Some Elements of Structure in Elliott Carter's "Insomnia" from a mirror on which to dwell (1)


Johanna Devaney


Elliott Carter's song cycle "A Mirror on Which to Dwell" sets the text of six poems by Elizabeth Bishop. Completed in 1975, A Mirror on Which to Dwell was followed by Carter's settings of the poetry of John Ashbery in 1978 and Robert Lowell in 1981. All three cycles share what Lloyd Schwartz describes as Carter's unique approach to text setting. Partially rooted in the vocal style of Bach's cantatas, Carter employs a style that is neither recitative nor speech, but rather lies somewhere in between. In his liner notes for Elliott Carter: The Vocal Works (1975-1981), Lloyd Schwartz comments that "Carter turns poetry - the poets' speech - into music; the singer has to make the music talk." (2) Carter's songs achieve this through the use of rhythmic patterns and accents whose sole purpose are to facilitate a reading of the poem. The primacy of the reading of the poem in the vocal line is emphasized by the syllabic style; few syllables are articulated with more than one note. Thus, in addition to the meaning of the text, the listener is left with a strong sense of the overall structure and balance of the original poem.

"Insomnia" is the fourth song of the cycle, and the poem from which the name of the cycle, A Mirror on Which to Dwell, is taken. The poem is organized into three verses, an organization which clearly underlies Carter's structuring of the piece. The first verse, dealing directly with the theme of insomnia, considers the moon's dual role as both a reflection of the insomniac - as seen through the bureau's mirror - and as an entity that is enviable to the insomniac as it is able to compensate for its nighttime sleeplessness with daytime slumber. The second verse takes up the theme of inversion and relates it to the reflected properties of water, expressed with the phrase "a mirror on which to dwell" which is particularly emphasized through the use of staccato and tenutos. Water has a dual role, not only being a means of reflection but also (as in the "well") as a disposal for her cares. Thus it is implied that there is some issue that the insomniac must confront and resolve before sleep may return. This issue is identified in the third, and final, verse which describes the inverted world within the water/mirror as a reversed, unnatural one, allowing an ironic admission of rejection by a former lover.

The moon in the bureau mirror

looks out a million miles

(and perhaps with pride, at herself,

but she never, never smiles)

far and away beyond sleep, or

perhaps she's a daytime sleeper.

By the Universe deserted,

she'd tell it to go to hell,

and she'd find a body of water,

or a mirror on which to dwell.

So wrap up care in a cobweb

and drop it down the well

Into that world inverted

where left is always right,

where the shadows are really the body,

where we stay awake all night,

where the heavens are shallow as the sea

is now deep, and you love me.


Figure 1: "insomnia" by Elizabeth Bishop (3)

"Insomnia" is scored for soprano, piccolo, marimba, violin, and viola. The preeminance of the vocal line is secured by the moderate pacing of rhythmic patterns which express the only developed melodic material in the piece. A slow moving polyrhythm provides a structural background for the poem's text, articulated for the most part by the piccolo and violin, but shifting to the violin and viola for a short while and the marimba and viola supply fast moving melodic commentary and harmonic fixations that further decorate and "harmonize" the vocal line.

David Schiff has argued that the interplay of "the high slow-moving lines of the piccolo and violin [with] the nervous rattle of the marimba and viola, [reflects] the poem's contrast of an insomniac with the reflected moon" (4).This evokes a lineage of moonlight-related works by Crumb, Schoenberg, Debussy, and Beethoven. The use of sustained high pitches to represent the moon was employed by Crumb in the piccolo and electric 'cello in the third part of his Night of the Four Moons; by Schoenberg in the violin parts of numerous sections of his setting of Pierrot Lunaire; and in different ways by Debussy where throughout much of Clair de Lune the high slow moving melody rises above arpeggiated chords, calling to mind the opening movement of Beethoven's "Moonlight Sonata". In Carter's "Insomnia" as in Crumb, and Schoenberg the effect is subtler than in Debussy and Beethoven and is really only emphasized in the opening bars. With the introduction of the vocal line Carter shifts the listener's attention to the declamation of the text to which the sustained notes provide an underlying framework, in contrast to the Debussy and Beethoven where the sustained notes perform a melodic function over a wash of arpeggios. In Carter's own oeuvre his 1980 work for solo piano Night Fantasies provides an interesting parallel; it contains slow sections that also employ sustained high pitches which are in turn emphasized by the extensive use of pedalling. The sustained high pitches serve a dual purpose in "Insomnia" however, as, in addition to their representation of moonlight, they also outline the large-scale polyrhythm.


