texture register

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Texture, Register, and Their Formal Roles in the Music of Witold Lutosławski Author(s): Michael Klein Source: Indiana Theory Review, Vol. 20, No. 1 (SPRING 1999), pp. 37-70Published by: on behalf of the Indiana University Press Department of Music Theory, Jacobs

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Texture, Register, and Their Formal Roles in the Music of Witold Lutoslawski

Michael Klein

BY texture I mean that part of musical structure conceived as a number of lines and their interactions, where a precise definition for the term line

remains open according to context. By register I mean the placement of

those lines in a pitch-space, whose span from low to high is segmented into equal parts by the octave. Following Wallace Berry, we might conceive of a coupling of texture and register into a single musical structure called texture-space.

Berry's definition of texture-space—"a two-dimensioned field setting out 'hori

zontal' and 'vertical' boundaries enclosing the element-successions which con stitute the musical work"—implies a temporal element that I shall leave relatively unexplored in this paper.1 His emphasis on registral boundaries, how

ever, resonates with properties defined in this paper that I find central to an understanding of form in the music of Witold Lutoslawski.

Texture-space takes on a role of heightened importance in much avant-garde

music after 1960, notably in the music of Lutoslawski, Krzysztof Penderecki, and

György Ligeti, among others. The dense pitch clusters that are common in this

music have generated a confusing array of terms in historical and analytical stud

ies, including textural music, cluster compositions, net-structure compositions (Ligeti),

and aleatorism of texture (Lutoslawski). In recent publications, some theorists have

offered detailed observations of how texture-space generates form in music of the

1960s, particularly in the music of Ligeti.2 Absent from this literature is any

exposition of how texture-space functions in the music of Lutoslawski, per haps because his method of organizing pitch (harmonic aggregates) and rhythm (ad libitum sections) complicates such a study.

1 Wallace Berry, Structural Functions in Music (Englewood Cliffs, NJ: Prentice Hall, 1976), 279.

2Among many examples are Miguel Roig-Francoli, "Harmonic and Formal Processes in

Ligeti's Net-Structure Compositions," Music Theory Spectrum 17, no. 2 (1995): 242—67; Jonathan

W. Bernard, "Voice Leading as a Spatial Function in the Music of Ligeti," Music Analysis 13 (1994):

227—53; Alejandro Pulido, "Differentiation and Integration in Ligeti's Chamber Concerto, HI," Sonus

9 (1988): 17—37; Bernard, "Inaudible Structures, Audible Music: Ligeti's Problem, and His

Solution," Music Analysis 6 (1987): 207-36; and Robert Cogan, "György Ligeti: Lux Aeterna," in

New Images of Musical Sound (Cambridge, MA: Harvard University Press, 1984), 39—43.



38 Indiana Theory Review Vol. 20/1

Perhaps the best-known research about the music of Lutoslawski is Steven

Stucky's book of 1981, which, though written well before the composer's death, is still a valuable introduction to his life and music.3 Charles Bodman Rae

(1994) has offered a similar study, expanding upon Stucky's work by including

brief analyses of the Polish composer's last compositions.4 Probably the most detailed published analysis of a single composition by Lutoslawski is Aloyse Michaely's 1991 article on the Symphony No. 3,5 while the most important body of analytical research comes from Martina Homma,6 who, in addition to writing nearly a dozen analyses of Lutoslawski's works, was responsible for cataloging the composer's sketches for the Paul Sacher Foundation.7 All of the analytical work mentioned above focuses on issues of pitch organization or dis cusses Lutoslawski's use of aleatory techniques.8 None of this work, however,

includes analysis of how the dense textures that are central to Lutoslawski's music after 1960 delineate form.

sSteven Stucky, Lutoslawski and His Music (New York: Cambridge University Press, 1981).

+Charles Bodman Rae, The Music of Lutoslawski (London: Faber and Faber, 1994).

sAloyse Michaely, "Lutosiawskis III. Sinfonie," Musik-Konzepte 71—73 (1991): 52—197.

6A complete list of Homma's work on the music of Lutoslawski is impractical here. Most of these publications draw on material from her published dissertation Witold Lutoslawski:

Zwöftonharmonik, Formbildung, "aleatorischer Kontrapunkt"; Studien zum Gesamtwerk unter Einbezie

hung der Skizzen (Cologne: Bela, 1995).

7The Paul Sacher Foundation holds Lutoslawski's sketches and manuscripts with the excep

tion of some fair copies (final manuscripts) that the composer gave to performers who pre

miered his works. Extant are sketches for nearly all of his music after 1960.

8In addition to this analytical work, there are a number of published interviews, includ

ing Irina Nikolska, Conversations with Witold Lutoslawski, trans. Valeri Yerokbin (Stockholm:

Melos, 1994); Tadeusz Kaczynski, Conversations with Witold Lutoslawski, trans. Yolanta May

(London: Chester Music, 1984); and Bâlint Andrâs Varga, Lutoslawski Profile: Witold Lutoslawski

in Conversation with Bàlint Andrâs Varga, trans, and ed. Stephen Walsh (London: Chester, 1976). Theses and dissertations about the music of Lutoslawski are numerous. Notable

theoretical studies among these include Michael L. Klein, "A Theoretical Study of the Late Music of Witold Lutoslawski: New Interactions of Pitch, Rhythm, and Form," Ph.D. diss.,

State University of New York at Buffalo, 1995; Douglas M. Rust, "Lutoslawski's Sym

phonic Forms," Ph.D. diss., Yale University, 1995; Gerald Evans, "The Development and Application of New Structural Procedures in the Works Chain 1, Chain 11, and Chain III by

Witold Lutoslawski," Ph.D. diss., Kent State University, 1990 (especially Part II); and Kathy Ann Russavage, "Instrumentation in the Works of Witold Lutoslawski," D.M.A. thesis, University of Illinois, 1988. A more complete bibliography appears in Martina Homma, "Auswahlbibliographie," Musik-Konzepte 71—73 (1991): 208—16.



Klein, Texture, Register, and Their Formal Roles in Lutoslawski 39

Clues to Lutoslawski's use of register or texture come from the composer himself, who, in a brief article devoted to the use of aleatory techniques, offers two

small graphs showing how the registral boundaries of one pitch collection can

expand or contract to form the registral boundaries of another pitch collection.9

Lutoslawski's concern with registral boundaries in these graphs reminds us of Berry's definition of texture-space, described above. In this paper, therefore, I

take Berry's conception of texture-space as a point of departure for an under standing of how such space functions in the music of Lutoslawski. I begin by outlining Lutoslawski's method of organizing pitch and rhythm, then proceed to

define some properties of texture-space (field, density, and compression) and some transformations of those properties that recur frequently in Lutoslawski's

music. The paper concludes with analyses of Trois poèmes d'Henri Michaux (1963) and Chain 1 (1983).

Lutoslawski's Compositional Elements

Beginning with his Five Songs on texts by Kazimiera Illakowicz (1957), Lutoslawski structured pitch through harmonic aggregates,10 which are ordered

pitch collections containing all twelve pitch classes, where each of the pitch

classes is fixed in a single register. Example 1 shows the first harmonic aggre gate that structures the piano part of "Morze" (The Sea), the first of the Five

Songs. We can represent a harmonic aggregate as an interval string indicating the succession of ordered pitch intervals between its pairs of adjacent pitches from lowest to highest. Such an interval string can also represent a class of harmonic aggregates, all of which are related by transposition in pitch space.

'Witold Lutoslawski, "Rhythm and the Organization of Pitch in Composing Techniques

Employing a Limited Element of Chance," Polish Musicological Studies 2 (1986): 37—53. In addi

tion, a study of Lutoslawski's sketches shows that some are written on pieces of graph paper,

on which the composer has drawn shapes showing how registral boundaries move from one

pitch collection to another. Such sketches support the type of registral analyses that I present

in this paper.

