"the Concept of 'Alea' in Boulez's 'Constellation-Miroir'

8/17/2019 "the Concept of 'Alea' in Boulez's 'Constellation-Miroir'

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The Concept of 'Alea' in Boulez's 'Constellation-Miroir'Author(s): Anne TrenkampSource: Music & Letters, Vol. 57, No. 1 (Jan., 1976), pp. 1-10Published by: Oxford University PressStable URL: http://www.jstor.org/stable/733804

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2/11

I S Candetters

JANUARY

1976

VOLUME LVII

No. i

MUSIC

AND LETTERSwas

founded

in

I920

by

the

late A. H.

Fox

Strangways. It

was continued by

the

late

Richard

Capell and is now the property of Music

and

Letters Limited,

a

Company Limnited

by guarantee

and

comprising repre-

sentatives

from

the Royal

Musical Association

and Oxford University Press

and

others.

BUSINESS

&

ADVERTISING ADDRESS:

44 Conduit Street, London, WiR oDE.

EDrrORIAL ADDRESS: Faculty of

Music, 32 Holywell, Oxford, OXi 3SL.

THE

CONCEPT

OF

'ALEA'

IN

BOULEZ'S

'CONSTELLATION-MIROIR'

BY ANNE TRENKAMP

THE USE

of chance techniques by contemporary composers has

bewildered

more than a few theorists and

driven others to silence.

Some

musicians

would

agree

with Edward T.

Cone

that,

since

chance

music

has

no

definitively

ordered

sequence

of

events,

it can

only

be

described,

not

analyzed.,

Others

would

agree

with

Anthony

Cross:

The

preoccupation with chance

on

the part of composers like

Stockhausen

and

particularly

Boulez,

pinpoints

the

chief problem

faced

by composers

of

the

so-called post-Webern school: with

the

abandonment

of

tonality,

of

all

pre-existing

language,

how

is

the

composer to achieve the meaningful articulation of form?2

The

problem

of chance

in

music

is

particularly crucial for twentieth-

century

scholars.

In

the

past, major

musical

issues

have

been avoided

by negative

means:

tonality

became

atonal;

themes became

athem-

atic; rhythm

became

arhythmic.

Only by linguistic feats such as

'open

form', 'circular

form' and

so on has form not become 'aformal'.

By examining

one

composer's

confrontation

of chance the relation-

ship

between the

articulation of

form

and

chance can be seen from a

more positive viewpoint.

Boulez

has

made a

distinction

between chance and alea

in

his

speeches

and

essays.

For

him,

al6a

is the use of

chance under

highly

controlled

circumstances. While this

distinction

appears

on

the

1

'Analysis

Today',

Probklms f Modern

Music, ed.

Paul H. Lang, New

York,

I960,

p.

38.

2

'The

Significance of

Aleatoricism

in

twentieth-century Music',

77ie

Music

Review,

xxix

(I968), 322.

I


3/11

surface to

be nothing

more than linguistic hairsplitting,

the

signific-

ance of

the differentiation becomes

apparent

in the analysis of a

work such

as 'Constellation-miroir',

the third

and central movement

of Boulez's Third Piano

Sonata.3

Close examination of

some ideas

Boulez wrote about at the time he was composing the sonata and an

analysis

of

'Constellation-miroir'

make clear

the

necessity

and

validity

of the

distinction.

In

addition,

an

analysis

of this movement

illustrates

one meaning of the term 'open

form'.

An earlier work

by Boulez,

Structures or

two

pianos

(I 95I-6),

illustrates the composer's

attempt

to serialize rhythm, dynamics

and

attack

in

addition

to pitch. During the completion

of Structures,

however,

Boulez was

already re-examining the

validity of

the strict

serial

procedures

he

was employing

at that

time; his

writings show a

concern with this problem until the composition of the Third Piano

Sonata

(c.

I

960).

First,

Boulez

challenged

the

conclusions

serial

composers

drew from Webern's

works and the

manner in

which

they

'extended' his

procedures:

The

model universally

chosen

is Webern: and

in

his

music the

principal

matter

for

study

is

the

organization

of the

musical

material.

Certain conclusions are arrived at, and

these are

then

deliberately

developed by

a

process

of extension.

