GOLDMAN, Boulez Explosante-fixe

8/17/2019 GOLDMAN, Boulez Explosante-fixe

1/37

C M ÉMORIALE : P A HS B’ ... EXPLOSANTE - FIXE ... musa_274 25..61

Analytical Rationale

In this article, Pierre Boulez’s Mémoriale (... explosante-fixe ... originel) (1985)will be analysed using various kinds of charts and tables.1 This work is anoutgrowth of a project called ‘Score Charting, Segmented Listening’ (‘Mise en

tableau, écoute segmentée’) undertaken by the Analysis of Musical Practices(APM) team at the Institut de Recherche et Coordination Acoustique/Musique(IRCAM) in which I have participated since September 2005. The approach Iadopt therefore emphasises the path leading from the score (as well as therecording) to the various charts in which different aspects of the score arerepresented.The APM team, directed by Nicolas Donin, is developing a softwaretool capable of producing multimedia charts, and in particular ‘audible’ para-digmatic analyses of musical pieces. In a way, of course, this project is an attemptto adhere to Nicolas Ruwet’s injunction to furnish explicit criteria for segmen-tation, grouping and any other analytical decisions which give rise to the processof interpretation.2 What will become apparent from the analysis provided here

is the use, in this piece as well as in others by Boulez from the 1980s onwards,of polar notes – that is, structural nuclei around which other pitches cluster likemoons around a planet – as the axial points of musical form. In Mémoriale, theopposition between groups of appoggiaturas and long polar notes is decisive forthe articulation of form. This in turn is related to one of the possible meaningsof the title ‘... explosante-fixe ...’.

It might seem unpromising to study works from Boulez’s later period bycompiling charts and tables.The chart is thought to be the precompositional toolof choice for works from the purely serial phase of the composer’s stylisticdevelopment, especially those from the brief period of the so-called generalisedseries, the emblematic work of which is Structures pour deux pianos (1952). Later

works by Boulez, as commentators such as Jean-Jacques Nattiez (1993) andCélestin Deliège (2004) have argued, reveal a new realm of stylistic freedom, andof corresponding unanalysability. It is generally thought that even if, in his laterworks, Boulez remains faithful to serial principles, the rigour and seemingautomatism of, for example, Structures 1a gives way to compositional freedom,on the one hand, and to accommodations made in favour of particular listeningstrategies – to what could be called an aesthetic prediction incorporated intothe poietic process – on the other. This amounts to a kind of compositional

DOI: 10.1111/j.1468-2249.2009.00274.x

Music Analysis, 27/ii-iii (2008) 25© 2009 The Author.

Journal compilation © 2009 Blackwell Publishing Ltd., 9600 Garsington Road, Oxford OX4 2DQ, UK

and 350 Main Street, Malden, MA 02148, USA


2/37


3/37


4/37

Ex. 1 ... explosante-fixe ...

Ex. 2 Originel idea from ... explosante-fixe ...

ORIGINEL (début ou fin)

28

Music Analysis, 27/ii-iii (2008)© 2009 The Author. Journal compilation © 2009 Blackwell Publishing Ltd.


5/37


6/37

Ex. 6 Element D (‘rapide, irrégulier, vacillant’)

4

Rapide, irrégulier, vacillant = 120/1325 5 5 5

5ralentir . . .jusqu’a

Ex. 7 Paradigmatic analysis of Mémoriale using score charting tool

11 5céder

5

5Modéré, Modulé = 90 = 60

= 90 ( = 120) rall. = 60

Rapide, stable = 1203

ralentir jusqu’à 1

Modéré. Modulé = 90

rall. = 60 ( = 120)


céder

Rall.


8


30



7/37

The Element C Passages: Progression from Clean to BlurryBefore interpreting the results of the paradigmatic analysis, some further obser-vations regarding element C are worthy of consideration due to its unique formalstatus. Altogether this quasi-cadential formula occurs six times, once at the veryend of the piece, while each of the other three elements (A, B and D) appearstwelve times. The process within which element C is embedded is in factconnected to the acoustic sense of the word ‘analysis’, that is, the decomposition

Ex. 7 Continued

12Rapide = 120/132 irrégulier, vacillant

10

Lent, souple = 60 en rallentissant suspendu

long

9ten.

3 3 3 céder ten.

6

Lent ( = 60)suspendu

long

73

3

Lent, souple = 60suspendu

long

4

Rapide, irrégulier, vacillant = 120/132rallentir 5 5

55

5

Rapide, irrégulier, vacillant = 120/132


33

33 3

33

C M ÉMORIALE 31

Music Analysis, 27/ii-iii (2008) © 2009 The Author. Journal compilation © 2009 Blackwell Publishing Ltd.


8/37

of a complex sound into its component parts. Boulez’s increasing interest in thescience of acoustics and its application to music may of course be traced to hisearliest proposals for the founding of IRCAM dating from the early 1970s.Indeed it was around this time that the electroacoustic transformation of soundbegan to leave a mark on his instrumental writing, albeit sometimes in a rathermetaphorical form, in the presence of adapted electroacoustic techniques such asfrequency shifting, phaser effects, filters, delays, harmonisers, resonators, and soon.

