carter,elliott_canon for 3 (à stravinsky)_ avec une analyse

7/27/2019 Carter,Elliott_Canon for 3 (à Stravinsky)_ avec une analyse

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Spatial Design tn

Canon

Elliott

for ·3

Carter's

1

THOMAS DELIO

E l l i o t t Car t e r ' s Canon fo r 2 was wri t t en in response to a

request from the Br i t i s h per iod ica l Tempo fo r a composi t ion

honoring the memory of Igor St rav insky . The work was wr i t

ten in 1972 and was s ubs equent ly publ is hed by Associa ted

Music Pub l i she r s . Despi te i t s b rev i t y , the canon unfolds ar ich and complex des ign and a f fo rd s a ra re oppor tun i ty to

gl impse , wi th in a most conc ise format , the working out of

va riou s ideas in a manner t yp i ca l of many o f t h i s composer ' s

recen t works. l

I : Prel iminary Observa t ions

The in s trum en ta tion o f t h i s canon i s l e f t unspec i f i ed .

In h is no tes preced ing the score , however, the composer does

make seve ra l recommendations: one, fo r a vers ion employing

th ree t rumpets each with a d i f f e r en t mute; and an oth er , fo r

a version with muted t rumpet , c l a r i ne t and oboe. 2The piece may be div ided in to two sec t ions : the f i r s t ,

mm. 1-16 and the second , mm. 17-26. In Section" One each

voice in tu rn presen ts the cano n's opening s t a t ement , which

cons i s t s of a s ing le twelve-note row. In mm. 1-5 the f i r s t

voice sounds PO; in mm. 6 - 1 0 ~ the second presen t s I 6 ; and,

of cou rse , in mm. 11-16 the th i rd repea t s PO.

D ACE A# B G

ISee David Sch i f f , "Car te r in the Seven t i e s " , Tempo,

(Boosey and Hawkes Pub l i she r s , Sep tember 1979, No. 130) , p .

5. This paper conta ins seve ra l noteworthy obse rva t ions with

r e spec t to spa t i a l design in the f i r s t song of Car t e r ' s cy

c le A Mirror on Which to Dwell .

2E l l i o t t C ~ t e r , C a ~ n fo r 2, (New York: Associa ted Music

Publ i shers ,1972) , p. 1.



2 INDIANA THEORY REVIEW

Canon for 3In Memoriam Igor Srravinsky

1

Playin.g Score jmeElliott Carter

(1971)

J.= ca .56

2

3

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~ I

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- j

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CW

p(poco)

1101~ - - - - - -- - , . ~ ~-----

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ub.

AMP-n03©Copyright 1972 by AssociatedMusic Publishers, Inc., NewYork

All Rights Reserved

Used by permission.Printed in U.S.A.



ELLIOTT CARTER'S CANON FOR 3 3

Playing Score in C

p fiftpp sempre

'" " .. .. .. • (;::.) 1(:> I,--- '""-l.....J poco \, ( : » ~mf ' ¢pp se,\pre r t - - - ~ ( ~ ) LI . - ( : > -+ - - --:-

~ . 1--'

poco e\ /, - - , , ' -- - p= p p ¢ppsempre

: > _ ~ - - -- ~ ~ ~ ~ --.:::::II l- " ..--::

"

I '-'" ~t!J ~ (» I:: p p>

11- !: » 'p.' .fL' .fL

t I \ ~ ~ ~ \ ~ \: m f f - ~~ ~ ~ ) / :>.. I

\ /l '(:» '-v· 7 n i f ~ ; ~ /,? -

(= j - - ~ ; --,. ~ ( : »1/1",

" I I :>

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[TI]rit, funza

--- r:'I -1\ -- -

/( ~ -,," ----- - ~ / _\ I

\ J O c o ~ p p rit.lZinga

\\ ( :», ~ ; 2 ~ ( ~ ) ( :» r:'I

. t ! J p o c o ~ ~~ p p s e m p r e ~ ) /

II ---'"

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So as to g ive

cons i s t en t among

remainder o f th e

s igns to each th e

these i n i t i a l s ta tements a p ro f i l e both

themselves and yet d i s t i n c t from the

mate r ia l o f Sec t ion One, th e composer as

same symmetr ical rhythmic pa t t e rn :

.(-- ~n, J ~ J, n. J. 1 J, n, l.

