Structur 2

7/25/2019 Structur 2

http://slidepdf.com/reader/full/structur-2 1/35

Pierre Boulez’sStructures 1a for Two

Pianos

An Analysis by Reginald Smith

Brindle

Presented by Michelle Keddy



Introduction

Boulez wrote two books of “Structures” for two pianos.Structures I consists of three parts and Structures II ofparts. (We will be discussing Structures Ia)

Structures Ia was written in 1!". #s al$ost e%er& asthe piece was predeter$ined' Structures was withoutwritten in the st&le of integral (total) serialis$. In fact'

Boulezs intention to $ake Structures a tetbook pieceintegral serialis$ in the sa$e wa& The Art of The Fugufor fugal writing.



*he *one +ow *he tone row Boulez used for Structures was based uptwel%e,note series deri%ed fro$ -i%ision 1 of essiaende valeurs et d’intensités.

#ll twel%e transpositions of the tone row plus the twel%transpositions of each of the deri%ed for$s (in%ersion'retrograde and in%erted retrograde) were used once eathroughout Structures 1a. *hus' a total of /0 rows appin the piece' each iano part containing "/ rows.



*he atrices2sing the tone row' Boulez created two $atrices3 theatri' and the In%ersion atri.

-To create the matrices, Boulez first assigned each of the notes in

the tone ro a number!

So "-flat became #, $ %, A &, A-flat ', ( ), etc!



The Matrices *he original $atri was then 5lled in b& transposing thoriginal row' beginning on each note in turn. *or e+aml

the second note of the series as $, so the second ro of the matri+

as formed by eeing the inter.al relationshis and starting on a $!

The second ro of the matri+ thus reads % / ' ) 0 ## # 1 #% & 2 #3!

The third note of the series as A, so the third ro of the matri+

as formed by eeing the inter.al relationshis and starting on A!

The third ro of the matri+ thus reads & ' # % / 1 #3 ) 0 2 #% ##



*he atrices4nce all twel%e transpositions are deter$ined' the& arinto the $atri. +eading fro$ left to right gi%es the orirow and its transpositions' and reading fro$ right to lethe retrograde rows.



*he atrices *he second $atri is created b& deter$ining the in%erthe original row and its transpositions.

*hus' the 5rst row of the In%ersion atri reads31 6 7 18 1" " 11 9 / 0 !



*he atrices *he in%ersion transpositions are deter$ined in the saas the for the 4riginal atri. *he& are then 5lled intoIn%ersion atri. +eading fro$ left to right gi%es thein%ersion rows' and reading fro$ right to left gi%es the

retrograde in%ersion rows.



*he atrices*hese two $atrices were used to deter$ine all note duratid&na$ics' and $odes of attack. *he& also deter$ined thein which the rows were used and for$ed a plan for note du



:ote -urations

In Structures 1a' Boulez uses the thirt&,second note abasic ti$e unit. *o deter$ine note durations throughwork' the thirt&,second note is $ultiplied b& the nu$

each of the row of the $atrices. *or e+amle, a note duratiseries based on the original ro ould loo lie this4

A &%nd note + #5 a &%nd, a &%nd + % 5 a #0th, a &%nd + &5 a dotted #0th,

etc!



:ote -urations

In Piano I, the iece begins by laying note durations of

the RI) ro 6#% ## 1 #3 & 0 2 # % / ' ) 7! This results in

the folloing rhythm4

Piano II lays note durations of the R #% ro 6) / 0 ' & 1 % # 2

## #3 #%7! This multilication concet is alied to all '/ of the

ros, each resulting duration series being used once during the iece!



-&na$ics *o deter$ine d&na$ics' Boulez chose twel%e di;erentd&na$ic %alues and assigned each one a di;erent nu

#5 ,,,, )5 8uasi , 15 f

%5 ,,, 05 m, #35 ff

&5 ,, 25 mf ##5 fff

'5 , /5 8uasi f #%5 ffff



-&na$ics *he order in which the d&na$ics were used was deterfro$ the diagonals of the two $atrices. *he 4riginaldeter$ined the order of d&na$ics for iano I.



-&na$ics *he diagonals fro$ the 4riginal atri resulted in thefollowing ordering of d&na$ics3

1" 6 6 11 11 ! ! 11 11 6 6 1"

;; $f $f ;f ;f <,p <,p ;f ;f $f $f ;;

" 7 1 9 6 6 9 1 7 "ppp pp pppp $p f $f $f f $p pppp pp pp

=ach of the "/ d&na$ics were applied in this order to trows that $ade up the part of iano I. (*he 5rst row uwas ;;' the second series was $f' the third was $f' et



-&na$ics *he In%ersion atri deter$ined the d&na$ics for ia



-&na$ics *he diagonals fro$ the In%ersion atri resulted in thfollowing ordering of d&na$ics3

! " " 0 0 1" 1" 0 0 " " !