Ex. 7 Continued

17


16accel.120

sub.

tempo = 60

rall. accel. ralentir ten.

rall.

13

Modéré, Modulé = 90

accel.

3

19

accel. rit. tempo . = 120

= 60

. = 120 . = 90 = 90 jusqu’á

120

accel.

ModéréModulé

= 90 = 90

tempo

ModuléModéré

. = 90 . = 120 . = 90

32



9/37

During his 1991 lecture, the composer explained that the accompanyinginstruments in

Mémoriale had been chosen so as to create a continuum between

what might be termed a ‘straight’ sonority (by which was meant a clean, focused,non-vibrato sound) and a more ‘fuzzy’ one (involving blurring or muffling effectssuch as vibrato, tremolo, muting or flutter-tonguing). As Mémoriale progresses,the overall sound envelope consequently follows a trajectory from clean to blurryor blurry to clean, depending on which motivic cells are being considered. Thehorns, according to this schema, remain at one extreme of the clean sound, whilethe flute, which for much of the piece plays using trills or flutter-tonguing

Ex. 7 Continued

3

3

3 33 3

3

14Lent = 60

suspendu

long

15Rapide, irrégulier, vacillant = 120/132

3

3 33

33

3

33 rallentir

long

suspenduen ralentissant Lent = 5618

jusqu’á

souple

C M ÉMORIALE 33



10/37

technique, occupies the other. Due to the variety of playing styles available to it,the string group fluctuates between these two outer limits, approaching thetimbre of the horns when adopting a naturale and non-vibrato playing style, andthe timbre of the flutter-tongued flute when playing either

tremolo sul tasto or

trilled sul ponticello. Given this acoustic framework, music analysis and sonicanalysis may thus be felt to intersect in this work. With specific reference toelement C, the strings begin in a more ‘normal’ register prior to accommodatingan expanding range of tremolos, trills, sul ponticello and sul tasto techniques. Theprogressive effect may be gauged with reference to Exs. 8–10 as shown below.Thus in the third occurrence reproduced in Ex. 8 (C3), only one instrument,the first viola, is blurred. Ex. 9 by comparison summarises the string

Ex. 7 Continued

( = 90)rall. tempo = 90 rall.

5


3

33

céder

20

26

céder

28rall.

accel. rall.. = 120. = 90

. = 90 rall.. = 120

ten.


= 90 . = 90

Modulé . = 120Modéré

= 60

accel. = 60

34



11/37

accompaniment of each of the six occurrences, while the table shown in Ex. 10makes clear the near-linear progression.

Global Observations Arising from the Paradigmatic AnalysisA cursory examination of the three thematic elementsA, B and D reveals that eachtheme comprises a certain number of small note values or appoggiaturas followedby a longer note.This leads to the formulation of two potential hypotheses:

Hypothesis 1: These longer notes function as polar notes – in other words, thetrajectory of the piece is based on the sequential progression from long note tolong note.

Ex. 7 Continued

29

Lent, souple = 60en ralentissant beaucoup

morendo

27

3 3 3 3

3 33

3 3

33

3 3céder

25

21

Rapide, irrégulier, vacillant = 120/1323 3

3 3

3 céder .



C M ÉMORIALE 35



12/37

Hypothesis 2: There is a particular significance attaching to the playing style of these longer notes according to whether they are articulated naturale, tremolo, or asa trill.

Ex. 11 illustrates these hypotheses with instances drawn from elements A, B andD in each of the three possible playing styles. The first hypothesis implies that

Ex. 8 Third occurrence of element C

Fl. solo

10

Lent, souple = 60

long

3 Vns

Hns

2 Vlas

Vlc.

long

long

long

long

long

long

long

non vibrato

non vibrato pos. nat.

( sul tasto)

pos. nat.

pos. nat.

pos. nat.

non vibrato

non vibrato

non vibrato

Suspendu

en ralentissant . . . . . . . . . .

36



13/37


14/37

however, the long note at the end of each unit clearly carries a greater structuralweight than what precedes it, and so may be considered a polar note into whose‘aura’ (to borrow Boulez’s term) the remaining elements are drawn.13 While itconforms in part to this model, element C is actually more clearly articulated bythe chordal sequence which precedes its recurrent unison E.

Commenting on the role of extended trills in relation to this characteristicphrase pattern, Célestin Deliège has remarked that ‘among other procedures forabandoning a polar tone, one notes that Boulez often embellishes the tone with

a few brief decay-like tones; the opposite situation, that a trilled or otherwisesustained tone is simply followed by a rest, is actually quite rare’.14 One mightextend Deliège’s observation by asserting that the same statement is equally trueof the means by which such trills are approached. This type of melodic profilemirrors, on a macroscopic level, the tripartite impulse-resonance-decay structureof any sound and thus constitutes another example of acoustic metaphor inBoulez’s music.The three paradigms relating to elements A, B and D could thusbe subsumed under a higher-level bipartite paradigm akin to the first two of thesethree structural components. In this sense, shorter notes followed by long polarnotes could be likened to the impulse and resonance stages of a sound.Francesco Buscemi has taken this reasoning one step further by interpreting