I

>J n.In add i t i on , each s ta tement o f t h i s opening phrase i s marked

by f requen t and bold dynamic a r t i cu l a t i on qui te d i f f e r e n t

from the c o n st an t, u n in fl ec te d pianiss imo with which the

remaining mate r i a l o f t hese f i r s t s ix teen bars i s heard .

Sect ion Two (mm. 17-26) con tinues the canon between

voices bu t compounds th e s t ruc tu re through a r a the r dazz l ing

canonic t ou r -de - fo rce . In these mea su re s, w hile con t inu ing

to answer one ano ther in the manner ind ica ted above (second

voice inver ted a t the t r i t one ; th e th i rd a t th e unison) , the

th r ee vo ices a re combined, sounding t oge the r f i r s t th e in

ver ted t r ansposed answer o f th e second voice (heard

o r ig ina l l y in bars 6-10) , and then the unison answer (heardo r ig ina l l y in bars 11-15) .

mm. 17-21

P !if;'pp .empre

/_rJ-1b-l. • • ,(: »

, up.·

,

l ~ p p ~ m p r e ( » ~ , r ' ~ ~ ~ ~ \, \1 ~ " " . ~ ) / '=:.( :>+"-.- :- ~poco \ / ,V-

"'l» '--v· _\ ~ ~iIJpp sempre

1'1 : - - - - . . . :>'):: - : : : : ~----- >l •

r-....... . . . . . ' I : » ~,!J ~ . _.

I I -- -pp

Composi te o f mm. 17-21; c f . mm. 6-10.




,it. lunga

poco!lf-ppocoS£vn===;;;-pp-p

mm. 22-26r . ~ ~ • ~ f':<, -

I ~ m f f-;'\ /( ~ ....- II \ocoflJpp rit.

/. \ (r' IUllga

\I' (0 ) ) • ~ ; i ~ f ~ ) • ("'0» • f':<,

! ~ i > ~ / ~ ~ .' ' ' - (0 ) ) /

( ~ f ---

f 'p .. I ~ ' - ~ < nt.__.... IUllga-.....b :---. ~11." -,.-. -,.' L If':<,~ ~ - - = = - - - - ~ " i»

. ~ . ~-

Composite o f mm. 22-26; c f . mm. 1-5 and 11-15 .

ThUS, in S ec tion Two Ca rt er s imu lt an eou sl y recap i tu l a t e s and

ex tends h is preceding mate r i a l .

I I : Spa t i a l Design

The pre l imina ry observa t ions having been s t a t ed , the sub

j e c t o f t h i s paper may now be fu l l y addressed . In con

s ider ing th i s composi t ion ' s s p a t i a l des ign , one immediately

no t i ces the s t r i k i ng r e l a t i onsh ip between th e m a nip ula tio n

o f t h i s paramete r and the canon ic procedure i t s e l f . Con

s i s t e n t l y , one d i scove r s th a t c e r ta in sp a t ia l format ions

c ry s t a l l i z e over t ime as the var ious r e f l e c t i on s among the

voices a re heard in t h e i r s u cc es s iv e u n fo ld in g s. S ign i f i

can t l y , t h en , an exp lora t ion of the work 's s p a t i a l s t ruc tu re

may a lso revea l r ich new i n s i gh t s in to the use and meaning

of the c an on ic p ro ce du re i t s e l f .

By super imposing the i n i t i a l phrases of Voices One (or

Three) and Two in a no te -aga in s t -no te fa sh ion , a unique suc

cess ion of ve r t i c a l dyads is formed.




etc .

etc .

mm. 1-5

mm. 6-10 • b ~ ~~ ~ ~ ~ ~ : ~ t ~ n e ) ~ : Z j Z @ ~ : ~ ~ 3 ; ~ . ~ · " , ~ . ~ g ~ . " ~ . ~ ~ ' * ~ ~ : ~ .

