The treatment of rhythm as a central organising force is perhaps the mostenduring and characteristic aspect of Elliott Carter's compositional style.Throughout his long and productive creative life, he has been engrossed withmatters of musical time. As early as 1944, his perception was that `people hadforgotten that the really interesting thing about music is the time of it ± the wayit all goes along'.1

Carter's preoccupation with the notion of musical time led to an extendedexploration of innovative rhythmic techniques by which he could create musicthat flowed independently of the hierarchic organisation of regular metre. In1965 he confessed `it is toward this time dimension that my own interest hasbeen directed since about 1940, and whatever musical techniques I have usedare contributory to the main concern of dealing with our experience of time'.2

The anatomy of his rhythmic development is revealed in an essay by JonathanBernard, which presents the rhythmic devices found in each work from theCello Sonata of 1948 to the Double Concerto of 1961.3 It details how Carter'suse of successive tempi and speeds ± often associated with metric modulation ±developed gradually into the practice of juxtaposing simultaneous rhythmicformations.

In particular, Bernard discusses the structural significance of simultaneousspeeds in Carter's music. Here, `speed' refers to a measurable series of evenlyspaced attacks, and the focus is on the composer's concurrent use of severalsuch measurable speeds in different components of his multi-layeredcontrapuntal textures. An awareness of the distinction between speed andtempo is critical to an understanding of his use of speeds. Firstly, tempo isconsidered to be a general performance indication, whereas speed is thepresentation of a specific series of regular attacks. For example, at a tempo ofcrotchet=100, a series of semiquavers presents a speed of MM 400. Secondly,a tempo marking usually pertains to the whole ensemble, whereas, in Carter'smusic, a particular speed is frequently articulated by a single component of theensemble.

Frequently, in fact, Carter designs the entire rhythmic architecture of awork around a system of speeds. His Double Concerto, for example, is built ona large-scale plan of ten simultaneous `regular speeds', the distribution of

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BRENDA RAVENSCROFT

SETTING THE PACE: THE ROLE OF SPEEDS IN ELLIOTT CARTER'S

A MIRROR ON WHICH TO DWELL

which he charts in `The Orchestral Composer's Point of View'.4 Furthermore,his rhythmic structures rarely operate independently of other musicalparameters, and Bernard also elucidates how he often weds rhythm and pitchby pairing each speed with a specific aspect of pitch, such as with a smallrepertoire of intervals.5

Bernard's discussion of Carter's rhythmic practice is necessarily limited toinstrumental music, as he did not write for the voice in the decades addressedby the essay. It is intriguing, however, to consider how speeds could functionin vocal music, where there is, as Carter put it in the late 1960s when hisaversion to text-setting began, `a whole other time-structure to be thought ofand dealt with'.6 By the time he did return to vocal composition in 1975, after ahiatus of nearly thirty years, his technique of using speeds as a means ofcontrolling rhythm was well established. Moreover, it was evident that speedscould play a special role in terms of text expression: the added dimension oftext-setting would allow him to use speeds to convey his interpretation of thepoem and to set the pace at which the poem unfolds.

Carter's first vocal composition of this period is the cycleAMirror on Which toDwell, a setting of six songs for soprano and chamber orchestra.7 He selectedpoems by his contemporary, Elizabeth Bishop (1911±79), a poet whosepreoccupation with the passage of time resonated intimately with his owninterest in temporal issues.8 Bishop's focus is on how time shapes humanexistence ± for example, in the conflict between time and distance in `Argument',or the painful observation of each successive breath in `O Breath'. Believing thattiming and articulation are critical in poetry, she states her goal as being to `catchand preserve the movement of an idea ± the point being to crystallize it earlyenough so that it still has movement'.9 Her interest in the way one's perspectivechanges over time reflects Carter's concept of the `time screen', where one's focusshifts as events are projected through time and motion.

In his notes for the Speculum Musicae recording of the Mirror cycle, Carterwrites of Bishop's poems: `I was very much in sympathy with their point ofview, for there is almost always a secondary layer of meaning, sometimesironic, sometimes passionate, that gives a special ambiance, often contra-dictory, to what the words say.'10 These layers of meaning find their musicalexpression in his `simultaneous streams of different things going ontogether',11 a concept developed from his idea of musical time whereby thecomplex motion of life is reflected in a kind of musical motion in which layeredmusical events proceed simultaneously.

The purpose of this article is to examine the role of speeds in A Mirror onWhich to Dwell by analysing two songs from the cycle. `Anaphora' (the openingsong) and `Sandpiper' (the third song) contrast rhythmically in many respects;together they embody all of the most important ways in which Carter usesspeeds in the cycle. The analysis will focus on the speeds that are projected in

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254 BRENDA RAVENSCROFT

each song: on how these speeds shape the large- and small-scale rhythmicstructure, on the relationship between speed and other parameters such aspitch and timbre, and, most significantly, on the fundamental and intricate rolethat speeds play in his setting of the text.

Speed as Representation: `Sandpiper'

In his 1983 interview with Charles Rosen, Carter acknowledged the centralrole of speeds in `Sandpiper' by describing the structure of the song in terms ofits speeds and their associations with the text: `. . . the sandpiper . . . is seeingthe world in a grain of sand, and the sandpiper is totally oblivious to the wavesand the dangers of the sea. So he is continually moving around, always at thesame speed, while the rest of the song is always changing in speed as the poetconsiders various aspects of the scene'.12 The poem presents the figure of thesandpiper ± fastidious, myopic, obsessed with details ± in contrast to the vastand threatening natural world around him, the ocean and the beach.

The roaring alongside he takes for granted,and that every so often the world is bound to shake.

He runs, he runs to the south, finical, awkward,in a state of controlled panic, a student of Blake.

The beach hisses like fat. On his left, a sheetof interrupting water comes and goesand glazes over his dark and brittle feet.

He runs, he runs straight through it, watching his toes.

Watching, rather, the spaces of sand between them,where (no detail too small) the Atlantic drains

rapidly backwards and downwards.As he runs, he stares at the dragging grains.

The world is a mist. And then the world isminute and vast and clear. The tideis higher or lower. He couldn't tell you which.

His beak is focused; he is preoccupied,

looking for something, something, something.Poor bird, he is obsessed!

The millions of grains are black, white, tan and gray,mixed with quartz grains, rose and amethyst.

The sandpiper is represented musically by the oboe.13 Although he describesthe bird's movement as being `always at the same speed', Carter's musical settingdraws a distinction between the oboe's underlying speed (which is constant) and

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CARTER'S A MIRROR ON WHICH TO DWELL 255

its surface rhythm (which is more varied). Based on the oboe's rhythmicsubdivisions, the underlying speed is fixed at MM 525 (or very close to that)throughout the song, remaining constant across several metric modulations.14 Inother words, after the oboe establishes its speed in the opening bars byarticulating quintuplet semiquavers at a tempo of crotchet=105, its rhythmicsubdivisions change every time there is a metric modulation in order to maintainthe same speed. Ex. 1 shows one such instance. In bar 22 the overall tempo isminim=75 and the oboe's subdivisions are in septuplet semiquavers,articulating a speed of MM 525. When the tempo modulates to crotchet=131,the oboe proceeds with regular semiquavers. Strictly speaking, this articulates aspeed of MM 524 (not 525), but the difference is imperceptible.