<,p ppp ppp <,f <,f ;; ;; <,f <,f ppp ppp<,p

6 7 1 9 " " 9 1 7 6

$f pp pppp f $p ppp ppp $p f pppp pp $f =ach of the "/ d&na$ics were applied in this order to trow that $ade up the part of iano II.



-&na$ics:ote that in iano I' the nu$bers /' 0 and 18 do not oin the 4riginal atri diagonal nu$ber series' and thethe d&na$ics p, quasi f and do not occur in the partiano I. Si$ilarl&' the d&na$ics p, and f do not oc

part of iano II. >owe%er' these discrepancies causedBoulez to $ake a few uni$portant de%iations fro$ his



odes of #ttackBoulez assigned $odes of attack (articulation) in $ucsa$e fashion as he assigned d&na$ics. >e assigned adi;erent $ode of attack to each of the following nu$b1 " 7 ! 9 6 0 11 1". (Since neither / nor 18 ap

in the diagonals of either $atri' he did not assign thonu$bers a $ode of attack.



odes of #ttack4nce again he used the 4riginal atri to deter$ine iand the In%ersion atri to deter$ine iano II. (the opdiagonals were used' howe%er.)

?enerall& one $ode of attack is used per 1",note seri

though there are $an& irregularities.



4rdering of the :ote

Series *he two $atrices deter$ine the order in which the di;erows are heard during the piece. =ach indi%idual row isonce' so there are a total of /0 rows sounded. =ach pia

pla&s "/ of these rows. Structures 1a is di%ided into twparts' # and B' in which twel%e rows are used b& each p *he following chart shows how the rows are di%ided betthe two pianos3



4rdering of the :ote

SeriesPart A Part B

Piano IAll 9:; series

in order!

I

#

All 9RI; series

in order!

RI

#

Piano II

All 9I; series

in order!

:

#

All 9R; series

in order!

R

#



4rdering of the -urationSeries

# si$ilar chart is also used for the duration series.

Part A Part B

Piano I All 9RI; seriesin order!

RI#

All 9I; seriesin order!

R #

Piano II

All 9R; series

in order!

R #

All 9:; series

in order!

RI#



4%erall @or$Structures 1a can be broken into two $ain di%isions' cand B. =ach of these sections can be further broken dinto s$aller sections. *here are a total of ele%en sectiall' which are deter$ined b& te$po. # has ! sections a

has 9. *here are three te$pos which occur throughoupiece3 lent (slow)'$odArA' pres<ue %if ($ediu$)' and t$odArA (fast). *he order of te$pos is3

(section) 1 " 7 / ! 9 6 0 18 11(part #) @ S @ (part B) S @ @ S



4%erall @or$ *his can be rearranged as two partl& o%erlapping s&$$c&cles centered around section ! (section ! in fact beingcrucial $o$ent of the piece).

1 " 7 / ! 9 6 0 18 11 @ S @

S @ S @

>owe%er' it is i$portant to re$e$ber that the o%erall fostructure is reall& a free conception.



4%erall @or$Section Bars Tem,o <ength# #-2 Tr=s mod>r> #3 sec

% /-&# Mod>r>,

res8ue .if

&3 sec!

& &%-&1 <ent %3

' '3-)0 Mod>r>,

res8ue .if

%3

) )2-0' Tr=s mod>r> #3

0 0)-2% <ent '3

2 2&-/# Mod>r>,

res8ue .if

#3

/ /%-/1 Tr=s mod>r> #3

1 13-12 Mod>r>,

res8ue .if

#)

#3 1/-#3) <ent %)

## #30-##) Tr=s mod>r> #)

*rs $odArA30th noteC1"8

odArA' res<uDif30th noteC1//

Eent319th noteC1"8



4%erall @or$While Structures 1a can be di%ided into two $ain partB' and then further di%ided into ele%en sections whichdeter$ined b& te$po' so$e of these sections can be f di%ided into subsections. Subsections are deter$ined

length. =ach subsection is 60 thirt&,second notes longlength of one duration series. @or ea$ple' the te$posection 1 is très odéré and it is 60 thirt&,second notetherefore it cannot be broken into an& further subsecti

te$po for section "' howe%er' is odéré, presque vif aa total of "7/ thirt&,second notes long. *herefore sectis broken into three subsectionsF "a' "b and "c. Both s" and / can be broken into subsections.