~ . ~One immedia te ly notes the fol lowing r epe t i t i on s :

-a .. " · · · · · ~•

With t h i s in fo rm atio n th e fo llowin g th ree ca t ego r i e s may be

i d en t i f i e d :

a) The unison or oc tave dyads:

unison dyads

b) The r e g i s t r a l l y f ixed dyads ( t ha t i s , a l l pa i r s

which recur in th e same r e g i s t r a l pos i t i on ) :

f ixed dyads



ELLIOTT CARTER'S CANON FOR 3

c) The inver t ing dyads ( t ha t i s , those dyads which

recur in inver ted spa t i a l pos i t ions ) :

7

b ~inver t ing dyads

t h a t the r eg i s t r a l d i spos i t i on

fills the en t i r e space

(N ote, each pa i r i s f i r s t heard in i t s closed

pos i t i on , then in i t s open form.)

In add i t i on , one might note

o f tones a lmos t comple te ly

es t ab l i shed .

~-i.-

- ~ .a{ gJ- ( J••17t2Only two tones a re never heard. The importance of t h i s wil l

become c l e a r p resen t l y .

Having ex t rac t ed th i s da ta , one now begins to unders tand

the work ' s s p a t i a l des ign . F i r s t , it should be observed

t h a t c5

i s r e g i s t r a l l y th e cen t r a l tone in the spa t i a l

f i e l d .3

Each of the o the r dyads and so , o f cou rse , the

en t i r e co l l ec t ion - - i s ar ranged symmetr ica l ly around t h i s

pa r t i c u l a r C.

3Notat ion o f r eg i s t e r s : middle C i s l abe l l ed c 4 , the C

one oc tave higher is c5and so fo r th ; the C one octave lower

i s c3and so fo r t h . All tones between Ci and c j , where i

and j are ad jacen t i n t ege r s , a re given the supe r s c r i p t i andso f a l l wi th in r eg i s t e r i .




a}

c}

(Here , each dyad i nve r t s symmetr ica l ly around c5 . )

The importance of C5

is emphasized in the composi t ion in

va r ious ways. I t i s the only tone repeated by th e th ree

voices in unison . Also, wi th in the f i r s t phrase o f each o f

the t h ree voices the compose r marks a crescendo up to t h i s

tone a t which po in t the volume s ud de nly d ro ps to piano (m.

4 , f i r s t voice ; m. 9, second voice ; m. 14, t h i rd vo i ce ) ,

t h ree t imes ca l l ing a t t e n t i on to i t s s t r uc tu r a l impor tance.

In add i t i on , it i s importan t to note the spec i f i c ro l e s

occupied by sev e ra l o f the dyads ca tegor ized e a r l i e r . F i r s t

of a l l , it seems c le a r th a t a t te n t io n has been brought to

two spec i f i c tones by t h e i r unison or oc tave pai r ings : C,

th e impor tance of which has been made c l e a r from the

foregoing d i scus s ion , and F#, th e impor tance of which wi l l

become c l e a r as the ana lys i s proceeds . Clea r l y , however, i f

F# i s to be s i tua t ed symmetr ica l ly about C it must be pa i r ed

with i t s e l f a t some oc tave t r a n spos i t i on , a s i t u a t i on which

r e su l t s from the composer ' s i n i t i a l cho ice o f row forms Po

and 16

both of which yie ld F# in the same pos i t ion wi th in

the t o t a l succession o f twelve p i t ches .4

With r e spec t to the s e t o f f ixed dyads it should be noted

t h a t t hese occupy c r i t i c a l pos i t ions wi th in the work 's

s p a t i a l des ign . These pa i r s , B4_D

b5and D

4_B

b5a r e , re spec -

t i v e l y , th e dyads c l o s e s t to and f a r t he s t from the cen t e r ,

C5• In add i t i on , D

4and B

b5a re , re sp ec t iv e ly , the lower

and upper ex t r emi t i e s of the en t i r e compos i t ion , l im i t s

which would , by the way, be superceded i f the dyad B4_D b5

were ever i nve r t ed . Thus, the cen te r o f the f i e ld and i t s

ex t r emi t i e s are l inked to one ano ther in t h e i r i nva r i an t

4See : Mil ton Babb i t t ,

pos i t i ona l Dete rminants" ,

Henry L ang, ed . (New York:

"Twelve-Tone Invar ian t s as Com-

in Problems of Modern Music, Paul

W.W Norton , 1 96 0), p . 116-117.




spa t i a l deployments .In l i g h t o f t h i s , it i s also impor tant to note t h a t these

two dyads are always ad j acen t .

" ' ~ b . 1& ~l.._ iAo,..