Mémoriale as having a bipartite form consisting of ‘impulse’ (

impulso) followed by

‘resonance’ (risonanza).This reading has the merit of elevating the appoggiatura– long note contour to a higher level of structure – in fact to a kind of paradigm of paradigms for the entire work. In Buscemi’s view, it is necessary to take as validthe hypothesis that the slow sections, that is, those demarcated by element C,delimit the form, ‘since the first five occurrences are practically equidistant,whereas the last one (which coincides with the end of the piece) appears muchlater. A preliminary division would therefore be: 0–18 (impulse): 19–29 (reso-

Ex. 11 Appogiatura + polar notes (explosante + fixe)

4


5 5 5 55

ralentir

1


rall. accel.

3


38



15/37

nance)’.15 Of course this produces a rather summary segmentation, but alsocarries the distinct advantage of highlighting the ‘explosante-fixe’ contour onseveral structural levels.

Analysis of the Pitch Content of the Polar Notes

With respect to the process of paradigmatic analysis, it is appropriate at this pointto make a more precise examination of pitch organisation using the samesegmentation but replacing the complete musical units with the name of theircorresponding pitch centres. Ex. 12, which applies the two hypotheses advancedabove, presents a series of syntagmatic symbols (A1, A2, B1, B2, and so on) inorder to distinguish each individual long note along with its specific playing style.

Ex. 12 Paradigmatic analysis with syntagmatic symbols showing pitches of polar

notes and associated playing style

Element A Element B Element C Element D

A1=C nat.B1=E trem.

B2=E trem.

A2=D nat.

A3=B nat. C1=E trem./trill D1=A trill

B3=A trill C2=E trem./trillD2=D nat.

D3=D nat.

A4=E trem.

A5=F trem. D4=B nat.

C3=E trem./trill

A6=G trill D5=E trem.D6=D trem.

B4=A nat.

B5=C nat.

B6=C nat.

C4=E trem./trill D7=A nat.

D8=F nat.

D9=A nat.

B7=E trill

A7=B trem.

A8=B trem. C5=E trem./trill

B8=C trem.

B9=D trem.

A9=F nat.A10=C nat.

A11=A nat.D10=B trill

D11=A trem.

A12=C trill D12=A trem.

B10=F nat.

B11=G nat.

B12=E nat. C6=E trem./trill

C M ÉMORIALE 39



16/37

(Discussion of the element C paradigm will be deferred for the time being.) Asshown in Ex. 13, a total of 36 long notes may be assembled; considering these assix hexachords and labelling them S1, S2, ... , S6 then produces the result shown

in Ex. 14. Although these six series have little in common with each other interms of transpositional, inversional or retrograde equivalences, their mutualderivation can be confirmed by returning to the originel epigram whose pitchesare G, D, A, B and E, preceded by the encased E (see again Ex. 2).Transposingthis series onto each of its elements yields the outcome shown in Ex. 15.

Each series is identified by a label (S(E), S(G), and so on) in which the pitchclasses in parentheses indicate their respective first notes. For each line, the sixnotes which follow the parenthetical note correspond to the pitch content of oneof the Sn series defined by the polar notes of Mémoriale as shown in Ex. 14; theprecise correspondence is specified in the column on the far right.16 As can beseen, each line of this transpositional matrix represents one of the six hexachords

which make up the polar notes of Mémoriale (modulo their order within eachseries). Since the registers are fixed, they can be represented as six harmonies,

Ex. 13 Pitches of the 36 polar notes of Mémoriale

C E E D B A A D E E F B

G E D A C C A F A E B B

C D F C A B A C A F G E

Ex. 14 Six hexachords derived from the polar notes of Mémoriale

S1: C E E D B A

S2: A D E E F B

S3: G E D A C C

S4: A F A E B B

S5: C D F C A B

S6: A C A F G E

Ex. 15 Correlation between the originel matrix and the six hexachords derived from Mémoriale’s polar notes

S(E ) [E ] [G] [D] [A ] [B ] [A] [E] S

S(G) [G] B F C D C A S5

S(D) [D] F C G A A E S6

S(A ) [A ] C G C E D A S3

S(B ) [B ] D A E F E B S2

S(A) [A] C A D E E B S1

S(E) [E] G E A B B F S4

40



17/37

each associated with the note that generated it in the manner of an operator(Ex. 16). Shading these harmonic fields on the paradigmatic analysis yields thechart shown in Ex. 17, which shows the distribution of these notes across the six

hexachords. Once shaded in this way, the paradigmatic analysis reveals a verysimple structure: each harmonic zone contains six polar notes, of which one noteis trilled, two are played as tremolos and three are naturale, resulting in a patternof 1 + 2 + 3.

Ex. 16 The six harmonic fields of Mémoriale

S = S(A)1 S = S(B ) S = S(A ) S = S(E) S = S(G) S = S(D)2 3 4 5 6

Ex. 17 Paradigmatic analysis with shaded harmonic fields


A1=C nat.B1=E trem.