""There is little consistency in the terminology used to describe these chords in pub lished analyses. Stucky uses the term harmonic aggregate. Rae uses the terms 12-note chord and

chord-aggregate. Homma, whose work on Lutoslawski's music is enormously detailed, uses

the term Zwölfion-Harmonik (12-tone harmony). Lutoslawski, who was fluent in English, was inconsistent with his use of terms as well. For more detailed treatments of the structure of

harmonic aggregates, see Homma, Witold Lutoslawski; Klein, "A Theoretical Study of the Late

Music"; Rust, "Lutoslawski's Symphonic Forms"; Rae, The Music of Lutoslawski; and Stucky, Lutoslawski and His Music.




EXAMPLE 1. Harmonic aggregate from "Morze"

o i«> °

i —o

9* t°jl' 3 t <6, 1, 2, 5, 8, 9, 0, 3, 4, 7, T, E>

7-1-3-3-1-3-3-1-3-3-1

, Q i i— .. « Ä 1 fe tide ' ïo w «> i° rsyoi; #«. o ■ 1 jo

3 t <6, 1, 2, 5, 8, 9, 0, 3, 4, 7, T, E> 7-1-3-3-1-3-3-1-3-3-1

In order to show the twelve distinct pitch classes in harmonic aggregates, we can also represent them as an ordered set of integers (C — 0) separated by com mas between brackets < >. An arrow to the left of the brackets indicates that

the integers represent pitches ordered in pitch-space from lowest to highest, and a number to the left of the arrow indicates the octave in which the lowest

pitch of the harmonic aggregate appears. It is important to note that this second

type of representation does not account for the number of octaves that may appear between adjacent members of the harmonic aggregate. Thus more than one interval string may map onto this representation. Both types of numerical

representation appear below the harmonic aggregate in example 1.

With the premiere of his Jeux vénitiens (1961), Lutoslawski began to set harmonic aggregates in ad libitum sections, in which limited aleatory techniques affect the rhythmic coordination of the various parts in the ensemble.11 In these

sections, Lutoslawski notâtes the pitches, rhythms, articulations, dynamics, and

even the entrances of the various instruments, but he leaves to the performers

the exact rhythmic coordination of the various parts. Ad libitum sections gener ally lack a common meter, and in describing performance practice for these sections Lutoslawski demands that the musicians play their parts with the same

"Among the terms used to describe Lutoslawski's aleatory techniques are limited aleatory, controlled aleatorism, aleatoric counterpoint, aleatorism of texture, collective ad libitum, and ad lib

technique. Lutoslawski himself is not consistent in his use of these terms. His scores usually

indicate aleatory sections with the words ad libitum, or ad lib, but sometimes use only an arrow

to mark the beginning of an ad libitum section. In writings and conversations Lutoslawski

claimed to prefer the term limited aleatory-, however, he often referred to such portions of his

music simply as ad libs. The latter term is unfortunate since it can imply either that the per

former may choose to skip a passage, or that the performer can improvise pitches and/or rhythms; neither of these meanings ever applies to Lutoslawski's music. Despite the difficul

ties implicit in this array of terms, I will continue to use them all interchangeably.




expressive freedom of a solo or a cadenza.12 During ad libitum sections the conduc

tor ceases beating time and uses the baton only to indicate cues or to show the

beginning of a new section that may be either in battuta (measured) or ad libitum

style. The end of an ad libitum section often includes repeated patterns, which the

player is to perform until the conductor cues the entire ensemble to begin the next

section. Several notational consequences arise as a result of Lutoslawski's limited

aleatory technique: first, he indicates the lengths of many ad libitum sections in

numbers of seconds; second, all accidentals apply only to the pitch that immedi

ately follows (this is true of ad libitum as well as battuta sections); finally, in all ad

libitum sections any visual coordination of parts in the score is purely incidental and

should not be interpreted as a rhythmic coordination preferred by the composer.

Lutoslawski was quite open about his method of presenting pitch material in ad libitum sections:

Within an aleatoric section, pitch can be stricdy fixed. That may appear

strange if you think of the loosening of time relations between sounds... .

This is the simplest way of organising pitch within an aleatoric section. We compose a twelve tone chord, which serves as the basis of

that section. The instruments only play the notes belonging to that chord. It may occur that the chord never actually sounds in its entirety

—it is supplemented by our memory and imagination.13

Only one harmonic aggregate unfolds within each ad libitum section, and because

of this one-to-one correspondence we can define both microrhythmic and macrorhythmic structures in Lutoslawski's music. Mictorhythm includes all of the attack points unfolding in the course of a single ad libitum section, analo gous to the most surface or foreground rhythm in non-aleatoric music. Macroihythm is created by the change from one harmonic aggregate to the next,

often corresponding to the changes from one ad libitum section to the next.14

l2Witold Lutoslawski, interview by author, 24 October 1993, Toronto, Canada.

"Varga, Lutoslawski Profile, 24—25.

"Discussion of micro and macrorhythm in Lutoslawski's music first appears in Stucky, Lutoslawski and His Music, 128. Stucky's definition of macrorhythm is broader than mine. He describes macrorhythm as the "relationships in time between whole sections of music,"

without defining precisely what these large sections are, although in some cases it is clear that

he is talking about harmonic rhythm as defined by a change from one harmonic aggregate to the next. In his later music, Lutoslawski tends to use ad libitum sections less frequently. In

such music, harmonic aggregates may unfold in the course of battuta sections, in which they would still define macrorhythm. In the latest music, harmonic aggregates cease to structure the

entire pitch content of his compositions.




A clear distinction between macro- and microrhythm is more difficult when

dealing with battuta sections, which are not always governed by harmonic aggre

gates, especially in Lutoslawski's later works. My primary interest in this paper, however, lies with Lutoslawski's most textural music (those works from the 1960s and 1970s), in which case the distinction is less difficult to make. In addi

tion, I am concerned with macrorhythm, and the graphs that follow show the

placement in register of harmonic aggregates, each of which might unfold over the course of a different ad libitum section.

Another result of the one-to-one correspondence of harmonic aggregates and ad libitum sections is that pitch, timbre, and register remain static through

out such sections. Lutoslawski freely discussed these consequences, saying:

One can't deny that the controlled aleatory technique enriches the music's rhythm and expression, and transforms the musical content

from a kind of versified speech into prose. But it also impoverishes the

musical matter to some extent. This impoverishment affects the har

monic flow, which inevitably slows down in all the sections played ad libitum; and that in turn produces a somewhat static effect.15

Although the composer does not discuss the extension of stasis into the realm of

register, he surely must have known that if pitches are fixed throughout an ad libitum section, so too are registers. But I suspect that, at first, Lutoslawski con

sidered this static effect to be a positive attribute. In fact, given the emphasis in

music of the 1960s on the generation of form through texture, timbre, and reg

ister, Lutoslawski may well have thought of ad libitum sections as liberating forces that allowed him to focus on the coordination of blocks of sound.

Texture-Space

The combination of harmonic aggregates and their presentation in ad libitum

sections has a profound effect on the use of texture-space in Lutoslawski's music.

In order to pinpoint this effect I shall define some properties and their transfor

mations that organize texture-space. Although there is no doubt that studies of

pitch and rhythm make up a large percentage of music-analytic writings, a grow

ing body of literature focuses on register and texture, or what I have been railing

texture-space. I have already mentioned Wallace Berry's study of texture in his Structural Functions in Music. In addition, Robert Cogan and Pozzi Escot have

5Kaczynski, Conversations with Witold Lutoslawski, 48.




devoted a large portion of their Sonic Design to explaining the correlation between

historical conceptions of perspective in the pictorial arts and composers' use of

texture-space in music.16 Jonathan Bernard's work on the music of Varèse con

tains substantial development of a theory for that composer's use of register.17

Both the work of Cogan and Escot and that of Bernard use a grid notation to illus

trate the structure of texture-space. In these grids the vertical axis represents the

total available registral spectrum from CO to C8, and the horizontal axis repre

sents a movement through musical time. I will use a similar grid notation to illus

trate how Lutoslawski structures texture-space in the creation of musical form.