With

real

frenzy

we set about

[serial]

organization as

if

we were on

the

threshold

of

undiscovered

worlds ... Webern organized only intervallic relationships; we now

subject rhythm,

tone-colour and dynamics

to

[serial]

organization.

All

this serves as

fodder for the monstrous

multiple

organization

which must

be renounced forthwith

if we are

not

to

condemn

our-

selves to deafness.4

Second,

he

questioned

the

relationship

between the

serialized

elements

and

the

perception

of

the

total form:

Each system,

carefully

worked

out in its own

terms,

could

only

cohabit with the others through a miraculouscoincidence. The works

of this

period

also

show

an

extreme

inflexibility

in all their

aspects;

elements

in

the

'magic squares'

which

the

composer,

with his

magic

wand, forgot

at

the

birth

of the

work,

react

violently

against

the

foreign

and

hostile

order

forced

upon them; they get

their own

revenge:

the

work does

not achieve

any

conclusively

coherent

organization;

it sounds

bad and

its

aggressiveness

is

not

always

intentional.5

These

are bitter

thoughts

from

one of

the

technical

masters of

'total serialism'. What Boulez specifically attacked was the applica-

3 Only

two

of the proposed

five

movements

have

been

published:

'Trope'

and

'Constellation-miroir'.

The

latter is

designed

to

be

played

either

forward

or in retrograde,

but only

the

retrograde

has been published.

Both were

completed

by

I96o.

'

In

German

in

'Einsichten

und Aussichten',

tr.

Hilde

Strobel,

Melos,

xxii

(I955),

i62.

?

Boukz on Music

Today,

tr. Susan

Bradshaw

and Richard

R.

Bennett,

London,

197I,

p.

25.

2


4/11

tion of twelve-note

pitch technique

to the

materials of

rhythm, colour

and dynamics,

because

each

of these materials

has a

different inner

structure.

Pitch material in

this style

is

a

closed

system

of

twelve

chromatic pitches whose different

permutations

produce associative

elements at will. Rhythm, on the other hand, does not contain such

a closed

system

of

separate elements; to

enforce upon

rhythm the

same

procedures that

govern pitch

cannot

produce the same

necessary conclusions.

This

point

of

logic applies to colour and

dynamics

as

well.,

When

composers

tried to use the

same

procedures

for

all four

elements mentioned

above,

there

was no

logical

or

necessary

relationship

between

them.

The

resultant 'chance

by

inadvertence'

occasionally produced

homogeneous and logical

simultaneities,

but not

by

rule of the

composer.

Boulez, however, did not reject serial technique completely; his

arguments

primarily reject

the

excesses

of a

system

which

re-

linquished compositional

decisions to a series of

calculations and

tables.

For

Boulez,

the

extents

and limits

of

serial technique

displayed

in

Structures rovided not

a

dead end,

but a new begining: 'Serialism

provided me with

a

syntax.

In

"Le Marteau",

I

used it

to formulate

thoughts'.7

The

syntax provided

by

Structureswas

actually

a re-definition of

the role of

the

series.

In

'Musical

Technique'

Boulez

presents

still

another definition of the series that illustrates this role; he stresses

the

importance

of

hierarchy

within the series

rather

than

the

primacy

of

pitch-order:

The

series

is

...

the germ of a developing hierarchy...

,endowed

with a

greater

or

lesser

selectivity,

with

a

view

to

organizing

a

FINITE

ensemble of creative

possibilities

...

;

this

ensemble

of

possibilities is

deduced

from an

initial series

by

a

FUNCTIONAL

generativeprocess

(not simply

the

consecutive exposition of a certain

number of objects,

permutated according to restrictive numerical data)."

Boulez's

redefinition

of the series has

direct

bearing

on

the

analysis

of

'Constellation-miroir'.

First,

the

recognition

of interval-

class

and/or pitch-class hierarchy

as

opposed to pitch-order demands

a

reformulation of the

role

of pitch within a piece.

Second, since it is

the interaction between

musical

elements that

produces form, any

change

of

approach towards one

or

more elements is

bound to affect

the

manner in

which a

composition

as a

whole is

organized. Thus,

the new role of

pitch

and

the

disavowal

of the

serialization of other

elements invite

special

attention

to the

formal

organization.