B2=E trem.

A2=D nat.

A3=B nat. C1=E trem./trill D1=A trill

B3=A trill C2=E trem./trillD2=D nat.

D3=D nat.

A4=E trem.

A5=F trem. D4=B nat.

C3=E trem./trill

A6=G trill D5=E trem.D6=D trem.

B4=A nat.

B5=C nat.

B6=C nat.

C4=E trem./trill D7=A nat.

D8=F nat.

D9=A nat.

B7=E trill

A7=B trem.

A8=B trem. C5=E trem./trill

B8=C trem.

B9=D trem.

A9=F nat.A10=C nat.

A11=A nat.D10=B trill

D11=A trem.

A12=C trill D12=A trem.

B10=F nat.

B11=G nat.

B12=E nat. C6=E trem./trill

C M ÉMORIALE 41



18/37

This schema makes use of six transpositions of S(E); but what of S(E) itself,that is, the originel series? In fact it is reserved for the ‘cadential’ C sections, withthe relevant six notes presented here in order as Ex. 18. Each of these rows is asubset of S (E), the originel series, and each successive row presents one more

note in the series; the final one contains all seven of the notes that constituteelement C in its complete form. Moreover, the first six polar notes encounteredin Mémoriale belong to S1, which was defined as the series transposed onto A, inother words S(A). C1 contains the notes A and E, that is, the first note of C1 isthe pitch class which generates the six notes used throughout that section.Extending this principle, it can be assumed that for all series S1 to S6, if the firstnote of the C section is any note x, then the six polar notes in the same sectionwill equate to pitches drawn from S(x). A kind of ‘centre-absence’ game seems tobe at work here:17 for instance, the six notes of the series engendered by A areintroduced, but only then does A appear as the first note of the cadential elementC.18

The series S1 to S6, then, map out the trajectory of the piece from one polarnote to the next, creating six harmonic fields through which the flute travels frombeginning to end. The shaded regions of Ex. 17 show the extent to which theparadigmatic segmentation agrees with the serial segmentation. As previouslynoted, each harmonic field contains three statements of one thematic element,two of another, and one of a third, as well as a single occurrence of element C.As is shown in Ex. 19, the question of which thematic element is representedthree times, which twice and which only once in any given harmonic field is afunction of the mode of articulation accorded to each polar note. Representingthese modes in shades of grey on the initial transpositional matrix of the sixharmonic fields (from naturale as the lightest shade through to the trill as thedarkest) yields the result shown here. Besides one exchange of values in S

5, for

each seven-note series Boulez always uses positions 1, 3 and 6 for naturale notes,4 and 5 for tremolo notes and 2 for trills. This can be mapped another way inorder to bring out which of the three themes, A, B or D, is assigned to either thethree naturales, the two tremolos or the single trill for each of the six harmonicfields (Ex. 20). Overall this pattern corresponds to two cyclic permutations tothe left (anticlockwise), followed by three cyclic permutations to the right (clock-wise) as illustrated in Ex. 21.

Ex. 18 Pitches of element C in relation to shaded harmonic fields

S(A)=S1 A E C1

S(B )=S2 B E C2S(A )=S3 A B A E C3

S(E)=S4 E A A B E C4

S(G)=S5 G B A E A E C5

S(D)=S6 D G E A B A E C6

42



19/37

Analysis of Durations

Until this point, no attempt has been made to interpret the durational valuesof the polar notes. Represented in semiquavers and arranged on the paradig-matic chart shown in Ex. 22, adjacent polar notes with the same playing stylein fact appear to be of largely similar duration – indeed to within the length of a single semiquaver. Adjustment of these values produces the schema shown inEx. 23 (the number of exceptions is indicated with the abbreviation ‘exc.’).Expressing these durations in quaver values while at the same time represent-ing the symmetry between the two parts of the piece through shading yieldsthe outcome illustrated in Ex. 24, a pattern whose contours in turn reveal anearly arithmetic progression as indicated in Ex. 25 (only the value of four isrepeated).