Berry has made a useful distinction between quantitative and qualitative accounts

of texture-space.18 Thus the difference between monophonie and polyphonic textures is primarily quantitative (one voice versus two or more voices), while that between polyphonic and heterophonic textures is primarily qualitative (two or more independent voices versus two or more voices with hetero melodic structures).19 The qualitative aspect of a texture entails an account of the interaction of its voices, especially in regard to the relative independence of

their melodies, rhythms, timbres, contours, registers, and so on. The quantita

tive aspect of a texture entails a numeration of the span, voices, and thickness of

the textural fabric. I shall consider primarily quantitative characteristics of tex

ture-space when analyzing Lutoslawski's music, and among such characteristics

I shall make reference to three: field, density, and compression. Thefield of any

texture-space is the expanse of its register from the lowest to the highest notes

in that space.2 The density of any texture-space can be, according to context, the

"Robert Cogan and Pozzi Escot, Sonic Design: The Nature of Sound and Music (Englewood Cliffs, NJ: Prentice Hall, 1976).

"Jonathan W. Bernard, The Music ofEdgard Varèse (New Haven: Yale University Press,

1987). Earlier versions of this material appear in his "Pitch/Register in the Music of Edgard

Varèse, Music Theory Spectrum 3 (1981): 1—25; and in his "A Theory of Pitch and Register for the

Music ofEdgard Varèse," Ph.D. diss., Yale University, 1977. "Berry, Structural Functions in Music, 185.

"There is little agreement both on how many voices must be present to create a texture

and on how to define the term voice. For example, John White, The Analysis of Music (Engle

wood Cliffs, NJ: Prentice Hall, 1976) asserts that "two or more voices . . . produce a texture,"

(185) while Berry allows textures to be made up of one voice. In the interest of both musical

and mathematical thoroughness I define textures as the product of zero (silence) or more

voices. For a more thorough discussion of the term voice, see Monte Tubb, "Textural Con structions in Music," Journal of Music Theory Pedagogy 1, no. 2 (1987): 201—24.

20Cogan and Escot, Sonic Design, define fields as "frequency areas of any width—from the

narrowness of a single frequency to the width of the entire available frequency range" (52).




number of voices or the number of pitches in the textural field. Finally, compression

refers to how tightly packed the voices are within a textural field.21 A more thorough and heuristic exposition of these three terms follows.

Our measurements of a textural_/ï'eU may be approximate or precise. Approxi

mately, we might measure the field of a texture-space by the entire register or registers that it spans, where a fixed interval (traditionally the octave) marks the

boundary from one register to the next.22 The pitches shown in example 2 all fall

within a three-octave range, therefore the approximate field of the collection is

three octaves. The most precise measurement of the field of a texture-space, however, is the total number of semitones from the lowest to highest pitches in that space. Under this measurement the pitch collection of example 2 has a field of 26 semitones. Note that the measurement for this field (and all of those that fol

low) has been from the lowest to highest pitches inclusive. Thus, a texture-space

that consists of one pitch has a field value of 1, not 0. The reason for this type of

computation will become clearer during the discussion of textural compression.

EXAMPLE 2. Measurements for textural field

f o $ -ÖP O

rf> »

Approximate Field: pitches fall within 3 octaves

Exact Field (number of semitones, inclusive): B2-C5 /= 26

2'Berry, Structural Functions in Music, 184 uses the terms density-number and density - compression to refer to what I am calling density and compression respectively. 1 have resorted to

unhyphenated versions of these terms in order to use a simpler locution. Patrick McCreless

has pointed out to me that in the sciences the term density has a meaning that is closer to what

I am calling compression. The problem is that the term density is already used in musical writ

ings to refer to a number of lines or a number of pitches in a texture (as in Cogan and Escot, Sonic Design-, see also Richard Delone, Vernon L. Kliewer, et. al., Aspects of Twentieth-Century

Music, ed. Gary Wittlich [Englewood Cliffs, NJ: Prentice Hall, 1975]; and Monte Tubb,

"Textural Constructions in Music"). I do not wish to cause confusion by using an old term in

a new way, nor do 1 wish to resort to possessive pronouns (my density versus their density) in

order to make this material clear. Therefore, I shall continue in a tradition of using the term density to refer to a number of lines or pitches in a texture.

22By convention, we use the octave as the width of each register; however, we might read

ily define registral bandwidths by larger or smaller intervals. Robert Morris outlines this possi bility in his Class Notes for Atonal Music Theory (Roxbury, MA: Ovenbird Press, 1991), 10—11.



Klein, Texture, Register, and Their Formed Roles in Lutoslawski 45

The term density is commonly invoked when quantifying texture-space, although the exact use of this term can vary according to musical context. Cogan and Escot, for example, use the term density to refer either to the num

ber of voices in a section of music or to the number of notes in a sonority.23 The

difference between these two conceptions of density is not at all moot. Taking as an example the first measure of Chopin's Etude in C minor, op. 25, no. 12 (example 3), we can consider the density to consist of two voices, represented by the single lines of sixteenth notes in both the right and left hands, or we can

consider the density to consist of all the notes (32) that appear during the course of this measure, or even as the number of pitches (6) that make up the first chord before its replication an octave higher. A similar problem arises when determining the density of texture-space in Lutoslawski's music, espe cially in ad libitum sections.

EXAMPLE 3. Opening measure of Chopin Etude op. 25, no. 12

( it trh d* -== TT ^ Pi h 1 (fa g U IP

/ i rj. n *

1 J

=rff

—m J J J1 w

y ' ^ i, ^—r' r \jBst Lüj

Lutoslawski's limited aleatory technique creates a high degree of independ ence among a relatively large number of voices. Often these voices will be homo- or heteromelodic, yet the absence of a common meter results in what

Lutoslawski called a "richness of rhythm,"24 which is a qualitative characteristic

that contributes to textural complexity. Although the absence of a common meter in limited aleatory sections is a solution to a compositional problem, it presents an analytical problem in quantifying textural density. While the num

ber of voices (instrumental lines) remains constant with each performance of any ad libitum section, the precise number of notes within each section will

change from performance to performance. When quantifying the density of the

2iCogan and Escot, Sonic Design, 28—68. 24Lutos}awski, interview by author.




sonority of an ad libitum section, therefore, I will often consider its macrostruc

ture as a chord that has been composed out with the limited aleatory technique.

Borrowing an analogy that Lutoslawski makes between his ad libitum sections and the Alberti bass of much eighteenth-century music,25 we might say that just as the Alberti bass activates a triad, or three-voiced texture, so the limited alea

tory technique activates a harmonic aggregate, or twelve-voiced texture.

This conception of density as the number of pitches in a sonority, however,

leads to a second problem when analyzing Lutoslawski's use of texture-space. Since harmonic aggregates form the macrostructure of much of his music, the

density of texture-space remains constant with a value of twelve. Therefore,

we need a way to compare how such pitch structures organize texture-space. Compression will enable us to compare harmonic aggregates; compression will be

the number of pitches per unit of space within the field of a pitch collection and

will be calculated by the following formula,26 where c = compression, d = den sity, andJ— field:

c-d/j

For example, given a pitch collection with a density of 4 pitches and a field of 11

semitones, the compression of that collection is 0.36 (0.36 = 4/11).27 Example 4 shows calculations for the compressions of two pitch collections. When con

sidering values for compression, higher values correspond to higher compression, and the greatest possible compression of any pitch collection yields a value of c

— 1. If a collection has a compression value of 1, then every available pitch within its field is present. In a metaphorical sense, we can think of compression

as the opacity of a pitch collection. In example 4 the second harmonic aggregate

has a higher value for compression than the first; therefore, it has greater com pression, and we might think of it as being more opaque than the first harmonic

aggregate. Generally, we might contend that pitch structures with the extreme

compression value of 1 are central to the musical language of the 1960s. This observation often extends to sections of music that focus on only one pitch. Such sections have a small field of 1 but an extreme compression of 1. An example

appears in the first movement of Ligeti's Cello Concerto, whose opening pitch material is limited to a single sustained E4 and whose textural field expands from

this E4 rather slowly. Lutoslawski's Chain 7, to be analyzed later in this paper, illustrates a second such example.

2!Varga, Lutosiawski Profile, 25.

26I am indebted to John Clough for simplifying an earlier formula that I used for compression. 27,

Values for compression will be rounded to two figures after the decimal point.