Large-scale polyrhythm

Carter has long made use of large-scale polyrhythms. (5) These are generally articulated by accented and/or sustained notes and are intended to provide a slow moving rhythmic pattern independent of any small scale meter - a rhythmic pattern that is available to the listener but which does not command their constant attention. The existence of such a substructure is advantageous as aspects of the composition, such as the primacy of certain pitch classes or the features of the rhythmic structure itself, can be defined subtly and fluidly through the polyrhythm.

The polyrhythm in "Insomnia" is presented discontinuously in the piccolo and violin in mm. 2 - 7, 8 - 14, and temporarily in the violin and viola in bars 19 - 24 before returning to the piccolo and violin in mm. 25 - 33: it is absent in mm. 1, 8, and 15 - 18. The presence of these lines is subdued as they are generally played at pp or ppp; one only becomes fully aware of the rhythmic relevance of this very subtle texture when it returns in measure nine after its one and a half bar hiatus.

The polyrhythm is determined by the ratio of seventeen quintuplet sixteenths to fourteen sextuplet sixteenths or a pulse duration ratio of eighty-five to eighty-four. At the prescribed tempo, of q  = 54 the real-time ratio of the polyrhythm is 3.14 seconds to 3.11 seconds, approximately MM 19.3 and MM 19.1. Although the total time needed to complete one cycle of the polyrhythm is 285.6 seconds (4 minutes and 45.6 seconds), the total running time of the piece is 2 minutes and 22.2 seconds, less than half the time needed. Thus the cycle's delayed entrance and its multiple interruptions further reduce the available time for it to unfold and there are only thirty-two articulations of the sextuplet rhythm and thirty-five articulations of the quintuplet rhythm, far less than half a full cycle. It becomes clear however through further analysis, that Carter's use of the polyrhythm, both in it's presence and it's absence, serves to emphasize the verse and thematic structure of the poem. The polyrhythm of "Insomnia" is abstracted in its pitch and rhythmic content in Figure 2.


Figure 2: Large-Scale Polyrhythm of "Insomnia".

Note: polyrhythm is absent in mm. 15 - 18 and stars indicate pitch classes in referential hexachord (F#. G# G#. A#. B. C).


Pitch content

Carter's approach to pitch material is characterized by variety more so than by obvious patterns. Thus David Schiff's brief remark, in The Music of Elliott Carter, that one particular hexachord plays a generating role in the whole song, offers a useful analytical hook for approaching the pitch material in the piece. Carter uses the hexachord identified by Schiff (F#, G, G#, B flat , B, C) , for setting the first two lines of poem in the soprano in bars four through six:


Example 1: "Insomnia" Vocal line, mm. 4-6.

I have developed this hint into a systemized analysis of the role of the hexachord as an untransposed collection of pitch classes. In addition to its role in the coherence of the vocal line, the hexachord provides a second unifying factor of the piece, as the frequent occurrences of elements of the hexachord in the instrumental parts connect with the vocal line.

Addressing the hexachord for a moment as a set of fixed pitches, rather than as a hexachord type, the following dyads and trichords can be isolated:

m2 (4) F#-G, G-G#, B-B, B-C

M2 (3) F#-G#, G#-B, B-C

m3 (2) B-B G#-B

M3 (2) F#-A#, A-C

P4 (2) F#-B, G-C

X4 (1) F#-C


(0,1,2) (2) F#-G-G#, A#-B-C

(1,2,3) (2) G-G#-B, G#-A#,B

(0,1,4) (4) F#-G-B, G-G#-B, G-A#-B, G#-B-C

(0,1,5) (4) F#-G-B, G-G#-C, F#-A#-B, G-B-C

(0,1,6) (2) F#-G-C, F#-B-C

 For the purposes of this analysis I have adopted the following terminology of "included" dyands or trichords for sets of pitch classes which are wholly within the source set, "overlapping" for sets which consist of pitch classes both within and outside of the source set, and "excluded" for sets which consist of wholly of pitch classes outside of the source set.