Ex. 19 Playing style as a function of position in the series

1 2 3 4 5 6

nat. trill nat. trem. trem. nat.[E ] G D A B A E

G B F C D C A S5

D F C G A A E S6

A C G C E D A S3

B D A E F E B S2

A C A D E E B S1

E A E A B B F S4

Ex. 20 Correlation between playing style, harmonic field and thematic unit

3nat. 2trem. 1trill trem.\trill

A B D +C S1

D A B +C S2

B D A +C S3

D A B +C S4

A B D +C S5

B D A +C S6

Ex. 21 Cyclic permutation of thematic elements

Anticlockwise rotation: ABD DAB BDA

Clockwise rotation: (BDA) DAB ABD BDA

C M ÉMORIALE 43



20/37

Ex. 22 Durations of polar notes expressed in semiquavers


S1=S(A) A1=C nat. 12 B1=E trem. 6B2=E trem. 6

A2=D nat. 9

A3=B nat. 11 C1=E trem./trill D1=A trill 16

S2 =S(B ) B3=A trill 8 C2=E trem./trill D2=D nat. 10

D3=D nat. 8

A4=E trem. 13

A5=F trem. 14 D4=B nat. 8

S3=S(A ) C3=E trem/trill

A6=G trill 18 D5=E trem. 12

D6=D trem. 12

B4=A nat. 4

B5=C nat. 4B6=C nat. 4

S4=S(E) C4=E trem./trill D7=A nat. 8

D8=F nat. 8

D9=A nat. 8

B7=E trill 8

A7=B trem. 13

A8=B trem. 14 C5=E trem./trill

S5=S(G) B8=C trem. 6

B9=D trem. 6

A9=F nat. 10

A10=C nat. 10

A11=A nat. 10 D10=B trill 17S6=S(D) D11=A trem. 12

A12=C trill 17 D12=A trem. 12

B10=F nat. 5

B11=G nat. 4

B12=E nat. 4 C6=E trem./trill

Ex. 23 Durations of polar notes expressed in semiquavers and grouped by playingstyle

A B D

10 nat. (3 exx.) )llir t(61).mer t(6

14 (trem.) (1 ex.) ).xe1().tan(8)llir t(8

18 (trill) ).mer t(21).tan(4

14 (trem.) (1 ex.) ).tan(8)llir t(8

10 (nat.) ).xe1()llir t(61).mer t(6

18 (trill) (1 ex.) 4 (nat.) (1 ex.) 12 (trem.)

44



21/37

Notes on the Accompaniment: Unplugged Electronics and

Geometrical Serialism

Since the form of Mémoriale is essentially dictated by the solo flute part, the roleof the accompaniment was not deemed significant for the initial phase of para-

digmatic analysis. In a broader respect, however, the accompanimental dimen-sion offers an object lesson in Boulez’s notion of deduction: the solo flute line,composed in advance, gives rise quite methodically to the eight subordinatelines. As such, Mémoriale qualifies as a ‘didactic work’,19 a term likewise coinedby Boulez in the 1970s to describe certain very specific pieces by ‘the Webern of the series’.20 Although the derivation of the ensemble parts from one solo linereflects a conscious indebtedness to Berio’s Chemins projects, it also representsan expression of Boulez’s declared belief that ‘each note [in a work] has aresponsibility towards every other one’.21 Not surprisingly, the accompanimentalstratum of Mémoriale fulfils this dictum by drawing on the reservoir of pitchesinitially announced by the flute; moreover the rigidly fixed registration of the

piece adds to its being perceived as fairly limited in terms of harmonic material.

22

In addition, the accompaniment serves, as previously noted, to prolong, harmo-nise and enhance the flute line in the metaphorical sense of an unpluggedelectronic resource, aspects of which will be examined below.

Unplugged Electronics I: Resonator

At rehearsal number 4, the first of each pair of semiquavers in the flute part isnotated using light resonance marks.The upper strings then act as four separate

Ex. 24 Durations of polar notes expressed in quavers

A B D

5 nat. )llirt(8).mert(3

7 (trem.) (1 ex.) ).xe1().tan(4)llirt(4

9 (trill) ).mert(6).tan(2

7 (trem.) (1 ex.) 4 (trill) 4 (nat.)

5 (nat.) 3 (trem.) 8 (trill) (1 ex.)

9 (trill) (1 ex.) 2 (nat.) (1 ex.) 6 (trem.)

Ex. 25 Schema for polar-note durations

B D A

Nat. 2 4 5

Trem. 3 6 7

Trill 4 8 9

C M ÉMORIALE 45



22/37


23/37

depicted using either light or dark lines in Ex. 27).The composer may thereforebe understood to be employing timbral distinctions as a means of dividing theoverall registral space through the separate treatment of polar and non-polar

notes.Unplugged Electronics II: Delay and Retrograde Echo

As well as exploiting the possibilities of timbral resonance, Boulez also employsdelay and echo effects in his ensemble writing. The particular acoustic impres-sion illustrated in Ex. 28 could be likened to a retrograde echo in the sense thatif an echo’s repetitions may be perceived to become progressively more partial,then the repetitions of a retrograde echo are made successively more complete.

Ex. 27 ‘Resonator’ accompaniment, rehearsal number 20

Vlc.

pizz. 1. V.1. V.

1. V.

Vla 2

Vla 1

arco

Vn 2

arco

Vn 1

arco

53

3

3

Fl.

Vn 3

Hns

Céder Rapide, stable = 120

20

C M ÉMORIALE 47



24/37

The first viola reconstitutes only four notes of the nine-note flute phrase; it isfollowed by the second violin, which echoes six of the notes, and then the firstviolin, which repeats all nine notes: the outcome is a kind of reverse echoimpression reminiscent of certain tape-loop effects.