EXAMPLE 4. Compression of two harmonic aggregates

c = compression d = density / = field

c = d!f pxx

xx

n %? ptfN

i£»

= 12 /= 56 rf= 12 /= 32 c= 12/56 = 0.21 c= 12/32 = 0.38

m

c = compression d = density / = field

c = dt f VO

IX

« %F pige

d»

PTT

d= 12 /= 56 rf= 12 /= 32 c= 12/56 = 0.21 c= 12/32 = 0.38

Before focusing on transformations of these textural characteristics, it will

be helpful to show how field, density, and compression interact, and how those

interactions are limited by the structure of harmonic aggregates. In particular, I wish to note that if density remains constant, as it often does in Lutoslawski's

music, an increase in the textural field results in a decrease in compression, while a decrease in the textural field results in an increase in compression. Some simple examples will illustrate this inverse relationship. In the first pitch

collection of example S the field value is 8, density is 4, and compression is 0.S (hereafterJ— 8, d = 4, and c — 0.S), but in the second collection an increase in the field to 26 results in a decrease in compression to 0.15 because the value for

density remains constant. Example 5b illustrates the reverse case. Here all three

collections have a value of d — 2, but as the field decreases from f =18 to J =12

to j— 6, compression increases from c = 0.11 to c = 0.17 to c = 0.33. Example 5c shows that despite decreases in the textural field, the compression of the three pitch collections can remain constant if there are decreases in density. Here again the fields decrease from J— 18 to f =12 to f = 6, but compression remains constant at c = 0.33 because the densities decrease from d = 6 to d — 4 to d— 2.

The registral process outlined in example 5c is not a possibility in any music

by Lutoslawski structured solely with harmonic aggregates. Since the density of such music remains constant at d — 12, any decrease in the textural field will result in an increase in compression. In compositions like Chain 1, as I will show, Lutoslawski uses the types of textural motions that result in increases in

compression to create formal connections between large sections of music.




EXAMPLE 5. Interactions of field, density, and compression

a) b) -X -fe +TT J **>

-CT; 8

o frA* o

e

©

/= 8 /= 26 /= 18 /= 12 /= 6 </=4 rf=4 rf=2 </=2 </=2

c = 0.5 c = 0.15 c = 0.11 c= 0.17 c=0.33

I c)

¥

8

o

/= 18 /= 12 /= 6 rf=6 rf=4 <7=2

c = 0.33 c = 0.33 c = 0.33

a) b)

S

/= 8 /= 26 /= 18 /= 12 /= 6 <7=4 <7=4 <7=2 <7=2 <7=2

c = 0.5 c = 0.15 c = 0.11 c= 0.17 c=0.33

$ c)

¥ S

8

/= 18 /= 12 /= 6 <7=6 <7 = 4 <7=2

c = 0.33 c = 0.33 c = 0.33

However, Lutosiawski may have viewed the interactions of field, density, and compression as a compositional problem in music where density remains con stant. In a discussion of his music after 1980, Lutosiawski states:

One of the important steps here was to invent a method of writing thinner textures; I just reached it only a few years ago. Please notice that in the sixties my pieces employed large masses of sounds almost exclusively, as in the Second Symphony, and to a smaller extent in Livre pour orchestre, Three Poems by Henri Michaux, Jeux vénitiens [sic], etc.

It was so not because I delighted in sound masess [sic]—I simply lacked

suitable tools for writing in a thinner texture. . . .

I have always imagined that large masses should only constitute a cer

tain percentage of the music of a work, though out of necessity I have worked just with them . . . Meanwhile, thin textures, with a smaller num

ber of simultaneous sounds, were still a question for me. This issue, as I

say, clarified itself late, but luckily it did. And only then could set about

such pieces as the Concertofor Oboe and Harp, or now the Piano Concerto.2"

2SGregorz Michalski, "An Interview with Witold Lutoslawski," Polish Music 23, nos. 2—3 (1988): 3-21.




Lutoslawski's reference to large sound masses lacks the precision to allow us to conclude that he was thinking specifically of the property called density, although

the mention of "simultaneous sounds" is close to a definition of this property. If we

can trust Lutoslawsld's retrospective comments about his music from the 1960s,

we might conclude that he was concerned with the problem of altering density in

this music. In later examples, we shall see how Lutoslawski makes efforts to solve

the problem of constant density that results from the use of harmonic aggregates.

Transformations of Texture-Space ( 1 )—Expansion and Contraction

Since density often remains constant in Lutoslawski's works, field and compression will become the foci of an investigation of transformations of musical space. In Lutoslawski's music, we can often confine our observations to transformations of the textural field alone since an increase or decrease in the

field will result in the opposite effect in compression.

I refer to any increase in the textural field as an expansion and any decrease

as a contraction. If an expansion or contraction appears over a number of har monic aggregates, it can serve to delineate formal sections. For example, in the

opening of "Pensées," the first movement of Trois poèmes d'Henri Michaux (1963),

a field contraction unfolds over the course of six harmonic aggregates. Trois poèmes is scored for orchestra and SATB chorus, and in performance the orches

tra and the chorus require separate conductors. Lutoslawski notâtes the compo sition in two large scores, but provides an orchestral reduction in the choral score and a choral reduction in the orchestral score. Example 6 is based on Lutoslawski's reduction of the orchestral score and reproduces the harmonic aggregates that appear in the introduction. From example 6, we can see that the first

six harmonic aggregates represent a field contraction from f= 28 down to J — 12.

EXAMPLE 6. Reduction of opening of "Pensées"

sm m

$ i

f= 28 /= 12



SO Indiana Theory Review Vol. 20/1

Because the clef change may make it difficult to visualize this field contraction,

example 7 transfers these harmonic aggregates into grid notation. Here, we can

monitor visually the increase in compression from the first harmonic aggregate to the last by focusing on the amount of space between notes. As is the case in

much of Lutoslawski's music, the six harmonic aggregates in the introduction of

"Pensées" gradually contract to reach a registral goal with the extreme com pression of c — 1. Later in this paper, I will show how the vocal section that fol

lows the introduction uses pitch collections with the same compression (c = 1 ) to structure the first stanza of "Pensées."

EXAMPLE 7. Opening of "Pensées" in grid notation

01 1 1

Jn

1 |

: : 1 F#

! ! ! d: I 1

: ■

s ! 1 ] 1 I 1 c 1 i

B ■

Bb ' 1

A 1 i

Ab ! 1

C 1

H Aggregates 1




Transformations of Texture-Space (2)—Symmetric Expansion and Symmetric Contraction; Projection

In addition to expansion and contraction, which are broadly defined trans

formations of the textural field, I will consider two transformations that Jonathan

Bernard develops in his work on registral structure in the compositions of Varèse: symmetric expansion and symmetric contraction.29 I define symmetric expansion

as a transformation in the field of two pitch collections in which the highest note

of the second collection is the same distance higher than the highest note of the first collection as the lowest note of the second collection is lower than the low

est note of the first collection. I define symmetric contraction as the reverse

transformation of symmetric expansion. Since these transformations involve the

textural field alone, they can occur between pitch collections of different densi

ties and compressions. Also following Bernard, I will allow measurements over

relatively long time spans, so that we can measure the distances between the highest and lowest notes of two or more sections of music. Since I am inter ested primarily in the registral extremes of collections, and since Lutoslawski

uses large collections of pitches, I will sometimes plot only the highest and low

est notes of a collection in grid notation.

A good example of both symmetric expansion and contraction appears in the first movement of Jeux vénitiens (1961), the first composition in which

Lutoslawski uses the limited aleatory technique. This movement has a simple form, based on the alternation of material set in the ad libitum style and material

set in the battuta style. For this example, I am concerned only with the material in the ad libitum sections. The movement opens with an ad libitum played by the

winds. At each return of this opening material, a new group of instruments is added to the wind section. At the first repetition the percussion is added. At the

second repetition the brass is added, and at the final repetition two pianos are

added. Lutoslawski notâtes these sections within boxes, which appear together on one large page of the score. Table 1 lists the pitch material for each of these

ad libitum sections. Note that when all the sections are played together, during

the final repetition of the ad libitum material, the result is a harmonic aggregate

"Bernard often uses simply expansion or contraction without the modifier symmetric. In order

to avoid confusion between these techniques and the more general registral expansions and

contractions outlined earlier, I will always use the terms symmetric expansion and symmetric con

traction to refer to exact measurements between highest and lowest notes, as defined in Bernard's

work. The terms expansion and contraction without the modifier symmetric will refer to the

more general use of wider or narrower textural fields.