In terms of the oboe's surface rhythm, however, Carter's interpretation ofthe idea of speed is influenced by the exigencies of text expression. Althoughthe underlying rhythmic subdivisions are constant, the oboe line incorporatesboth local rests between attacks (as can be seen in Ex. 1) and longer periods ofsilence (which can be seen in Ex. 6 below). The former technique seems to bedesigned to invoke the `awkward' quality of the sandpiper's running motion,whereas, as we shall see later, the longer gaps in the oboe strand usually occurwhen he transforms the overall texture of the song in order to relegate thepresence of the sandpiper (oboe) to the background when another aspect of thepoetic scene is being described.15

3

3 3 3pizz.

3

secco

5 5

3

pizz.3

secco

= 131

(leggeriss.

3

)

7 7 7

= 131

3

= 75

=

22

ver his dark and brit tle feet. He

Sop.

Ob.

Vn

Va

Vcl.

Cb.

nn

7

3

Ex. 1 `Sandpiper', bars 22±3

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256 BRENDA RAVENSCROFT

From this discussion of the oboe part in `Sandpiper', it is apparent thatCarter uses speed as a means of providing continuity, linking different sections.The notation of his setting of the poem implies four sections, with eachsectional break signified by a metric modulation and a change of timesignature. (These musical divisions correspond to the semantic divisions in thepoem, where clear breaks in its semantic content occur at the end of the firstand third stanzas and after the third line of the second stanza, creating the kindof structural counterpoint that characterises Bishop's writing.) However, theoboe's consistent underlying speed and the instrument's prominent anddistinctive timbre conspire to obscure these notated and musical divisions, andto make the song appear through-composed to the listener.

Let us now examine what Carter means when he says that `the rest of thesong is always changing in speed'. While it is true that there are no other fixedspeeds operating on a large-scale level in `Sandpiper', it is also true that therhythms are not in a permanent state of flux. Instead, in order to achieve theeffect of changing speed, local steady speeds establish themselves for briefperiods of time, and then dissolve back into irregular rhythmic activity. Theopening of the song (shown in Ex. 2) presents several such measurable speeds,articulated by the piano and strings. In the piano, intermittent gesturescomprising sextuplet semiquavers articulate a speed of MM 630. Simul-taneously, in the strings, an irregularly accelerating series of attacks in bars 1±2culminates in the brief establishment of the speed MM 157.5 (an attack everysecond triplet quaver), which is initiated by the violin attack at the end of bar 2.A second example of the same speed, out of phase with the first, is articulatedagain in the strings, starting in mid-bar 3.

Although their rhythmic behaviour is quite different in terms of relativeattack density, the gestures in the piano and strings are similar in manyrespects, and both are used by Carter to suggest the ocean as it roars and swirlsover the sandpiper's feet. The characteristic registral and dynamic contours ofthe gestures ± rising then falling ± evoke the waves that ebb and flow alongsidethe bird, while the low tessitura connotes the depth and vastness of the ocean.The contrasting attack densities of the piano and strings invoke images ofwaves swelling and breaking at different rates. In this way, the gesturesembody the quasi-regular rhythmic quality of the ocean.

In the opening of `Sandpiper', the strings combine to articulate a steadyspeed, albeit fleeting. Ex. 3 illustrates another technique used by Carter toachieve the effect of `changing speed', in which one instrument articulates ameasurable speed while the other instruments surround it with irregularrhythms. In this excerpt, sustained notes in the viola present a speed of MM45 (successive attacks are separated by five triplet crotchets), while the piano,cello and bass imitate the sustained events without articulating a regularspeed.

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CARTER'S A MIRROR ON WHICH TO DWELL 257

In his comments about `Sandpiper', Carter mentions that speeds constantlychange `as the poet considers various aspects of the scene'. The composer thusshares the poet's perspective, and their common viewpoint is central to hismusical setting. The opening line of the poem presents the two main aspects onwhich the poet focuses her attention throughout the song: the ocean (`Theroaring alongside') and the sandpiper (`he takes for granted'). The bird is, ofcourse, omnipresent in the form of the prominent oboe line. But, on a more localscale, Carter also uses the voice and strings to portray the bird by articulating

33

3

3

3

8

36

3

MM 630

m6

m6

m6

M9

M9

M9

M9

m6

* n = normal fingering.o = fingering that produces a different

tone-colour than normal fingering.

MM 157.5

(senza sord.)

(senza sord.)

Moderato

Moderato = 105

= 105

Cb.

Vcl.

Va

Vn

Pno

Ob.

Sop.

The

sub.5 5 5 5 5 5

n n nm2 p5

m6

Ex. 2 `Sandpiper', bars 1±4

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258 BRENDA RAVENSCROFT

speeds associated with the sandpiper when the speaker describes him. In theexcerpt shown in Ex. 4 (the setting of `He runs, he runs to the south, finical'), thebird is represented by the speed MM 315 (triplet quavers at a tempo ofcrotchet=105) in the voice and the viola, cello and double bass. Unlike the slow,sustained string events that suggest the ocean, these fast pizzicato staccato stringattacks connote the bird's rapid and sharp movements. Carter is particularlyadroit at transcending timbre in this way: by using contrasting musical properties± rhythm, articulation and pitch ± he creates new `voices' in the same instrument.

33

3 3 3

3

3 3 3

3

6

3

6 3

3 3

roar ing a long side he takes for grant ed, and that ev ’ry so

3 meno

MM 315

5 5( )

5 5 55 55( )

n

333

MM 157.5

* suggested fingering

*

8ve key

E key

hole122

16

3 3

3

3

3

3

3 3

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CARTER'S A MIRROR ON WHICH TO DWELL 259

3 33

3

tranquillo

3 33

3 3

3 3 3 3

3 3

3 3

7 7 7

legato

tranquillo

MM 453legato

tranquillo

3

= 75

3 3

3

7 = 7

7 7 7 7

11

5

=

7

= 75

3

legato

The beach

hiss es like fat. On

Sop.

Ob.

Pno

Cb.

Vcl.