Boulez has

stated that his

concept of form at

that time was

6

See

Gyorgy Ligeti,

'Pierre

Boulez',

Die Reihe,iv

(i958),

38-63.

7

Peter

Heyworth, 'Pierre

Boulez', The

New

rorker,24

March

1973, p.

63.

$

Boulez

on Music

Today,

pp.

35-36.

3


5/11

influenced more by literature

than

by other composers,

especially

by Stephan Mallarme. 9

He felt that writers had explored structural

possibilities far more extensively

than composers, and

in

Mallarme

he found a system of organization suggestive of what he was

attempt-

ing in 'Constellation-miroir'. In 'Un Coup de des', the poem after

which 'Constellation-miroir' is modelled, two facets of poetic

usage

have bearing on this analysis.

First,

Mallarme

transposed words

from their everyday associations

into verbal objects with a poetic

function by concentrating

on phonemic qualities and by juxtaposing

words

in

a manner which gave them a multiplicity of

meanings.10

Boulez's

task was

not

dissimilar;

he transposed pitches

from

their

serial

matrix

into

the

phonemic

state of the smallest recognizable

unit of

pitch relationship,

serial or non-serial: the interval.

Second, Mallarme in 'Un Coup de des' segmented phrases and

arranged them on the page in such a way that the connections

between

phrases

would

be

ambiguous. For example, if

a

sentence

is

diagrammed in the traditional

way, the words are segmented and

additional words

are

joined

to them to designate their function.

Even if the words are presented

in an unusual order, the functional

designations make the meaning clear:

verb direct bject subject

took

the bread

I

uickly

to

my

house

adverb

prepositionalhrase

In

'Un Coup de

des',

the sentence is fragmented, but there

is no

explicit relationship between

the fragments, except for

a certain

typographical hierarchy:

LE

MAITRE

surgi

inf6rant

de cette

conflagration

que se

comme

on

menace

l'unique

Nombre

qui

ne

peut

pas

hesite

cadavre

par

le bras"

9

'Sonate,

que me veux-tu ?',

tr. D. Noakes and P. Jacobs, Perspectivesf New

Music,

i(1963),

32.

10

Hans R. Zeller, 'Mallarme

and Serialist Thought', tr. Margaret Shenfield,

Die

Reihe,

vi (I964), 7.

11

Mallarme,

ed. Anthony Hartley, Harmondsworth, I965,

p. 2I8.

4


6/11

Despite the

seemingly

fewer choices in the

Mallarme

poem,

the

musical continuity

in

'Constellation-miroir'

has been segmented

in

the same fashion, and the choices

of

segment-sequences

in

perform-

ance create

ambiguity similar to that

found

in the Mallarme poem.

Interesting as these artistic influences are, it is the process

through

which Boulez turned to aleatoric procedures that is im-

portant. Boulez

stated: 'Actually, the only thing

one can play upon

is the interaction between style

and form'.

12

He developed

a post-

serial style

and

sought-by

analogy perhaps-a formal procedure

with which it

could interact. The result of this

search was a particular

form

of chance

called alea,

in which the composer controls precisely

the

areas

in

which

chance

may enter into the composition."I Alea,

then,

was not an outside influence, used in

and for itself. Rather,

it

was the adoption of a literary viewpoint to create a formal procedure

which could interact with a particular style.

The intrinsic use of

alea

as a formal

device in 'Constellation-

miroir' can be seen by a glance

at the score. The idea of

an open-

form,

aleatoric

movement is

enhanced through the typographical

layout of the

movement.

The score consists of nine pages,

i8 ins.

x

24 ins.,

over

which

58 segments

of

varying

length

are

arranged.

These segments

are

printed

in either red or

green, red standing for

the chordal

blocs

sections and

green for the points sections of

pointil-

listic texture. Signs before and after each segment mark the routes

that

can

be taken.

In

addition

to the many

signs surrounding the segments,

two

different

types

of tempo

indications are used. First are the

specific

tempo

modifications often found

in

the

blocs

sections; these

may

indicate rapid changes of tempo

in a

short space,

as

in blocs i:

Ex.

