pythagoras and pierrot

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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

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2/30

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


3/30

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


4/30

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


5/30

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


6/30

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


7/30

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


8/30

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


9/30

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


10/30

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.


11/30

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


12/30

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


13/30

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.


14/30

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.


15/30

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=

"==


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


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


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


19/30

3

2

5 7

7

3

2

5

=

92

SIecT

I =

14,

ArS

5

TIME

PAN=4J

=

10=1


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,


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


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


23/30

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

%


24/30

1

9

7

5

=

9q=

1

9

=

9

i

1=

34,

(

l

=(

1s=(. 5s=(9

#

ift=&

f-=ie

-=.ie

S 1

=

7

7

7= 3

3 3

7

1

3

b

so=(lo

52)

=

o=

O

27

28

71

3

5

11

S

1

7 1

7

7

5

&

33

t12

S

54

C7 1T=

95

SCTiN

IAI

='14=

OAKS

TiM

PAN

70

=

7


25/30

SICTIOC

m

9

5

1

2 112

5=

1

( 2

7

1

3 9= 117

3 5

2

7

1=

=

=

C,,

29

=

LA)

-

-50)

(

~5--"-O

?

,

1 I

1 9

ft

lop

1

=

40

s

:?

Vauw

"

9 7

T

1

I

9 I

CEUO

2,

4(

" t

I,

5

7

F

' "=

"

9

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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.


30/30

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.

pythagoras and pierrot

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