Va

Vn

14

arco

7

Ex. 3 `Sandpiper', bars 11±16

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260 BRENDA RAVENSCROFT

If we look again at the musical setting of the opening line (Ex. 2), we cansee how the appearance of the sandpiper (`he takes for granted') introducesthe speed of MM 315 (triplet quavers) for the first time in the voice, togetherwith the associated staccato articulation. It is also clear that the two speeds ofMM 157.5 in the strings in bars 2±3 are related to this speed, being exactlytwice as slow (an attack every second triplet quaver), and that they fore-shadow the appearance of the bird.16 Soon afterwards, in bar 4, the stringscombine to present MM 315, and the characteristic staccato articulation isintroduced.

Carter's use of speeds to represent the sandpiper in the strings and voice isless strict in its application than it is in the oboe, where the underlying speed(MM 525) is held invariant across all of the modulations in tempo. Instead,speeds in the string and voice change with each metric modulation ± from MM315 and 157.5 (as we saw above), via MM 450 and 225 in bars 11±22(observable in the violin in Ex. 3), to MM 393 and 196.5 in bars 23±39 (see Ex.6 below). Thus, it is not so much literal speeds that serve to establish therepresentation as relative speeds (relatively fast in comparison with the slow

Cb.

pizz.

Vcl.

MM 3153

pizz.3 3

Va

pizz.

Vn

Pno

6

Ob.5 5

5 55 5

5 5

Sop.

7MM 315

He runs,

3

he runs to

3

the

3

south,

meno

fin i cal.

3

3

33 3

Ex. 4 `Sandpiper', bars 7±8

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CARTER'S A MIRROR ON WHICH TO DWELL 261

attack densities of the strings' `ocean music') and the distinctive staccatoarticulation.

Harmonic vocabulary is also associated with speed in `Sandpiper', as it is inall of the songs, and takes the form of featured pitch intervals (see Ex. 2, bars1±2). The oboe (sandpiper), whose underlying speed is fixed at MM 525, has alimited repertoire of intervals that includes minor and major seconds, minorthirds and perfect fifths only.17 The piano and strings, which, as we have seen,articulate various changing speeds in the role of representing the ocean, have amore flexible interval repertoire. They feature minor sixth and major ninthdyads, but are not restricted to those intervals.

Once these two exclusive interval repertoires are established, Carter treatsthem as resources from which other instruments can borrow. Both the voiceand the strings adopt intervals from the oboe (sandpiper) repertoire when theypresent their faster `sandpiper' rhythms. The soprano (the voice of the poetconsidering `various aspects of the scene') also emphasises intervals from thepiano/strings `ocean' repertoire and imitates its lower attack density when thespeaker describes the ocean and natural world surrounding the bird.

Carter's empathy with the poet's point of view ± her ability to see the worldboth from the sandpiper's restricted perspective as well as in terms of thelarger, invariant cycles of nature ± is made particularly clear through his settingof the vocal line, where the soprano's rhythmic behaviour and intervalliccontent are strongly influenced by the image she is currently depicting. In thepassage shown in Ex. 5, when the singer describes the misty, `vast' world andthe indistinct tide (`higher or lower') ± aspects of the scene that are beyond thebird's limited vision ± she imitates the `ocean's' slower attack density (andlegato articulation), and uses intervals from its repertoire, particularly minorsixths. However, when she focuses on the bird's `minute' world briefly in bar44, and when she describes his confusion (`He couldn't tell you which'), sheadopts speeds (MM 315 and 157.5) and intervals (minor and major secondsand minor thirds) from the oboe's (sandpiper's) repertoire, as well as itsstaccato articulation.

= 10540

The

m6

world

m6

is

3

a

m6

mist. And then

3

the world

m6

is

3

M2

mi

3

nute

m6

3

and vast

and clear. The tide is high er or low er. He could n’t tell you which.

3 3 3 3 3 3 3 3 3

=m6 m6 =M2m2

m2m3

Ex. 5 `Sandpiper', bars 40±49 (voice)

ß Blackwell Publishing Ltd. 2003 Music Analysis, 22/iii (2003)

262 BRENDA RAVENSCROFT

These examples have focused on individual aspects of the rhythmic scene,but, as Carter says, usually there are several `different things going on together'in the music. The passage shown in Ex. 6 exemplifies this approach. Here, thespeaker's attention is focused both on the sandpiper and on aspects of thenatural world he interacts with ± the water he `runs straight through' and the`spaces of sand' between his toes. Carter's musical setting reflects the textrhythmically. Speeds associated with both the bird and the ocean are presentsimultaneously, but one or the other comes to the fore and dominates themusical texture depending on the focus in the text.

Initially, in bars 23±5, music associated with the sandpiper predominates:the prominent oboe line moves at MM 524, and the voice and strings present`sandpiper music' by articulating speeds of MM 393 and 196.5, together withtheir associated intervallic and articulation properties. As the focus turns to`the spaces of sand' between his toes (bars 26±8), the bird recedes musically andthe ocean becomes more apparent. While his presence is maintained in thestaccato triplet figures of the voice and strings, the oboe gestures become verybrief and intermittent, and a slowly accumulating `wave' in the piano crests inbar 28. When the speaker directs her attention to the larger natural world (atthe start of the phrase `where . . . the Atlantic drains'), the `ocean music'pervades the texture as the voice and violin (bar 27), and the cello and bass (bar28) adopt the lower attack density and legato articulation associated with theocean.18

As well as using established speeds to represent characters and aspects of thepoem, Carter uses an accelerating speed in `Sandpiper' to connote a process ofintensification. The acceleration takes place in the oboe and functions tosymbolise the re-emergence of the sandpiper as the central figure in the scenefollowing an extended description of the ocean, as well as to depict the bird'sintensifying emotional state as his confusion grows. This passage is shown inEx. 7. Starting in bar 36, successive events (or gestures) are attacked at adecreasing multiple of a fixed metrical unit (the quintuplet semiquaver) untilthe end of bar 49, where the acceleration concludes as the period of peakemotional intensity is approached in the text, ultimately climaxing with thediagnosis, `Poor bird, he is obsessed!'19

The climactic period to which this acceleration leads (shown in Ex. 8)presents a striking instance of how powerful the representative role of speeds isin Carter's music, and how attuned he is to the inflections of Bishop's writing.By this point in `Sandpiper', the speeds that are associated with the sandpiperare well established. As the singer describes the bird's increasingly franticmovements and desperate mental state, the texture is distilled down to voiceand oboe. The oboe continues to articulate an underlying speed of MM 525,while the voice, in bars 51±2, establishes locally steady triplet speeds of MM315 and 157.5, and features oboe-repertoire intervals. The other instruments

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CARTER'S A MIRROR ON WHICH TO DWELL 263

3 3

( )

3

3

33

( )

3

3

3

(3

( )

)

3

(

3

)

3 3 3

3

( )3

Cb.

3

Vcl.

3 3 3pizz.

3

secco

Va

5 5

3

pizz.3

secco

Vn

= 131

MM 393 & MM 196.5

(leggeriss.

3

)

Ob.

7 7 7

Sop.

22

ver his dark and brit tle feet.