Geometric Orchestration

Just as the rigid structure of the six harmonic fields and the correspondingdurational schema together hark back to the experiments of integral serialism, sothe accompaniment also uses techniques explored most intensively in this samecreative context. For Boulez in the 1960s, orchestration could be approached asa kind of Cartesian geometry. Three specific types of distribution could beenvisaged: ‘symmetrical, asymmetrical, combined symmetrical-asymmetrical’,23

involving the translation into musical notation of forms plotted on a grid. Ex. 29shows one example of a geometric form drawn from Mémoriale. The stringaccompaniment here represents an inverted triangle whose apex is in the secondviola. Comparing the flute part with the first violin part, it becomes apparent that

Ex. 28 Reverse echo, rehearsal number 9

sul tasto

sul tasto

sul tasto

3 3

3

sul tasto

sul tasto tremol o

3

ten.9


Fl.

Hns

Vlc.

Vla 2

Vla 1

Vn 3

Vn 2

Vn 1

48



25/37

the latter takes two notes from every triplet figure of the former (with theexception of the added E in the second bar) and reconfigures them to producethe five groups of four semiquavers seen in Ex. 30. Labelling these five four-notegroups a1, a2, a3, a4 and a5 yields the result shown in Ex. 31. Each successive rowis formed through a process of retrogradation from which the middle element isomitted. A further axis of symmetry may also be discerned in this formationwhereby the rows of the pyramid are superimposed in such a way that theone-element row contains the same element as the one-element column, thetwo-element row contains the same elements as the two-element column, and so

on. In this respect, as in so many others, Mémoriale wears its deductions on itssleeve.

The Rhythmic Canon

According to the composer, the passage from rehearsal number 22 to rehearsalnumber 24 remains independent of the rest of the piece. Divorced thematicallyfrom the music which precedes it, this short section lasting no more than a few

Ex. 29 Geometric approach to orchestration, rehearsal number 21

21


3 3 3 33

C M ÉMORIALE 49



26/37

seconds outlines a closed ABA′ ternary form. It also depends in part on arhythmic canon that involves five of the nine instruments; this grouping thusprovides a kind of barely audible polyphonic accompaniment to the flute partthat is not only played at a constant pianissimo, but also with a pitch-obscuring sul tasto tremolo. Seeking to explore a seemingly secondary detail of this kindwithout necessarily attempting to integrate it into the surrounding framework isin fact a highly Boulezian strategy. Indeed for the composer himself,

analysis is not necessarily that global approach, that total and absolute capturingof the whole at which it often aims. Analysis can be short, searing and intuitive. Itneed not deal with the work as a whole in order to be conclusive. It can imme-

diately latch on to an apparently secondary detail; it can sometimes be the resultof a surprising, inspired encounter.24

Boulez first encountered the technique of rhythmic canon in his studies withMessiaen at the Paris Conservatory in the 1940s as well as from his examinationof late works by Webern, such as the Second Cantata, Op. 31.25 Its deploymentin this context is perhaps best interpreted as a kind of second nature whereby thecomposer sought to draw on techniques so ingrained in his mind that they

Ex. 30 Rehearsal number 21, excerpt

Vn 1

Vn 2

Vn 3

Vla 1

Vla 2

Vlc.

Ex. 31 Schema for accompaniment, rehearsal number 21

a1 a2 a3 a4 a5

a5 a4 a2 a1 (retrograde with middle element omitted)

a1 a2 a5 (retrograde with middle element omitted)

a5 a1 (retrograde with middle element omitted)

a1 (retrograde with middle element omitted)

50



27/37


28/37


29/37


30/37

Charting Mémoriale

The various illustrations presented here represent an attempt to give concreteexpression to the composer’s own concept of analysis. For Boulez, the musicalwork is the result of deductions effected on an initial gesture transcribed vianotation or écriture, which could be defined as a kind of graphic-symbolicreasoning. Music analysis, in turn, is ‘the pursuit, no doubt ultimately vain, of the labyrinth which joins the idea to its realisation’.26 Elsewhere, Boulez hasdescribed this analytical stance as essential to the composer’s work: ‘Since thework at once exceeds and sometimes even negates the initial Idea, the path fromthis initial Idea to the realised work is difficult, if not impossible to decipher.

Ex. 38 Second rhythmic canon, rehearsal number 24

sempre

progressivement vers le chevalet . . . . .

arco

poco

sul pont .

sempre sim.

5 6 24

Libre, continu.

= 108/120

.

.

.

di - mi - nu - en - do

.

.

.

.

arco sul pont .

sim.

sul pont .

sul pont .

sul pont .

arco

arco

arco

.

sempre

sempre

sempre

sempre

sim.

poco

poco

poco

poco

sim.

.

Fl.

Hns

1

2

Vns

1

2

3

Vlas

1

2

Vlc.

54



31/37

Ex. 38 Continued

.

.

.

.

.

.

.

.

cres. . . . cen. . . . do. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

..

. .

. 56

. .

.

. .

..

. .

.

.

.

