7
=3
11
2
8
74
,
fl=
+
1=
172= 5
1
2
11
1
7
~
3
7
7=
FLAG-.
5 5 9 1 3 I
SIlL
-
LEN Hoi
-
ZONT
12
{-+-+
'---
P
---------------
+
S5 7
2
3
6 7=
=3 9
fog 0=
1
3
1
8
5
3=
1=3
-
8/18/2019 Pythagoras and Pierrot
18/30
S=
=
)
1
Z
3
7
10.4
=
9
9
7
7 7
3
1
.19
-&
-
I
8
7
3 2
6
2
1 1
=
31 =
NACHTS
DER
MOND
IN
W0
-
CN
NIE-
DER,
5 7
5
7 = 27 =
,9
- - - --=10=
=
9)
=
=@
L0
-
8/18/2019 Pythagoras and Pierrot
19/30
3
2
5 7
7
3
2
5
=
92
SIecT
I =
14,
ArS
5
TIME
PAN=4J
=
10=1
-
8/18/2019 Pythagoras and Pierrot
20/30
Sect~oN
1
,i z
8
or
3
7l
1
G
'
7
7 7=
f
f
3
r1
z
7
79
39
=
FLvrE
~~
~F
If
>
lof,
A
(
,
,
@,
,L
5
5
1
&
(
tf
Cf
IOUN
RCITER
I
7 6 9
1
f
7
7
7
I
1
(o
7
"?u:.
f"
'=
. . . .
..OE,
-
.,
f
7
7
7= 9
,
-
9-.
2 3
,,
7
4
tow
I L
W.-
I
A
I,
-
8/18/2019 Pythagoras and Pierrot
21/30
f1
f
I2
2
1
f
=
7
9f
7
0=
1
f
577
3 7
7-
9
5
0o=
=
4 , =
iZ
=
(5
9
-
7
5
l
1
if
I
7 1
9
10
0
/
1
11=
3
9
7
1
5
2
1
1
15=-
LU
STE, SCAU ER IC
UND
SUs, DURC
43774.4.
.
.....5
32
I1
,"
".
-.,
?
1
&
7
3
4 7
1=
t
19t
1
-
8/18/2019 Pythagoras and Pierrot
22/30
67=
7
7
8
93235
o
9=j197
I SfI 9=
S
?t
I-
=
o;
4
=
=
-
=
6
7
11
1=
9 7
2
(
5
7=
7
7
9
S=
@
7
1O
=
3?
9
7
3
o
3
,
=
5
1
9
8
i
3CHwlMMEN
HNE
AHL
DIE
FLU
TEN DEN
EIN,rJ
AN
iT
ruaN
if
3
i
I
=
39
ft=lo
.o
-
8/18/2019 Pythagoras and Pierrot
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f
t if-
9f
1I
9
1
f
oD
39
*1
s
ii
9)
-------
b,
6
-
---
5
7
7
7
5
3
3=
f
3
9
f
= 1 9 6 9 I 8
-
W
9==
=
32
57
TAINKT,
GIESST
NACHTS
DER
MOND IN
OOEN
oiE-
DER.
26
-
io-
]
-k
i
S
=
9
2
8
f
9
11
7
1
7=
1 9
19=lo
J9=
=
3
41
f
I
I
w
~oP
%
-
8/18/2019 Pythagoras and Pierrot
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1
9
7
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8/18/2019 Pythagoras and Pierrot
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533
NOTES
ON
THE
ANALYTICAL CORE
Bar Beat
7
1 7
(flute)gainst (violin)
7
1,2
Throughout
he
core,
hord
ormationseceive heir
itch
alues
fromhe
umof
heir
omponents.
he
piano
hord
n
the
econd
beat
f his
ar,
10=
1
chord
with
n intervallic
alue f
11
(and
thus
he
mplication
f
21),
will
ater
erve s
the
22-
pedal
n
Section II.
10
1
"stillen"
eceives
pecial
mphasis
y
being
he
ingle
word
ung
in
Mondestrunken."ts
itch
alue s
5+8=
13, implying,erhaps,that hehorizon s not
only
till,
ut,
acking
he
aving
race
of
moonlight,
terile
nd
lifeless s
well.Such
an
interpretation
s
supported
y
the
phrase
n
the
right
and
of the
piano
part
beginning
n the
ast
ixteenth
ote
f
measure .
Its
itch
alue
s
13
(=4). Dovetailing
ith
he
13 of
"stillen,"
he
piano
13
is
transformed
nto
7,
after
dramatic
reak,
y
the
mysterious
3X
22
chords f
measure
0.
10
2
As
noted
n
he
core,
he
piano
hord
ere
hasa
pitch
alue f
2.
Its intervallicalue is also 22. Andwith henumbers
f its
component
itches,
t
becomes
veritable
ompendium
f
Pierrot
number
alues:
1+3+7+11=
22. In
addition,
his
eries
draws
attention
o the
process
by
which
he
original
wo
numbers f
he
title,
and
7,
generate
he
thersn
the
et:
3+7=
1;
3+7+1
=
11;
3+7+1+11=22.
-
8/18/2019 Pythagoras and Pierrot
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534
10
2 The solationf
he
iolin
and
the
act
hatt
s
the
nly
armonic
called for
n
the
ong
both
give
he
note
pecialprominence.
ts
function,oo,
s
significant:
s 8
it
transforms
he
phrase
which
precedes
t
from
pitch
alueof 11 to one of 10. "Power" s the
numerological
eaning
or .
Meanings
or 1 and 10
(1)
have
been
uggested
nthe
body
f
he ext.
As must e
apparent
rom
he everal ommentsmade on
the
activity
n
hismeasure
appropriately,
easure 0 of he
piece),
ts
significance
ould
best
be
explained
yreferring
o
the
numero-
logical
meanings
f
numbers nd to
Schoenberg's
personal
interpretation
nd
use
of
them.
A
thorough
xaminationf
this
subject
would
be
extraordinarily
evealing,
ot
only
for
Pierrot
lunaire,
ut
for
heentire
orpus
of
Schoenberg's ork.
uch a
project
s,
of
ourse,
uite
beyond
he
cope
of
he
present
tudy.
26
2
The
5
value as
the
total
or he
reciter's
itches
n
Section
I
is
equivocal.
Adding
tto
the7
total
f Section
results
n
12=3,
whereas
ombining
t
with he
otal f
ection
II
produces
6=7.
29
1 The number
fnotes
nthe
irst
hrase
f
he
ello ine s
11,
and
that f
he
econd
phrase
s
10.
11
+
10=
21
=3.
With
he
emitone
as theunit
f
measure,
he
ntervallic
aluefor he
first
hrase
s
34= 7. That or he econd
phrase
s 22. 7+22=29=
11.
29
1 The time
pan
for
he
ight
and
f
he
piano
part
romhe
econd
half
f
his
eatuntil he nd
of
bar
34
is
29
=
11.