=

= 131MM 393 & MM 196.5

3

He

3 3 324

runs, he runs straight through it, watch ing his toes. Watch ing,

MM 524n

n

n

Pno

3

3

Ex. 6 `Sandpiper', bars 22±8

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264 BRENDA RAVENSCROFT

3pizz. 3

pizz. 3 pizz.

26

3

3

33

3 3

3

33333

3 3

arco

( )

)(

( )

26

rath er, the spac es of sand be tween them, where (no

( )

n

31

36

28 24

20 14 16 13 12 11 10 9

8 7 6 5 4 3 4 1

5

5

555

55

5 5 5 5 5 5 5 55

55

5

attacks measured in Distance between 5

=

5

Ex. 7 `Sandpiper', bars 36±49 (oboe)

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CARTER'S A MIRROR ON WHICH TO DWELL 265

are silent. In this way the music, like the text, focuses intently on the bird as hisemotional crisis deepens. However, as the oboe and soprano crescendo to thedramatic climax in bar 53 (`he is obsessed'), Carter, like the poet, detacheshimself from the sandpiper's preoccupation, and stands back to observe thebird's obsession. The soprano (the voice of the poet/composer) abandons the`sandpiper's' triplet rhythms and characteristic intervals, articulating minorsixths from the piano/strings interval repertoire instead.

Although `Sandpiper' arguably presents the most unambiguous example ofCarter's use of speeds to depict poetic personae musically, this practice is afeature of all of the songs in the Mirror cycle. The only exception is theopening song (`Anaphora'), where the metaphorical correspondences are moreabstract, and where the primary function of speeds is to create the rhythmicframework.

Speed as Rhythmic Framework: `Anaphora'

In `Anaphora', Carter uses the constant presence of two steady speeds (orpulses) as the structural backbone over which all surface rhythmic activitytakes place. Both pulses are established in the opening bars, and theycontinue across a metric modulation through to the final bars of the song.The pulses are unrelated to the notated metre(s) or, more accurately, arerelated in unconventional ways. The first pulse (pulse A) comprises an attack

5 5

5 5 5

Ob.

5 5 55 5 5

55

Sop.

MM 315 & 157.5

51

(

oc

p5

)

cu

3

m2

pied,

3(

look

)

p5

3

ing

m2

for

3(

some

m2

)

thing,

3

some

m2

thing,

3

some

m2

thing.

=m2

3

Poor

3

m3

bird,

he is ob sessed!

53m6 =m6

Ex. 8 `Sandpiper', bars 51±3

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266 BRENDA RAVENSCROFT

every twenty-third semiquaver, which at a tempo of crotchet=90 articulatesa speed of MM 15.65.20 A metric modulation in bar 22 establishes a newtempo of crotchet=72, with the former semiquaver now the equivalentduration of the quintuplet semiquaver; the pulse continues with an attackevery twenty-third quintuplet semiquaver, maintaining its speed of MM15.65. The second pulse (pulse B) initially consists of an attack every twenty-two semiquavers, articulating a speed of MM 16.37.21 Following the metricmodulation in bar 22, this pulse is modified slightly to comprise an attackevery thirteen triplet quavers, which articulates a speed of MM 16.62. Thedifference between these two speeds (MM 16.37 and 16.62) is essentiallyinaudible, and they are thus perceived as a single `steady' speed generated bya `constant' pulse.

The two pulses ± A and B (MM 15.65 and MM 16.37/16.62) ± are also verysimilar to each other in terms of metronomic speed. Carter differentiates themclearly, however, through instrumentation and through the way each pulse isarticulated. `Anaphora' is scored for winds (alto flute, oboe and clarinet in B[),strings (violin, viola, cello and double bass), vibraphone and piano. As can beseen in Ex. 9, pulse A (MM 15.65) is articulated by the piano and pulse B (MM16.37/16.62) by the vibraphone. While the winds and strings participate freelyin both pulses during the song, pulse A is never articulated by the vibraphone,nor pulse B by the piano. The association of the two pulses with the piano andvibraphone is particularly consistent at the beginning (bars 1±21) and at theend of the song.

The way in which each pulse is articulated in bars 1±21 is also distinct. Inthese bars, Carter groups events in both instruments into multiple-attackgestures of relatively short duration that proceed intermittently.22 In eachinstrument, a single attack within each gesture is highlighted through dynamicintensity, that attack being the one that articulates the pulse (highlightedattacks are indicated by arrows in Ex. 9). The piano gestures have a decreasingdynamic curve, so that the initiating attack of each gesture articulates the pulse.In contrast, the vibraphone gestures have an increasing dynamic curve, withthe highlighted attack occurring towards the end of the gesture. He abandonsthis gestural format after bar 21, and from bar 22 to the end of the song thepulses are articulated by isolated single notes or chords.

It is evident from the full score that, in addition to the two ongoing pulses,other more transient speeds are also occasionally present; for example, in bars3±4 the violin, viola and cello proceed at a rate of MM 720. These speeds havea different function from the deep structural role of the cross-pulse, and serveinstead to create intermittent surface areas of high attack density that, as weshall see below, often relate to the text.

The relationship between speed and pitch in `Anaphora' is unusual forCarter, because, instead of associating each pulse with a unique aspect of pitch,

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CARTER'S A MIRROR ON WHICH TO DWELL 267

* all tremolos as fast as possible

( )

MM 720

[012478]

*

A MM 15.65

B MM 16.37

[012478]

( )

3

3

5

5

3

3

Each day

3

Although the voice participates in the ensemble, its line with theindicated dynamic shadings must clearly predominate throughout.Instrumental dynamics should be adjusted, wherever necessary,to produce this result.

. = 59–60

Sop.

A. Fl.

Ob.

B Cl.

Vib.

Pno

Vn

Va

Vcl.

Cb.

. = 59–60

Ex. 9 `Anaphora', bars 3±7

ß Blackwell Publishing Ltd. 2003 Music Analysis, 22/iii (2003)

268 BRENDA RAVENSCROFT

( )

pizz. arco

( )

5

[012478][012478]

( )

3

[012478] [012478]

3 3

( )

3 3

( )

( )

with so much cer e mo ny be gins.

5

3

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CARTER'S A MIRROR ON WHICH TO DWELL 269

both pulses are associated with the presentation of the same set-class (thehexachord [012478]) in different transpositions.23 The pitch universe withinwhich the song unfolds is a static one, with each of the twelve pitch-classesfixed in a specific register (within the range of the soprano) for the duration.Because each pitch-class occurs once only in this scheme, the concept of pitch-class, with its inherent qualities of equivalence, could be considered to beirrelevant in the song. However, Carter clearly organises his harmonic materialin terms of `chords' ± his term for the unordered collections theorists prefer tocall set-classes. Set-class [012478] is the `all-trichord' hexachord (ATH);although he frequently articulates the hexachord as two trichords, he neverfully exploits the ATH's unique property by presenting all of its possibletrichordal partitions. Instead, he focuses on a limited number of partitionings,which he distributes so as to reflect the structural design suggested by pulseand instrumentation.