.

très près du chevalet

Ex. 39 Durations in second rhythmic canon

total

I: 3=a2 8=a6 6=a4 7=a5 10=a7 4=a2 14=a8 5=a3 57

II: 14=a8 7=a5 5=a3 6=a4 8=a6 3=a1 10=a7 4=a2 57

III: 10=a7 6=a4 4=a2 5=a3 7=a5 14=a8 8=a6 3=a1 57

IV: 8=a6 5=a3 3=a1 4=a2 6=a4 10=a7 7=a5 14=a8 57

V: 7=a5 4=a2 14=a8 3=a1 5=a3 8=a6 6=a4 10=a7 57

C M ÉMORIALE 55



32/37

But to work back [through analysis] from the realised work to the concept whichwe have of the [initial] Idea, this is what guides us along our own path’.27

For Boulez, the initial gesture needs to be housed within some kind of system,

essentially a precompositional matrix of some kind, in order to allow it to emergeas a realised work. But the system is never to be adhered to uncritically; thingsalways intervene which lead to minor points of deviation. These Boulez calls‘accidents’,28 and they constitute the unanalysable quotient of the realised work,or what André Breton more evocatively called an ‘unbreakable kernel of night’that lies at its heart.29

The principle of paradigmatic analysis as applied here serves to differentiateparticular aspects of the compositional material. More directly, it defines whichelements can be grouped together thematically, but also, at a more detailed level,makes clear the fundamental distinction between the long polar notes, whosepitches form the harmonic underpinnings of the piece, and the short appoggia-

turas, which do not. Rendering explicit the system – that is, the six hexachordalharmonic fields and the arithmetic relationships between durations – highlightsthe actual écriture at work here in all its proliferational splendour: the flexibilityof the phraseology, the ornamental flourishes and the differentiation of thefigures. It allows us effectively to glimpse the creative networks which led Boulezdown the path from system to realisation; and this path, when travelled in theopposite direction, in turn actualises the composer’s own analytical ideal. In theend, chart making, by revealing compositional systems, can aid us in distinguish-ing figure from fond , to use terms from painting – separating the foregroundfigures, the écriture, from the background system. And as a declared strategy, thisapproach is itself grounded thoroughly and unapologetically in the spirit of

serialist logic.30

NOTES

All musical extracts of Mémoriale (... explosante-fixe ... originel) for flute andeight instruments used here are reproduced with the kind permission of Uni-versal Edition. © Copyright 1985 by Universal Edition A.G., Wien/UE 18657.

1. Parts of this paper were presented in collaboration with Nicolas Donin at theSociety for Music Analysis’s Autumn Study Day which took place at RoyalHolloway, University of London on 5 November 2005. Other parts were presentedat the Dublin International Conference on Music Analysis held at University

College Dublin in June 2005.2. See Ruwet (1972), p. 106.

3. ‘The System and the Idea’ (‘Le système et l’idée’ [1986]); published in Boulez(2005), pp. 339–420.

4. ‘Cela revient à considérer le système comme une aide ... sans lui, ne serait pasarrivée à concevoir réellement un monde rêvé: je choisis, donc je suis; je n’ai inventéle système que pour me fournir un certain type de matériau, à moi d’éliminer ou de

56



33/37

gauchir ensuite, en fonction de ce que je juge bon, beau, nécessaire’ (Boulez 2005,p. 407). All quotations from Boulez appear in the author’s own translation.

5. The original remark reads: ‘Ce qui m’intéresse ici, ce sont les permutations, les

variations, mais strictement contrôlées, numériquement contrôlées’ (Boulez 2004,p. 407).

6. Boulez acknowledged the influence of Berio’s Chemins in the course of a lecturedelivered at McGill University, Montreal on 23 May 1991. My article relies on acassette recording of this presentation held by the Pierre Boulez Archive at theUniversité de Montréal.

7. Although applied here in an informal sense, the term might be considered analo-gous to that favoured by Helmut Lachenmann, ‘musique concrète instrumentale’.See, for example, Lachenmann (1996), pp. 211–12.

8. This image is reproduced from the CD booklet of Boulez Conducts Boulez (DGG445 833-2).

9. For more on the concept of ‘puzzle’ form, see Boulez (2005), p. 502.

10. ‘Comme j’ai travaillé en même temps à ... explosante-fixe ... et à Rituel , les deuxœuvres sont parallèles. L’idée première, je l’ai prise des Symphonies d’instruments àvent de Stravinsky, où il y a au début l’appel de la clarinette dans l’aigu, puis cesaccords qui sont un long et un bref, mais toujours le même. Quand j’ai entenducette pièce de Stravinsky, je me suis dit: ‘il fait toujours ça, il repète exactement lamême chose, est-ce-qu’on ne pourrait pas varier ça? Par exemple en amenantl’accord, en lui donnant une désinence’ (Boulez 2004, p. 399). This quotation istaken from the unedited French transcript of this interview, obtained from Jean-

Jacques Nattiez, rather than the published Italian version.

11. See again n. 6. In his 1991 lecture, Boulez explained that the section between

rehearsal numbers 22 and 24 inclusive was constructed using a different systemfrom the rest of the piece. Consequently, it is not included in the paradigmaticanalysis, although its rhythmic structure will be examined in the later stages of thisarticle.

12. The tool was designed collaboratively by Nicolas Donin, Thomas Bottini, SamuelGoldszmidt and the present author (see also Donin 2004). An intended futurerevision will allow superimposed cells to be more precisely aligned. Cf.apm.ircam.fr/tableau.