TABLE 1. Pitch material in ad libitum sections of Jeux vénitiens: first movement

Timbre Pitch material

winds 3f <7,9,0,2,4,6, 8, 9, E, 1,3, 5, 8, T> 2- 3- 2- 2- 2- 2-1-2-2- 2- 2- 3-2

brass 4t<7,8,9,T> 1-1-1

pianos 1T <E, 3, 0,4,1,5,2,6> 4- 9-4-33-4-9-4

(9)

winds, brass, pianos It <E, 3,0,4,7,9,0,2,4,6,7,8,9, T, E, 1,3,5,8, T, 1,5,2,6> 4- 9- 4- 3- 2- 3-2-2-2-1-1-1-1-1- 2- 2- 2- 3- 2- 3- 4- 9- 4

Timbre Pitch material

winds 3Î <7,9,0,2,4,6, 8, 9, E, 1,3, 5, 8, T> 2- 3- 2- 2- 2- 2-1-2-2- 2- 2- 3-2

brass 4î<7,8,9,T> 1-1-1

pianos If <E, 3,0,4,1,5,2,6> 4- 9-4-33-4-9-4

(9)

winds, brass, pianos It <E, 3,0,4,7,9,0,2,4,6,7,8,9, T, E, 1,3,5,8, T, 1,5,2,6> 4- 9- 4- 3- 2- 3-2-2-2-1-1-1-1-1- 2- 2- 2- 3- 2- 3- 4- 9- 4

with twenty-four pitches, where each pitch class appears in two registers. Alter

natively, we might consider this final section to consist of two harmonic aggre

gates played simultaneously. The appearance of the twenty-four pitches in this final section doubles the density found in most other ad libitum sections. We

might view this doubling of density as a solution to the problem of constant density that occurs when music is based solely on the standard harmonic aggre gate with twelve pitches. Lutoslawski only rarely repeats this solution in his

later works, with one such example appearing in a section of his Fourth Symphony

(1992).30 The rare reappearance of this solution may be because it results in greater density, while the compositional problem that Lutoslawski claims to have been facing involved the writing of music with less density.

Lutoslawski's choice of registers for each of the three pitched orchestral

groups reveals a process of symmetric contraction and symmetric expansion with respect to the initiating wind section. The highest and lowest notes of each

of these orchestral groups appear on a grid in example 8. Since the winds first

perform alone, their highest and lowest pitches appear in the left part of the grid. The pitches of the brass section and the piano section are added to the

pitches of the wind section as we move through the grid from left to right, and the three different shapes in the grid represent the three different timbres (circle

i0The section in question appears at rehearsal numbers 53—58. Here Lutoslawski gradually

builds a harmonic aggregate with an octave duplication of each pitch, resulting in a harmonic aggregate with twenty-four pitches.




EXAMPLE 8. Grid notation for boundary pitches in Jeux vénitiens

F#

L i

+20 . -'

Bb 1

* *S , -12

"A Bb

<

1 1

1

G

1

1

G «

X' + 12

<

' ^. -20 '•v

* i L

B

I

Winds Brass Pianos Tutti

u Cm o

I o

F#

i ii

+20 . y

- '

Bb i

* *S , -12

"A Bb

it

1 1

1

G

II

II

G 1

X' + 12

it

' . -20 '•v

* i i

B

a


= winds, square = brass, and triangle = pianos). The grid shows that the boundary pitches of the brass section represent a symmetric contraction of the

boundary pitches of the opening wind section. When the pianos enter, their boundary pitches represent a symmetric expansion of both the wind section and

brass sections. In example 9 I literally "connect the dots" of the boundary pitches to produce a graphic representation of Lutoslawsld's use of timbre and

register. In this example, I have added the boundary pitches of both piano parts

because the four upper pitches of this timbre are widely spaced from the four

lower pitches. The resulting boxes in the graph of example 9 mirror the boxes

that Lutoslawski often uses to notate these ad libitum sections, and they pro

vide an image for the static effect of such sections. The graph also gives us a clear image of the interaction of timbre, pitch, and register. Only rarely in later



54 Indiana Theory Review Vol. 20/ 1

EXAMPLE 9. Registrai/timbrai boxes in Jeux vénitiens

Winds Brass Pianos

s u

o


compositions does Lutoslawski rely on such a mechanical melding of these three

musical elements, but often from the densest material we can separate layers of

registral or timbrai sound that provide a clue to his method of creating larger forms.

In addition to symmetric expansion and symmetric contraction, I will refer

also to a transformation called projection,31 A projection is the movement of a field

to a new pitch/registral level; as in Bernard's use of the term, the preservation

of internal detail (such as density, compression or even internal intervallic structure) is optional.

A return to "Pensées" offers an opportunity to illustrate the structural use of both symmetric expansion and projection. Previously, I focused on the

^Bernard, Edgard Varèse, 48.



Klein, Texture, Register, and Their Formal Roles in Lutosiawski S S

TABLE 2. Organization of the first stanza in "Pensées"

Section Rehearsal

numbers

Orchestration Harmonic aggregate

Orchestral in

troduction

1-28 winds, brass see examples 6,7

Line 1 28-29 SATB 3T<7,8,9,T,E,0, 1,2,3,4, 5, 6>

Line 2 29-30 SA 4T <5,6, 7, 8,9>

Line 3 (begin) 30-32 (SA)TB 3| <T, E, 0,1,2>

Line 3 (end) 32-34 (T)B 3t <3,4>

Orchestral

interlude:

part 1

35-45 winds 4f <2,3,4,5, 6, 7, 8,9, T>

Section Rehearsal

numbers

Orchestration Harmonic aggregate

Orchestral in

troduction

1-28 winds, brass see examples 6,7

Line 1 28-29 SATB 3t<7,8,9,T,E,0, 1,2,3,4, 5, 6>

Line 2 29-30 SA 4T <5,6, 7, 8,9>

Line 3 (begin) 30-32 (SA)TB 3î<T,E,0,1,2>

Line 3 (end) 32-34 (T)B 3Î <3,4>

Orchestral

interlude:

part 1

35-45 winds 4| <2,3,4,5, 6, 7, 8,9, T>

orchestral introduction, and here I expand that analysis to include the entire first stanza, in which three lines of text compare thought to an indistinct sea. Lutoslawsld devotes an ad libitum section to each of the first two lines, and he

devotes two ad libitum sections to the third line. The entire stanza is sung a cappella.

Following the first stanza, the orchestra enters briefly but then pauses before

setting up the choral entrance for the second stanza. Typical of Lutoslawski's music is the careful alternation of high and low voices to mark clearly the struc

ture of the stanza. This information, along with the harmonic aggregates that

appear in the ad libitum sections, is summarized in table 2. Under the entry for

"Line 3 (Begin)," the soprano and alto parts are enclosed within parentheses (SA) because their pitch material from Line 2 carries over into the third line of

the poem. Similarly, under the entry for "Line 3 (end)," the tenor part is en closed within parentheses (T) because it maintains the pitch material from Line

3 (begin). Together the pitch material for lines 2, 3 (begin), and 3 (end) form a

harmonic aggregate, and the compression values for all of the entries in table 2

are equivalent at c = 1. Since the harmonic aggregate is divided into three sub sets (in three ad libitum sections) that vary in their fields but share equivalent

compressions, this first stanza offers another solution to the problem of con stant density in works structured with harmonic aggregates.




In example 10, the information of table 2 appears in a grid in which only the highest and lowest notes of each pitch collection are plotted in order to show the fields of the material. The calibration of the pitch-space on the vertical

axis is exact in this grid, but the calibration of time on the horizontal axis reveals only the order of events and not their duration. The material for the orchestral

introduction is not included because it appears in example 7. The lowest and highest notes of the orchestral interlude also appear separately since this section

of the music begins with repeated notes on D4, the section's lowest pitch, and ends with repeated notes on Bt4, the section's highest pitch. Dark horizontal lines show that the highest or lowest notes of one pitch collection remain con stant into the next collection. Pairs of dark arrows illustrate projections, and dotted arrows illustrate a symmetric expansion.