The association of the two speeds with [012478] is especially clear in the firsttwenty bars of `Anaphora', where each pulse gesture in the piano andvibraphone comprises six pitches that form the ATH.24 These sets have beenbracketed and labelled in Ex. 9. (Although the other instruments inevitablydouble the pitches of the piano and vibraphone, there is no clear segmentationinto similar such [012478] hexachords.) Carter emphasises [027]/[037] ATHpartitioning in these bars, as can be seen in the vibraphone's repeatedpresentation of overlapping forms of these set-classes. The association of thetwo pulses with [012478] changes with the metric modulation in bar 22 (shownin Ex. 10a). Now each pulse is articulated by a single trichord in thevibraphone and the piano, and the ATH is completed by other, concurrentinstruments: the woodwind instruments combine with the vibraphone, and thestrings combine with the piano. After bar 22 the instrumental profiles of thetwo pulses become less consistent, and the harmonic focus shifts to [016] andits ATH-complementary trichords.

Towards the end of `Anaphora', there is a return to the clear associationbetween pulse and instrumentation and a restoration of the partitioning focuson the [027]/[037] trichordal pair. From bar 59 (shown in Ex. 10b), the pianoand vibraphone pulse attacks each present one of the two trichords, whichcombine to form the [012478] hexachord.

The two speeds in `Anaphora' function, in a sense, like metre ± theirmeasured, unwavering presence creating the rhythmic framework over whichmore local rhythmic activity is projected. Unlike metre, however, there is nohierarchy of strong and weak beats. In addition, the fact that there are twoconcurrent pulses gives rise to another dimension of temporal relationshipscreated by the interaction of the pulses. Not only does the cross-pulse formedby the two pulses have a cycle ± the length of time it takes for the two pulses toget back in phase (to return to exactly the same position in terms of their

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5 5 to the fore

55

=

=

225

5

Moderato

( = 70–72)

5 5

[012478]

9

5 5

3

3

5

3marc.

3

[012478]

3

marc. 3

3

marc.

3

5have missed?’

522

Moderato

( = 70–72)

Sop.

A. Fl.

Ob.

B Cl.

Vib.

Vn

Va

Vcl.

Cb.

Pno

Ex. 10a `Anaphora', bar 22

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temporal relationship to each other) ± but within that larger cycle the twopulses have regions where they converge and diverge.

Carter does not allow the cross-pulse to complete a full cycle, ending`Anaphora' prematurely about three quarters of the way through. The lengthof the complete cross-pulse cycle (calculated from the relationship between thetwo pulses) is 299 crotchets. The two pulses are in the ratio 65:69,25 making thelength of the complete cross-pulse cycle: 65 x 69 15=299 (in bars 22±65 notevalues). The actual length of the cross-pulse is 224 1/5 crotchets (calculated asthe sum of two sections) following and preceding the metric modulation:

175 + (61 1/2 � 4/5)26=224 1/5 (in bars 22±65 note values)

The actual length of the cross-pulse (224 1/5 ) is therefore about three-quarters of the complete cycle length (299 ), meaning that the cross-pulsecycle is longer than the actual length of the song. The significance of thisrelationship will be discussed below.

Within this extended cycle, there are several areas where the two pulsesconverge on each other and diverge from each other without attaining exactlythe same phase state (this would only be achieved after the completion of thewhole cross-pulse cycle). These regions are charted in a simplified form inFig. 1, together with rhythmic reductions showing the precise relationshipbetween the pulses in those areas. Three areas of convergence ± in bars 23 (theonly occasion that the two pulses are attacked simultaneously), 41 and 60±61 ±alternate with three areas of maximum divergence in bars 7±9, 32±3 and 51±2.Thus, the larger cross-pulse cycle embodies three smaller cycles of divergence/convergence.

The above discussion has made clear the fundamental role that speeds, inthe form of two concurrent pulses, play in organising rhythm in `Anaphora',and has elucidated how these speeds relate to other musical parameters such astimbre and pitch. Let us turn our attention now to the relationship between

5 55

5

33

Vib.

Pno

[012478] [012478]

5

5

Ex. 10b `Anaphora', bars 59±60 (vibraphone and piano)

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speed and text, first by mapping the regions of pulse convergence anddivergence onto the poem. In Fig. 2, convergence is indicated by the symbol! , and divergence is indicated by the symbol !.

The poem describes the progression of a day, from dawn to sunset, in termsof the ebb and flow of energy. Although only one day is described, it is clearlyrepresentative of all days, and, as such, is part of a cycle that will recur in`endless' repetition.27 The high energy of the early-morning scene ± depictedaurally (`birds', `bells' and `whistles' that generate `the music') and visually(`white-gold skies' and `brilliant walls') ± undergoes a transformation as soon asthe `ineffable creature' appears, and starts to decline. Although this creature(the personified sun, whose energy dissipates from dawn to dusk) is nothuman, he assumes human qualities (`memory' and `mortal fatigue'); and beingsubject to human frailties, he loses his transcendent quality and starts todegenerate.

As the decline of energy continues in the second stanza, the ineffable creaturebecomes visible (`falling into sight') and starts to interact with humanity,culminating with his subjection to our `uses and abuses'. The creature'sdownward trajectory then takes him through `the drift of bodies' and of `classes'until he reaches his nadir at `evening'. Here, in the identical position as he

Vib.Pno

23 41

5

360

5

3

5

3

convergence

divergence

total

1 5 10 15 20 25 30 35

bar

40 45 50 55 60 65

Vib.Pno

73

32

3 5 5

351

Fig. 1 `Anaphora': regions of convergence and divergence of the piano andvibraphone pulses

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initially appeared in the first stanza (line 9), the Apollonian figure assumes amortal form as the `beggar in the park', whose appearance heralds the reversal ofthe declining energy. Although the figure of the `beggar' suggests the lowest,most impoverished form of humankind, whose `studies' must be performedwithout the aid of light or books, the `beggar' also represents the artist (poet/composer), who, out of the detritus of society, constructs the work of art thatenergises all human endeavour (as the sun does).28 In the closing quatrain theenergy being described in the poem starts to increase again, as Bishop describeshow the beggar's `stupendous studies' recreate the energy of the dawn (`the fieryevent'). The final quatrain of the poem anticipates the regeneration of the sun andthe repetition of the cycle, and draws the reader back to beginning of the poem,where the high-energy event was first described.

Each day with so much ceremonybegins, with birds, with bells,

with whistles from a factory;such white-gold skies our eyesfirst open on, such brilliant wallsthat for a moment we wonder‘Where is the music coming from, the energy?The day was meant for what ineffable creaturewe must have missed?’ Oh promptly he

appears and takes his earthly natureinstantly, instantly fallsvictim of long intrigue,assuming memory and mortalmortal fatigue.