1.

126

Vif

J126 s *

1

t;= J126 J5

~~~~ Il~~~~~~

sffz

___

uJ

iPed.

sffz a----- U{.C.

12

Lecture

at Case

Western

Reserve

University,

Cleveland,

Ohio,

March

1971.

13

Pierre

Boulez, 'Alea',

La Nouvelle

Revue

ranfaise,

xlix (I

957),

845. In

this article

Boulez distinguishes

between

the

different

uses of chance

in

music

by

the

composer's

intent.

Two other uses

are

'chance

by

inadvertence'

or total

serialism

(p.

839)

and

random

techniques

(p. 841).

There

is no ready-made

noun

to go with

the

adjective,

aleatory.

Mr.

Cross

prefers 'aleatoricism',

while I would

like

to see the word

alia

taken

into

the English

language.

5


7/11

Second

are the

'if. . .

then'

tempo

markings,

those

which

are indica-

ted

by

the

same

sign that indicates

the choice

of

segment.

They

state,

in

effect,

that if

the

composition

is

to proceed

from

segment

x to

segment

y,

the

latter segment

must

be

played

at z tempo;

on

the

other hand, if the composition is to proceed from segment q to

segmenty,

the latter

must be

played

at

w

tempo,

as

in

pointS

2:

Ex. 2.

7

J

80 (mobile)

4=76

-(stable)

=

5

-

=86

- (mobile)

J=

96

tres

ecet

rapide

* b

-

.|

absolument

sants

--

Pedale

All of these

signs add

to

the

visual

complexity

of the

score.

The use

of

different

colours

and the

resemblance

of

the

layout

of

the score

to extra-musical

elements

provide

additional

amusement

for the

performer;

the

multiplicity

of

signs

gives

the

illusion

that

the

pianist

has

more choices

than

are

really

important

or available.

At

the highest

level

of

organization

there

are six

sections:

Melange,

points

3,

bloCs ,

points 2,

blocs

and points

;

these

sections

must

occur

in the order

stated.

At the

next

level,

individual

segments

are

linked

together by the other segments in whose company they are allowed

to

occur.

Thus,

although

a

section

may

have twelve segments,

these

linkings

may cause

the

segments

to create

three

units.

Within

these

units,

the

choice

of order

for

individual segments

may

remain

free.

For example,

Milange

has six segments.

The

pianist

must

start

with

the first segment

and end

with

the sixth.

Of the

remaining

segments,

the

third

must follow

the second

and

the

fifth must follow

the

fourth.

Segments

2

and

3

belong

to

one

textural

density

and

segments

4

and

5

to

the

other.

Thus

there

are

only

four

units

and

only

one

choice;

the choice is whether segments 2-3 will precede or follow segments

4-5,

or,

in

other words,

which

density

will

come

first.

The

other

sections,

by

the

very

nature of

the

signs

which

surround

them,

divide

into

units

in the

same

way.

When

unit

groupings

are

taken into

account,

there

are

actually

only

17

units,

although

there

are

58

segments.

The following

table

shows

the number

of

segments

and

units

in each section:

6


8/11

SECTION

SEGMENTS

UNITS

Mllange

6

4

points

IO

2

blocs2 24 3

points

2

8

3

blocs

I

I

2

points

3

3

Tempo does not really

affect the

number of units. Of the

two

types of

tempo

modification discussed

earlier the first occurs within

a

segment. The

frequent changes

in tempo

measure the time

relation-

ship between

chords or pitches

(see Ex. i). In music

with

a

basic

pulse this measurement is accomplished by the rhythmic values

assigned

to pitches. In his

earlier

compositions Boulez's notation

was

characterized by

highly

complex rhythms in music

that sometimes

lacks a

basic pulse. He found

that the

realization of these rhythms

in

performance was an

approximation of the

notation and that

simpler

notation,

combined with

fluctuating

tempo, would serve

him

better.

1

As

a

result, the

rhythmic

notation in this movement

has

actually been

simplified.

Fluctuations in tempo

replace many of

the

earlier,

complex

rhythmic patterns; in

their place

one finds

simple

quavers or semiquavers.

The connective,

'if . . . then' tempo

indications

between two

segments (see Ex.

2) might

appear to be a further

usage of chance

techniques, but

their primary

purpose is to assure a

smooth

transition

from one segment

to the next.

Since the order of