EXAMPLE 10. Grid notation for first stanza of "Pensées"

+ 4 semit ones

F#

A

> "J (

(

A

:-s. ► 4

D > <

— -> <

>

t Bb

< C

> —^ (

Bb

'■V *D#

-4 ;emitones

SATB SA (SA)TB (T)B Winds Winds (End)




The grid also reveals that the texture-space of the first stanza—from the opening choral part to the close of the orchestral interlude—undergoes the transformation of symmetric expansion. At the opening of the stanza the high

est pitch of the choral part is F#4, and by the end of the stanza the wind section

expands this note up four semitones to BM-; similarly, the lowest pitch in the

opening choral part is G3, and by the end of the stanza the basses expand this

note down four semitones to DÜ3. Despite the large ensemble required for per

formance of this work, Lutoslawski contains the opening stanza of "Pensées" within a texture-space whose narrowness is matched by the extreme compres sion of the individual pitch collections. The music navigates through this narrow

texture-space through two projections. In the first projection the sopranos and

altos expand the higher register of the musical space to A4, which is nearly the

highest pitch of the entire first stanza. In the second projection, the tenors and

basses mirror the expansion of the sopranos and altos by reaching down to Dit 3, the lowest pitch of the first stanza.

Analysis 1: Trois poèmes d'Henri Michaux, "Repos dans le Malheur"

Having defined characteristics of texture-space and having illustrated trans

formations of these characteristics in excerpts from Lutoslawski's music, I will

turn now to an analysis of an entire composition, "Repos dans le Malheur," the

third and final movement of Trois poèmes d'Henri Michaux. I have already com

mented on this score's complexity, which arises both from the sheer number of

required performers and from the nearly total reliance on the ad libitum technique

in both choral and instrumental parts. Trois poèmes, along with Lutoslawski's next

composition, the String Quartet (1964), represents his most thorough use of lim

ited aleatory techniques. Combining the materials of two scores in preparing an analysis of Trois poèmes presents numerous difficulties, but the third movement

presents fewer challenges since the chorus maintains an a cappella style and, with the exception of a brief instrumental climax, the orchestra is reduced to

two pianos and harp, which serve to introduce divisions of the text.

Steven Stucky argues for a fourfold division of this movement on the basis

of four solo harp entrances in which a single pitch is repeated.32 I agree with

Stucky that the harp entrances provide a clue to the formal plan of "Repos," but

in the analysis that follows I also maintain that, in addition to any importance

they may have for the pitch content of this movement, the harp pitches also

2Stucky, Lutoslawski and His Music, 146.




EXAMPLE 11. Four structural pitches of "Repos dans le Malheur"

function to articulate Lutoslawski's structural use of texture-space. Example 11

shows the four pitches in the registers in which they appear in "Repos." Just as

the four pitch classes mark a path up to Ftt, the three different registers that they

represent are balanced around the fourth octave, with the first two pitches appear

ing in the octave above FÄ4 and the third pitch appearing in the octave below.

In order to reveal the ramifications of this registral balance around the fourth octave, I offer example 12, a grid analysis of the texture-space of the entire movement. In this grid I have plotted all of the pitch material but have only labeled the highest and lowest pitches of each vertical collection. As with some of the other grid examples, time has been flattened somewhat in this exam

ple; that is, events to the right occur after events to the left, but the relative dura

tions of these events are not graphed. I have shown timbre in the grid through the

various shapes of the pitches: circles represent the harp, triangles (sometimes stacked upon each other) represent the pianos, boxes represent the voices, and diamonds represent the full orchestra. Arrows show projections, and pairs of lines show symmetric expansions and contractions. Rehearsal numbers appear at the bottom of the grid, and the first words of each of the two stanzas of the

poem appear at the top of the grid precisely where they occur in the music.

The two most striking transformations of texture-space in example 12 are the series of symmetric expansions and contractions near the end of the move

ment and the sustained projection near the opening of the movement. I will turn first to the symmetric expansions and contractions at the movement's cli

max. At rehearsal number 29 the winds, brass, percussion, and piano play Ft through a full seven octaves. Ft+ is the central octave in this registral spectrum,

an octave to which Lutoslawsld points by gradually removing instruments and octaves from the texture. The culmination of this symmetrical contraction appears

at rehearsal number 32, where the solo harp repeats the pitch F#4. More sub jectively, the octaves in this passage, coming with the words "dans ton horreur"

(referring to the narrator, who loses himself in misery), have a devastating emotional effect, matching the tone of the poem. Remember that harmonic aggregates lack octaves; therefore, with the introduction of octaves at this point




EXAMPLE 12. Grid notation for "Repos dans le Malheur"

Le i^alheur mon grand l^boureur... Mon grand theatre.. ^

Ob ±

ffl

D

\Bb Eb f Efb • i || SI eb!^ Is M IS II |K •

11 At? u

A#

■

G# i.l *# A# A

R #: 1 2 3 4 5 6 7 8 9 10 11 12 13 18 20 21 24 26 29 R ff: 1 2 3 4 5 6 7 8 9 10 11 12 13 18 20 21 24 26 29

in the music, the expanse of pitch-space collapses into modular pitch-class space, perhaps mirroring the collapse of the soul in the face of boundless misery.

The final vocal entrance begins on FÏ4 and then the voices fill pitch-space from this note down to C$4-. Against this pitch collection, in the only instance in

this movement in which the vocal part is accompanied, the pianos engage in a symmetrical expansion, performing pitch classes G, Gf, and A in three octaves

starting at exactly one octave and one semitone above the vocal FÜ4, and pitch classes C, B, and Bt> in three octaves starting at exactly one octave and one semi

tone below the vocal Ct4. Thus, the pitches of the vocal part become not only the center of pitch focus, but also the center of registral focus. The fourth octave

is the central register in these symmetric expansions and symmetric contrac tions, and the same octave is the center of registral balance for the four solo harp pitches that appear throughout the movement.

On the basis of the transformations of texture-space at the end of "Repos," I

will posit the fourth octave as the goal of registral motion throughout the movement. By turning to the opening of "Repos," we can see how the music achieves this registral goal. Here, the solo harp establishes the fifth octave as a

registral starting point. Disregarding the piano solo for a moment, we see that

the vocal part begins in the same register and gradually fills the lower register

through a projection of a textured field of eleven semitones. Through rehearsed




number 10, the lowest and highest notes of the vocal part are Eh3 and EhS. Octaves 3 and S he on either side of octave 4, which will be the final register of

the entire movement. The total registral space that unfolds within this section is

a contraction of the solo piano part that precedes it. Notice that here the con

traction is not symmetric since the highest pitch of the piano part, C6, lies nine

semitones above the highest vocal pitch, and the lowest pitch of the piano part,

Al>2, lies seven semitones below the lowest note of the vocal part. However, we can characterize the piano part as establishing a textural space from octave

6 to octave 2, which the vocal part contracts to a range of octave S to octave 3

through a gradual downward projection. Due to the extreme compression of the vocal pitch collections up to rehearsal

number 10, the graph does not reveal well the gradual increase in density that

accompanies the projection of this section. Each vocal pitch collection contains

one more pitch than the previous one, starting with the opening collection of seven notes. The only exception occurs precisely at the completion of the pro jection at rehearsal number 8, where there is a move from a collection of ten

notes directly to the full aggregate. Following the completion of the projection,

the density decreases and the field of the vocal part undergoes two symmetric

contractions so that the end of this section is reduced to a single pitch, G#3, which is part of the dyad {Gif, A} that lies at the center of the previous pitch

collection, G through At.

Following this single Gtt, the return of the solo harp playing repeated pitches implies a new musical section parallel to the opening of the movement. This formal division receives support in the structure of the poem, since the G#

in the vocal part at the end of rehearsal number 10 marks the end of the first

stanza. We might characterize the entire first stanza as establishing a texture space between octaves 3 and 5 through a steadily descending projection of pitch

collections with equivalent compressions and ever-expanding fields and densities.

Upon reaching the lower register, these pitch collections contract to a single pitch in the third register, mirroring the single pitch in the fifth register at the

opening of the movement.