13. For more on the concept of ‘aura’, see Boulez (2005), p. 401.

14. ‘Parmi d’autres procédés d’abandon d’un son porteur de polarité, on remarquefréquemment que Boulez l’orne de quelques valeurs brèves désinentielles; il estplutôt rare qu’un son soutenu et trillé soit purement et simplement suivi d’unsilence’ (Deliège 1988, p. 65).

15. ‘[S]i nota come tra queste le prime cinque siano praticamente equidistanti, mentrel’ultima (la quale coincide pure con l’ultima sezione del pezzo) appare assai dopo.Una prima divisione può quindi essere: 0–18 (impulso) 19–29 (risonzanza)’(Buscemi 2003, p. 4). My translation.

16. Boulez is partial to seven-note series. Over and above the existence of other piecesbased on the number 7 (for example, Anthèmes (1992) for solo violin), another

C M ÉMORIALE 57



34/37

interesting piece of evidence demonstrates Boulez’s fondness for this number: in1972, on the occasion of Pierre Souvtchinsky’s 80th birthday, Boulez sentSouvtchinsky a little composition called ‘Sept interjections pour pierre souvtchinskyde pierre boulez’ and dated ‘Paris, le 19 octobre, 1972’. The piece, clearly derivedfrom material from Rituel and/or ... explosante-fixe ... , bears the following inscrip-tion: ‘Cher Pierre / De Londres à NewYork, et de NewYork à Londres / ma penséen’oublie pas l’ami de toujours. La circonstance exceptionnelle me la fait souligner/ ces interjections sont sept, chiffre, en principe, magique! Cette magie, je la désirepropice pour vous / Cher Pierre’ (from the Dossier Souvtchinsky consulted at theBibliothèque nationale de France; I wish to thank Peter O’Hagan for pointing metowards this document).

17. The term refers to a lecture Boulez gave at Donaueschingen in 1979 entitled‘Poésie-centre et absence-musique’; published in Boulez (1995), pp. 467–84.

18. The compositional rationale expressed by S(x) is reminiscent of ideas expressed inBoulez (1964) in which the composer cites the logician Louis Rougier as stating

that the structure of the world is knowable in terms of relations and functions, notsubstances and accidents. Boulez subsequently entreats his fellow composers toadopt this approach in their work: ‘Let us not start from the “substances andaccidents” of music, but rather let us consider it in terms of “relations and func-tions” ’ (‘[Ne] partons point des “substances et des accidents” de la musique, maispensons-la “en termes de relations, de fonctions” ’ (Boulez 1964, p. 31).

19. ‘Œuvre didactique’; see Boulez (2005), p. 72–3.

20. ‘Le Webern de la série’; see Boulez (2005), p. 73.

21. ‘La responsabilité de tout élément par rapport à un autre dans un système cohérent’(Boulez 2005, p. 89).

22. For graphs of the fixed registers in Mémoriale, see Labussière and Chouvel (1997),p. 56.

23. The original observation reads: ‘Trois types de répartitions son possibles:symétrique, assymétrique, combiné symétrique-asymétrique’ (Boulez 1964, p. 59).

24. ‘[L]’analyse n’est pas forcément cette approche globale, cette saisie totale et absoluequ’elle se donne souvent comme but. L’analyse peut être courte, fulgurante, intui-tive. Elle n’a pas besoin de porter sur l’ensemble d’une œuvre pour être détermi-nante. Elle peut s’accrocher immédiatement à un détail apparemment secondaire;elle est parfois le fait d’une rencontre inspirée, surprenante’ (Boulez 2005, p. 75).

25. See Bailey (1991), pp. 119–46, for a description of canonic writing in Webern’sSecond Cantata, and Galaise (1991) for a reconstruction of Boulez’s analysis of itfor his students at the Basel Academy of Music, where the composer lectured from1960 to 1962. Additional remarks on Webern’s Op. 31 may be found in one of thecomposer’s earliest essays dating from 1948 entitled ‘Propositions’; see Boulez(1995), pp. 253–62; Eng. transl., ‘Proposals’, in Boulez (1991), pp. 47–54.

26. ‘C’est pourquoi l’analyse est la poursuite – vaine, sans doute, dans l’absolu – dulabyrinthe qui joint l’idée à la réalisation’ (Boulez 2005, p. 74).

27. ‘L’œuvre étant à la fois dépassement de l’Idée première et même sa négation, lecheminement vers cette réalisation depuis l’idée première est difficile, sinon impos-

58



35/37


36/37


37/37

AUTHOR QUERY FORMDear Author,

During the preparation of your manuscript for publication, the questions listedbelow have arisen. Please attend to these matters and return this form with yourproof.

Many thanks for your assistance.

Query

References

Query Remark

q1 AUTHOR: Goldman Jonathan, 2006 has not

been cited in the text. Please indicate where it

should be cited; or delete from the Reference

List.

SNP Best-set Typesetter Ltd.

Journal Code: MUSA Proofreader: Elsie

Article No: 274 Delivery date: 1 September 2009

Page Extent: 36

Documents

GOLDMAN, Boulez Explosante-fixe