segments within a

unit

is

not

predetermined, tempo must

be

considered within the

multiple

possibilities of contexts

for each

segment. This planning

can

be

seen

in

the two

choices offered by

Boulez for the

main unit of

points2 (in

the

diagram each crotchet or

quaver

represents a segment):

Ex.

3

---j

138

3 4

t

A J---~~~41-26-121

72

endu

126,-152

1/J

52- 26

------------s2 -

8

1---------

_

The

pianist,

then, actually

has far

fewer

choices

than one

would

expect from

the

notation of

'Constellation-miroir'. While there

is

choice

among

individual

segments,

the

organization of

these

segments

into

units

prevents

random

chance and

provides a

sub-

formal

structure.

In

addition,

the

tempo markings,

which at

first

14

iAl6a', pp.

841-2-

7


9/11

glance

appear to promote the

use of chance,

perform two long-

established

functions:

the control of the

rate of musical

events; and

the control

of smooth transitions

between

segments.

To this point we have eliminated some misunderstandings about

the use

of

chance in 'Constellation-miroir'

and have determined

how

many genuine

notational choices

are given.

In short, it has been

shown

that Boulez has loaded the dice.

To determine the extent

of

the loading

an

examination of the pitch

structure

is necessary.

Boulez has stated that

his prime

concern with serial organization

in

this

piece

was

to

create

horizontal

and vertical

sonorities related

to

each other

in

a

manner that could be perceived

by the listener.

15

If

this movement

is

to

be considered serial, it

must

be considered so in

light

of Boulez's definition

of the series,

with its emphasis

on

hierarchy as opposed

to pitch-order.

The

pitch organization

of 'Constellation-miroir'

is similar to that

of 'Trope', the

other

published

movement of the

Third Piano Sonata.

The same series

can

be considered

the foundation

from which Boulez

develops

his pitch

material:

I

2

3

4

IEFF#BI

G#

I

GAA

CA

I

CDD#I

The

four

main subdivisions

of

the chromatic

set,

when reduced

to

an

unordered,

elemental

state,

consist

of:

(a) two semitones

and

a

perfect fourth; (b)

an isolated

pitch; (c)

a

pattern

of

tone, semitone,

tone;

and

(d)

two semitones.

In

addition,

the

second

and

fourth

elements

of the series

can be

combined,

forming exactly

the same

intervallic relationships as the first element.

From

these initial

pitch

elements

Boulez creates

short,

easily

recognizable

patterns

that

are

repeated

vertically

or

horizontally

at

random;

the

only

hierarchical

organization

is the

inclusion

or

exclusion

of

certain

intervals,

or the

favouring

of a few

intervals,

such

as

the

minor second.

This

type

of

technique-the

use of

basic,

simple

intervallic

structures

as

a

replacement

for the

more

highly

organized

serial

pitch

structure-has

been

seen

as an extension

of

Webern's

ideas.

16

It has also

been considered

related

to the

investiga-

tion of the phonemic quality of words by Mallarme.'7 The pitch

structure

results

from

units

so basic

that

they

can

not be

broken

down

further:

15

Lecture

at

Case Western

Reserve

University,

March

1971.

16

Zeller,

'Mallarme

and

Serialist

Thought',

p.

7.

17

Ibid., p.

sO.

8


10/11

EL 4.

Vif

4=126

accel

J152.

-w

C

?ts0u:F--t; ft -j127

xxf

~v gf

I h

f

fff

Mf

ff ff

ff

sYffr

S

Discussion of prominent pitches and intervals alone does not lead

to

significant insights

about

Boulez's

piece.

Two

points

should be

noted,

however.

First,

the

lack

of

definitive,

hierarchical

pitch

organization

results in a bland

uniformity

of horizontal and vertical

pitch structures.

This

uniformity

allows basic sonorities to be

easily

grasped by the

listener,

unless the texture becomes too dense.

At

the

same

time it offers an ideal

background

for textural

manipulation.

The

absence

of

a

strong

hierarchical

plan

makes

possible

the

reduction

in

emphasis

of the

very

element to which we are most

attuned: pitch. Second, there is a basic difference in the pitch

organization

of the

principal

points

and blocs

sections.

The

points,

through

their

sparser

texture and concentration on the

horizontal,

allow

the listener