.."I' • .,,- .. .

I

The manner in which th es e a dja ce nc ie s a r i s e i s also qui te

impor tan t . In each case th e success ions are formed by l eaps

of a major s ix th . The pa i r 84_D b5 s urro un ds th e cen t r a l c5

a t the d i s t ance of a semitone and , in add i t i on , each member

of t h i s dyad i s also l inked with one of the ex t remi t i e s

through th e inve rs ion o f t h i s same semitone di s t ance .

As a r e su l t , t i e s between the core o f th is sp at ia l f i e ld and

i t s ex t remi t i e s are s t r eng thened , t i e s which wi l l be re in

forced as the composi t ion proceeds .

At t h i s poin t it would be usefu l to r eca l l t h a t the dyads

out l ined above never ac tua l l y sound as s imu l t ane i t i e s .

Rather , they are formed over t ime as the p ie ce u nfo ld s. As

the f i r s t i ns t rument presen t s i t s f i r s t twe lve -no te s t a t e

ment , it ou t l ines an incomplete f i e ld which i s c ry s t a l l i z ed

only a f t e r the second voice adds i t s spa t i a l l y complementary

tones . Simi la r ly , th e second voice i s i t s e l f completed as

the o r i g i na l s e r ie s is r e i t e r a t ed by th e t h i rd voice .

Within these opening bars the composer deve lops a complex

spa t i a l mosaic which i s a t once both s t a t i c and dynamic.

All dyads are f ixed symmetr ica l ly about one cen t ra l tone ,

though some remain unchanged whi le o the r s i nve r t around t h i s

spa t i a l co re .

Now t h a t some of the re l a t ionsh ips between the i n i t i a ltwe lve -no te s ta tements o f each voice have been i d en t i f i ed ,

the remainder o f the canon may be discussed . One of the

f i r s t poin ts to be noted is t h a t the use of s t r i c t twelve-

note success ions i s n ot c on tin ue d. Rathe r , th e co l l ec t ion

of ve r t i c a l dyads genera ted by th e two se r i e s in t roduced in

the f i r s t phrase i s maintained with r ig o ro u s co n si st en cy ,

admi t t ing on ly one, a l be i t ext remely impor tan t , add i t ion .

Continuing the procedure es tab l i shed ea r l i e r , super im-

pos ing the f i r s t voice with i t s inverse yie lds the fol lowingsuccess ion of dyads :




Phrase 2 Phrase 3 Phrase 4 Phrase 5

• •Immediate ly i n t h e second phrase t h e composer i n t r o d u c e s t h e

s i n g l e new dyad, Bb4 _D S and, so as t o emphasize i t s im-

p o r t a n c e , he s t a t e s it twice i n immediate s u c c e s s i o n . This

p h r a s e c o n t a i n s t h e on ly a pp ea ra nc e o f t h i s dyad i n t h e

canon , and i t s p re se n ce h er e i s q u i t e r e v e a l i n g . F i r s t , one

should observe t h a t t h e two t o n e s i n t r o d u c e d here were t h e

o n l y two excluded from t h e opening (Phrase 1 ) . As s u c h ,

t h e i r appearance marks t h e f i n a l , complete f i l l i n g - i n o f t h e

e n t i r e space o f t h e p i e c e .

i · - i · · ·..

t t

In a d d i t i o n , t h e s e two t o n e s c o n s t i t u t e t h e i n v e r s e o f one

o f t h e p r e v i o u s l y f i x e d dyads , t h e dyad which, s i g n i f i c a n t

l y , c o n t a i n s t h e upper and lower e x t r e m i t i e s o f t h e p i e c e .

As was t h e case with i t s i n v e r s e , t h i s new dyad i s l o

c a t e d a d j a c e n t t o t h e o t h e r f i x e d dyad heard i n t h e f i r s t

p h r a s e , B4_D

bS• T h i s , as may be r e c a l l e d , i s t h e p a i r

c l o s e s t to cS

and c o n s t i t u t e s t h e c ru c i a l l i n k between t h e

c e n t e r and t h e e x t r e m i t i e s .