:.erall *orm

1 ( M )

2 a 2 b 2 c

2 ( F ) 3 ( S )

4 a 4 b

4 ( F ) 5 ( M )

P a r t A

6 ( S ) 7 ( F ) 8 ( M ) 9 ( F ) 1 0 ( S ) 1 1 ( M )

P a r t B

S t r u c t u r e s 1 a

KeyM=très modéré F=modéré, presque vif S=lent purple=78 thirty-second notes long



-ensit&Because the piano is capable of pla&ing se%eral di;ere$usical lines at once' it is possible for one section or osubsection to contain $ore than one %ersion of the ton#s an arbitrar& ea$ple' the piano pla&er could pla& t

original tone row in the right hand and a transpositionoriginal row in the left. 4r the piano pla&er could pla&the original row and the in%ersion with the right hand'retrograde row and retrograde,in%ersion with the left.

Structures 1a is written for two pianos' there are $an&di;erent possibilities for density (the nu$ber of rowsare pla&ed in one section or subsection).



-ensit&In Structures 1a' each piano contributes a total of 1" rboth arts # G B' $eaning that each part contains antotal of "/ rows. =ach piano sounds either one' two orrows per section or subsection' and re$ains silent in o

*he following chart shows the densit& of Structures 1a.Part A Part B

Section # %a %b %c & 'a 'b ) 0 2 / 1 #3 ##

# of Rows

Piano 1

Piano 2

#

#

%

%

%

# #

&

&

#

#

%

&

# &

%

#

%

%

%

%

%

#

#

&

&

Total #

of Rows

% ' & # 0 % ) # ) & ' ' % 0

24 2



-ensit& *he densit& of Structures 1a can also be represented ifor$ of a graph.

0

1

2

3

4

5

6

7

1 2a 2b 2c 3 4a 4b 5 6 7 8 9 10 11

Sections

u !

" e r o # $ o % s



:on,redeter$ined

=le$entsSe%eral ele$ents of Structures 1a were not predeter$ *he& are3 1) octa%e registerF ") restsF and 7) $etre.

4cta%es3 Boulez did not assign an& particular octa%e rto an& particular note' row' d&na$ic' etc. *hus' the ocregisters used were deter$ined as the piece was beinco$posed. >owe%er' two principles can be obser%ed3

each part' successions of notes are generall& spread owide registerF and ") whene%er the sa$e note occurssi$ultaneousl& in two rows' it is pla&ed in unison' thera%oiding octa%es.



:on,redeter$ined

=le$ents+ests3 In staccato passages' fre<uentl& the notes will bindicated b& either a thirt&,second or a siteenth,note'the re$ainder of its duration 5lled out b& rests' as oppto using the staccato s&$bol. *his also occurs in pass

with these s&$bols3

4therwise' rest signs usuall& arent used' unless the&the part writing.

etre3 *he $etre changes fre<uentl& in Structures 1a'onl& purpose is to aid the perfor$er. When listening tpiece there does not see$ to be a sense of $etre at al



HonclusionStructures 1a was organized with etre$e care' lea%ingele$ents to chance. >owe%er' listening to the piece' itlike total rando$ness. -onald itchell sa&s “:e%er wasso o%er,deter$ined' and ne%er so dicult to hear as an

epression of order in ter$s of sound. Boulez Structur assu$es (because one has not succeeded in eperienciorganization as sound)' are Jabout nothing other than tstructures. But e%en the $ost open and ad$iring ear (

recognizes the brilliance of Boulez $usical personalit&)baKed in perfor$ance b& the absence of audible se<ueor logic.” (p.1"0)



HonclusionBoulez hi$self realized that Structures was pushing thtechni<ue of integral serialis$ to its absolute li$it. >einscribed a pro%isional title on the 5rst page of Book Ihe took fro$ a aul Llee painting3 “# lM li$ite du fertile

(eaning' “#t the li$it of fertile ground.”



Bibliograph& *his presentation was $ainl& based upon3Smith Brindle, Reginald! The New Music: The Avant-Garde since

1945. <ondon4 :+ford ?ni.ersity Press, #12)!

4ther books used3(riffiths, Paul! Boulez ! <ondon4 :+ford ?ni.ersity Press, #12/!

@ameu+, $omini8ue! Pierre Boulez. Translated by Susan Bradsha

ambridge, Massachusetts4 ar.ard ?ni.ersity Press, #11#!Mitchell, $onald! The an!ua!e o" Modern Music. <ondon4 The

"nglish ?ni.ersities Press <td!, #10/!

Peyser , @oan! Boulez ! Ce Dor4 Schirmer Boos, #120!

Documents

Structur 2