to

perceive

at

least

part

of the

pitch

structure.

Many

of

the

blocs,

on the

other

hand,

are

so dense that

pitch compre-

hension is impossible; these dense sections correspond

in

Boulez's

terminology

to

ordered

chaos.

In

this

manner

the

pitch

structure

does

support

the main

structural

divisions

while

remaining

a

secondary

element

suitable for textural

manipulation.

Each texture is further reinforced by dynamics and range. The

points

sections

employ

moderate

dynamics

and

a

middle

register,

while the blocs

use

extremes

of

both

dynamics

and

range.

Within

each section various

facets

of each

type

of

texture may

be

presented,

allowing

subtle

differences

in

texture.

The

structural organization of

this

work, then,

depends upon juxtapositions

of

textures.

Since

pitch

organization is not

a

major determinant, especially at the subformal

level, the options left open to the performer are really of little

significance.

To be

sure,

different

routes will

cause higher or lower,

slightly more dense sonorities to be heard in different orders, but

since

textural

organization

does not

create the

same degree of

expectation

as

pitch organization the choices have a minimal effect

on

the

perception

of

form.

The

basic six-part structure of alternating

textures remains

primary.

This is the way Boulez has

loaded the dice of chance: he has only

conceded

to

the

performer the things that do not matter; the

9


11/11

perceptible

structure

is

decided by

Boulez himself.

The

structure of

this movement

is no

more 'open' than

the other

compositions

were

'closed' structures,

unless

one

is to substitute

'pitch-orientated'

for

closed and 'non-pitch-orientated'

for

open.

The composition has

an

ordered succession of textures. The movement consists of six sections.

The

first, Milange,

introduces

the

two textures, the

first

of which can

be described

as

sparse

and

pointillistic,

and the second as

more

dense

and chordal.

These two

basic textures

are

presented in

alternation

for

the rest

of the movement,

ending with

a pointillistic

section.

The

variety of orders

possible

within each

section

gives renewed

interest

to each

section

without

removing

a

sense

of structure.

The conclusion

is inescapable

that 'Constellation-miroir'

is

composed

within a strong

structural

framework.

Aleatoric

proced-

ures do not weaken the structure, especially at the highest formal

levels. The term

'open form'

has

no relevance

here,

unless it is

re-defined

as referring to

a composition

whose

structure is

determined

primarily

by elements

usually

given secondary

status.

This is

a piece

whose form is

articulated by

what are generally

considered

the lesser

materials

of music: texture

and timbre (in

the sense of

range, spacing

and specially

devised

effects for the piano).

This is the

essence

of Boulez's

search

for a type

of controlled

chance,

or

alia.

In

the

past,

while

reaching

for

new means

of

organiz-

ation, he relied only on musical elements to which past history

assigned

certain expectations:

pitch

focus, symmetry,

rhythmic

periodicity

and so forth.

If these elements

were to serve

as both

the

newly organized

elements

and the organizational

basis

of the

composition,

it

was possible

for

chance

to combine

these

elements

and

purposes

in

such

a

way

that

unintentional distortions

appeared.

The solution

was twofold:

first,

to

recognize

chance

as

an

adversary

and plan every

point

at which

it

might enter;

and second,

to base

the

musical structure

on a

non-expectational

element, such

as

texture.

If

chance engaging

with

structure

is seen

from this

perspective,

it

becomes

clear

that the

analyst's

job

is not to

engage

in

fruitless

pursuits

of various

routes

through

a

composition,

nor

to

endlessly

count

pitches

in

search

of even

a

changing

hierarchy

of

pitches.

His

task is

to

recognize

the tremendous

vitality

of these collections

of

pitches

as

textures

and to

begin

to

develop

a

vocabulary

suitable

first for describing,

then

for

analyzing

them.

I0

"the Concept of 'Alea' in Boulez's 'Constellation-Miroir'

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