The second phr as e immed ia te ly f o c u s e s upon t h e s e c r u c i a l

r e l a t i o n s . In it t h e composer underscores t h e s e r e g i s t r a l

c o n n e c t i o n s by f i r s t i n v e r t i n g t h e dyad c o n t a i n i n g t h e ex-

t r e m i t i e s , then sounding t h i s i n v e r s i o n once a g a in , a d j a c e n t

t o B4_D

b5, and f i n a l l y proceeding immediately t o t h e c e n t e r ,

cS •




~ . ~ ~c l o s e s t i n v e r s e o f

d y a d e x t r e m i t i e s

t o cS

•

\c e n t e r

T h i s s i n g l e b r i e f p a s s a g e s e e m s t o c r y s t a l l i z e many o f t h e

s u b t l e c o n n e c t i o n s among t h e c r u c i a l t o n e s o f t h e s p a t i a l

d e s i g n e n c o u n t e r e d e a r l i e r i n t h e c o m p os it i o n .

The t h i r d p h r a s e i s e q u a l l y r e v e a l i n g , a s it r e v e r s e s t h e

m o t i o n o f i t s p r e d e c e s s o r , u n f o l d i n g o u t w a r d s y m m e t r i c a l l y

f r o m t h e C w h i c h c o n c l u d e d t h e s e c o n d p h r a s e . T h i s it a c -c o m p l i s h e s t h r o u g h a s u c c e s s i o n o f m i n o r t h i r d s :

Of c o u r s e , had t h i s s u c c e s s i o n b e e n c a r r i e d o n e s t e p

f a r t h e r , t h e m o t i o n o u t w a r d wo u ld h a v e a r r i v e d a t C4 a nd C6

an d s o p o s s i b l y s u g g e s t e d a t r a n s f e r o f t h e o r i g i n a l c5s i m u l t a n e o u s l y o n e o c t a v e i n b o t h d i r e c t i o n s . S

S In a d d i t i o n , s u c h a m o t io n o utw ard s u g g e s t s o n e p o s s i b l ee x p la n a ti o n f o r t h e e m p h a s i s g i v e n t o t h e t o n e F* a s t h e o n -

l y o t h e r u nis o n d ya d . The tw o F # ' s e m p l o y e d i n t h e ~ i e c es y m m e t r i c a l l y d i v i d e t h e s p a c e o u t l i n e d b y c4 , cS and C •

As s u c h , t h e y s t r e n g t h e n t h e i m p l i c a t i o n o f m o ti on o utw ar df r o m cS t o t h e o c t a v e C4_C 6 .




=:

However, the canon c on sp ic uo us ly a vo id s t he se t one s . I t s

boundar ies remain D4_B b5 and whenever the piece r eaches

t hese l imi t s it f o l d s back in to the cen t e r v ia the B4_D

b5

dyad. Thus, r a t h e r than as boundar ies o f a s t a t i c f i e l d ,

one might th ink o f the ex t r em i t i e s as two c r i t i c a l p ivo t

p oin ts w ith in a dynamic spa t i a l evo lu t ion .

Once aga in , the cen te r and ex t remi t i e s are linked in an un-

broken spa t i a l cont inuum.The four th phrase of the composi t ion begins with th e dyad

B4_D b5 and p ro ce ed s outwar d, r ec ap tu ri ng s ev er al more of the

dyads f i r s t genera ted by the opening twe lve-no te s e r i e s .

The f i f t h and l a s t phrase sounds the s ing le remaining dyad

(Ab4 _E 5 ) not ye t heard in the second through f i f t h phra se s ,

complete ly f i l l i ng in the space of the compos i t ion fo r asecond t ime . S ign i f i c an t l y , th e very l a s t phrase i t s e l fco nclu de s w ith a con f i gu ra t i on which qu i t e succ inc t ly and

dramat ica l ly focuses upon the composi t ion ' s most impor t an t

e l emen t s .

As the foregoing ana ly s i s shows, El l i o t t Car t e r ' s Canon

fo r l unfolds a unique and complex spa t i a l des ign . The in t e rp l ay between s t a t i c and dynamic e lements f ash ions a

s t r ik ing mosaic in which the r eg i s t r a l deployment of tones

i s organized with rema rk ab le sub t l e t y . The compos i t ion i s a

ra re gem, th e b rev i t y of which be l i e s the r ichness of i t s

ingenious s t ruc t u r e .

carter,elliott_canon for 3 (à stravinsky)_ avec une analyse

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