The use of texture-space in the second stanza represents a wider field but

less compression than the texture-space of the first stanza. The lower range of

the vocal part extends to include register 2, which has a counterpart in the use

of register 6 in the piano part that opens this stanza. The use of a wider field in the vocal part culminates in the pitch collection that extends from A2 to FS

immediately before the climactic Fits. The sudden collapse of register to the sin

gle FÜ4 in the solo harp highlights the climax of the movement.



Klein, Texture, Register, and Their Formal Roles in Lutosiawski 61

EXAMPLE 13. Centers of registral balance for stanza 2 of "Repos dans le Malheur"

R#: 11 12 13 18 20 21 24 26

a

u

SS 3 >

2 y O 2

R#: 11 12 13 18 20 21 24 26

We can trace a rough contour of the second stanza up to the climax by con

sidering the central register around which each of the pitch collections is bal anced. Example 13 replaces each of the pitch collections in the opening of stanza 2 with a single pitch that represents a center of registral balance for those

pitch collections. In graphing the collections in this way, I have collapsed the tex

tural field into a single pitch representative of register. The example illustrates

that the pitch collections of stanza 2 trace a center of registral balance that begins at octave 5, descends to octave 3, and comes to rest at octave 4. Thus both the

first and second stanzas trace a registral movement from octave 5 down to octave

3, though this registral path is more abstract in the second stanza. Example 14

illustrates these registral motions for the two stanzas. The thick lines reveal the

basic registral motion, while the thin lines show intermediate goals of registral

motion. In both stanzas register 4 is a passing register connecting endpoints of a

single registral descent. It is only at the end of the second stanza that the registral

motion is completed by a centering of pitch material at register 4. The registral

motion of the first stanza represents an incomplete replication of the large-scale

3iIn Richard Delone et. al., Aspects of Twentieth-Century Music, 87, a similar idea is discussed

in relation to register. The authors use the metaphor of a center of gravity, which is defined as

the midpoint of the total tessitura of a section of music.




EXAMPLE 14. Registrai graph of "Repos dans le Malheur"

Stanza 1 Stanza 2

5% II

registral shape of "Repos". This incomplete motion may represent a kind of for

mal analog to the two-part tonal form that Heinrich Schenker describes as an interruption in the fundamental line, although here the fundamental line is one of

register, and it is not given a priori but develops from the texture of the entire

composition through repetitions in timbre (the four harp pitches). Because of the

similarity to interruption form, I have borrowed the symbol of parallel lines that

Schenker uses to mark an interruption and placed it between the two stanzas.

Analysis 2: Chain 1 (1983)

The perception of musical structure depends upon memory. When musical ideas are vivid, their impressions allow for a rich network of associations, creat

ing senses of expectation and fulfillment that are central to musical experience.

In much of Lutoslawsld's music, the vivid use of texture-space cuts across time,

allowing us to hear connections between ideas even when an expanse of mate rial separates them. Consider two sections from Chain 1 for fourteen instru

ments (1983). Each of these sections has been reproduced in piano reduction as example 15.34 The first is the opening of the work, and the second is the climax,

"The two reductions show pitch only. No attempt has been made to notate the rhythm of the passages (a highly difficult task in any case, given their notation as ad libitum

sections). Lutoslawski himself uses similar rhythmless reductions in the scores (vocal and instrumental) of his Trois poèmes d'Henri Michaux.




EXAMPLE 15. Reductions of opening and climax of Chain 1

Opening Rehearsal no.: 1 2 3 before 4

ka.

pi pP «*>

Climax Rehearsal no.: 46 47

i 1? a t|a 4^ T T Wfo ^ M i>o simultaneity * \ total

\ chromatic

Opening Rehearsal no.: 1 2 3 before 4

ko.

jf to pi pP

Climax Rehearsal no.: 46 47

1? t|Ä ÛS nfë T ,

i ko

simultaneity ^ \ total \ chromatic

m

shortly before the end of the work. Both sections appear as a series of ad libitum

sections in the full score, and given their considerable rhythmic activity we may

at first focus our attention on their registral shapes. The opening passage begins on a single pitch from which the texture-space expands in both directions, only to collapse again onto a single pitch, like the unfolding and infolding of the wings of a large bird of prey. The climactic passage begins with a wide tex

tural field that collapses onto a single pitch, only to expand and then collapse again onto a chromatic cluster. Here, the extremely active rhythm and dynamic

intensity might suggest that a more appropriate image is that of a dying sun, col lapsing and expanding, only to gather energy one last time before a violent ex

plosion leaves behind a single dense black hole. The two passages express similar registral ideas that cut across time, forging a connection between the opening and climax of this remarkable music. Although the images I have drawn above may help to bring these passages to life for the reader, the textural char

acteristics of field and compression may lead to a richer, if less poetic, under standing of this music.




In example 16 the two harmonic aggregates of the introduction appear in grid

notation to illustrate the use of texture-space. Example 17 reproduces the harmonic

aggregates at the climax of Chain 1 in the same grid notation. A cursory comparison

of the two examples reveals that in both the introduction and climax of Chain 1,

there is the same basic shape in which the textural field expands and then contracts.

The shape of the introduction is perhaps more readily perceived since it takes place

over the course of a brief ad libitum passage ftamed by single pitches that highlight the

expansion and contraction. The shape of the introduction is composed out in the

climax, where the expansion occurs over the course of six lengthy ad libitum sections.

The single pitch, Bl>4, that appears at rehearsal number 46 draws our attention back

to the single pitches that opened the composition. The sudden collapse of the tex

tural field at rehearsal number 46 nearly mirrors the collapse of the field to the single

pitch, B3, at the opening of Chain 1. In addition, the final three events at rehearsal

numbers 46-47 mirror the registral shape of the introduction. However, the com

posing out in the climax of material from the introduction goes beyond the basic

shape of the two passages, as the more detailed analysis that follows will reveal.

The introduction (example 16) begins with the fourteen instruments of the

ensemble playing a single pitch that expands immediately to the first of two harmonic

aggregates. The second harmonic aggregate is a symmetric contraction of the textural

field of the first harmonic aggregate, and the concluding singleton is a contraction that

balances the opening expansion. The symmetric contraction is achieved by maintaining

the middle six pitches of the first harmonic aggregate through the second harmonic

aggregate. Dashes in example 16 represent these six pitches. The remaining six pitches

in the second harmonic aggregate result from an octave transfer of both the highest and

lowest trichords from the first harmonic aggregate. The dotted arrows in example 16

represent the octave transfers of the outer trichords from the first to the second har

monic aggregate and thus the symmetric contraction of the textural field.

The single pitches that frame the introduction also imply an octave transfer.

The B3 that completes the introduction appears in the octave lower than the A4

that opened the introduction. These two pitches together nearly bisect the field of

the first harmonic aggregate, which represents the widest field of the introduction.

B3 is 22 semitones distant from Dt2, the lowest note of the introduction, and A4 is

twenty-three semitones distant from Ak>, the highest note of the introduction.

An exact bisection of the highest and lowest notes would require Bt4 instead of A4,

resulting in the two pitches Bb4 and B3. These are the exact pitches that form the

outer boundaries of the final harmonic aggregate that occurs at the climax of Chain 1

at rehearsal number 47 (example 17). The field of this climax, J — 12, Ls the same as

that of the trichords that participate in the octave transfers in the introduction.




EXAMPLE 16. Grid notation for opening of Chain 1

<

D <

Ab

A <

F 1

*• <

Ab i

■ F »

A < „ A# Ff .

D#

( ; a# ■ F#

■ D#

B

E ■

!

/ ((

(

• B <

l

. E

i

► B

C

G <

(

i /'

i

D

D

u Cm O CA a» >

2 CJ

o

<

D <

>Ab

»

A <

F 1

\ <

Ab i

■ F »

A < „ A# Ff .

D#.

( ; a# ■ F#

■ D#

I 1 ' m lu

i

/ / ■ / ■

i

• B <

I

. E

i

► B

C

G<

(

\ /

i

D

D

Dashes — pitches that remain constant

Dots — pitches that move by octaves

Diamonds = first and last pitches




EXAMPLE 17. Grid notation for climax of Chain 1

d!

t

r A ! • ' A

\

\\ \ > \ \ \ \

s \

\ \

N N

\

E

#

F # ►

•

•

• i

\ \

-23 V

\

^ I V

Bb t

t

|

*

# <

•

>

. *

•

•

Bb Bb

*

C

•

•

-23 I

\

V \ I \

-A B /

/ /

/ /

c $ G

B

c# t

R#: 41 42 43 44 44 45 46 46 47

5 O

M (V 4 > (0 ■M U O

3

Ai

c .