More slowly falling into sightand showering into stippled facesdarkening, condensing all his light;in spite of all the dreamingsquandered upon him with that look,suffers our uses and abuses, sinks through the drift of bodiessinks through the drift of classesto evening to the beggar in the parkwho, weary without lamp or book

prepares stupendous studies:the fiery eventof every day in endlessendless assent.

divergence

divergence

divergence

convergence

convergence

convergence

Fig. 2 `Anaphora': regions of pulse convergence and divergence mapped ontothe poem

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Mapping the regions of pulse convergence and divergence onto the poemreveals the relationship between the cross-pulse and the text. Carter ensures thatthe rate at which the poem unfolds against the clock-time of the pulses results inthe coincidence of areas of convergence and divergence with importantmoments inthe text, particularly those that signal a change in the energy that is beingdescribed. The most significant of these moments are associated with theApollonian figure. In the first stanza the introduction of the `ineffable creature'(`Oh promptly he appears') signals a decline in the high, pre-dawn energy of theopening, and is immediately preceded by the point of maximum convergencebetween the pulses in bar 23. Similarly, the figure's transformation into the `beggarin the park' in the second stanza signifies a reversal in the fall of energy in the poem,and coincides with the region of divergence in bars 51±2.

Two other important moments in the poem are similarly highlighted. In thesecond stanza the culmination of the sun's energy-draining interaction withhumans occurs with the phrase `uses and abuses', and coincides with theconvergence of bar 41. The third and final convergence of pulses in `Anaphora'occurs in bars 60±61 with the words `the fiery event', emphasising the creationof the beggar/artist that foreshadows the renewal of energy and the repetitionof the cycle.29

The large-scale cross-pulse cycle is also associated with the text, in that theincomplete cross-pulse cycle corresponds to the incomplete cycle described inthe poem. As was discussed earlier, the actual length of the cross-pulse in`Anaphora' is about three quarters of the length of the complete cycle.Furthermore, Fig. 1 shows that three cycles of pulse divergence/convergenceoccur in the duration of the song without the two pulses getting back in phase.For the phase state to be achieved, a fourth such cycle must be extrapolated,reinforcing the ratio of 3/4 (present) to 1/4 (absent). The presentation of threequarters of the complete cycle can be seen as a metaphor for the cycle describedin the poem, where only about three quarters of the 24-hour day is depicted ±pre-dawn through to evening ± with the inactive night being the silent quarterthat completes the solar cycle.

The voice in `Anaphora', which has thus far been excluded from thediscussion except as a means of conveying the words, does not participate inthe presentation of the two speeds except for on one notable occasion. In bars57±8, on the word `stupendous [studies]', the voice articulates the two pulseattacks for the first and only time in the song, the anomalous instrumentationof the established speeds thus serving to emphasise the text. Moreover, thesefortissimo events cover the widest possible registral range, articulating thehighest pitch (B[2) and the lowest pitch (b) of the pitch/register repertoire ofthe song. Although all of these factors conspire dramatically to highlight thesuperlative quality of the beggar/artist's activities, the effect is curiouslyhollow. The exaggerated way in which Carter stresses the word `stupendous' (a

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rather overwrought adjective) suggests that the composer is responding to thepoet's ironic view of the artist's endeavours: the unlikelihood that the self-absorbed, esoteric activities of an artist could possibly influence the globalforces of nature by reversing the fall of the sun!

The overall cyclical design of the poem is paralleled in the music by thestructural curve articulated by Carter's association of pulse, instrumentationand trichordal partitioning described earlier. The vibrant energy described inthe opening of the poem coincides with the pulses being clearly articulated bypiano and vibraphone, each of which presents the ATH, with the vibraphonedistinguishing the [027]/[037] pair. As the energy described in the poem wanes,the established relationship between pulse, instrumentation and ATHpartitioning weakens and dissolves. Then, at the end of the song, the recreationof energy in the poem corresponds to the re-establishment of distinct piano andvibraphone pulses, each of which presents one of the original trichords.

One final function of speed in `Anaphora' remains to be discussed ± Carter'suse of speeds, often in the generalised form of attack density, to portray aspectsof the text in a more literal fashion.30 Most commonly, as we saw in theopening bars of the song (Ex. 9), relatively high attack densities depict the highenergy described in the text. Although local speeds can be discerned (such asMM 450 in the alto flute, clarinet and violin in bar 1, and again in the oboe,viola and cello in bar 2), they are masked by other concurrent speeds that alsocontribute to the overall high attack density.

Not only does Carter set the parts of the poem that describe more subduedenergy levels to correspondingly lower attack densities, but in two cases he usesritarding speeds to connote a process of slowing down, so symbolising thegradual loss of energy. Ex. 11a shows the opening bars of a rhythmicdeceleration in the oboe, and Ex. 11b shows the voice undergoing a rhythmicretardation as the time-spans between the attack points of successive words (orsyllables) become increasingly longer.

3

26

3 3 4 4 6 7 12 12 13 14

302523191715

3 3

33

attacks measured inDistance between

3

Ex. 11a `Anaphora', bars 22±30 (oboe)

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These decelerations are closely linked with the process of energy depletionthat is described in the poem. The oboe series starts as the sun appears (`takeshis earthly nature') ± the step that precipitates the reversal in the poem's highenergy levels ± and the distance between successive attacks continues tolengthen as the poem depicts the interactions that gradually exhaust the sun'spotential. The decelerating rhythmic processes in both oboe and voiceconclude just before these interactions culminate with the dramatic phrase`suffers our uses and abuses'. The moment of arrival is reinforced both by theculmination of the ritardations, and by the pulse convergence in bar 41.

Concluding Remarks

When Charles Rosen suggested to Carter that, in his music, `the emotionalcharacter comes from the combination of different kinds of tempo, differentkinds of time', his response was simply to affirm, `Yes, I think it does'.31 Buthis use of temporal devices goes still further in his vocal music. In addition toliteral `characters' in the poems being suggested by individual speeds, and theirinteraction connoted by the conjunction of those speeds, the combination ofdifferent speeds also provides deeper, more metaphorical connections to thetext. A brief summary of salient points from the analyses of `Anaphora' and`Sandpiper' reveals the gamut of ways in which he relates speeds to the text.