C# t

Bb

^3—t -23

Bb]

-23 «

Bb

-A B

R#: 41 42 43 44 44 45 46 46 47

I have already mentioned the contraction from a harmonic aggregate at rehearsal number 45 to a single pitch at 46, which is the most striking feature

of the climax shown in example 17. Following the harmonic aggregate at 46, the climax closes with a final harmonic aggregate that falls within the narrowest

possible field of 12 semitones. These final four pitch collections, rehearsal num

bers 45^47, replay some of the same registral processes found in the introduc tion of Chain 1. Lutoslawski sets this final section apart from the rest of the

climax by the sudden reduction in the use of the lower register and by the onset of repeated notes that will continue through the end of the climax.




The final harmonic aggregate returns to the register defined by the two sin

gle pitches of the introduction of Chain 1. Indeed, the lowest pitch of the final

harmonic aggregate, B3, is the same as the final pitch of the introduction, and the

highest pitch, Bt4, is only one semitone higher than the opening pitch of the introduction. This final harmonic aggregate nearly bisects the textural field of the

previous harmonic aggregate at rehearsal number 46. The lowest pitch in the final harmonic aggregate, B3, is twelve semitones higher than the B2 of the pre

vious harmonic aggregate, and the highest pitch in the final harmonic aggregate,

BU-, is eleven semitones lower than the A5 of the previous harmonic aggregate.

Lutoslawski might have achieved a perfect bisection of texture-space here by

making A4 the highest note of the final harmonic aggregate. In that case, the

highest and lowest pitches of the final harmonic aggregate would correspond to

the single pitches that frame the introduction but would sacrifice a complete harmonic aggregate, since all twelve pitch classes cannot appear within the field whose boundaries are B3 and A4. A perfect bisection of the textural field does

occur at rehearsal number 46 with the single pitch Bi>4 that is twenty-three semitones lower than the highest pitch of the previous harmonic aggregate and

twenty-three semitones higher than the lowest pitch of the following harmonic

aggregate. This registral relationship between the single pitch and its surround

ing harmonic aggregates helps us hear these final four events as part of a single formal component.

The register of the final harmonic aggregate involves two octave transfers. These are shown in example 17 as dotted arrows. The first octave transfer occurs

between the highest note of the harmonic aggregate at rehearsal number 45 and

the highest note of the harmonic aggregate at 46. The second octave transfer occurs between the lowest note of the harmonic aggregate at rehearsal number

46 and the lowest note of the final harmonic aggregate. Recall that in the intro

duction octave transfers served to produce a symmetric contraction between two harmonic aggregates. In the climax the contraction appears between three

harmonic aggregates; however, the contraction is still symmetric in that it involves

a reduction of one octave in both the highest and lowest registers.

The symmetry of the contraction is difficult to see in example 17 because

there is a phase-shift of register in the final four pitch collections. Example 18

shows a version of the same passage in grid notation, but here the contraction is

used to put the passage back in phase. In the example only the highest and low

est pitches are shown with the Bl>4 that bisects the field of these pitches. This

Bt>4 appears in all four of the final pitch collections of the climax. On the left




EXAMPLE 18. Phase-shift in climax of Chain 1

< , A <

1J < , A

-J < ,A

- - - <

B

h < i—

B B B B

(

y] i

B yl' i

B

i i

B i >

B

In Phase Phase Shift

5

O

S 4 >

2 u

O 3

i , A <

iJ <

-J 1 , A

- - - <

B

h < i—

B B B B

(

71 i

B 71' i

B

i i

B i >

B

In Phase Phase Shift

Diamonds — pitches that remain constant

Dots — pitches that move by octaves

side of example 18 the passage appears in phase with the octave transfers occur

ring simultaneously. On the right side of the same example the lower register

of the graph is shifted one segment of time to the right. The result of this phase

shift matches the use of register with its use in example 17. Returning to the

left side of example 18, we note that the symmetric contraction arising from the octave transfers mirrors the symmetric contraction at the introduction of

Chain 1. Thus, the use of register in the climax of Chain 1 is a transformation of

the use of register in the introduction of Chain 1.




Conclusion

I would like to conclude this paper by making explicit the nature of the claims I am making about register and texture in the music of Lutoslawski. In

order to do this, it will be useful to make reference to a well known tripartition

of musical facts into areas focusing on the composer, the material form(s), and

the listener, or, roughly, what Jean-Jacques Nattiez calls the poietic, immanent, and esthesic dimensions.35

Most of the claims in this paper involve the immanent dimension. In other

words, I am describing structures and the ways in which they connect large sec

tions of Lutoslawski's music. These structures involve texture-space, with a particular emphasis on registral boundaries. In the pursuit of spatial metaphors

with which we can imagine this music, I have had to marginalize many details

that some might find worthy of more attention. For example, although I have

demonstrated how harmonic aggregates have a profound effect on the treat ment of texture-space, I have ignored the internal details of these pitch struc

tures and their precise unfolding in ad libitum sections in order to highlight large-scale registral connections. A more complete theory for the music of Lutoslawski will have to contend with the difficulty of coordinating these regis tral events with the enormous detail and complexity within the individual ad libitum sections. In addition, such a theory will have to address the question of how Lutoslawski writes the thinner textures that characterize his music in the

1980s, when harmonic aggregates cease to be the sole source of pitch organization.

I have made no claims in this paper about the perceivability of the registral motions that I describe (the esthesic dimension). Such claims would need the

support of research and/or experimentation in cognition and perception. How

ever, I do believe that most of these transformations are easy enough to hear.

Simply put, such hearings require that the listener attend to the registral boundaries of some static sections of music, and that she notice the ways in which those boundaries expand or contract from section to section.

Finally, although I cannot yet make solid claims about how the registral procedures I describe match Lutoslawski's creative processes (the poietic dimen

sion), I have tried to develop a theory that is sensitive to the composer's con

cerns. Among much documentary evidence implying that texture and register

were of primary importance to Lutoslawski, his description of how he began to

write texture music seems worth repeating here:

?5Jean-Jacques Nattiez, Music and Discourse: Toward a Semiology of Music, trans. Carolyn

Abbate (Princeton: Princeton University Press, 1990).




Composers often do not hear the music that is being played: it only serves as an impulse for something quite different—for the crea

tion of music that only lives in their imagination. It is a sort of schizo

phrenia—we are listening to something and at the same time creating

something else.

That is how it happened with Cage's Piano Concerto. While listen

ing to it, I suddenly realized that I could compose music differently from that of my past. That I could progress toward the whole not from the little detail but the other way round—I should start out from

the chaos and create order in it, gradually. That is when I started to compose Jeux vénitiens.36

Although, like any passage, this one is open to many interpretations, I believe that

the description of working from the whole to the little detail may suggest that

Lutoslawski began his compositions of the 1960s by sketching out long-range regis tral motions; only later in the process did he flesh out these motions within each ad

libitum section. This contention is supported by a look at Lutoslawski's sketches,

which are often drawn on graph paper and include geometric shapes. A fuller account of these types of sketches, however, is too broad a subject for this paper.

The analyses included here give us clues to the types of textural and regis tral procedures that Lutoslawski favors in his music after 1960. For example,

pitch collections with extreme compression are often the starting points or goals of formed motions in texture-space. In the first and third movements of

Trois poèmes compressed pitch collections expand the registral field through pro jections and symmetric expansions, and in Chain 1 compressed pitch collections create an association between the introduction and the climax. Reference to the

properties of texture-space that I have defined (field, density, and compression)

may be useful for understanding the music of other composers active during the 1960s and '70s as well. In this regard, I have already mentioned the Cello Concerto

of Ligeti, but I could extend this reference to include the music of Xenakis, Penderecki, and others.

,6Varga, Lutoslawski Profile, 12—13.



texture register

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