In `Sandpiper', specific speeds signify characters in the poem by connotingtheir motion. A constant, fast underlying speed in the oboe represents thesandpiper's continuous running, with the exception of one passage in which anaccelerating speed is used to portray his intensifying emotional state. `Changingspeeds' (in the form of recurring local steady speeds in the strings, piano andvoice) represent the different aspects on which the speaker focuses (the bird andthe ocean) and the varied combinations of all these speeds portray the interactionsbetween the bird and the ocean described in the poem. In `Anaphora',connections between speeds and the text are more abstract. Regions where twolong-range pulses converge and diverge coincide with important moments in thepoem (where transformations occur in the energy levels being described), and theincomplete cross-pulse cycle is a metaphor for the unfinished solar cycle of the

339

(-dered) up on him with that look, suf

Distance betweenattacks measured in

33

6 (+ 2 )

3 3 33

54321

Ex. 11b `Anaphora', bars 38±41 (voice)

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poem. A decelerating speed suggests a process of slowing down that depicts theenergy loss described in the poem, and general attack densities ± high or low ±connote corresponding energy levels in the text.

Not only do speeds play a crucial role in projecting Carter's interpretation ofthe poems in A Mirror on Which to Dwell, but they also shape large-scalerhythmic form and control small-scale rhythmic activity. In `Anaphora', thetwo slow-moving pulses form a trajectory over the song's duration, creating itsrhythmic framework. In `Sandpiper', local steady speeds, repeatedlyestablished for brief periods, interact with a continuous fixed speed as wellas with other concurrent irregular rhythmic activity.32

Moreover, speeds do not operate in isolation, but are closely related to othermusical parameters such as pitch, timbre and articulation. Bernard'ssuggestion that Carter's method of integrating rhythmic innovation with pitchstructure `is hardly formulaic' is amply borne out in the two songs examinedhere, where speeds are associated with set-classes in `Anaphora' and with pitchintervals in `Sandpiper'.33 Nor is the relationship between speed and timbreand articulation prescribed. Although individual speeds are associated withspecific instruments for most of `Anaphora' (piano and vibraphone), thesespeeds are also articulated by other instruments in the ensemble. In`Sandpiper', other than the oboe, the connection between speeds andinstruments is even more variable. Both the strings and the voice presentdifferent speeds at various times in the song, each of these speeds beingassociated with specific intervallic repertoires and methods of articulation.

The predominant quality that strikes one when examining Carter's rhythmicorganisation, as exemplified by his use of speeds in these songs, is its flexibility.It is hard to think of a contemporary composer whose system of rhythmicdesign is as nuanced, as varied in its applications, and as adept at bothgenerating local activity and creating long-range motion. Carter focuses on therole of rhythm when he characterises his compositional goals in the followingstatement: `I'm constantly concerned with discovering new types of movement:changing from one speed to another, progressing from one kind of harmony toanother. It seems to me that that's what music is all about.'34

NOTES

I am grateful to Jonathan Bernard for his advice on an earlier draft of thispaper. Excerpts from Carter's A Mirror on Which to Dwell copyright ßAssociated Music Publishers, Inc. (BMI). All rights reserved. Used bypermission of G. Schirmer Ltd. 8/9 Frith Street, London W1D 3JB. Thepoems of Elizabeth Bishop are used by permission of the Random HouseGroup Ltd.

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1. Allen Edwards, Flawed Words and Stubborn Sounds: a Conversation with ElliottCarter (New York: Norton, 1971), p. 90.

2. `The Time Dimension in Music' (1965), in Jonathan W. Bernard (ed.), ElliottCarter: Collected Essays and Lectures, 1937±1995 (Rochester, NY: University ofRochester Press, 1997), pp. 224±5. Carter's development of new rhythmictechniques was in part a reaction to the treatment of rhythm by his immediatepredecessors and contemporaries, Ives, Cowell and Nancarrow, whose innovationsinspired but did not satisfy him. He discusses their contributions in his 1955 article,`The Rhythmic Basis of American Music' (Collected Essays, pp. 57±62).

3. Jonathan W. Bernard, `The Evolution of Elliott Carter's Rhythmic Practice',Perspectives of New Music, 26/ii (1988), pp. 164±203. A more recent, but far lesscomprehensive study of rhythm in Carter's music is presented in Yayoi Uno,`The Tempo-Span GIS as a Measure of Continuity in Elliott Carter's EightPieces for Four Timpani', InteÂgral, 10 (1996), pp. 53±91. Using David Lewin'stheory of generalised interval systems as a model, she proposes a systematicmethod for understanding Carter's metric modulations, but restricts her analysisto music with very limited texture (namely two of the Eight Pieces).

4. Elliott Carter, `The Orchestral Composer's Point of View' (1970), in Bernard(ed.), Collected Essays, pp. 235±50.

5. The Double Concerto exemplifies this compositional practice: Carter's chart ofspeeds also indicates the pitch interval (and instrument) associated with eachspeed.

6. Edwards, Flawed Words, p. 106.

7. Although his last vocal work prior to the Mirror cycle was the song Emblems(composed in 1947), Carter's lifelong interest in poetry is well known, and severalof his larger instrumental works were inspired by literature. For example, thelarge-scale plan of his Double Concerto is modelled on the dramatic plan of Dererum naturae (Concerning the Nature of Things) by Lucretius and on Pope'sDunciad, and many aspects of his Concerto for Orchestra were suggested to himby the prose poem Vents by Saint-John Perse.

8. David Kalstone puts it succinctly in his book Becoming a Poet: Elizabeth Bishopwith Marianne Moore and Robert Lowell (London: Hogarth Press, 1989), when hewrites that `in Bishop's work, time provides the plot' (p. 94).

9. Thomas J. Travisano, Elizabeth Bishop: Her Artistic Development (Charlottesville:University Press of Virginia, 1988), p. 70.

10. Liner notes for A Mirror on Which to Dwell (Columbia Masterworks M35171,1980).

11. Edwards, Flawed Words, p. 101.

12. Charles Rosen, The Musical Languages of Elliott Carter (Washington, DC:Library of Congress, 1984), p. 41.

13. David Schiff, in The Music of Elliott Carter, 2nd edn (Ithaca, NY: CornellUniversity Press, 1998), points out that Carter studied the oboe while at Harvard

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University, and suggests that the oboe `parodistically represents the composerfanatically choosing and placing notes, trying to impose order on a chaotic world'(p. 175). The sandpiper (`a student of Blake') also represents the poet, an analogyreinforced by Bishop's likening herself to her bird in her acceptance speech forthe 1976 Books Abroad/Neustadt International Prize for Literature. VictoriaHarrison, in Elizabeth Bishop's Poetics of Intimacy (Cambridge: CambridgeUniversity Press, 1993), discusses at some length the ways in which Bishop'sbehaviour and attitudes were similar to that of the bird in the poem (pp. 40±41);whereas Susan McCabe describes `Sandpiper', in Elizabeth Bishop: Her Poetics ofLoss (University Park, PA: Pennsylvania State University Press, 1994), as `a kindof self-portrait', comparing the `absolute indeterminacy' of the bird's world(looking for `something, something, something') to Bishop's thwarted desire tofind a home, both geographical and psychological (pp. 219±20).

14. Although, as Bernard has pointed out, the term `metric modulation' is actually amisnomer (as the objective of the transformation is a modulation of tempo), I willuse the term here because it has established itself as the term of choice intheoretical literature.

15. On one occasion the gaps in the oboe line are a result of a systematic acceleration,used to depict a process of intensification portrayed in the poem (see Ex. 7).

16. Bernard explains how speeds are related by being multiples of each other (`ElliottCarter's Rhythmic Practice', p. 174).

17. Although the context is atonal, it is more appropriate to use traditional terms todescribe these intervals than to identify them using integers (intervals 1, 2, 3 and7). Carter himself uses the traditional terms, and in the score he almost alwaysnotates them as such.

18. Beginning at bar 29, the prominence of the ocean is further reinforced by `oceanmusic' events in the piano and strings being marked on the score with the playinginstruction `bring out (solo)'.

19. As the metric modulation at the end of bar 39 specifies that the forthcomingquintuplet semiquaver is of equal duration to the preceding semiquaver, thetime-spans between attacks are multiples of both quadruple semiquavers andquintuplet semiquavers. In Ex. 7, for simplicity, all the time-spans are specifiedas multiples of the quintuplet semiquaver.

20. The tempo indication for bars 1±21 is crotchet=88±90; I have chosen, forconvenience of calculation, to limit this range to the specific tempo ofcrotchet=90. Similarly, the tempo indication at bar 22 is crotchet=70±72,which I have fixed at crotchet=72.

21. Occasionally, instead of an attack every twenty-two semiquavers, Carter uses adurationally similar combination of semiquavers and triplet semiquavers ± forexample, twenty semiquavers plus two triplet semiquavers, or twenty-onesemiquavers plus one triplet semiquaver. Judging from similar such anomaliesin the other songs, he appears to be more concerned with the perception ofregularity than with unwavering accuracy.

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22. Gestural unity is supported by the use of the sustaining pedal during thesounding period in all of the vibraphone gestures and in some of the piano ones(e.g. in bars 6±7).

23. The pitch structure of `Anaphora' has been discussed in detail in Craig Weston'sunpublished paper, `Text and Conceptual Modelling in ``Anaphora'' from ElliottCarter's A Mirror on Which to Dwell' (presented at the annual conference of theSociety for Music Theory, Austin, TX, 1989) and in his `Inversion, Subversionand Metaphor: Music and Text in Elliott Carter's A Mirror on Which to Dwell'(DMA diss., University of Washington, 1992), Ch. 3.

24. On the other hand, Carter's interest in interval, as opposed to interval-class, ismanifested in the frequent articulation of the pitches within each gesture asperfect fifth dyads.

25. The ratio is calculated by expressing the duration of each pulse in terms of acommon denominator. In other words, the piano pulse of 23 5 is expressed as 69

15 and the vibraphone pulse of 13 3 is expressed as 65 15, yielding a cross-pulseratio of 65:69.

26. 4/5 is the ratio between the durational units governing the metric modulation,where the semiquaver `becomes' the quintuplet semiquaver.

27. The theme of repetition pervades the poem, constantly making explicit the title(which refers to the repetition of a word or a phrase in successive clauses).Anaphora occurs, for example, in the phrases `instantly, instantly falls' and`mortal/mortal fatigue' in the first stanza, and in the repetition of almost theentire line in the second stanza (`sinks through the drift of . . .').

Musically, the theme of repetition underlies the pitch/pc structure in terms ofthe fixed pitch repertoire, and the repetition of hexachord [012478] in differenttranspositions. Furthermore, repeated intervals are associated with repeatedwords in the poem, and with words that rhyme. For example, the word `sinks',which is repeated at the beginning of two lines, is highlighted through being setmelismatically as a falling minor second in both cases, and the words `intrigue'and `fatigue' are both articulated by falling minor thirds.

28. Schiff also identifies the beggar as a symbol for the poet. However, for Schiff, thebeggar's reversal of the fall of energy `suggests the poet's willed, even deceptive,inversion of reality' (Music of Elliott Carter, p. 171).

29. Metaphorical connections can also be made between the text and other salientregions of pulse interaction. The repeating cycle of divergence/convergence(which was made explicit in Fig. 1) begins in bars 7±9 when maximum divergenceoccurs for the first time with the words `begins, with birds', just as the ritualistic,repetitive activities of the day begin. However, this cycle is only really establishedas such once the second region of divergence occurs in bars 32±3; like the sun,which is `falling into sight', the divergence/convergence cycle `falls into' being.This is also the point at which, possibly, the cycle enters the listener's awareness.

It is difficult to predict how perceptible these relationships in fact are to the listener.What is clear, however, is that the convergence of the two pulses often emergesperceptually out of a texture in which the cross-pulse is masked by surface activity.

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This phenomenon is consistent with statements that Carter has made about the roleof cross-pulses in his music. Although they are frequently present, he does notbelieve that the cross-pulses need to be perceptible all of the time. In his words, `asthese beats begin to converge toward a unison, you begin to become aware of theirpattern and to grasp the emerging rhythmic convergences' (Edwards, FlawedWords, p. 114). In this way, a cross-pulse can fade in and out of `perceptible order'.

30. Attack density is the number of attacks in a fixed, relatively short temporal unit.Although it can be described numerically, it is more useful to describe it inrelative terms as high or low.

31. Rosen, Musical Languages, p. 43.

32. Speeds play similar roles in other songs from the Mirror cycle. The contributionof two long-range pulses to the large-scale rhythmic structure of `Insomnia' isexamined in Brenda Ravenscroft, `The Moon and the Insomniac: MusicalPersonae in Elliott Carter's `̀ Insomnia''', South African Journal of Musicology,19/20 (1999/2000), pp. 57±70. In `O Breath', three continuous pulses interactwith each other to shape the song's overall form, as discussed in Ravenscroft,`The Anatomy of a Song: Text and Texture in Elliott Carter's `̀ O Breath''', ExTempore, 9/i (1998), pp. 84±102.

In the two songs that complete the cycle (`Argument' and `View of theCapitol'), rhythmic continuity and contrast are achieved through the recurrenceof intermittent local speeds presented in various components of the texture. AnneShreffler, in ```Give the Music Room'': Elliott Carters ``View of the Capitol fromthe Library of Congress'' aus A Mirror on Which to Dwell' (in Felix Meyer (ed.),Quellenstudien II: ZwoÈ lf Komponisten des 20 Jahrhunderts (Basle: Amadeus,1993), pp. 255±83), examines Carter's sketches for `View of the Capitol' todemonstrate how he assigns three recurring speeds to signify aspects of hisinterpretation of the poem.

33. Bernard, `Elliott Carter's Rhythmic Practice', p. 198.

34. Jonathan W. Bernard, `An Interview with Elliott Carter', Perspectives of NewMusic, 28/ii (1990), p. 197.

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