As mentioned, the pitch material of the marimba and viola parts provides support for the vocal line and the polyrhythmic framework. It is interesting to note the absence of any direct tritones in either the voice or marimba/viola lines. Tritones however are common in the polyrhythm. While (0,1,6) trichords occur in the viola/marimba figures, the (0,1,6) is the only trichord which is completely absent from the vocal line.


Sectional Analysis

The piece can be effectively analyzed in three sections, each corresponding to a single verse. These sections are characterized, not only, by the overall activity of the polyrhythm and use of harmonic source pitch classes, but also by the rhythmic and harmonic activity of the marimba and viola, and the articulatory character of dynamics and accents in all of the instrument parts. These characteristics are demonstrated in the following analyses of each section.

Section One (mm. 1 - 15)

The first verse of poem is set in mm. 4 - 15, the end of the verse being the terminal point for the first section. This first section divides into two subsections: the first in mm. 1-9, and the second in mm. 9-15. These are characterized by the articulation of the polyrhythm by the piccolo and violin, the dominant intervals in the marimba and viola, and the general rhythmic character and function of the viola.

The first subsection sets the first four lines of the text (see Example 2); as discussed above, the first two lines are expressed entirely with the harmonic source pitch classes (see Example 4). The last two lines outline the perfect fourth between D and G, using all the chromatic pitches in between. The polyrhythm is present in mm. 2 - 7; its silence in mm. 7,8, and 9 corresponds with the parenthesis in the poem.

The harmonic source pitch classes B, C, G, and F# are introduced in the instrumental parts prior to the introduction of the vocal line. They occur in conjunction with a various emphases on E, producing a number of "included" and "overlapping" dyads and trichords. E, in fact, is aurally prevalent in this section both by being the first pitch class of the piece and through it's insistence in the figuration. The intervals of the perfect fourth and perfect fifth (in particular E-B and B-E) similarly pervade this opening subsection with the E seeming to serve as a preparation for the sustained B naturals in the vocal line in m. 6, (see Example 1).


Example 1: Marimba and Viola at Opening

Perfect fourths and fifths occur elsewhere in the marimba/viola (G-C in mm. 2-3), the viola (B-E in m. 6), the marimba (A-D in m. 7), and the viola (D#-G# in m. 8). In these fourths, only harmonic source pitch classes F# and B are not represented, and all of the fourths except for one (A/D) contain at least one of the six source pitch classes. It is interesting to note that the articulation of the A/D perfect fourth in bar seven occurs only once, on a weak beat and in the middle of the sequence D-B-D-B-A-D-A-B (see Example 3).

Example 3: Marimba at m. 7


Example 2: "Insomnia" Vocal Line mm. 4 - 13

During this sequence B is repeated twelve times immediately following the occurrence of the D/A perfect fourth. Prior to this D and A, the pitch classes seem to function as a path to move from the high B. Thus it appears that this, the one fourth that doesn't use any of the source pitch classes, is not only the least emphasized of the five fourths in terms of rhythmic placement but that its primary directed toward the B natural.

The section is very quiet - all dynamic markings in the instrumental parts are either pp or ppp. The only accents or tenutos in the instrumental parts occur in the marimba, but all are in fast moving figures where they have little impact on the overall hushed impression.

The second subsection of this first section sets the last two lines of the verse (see Example 3). The harmonic source once more dominates the vocal line, each pitch class is used at least once. The polyrhythm, which had ceased for the previous two lines, re-emerges with its series still intact; merely offset by the seven quarter-note rests in both parts. The harmonic source pitch classes occur primarily in identifiable vertical dyads and trichords in mm. 10 - 13. This is in marked contrast to the first subsection where the occurrences were primarily horizontal dyads and trichords. The general character of the viola in this second subsection is also different from the first. In contrast with the fast moving figures of the earlier subsection, here the viola plays sustained double stops offsetting and interacting with the polyrhythm, thus isolating the activity in the marimba.

Another point of contrast with the first subsection is that there is no longer the same prevalence of a single interval in the viola and marimba parts in this section. Also, neither the perfect fourth nor any other perfect intervals occur. Instead, the subsection is dominated by major seconds, major and minor thirds, and major sevenths - all of which include at least one of the harmonic source pitch classes. A significant dynamic development is seen in the marimba with the viola as its figures gradually increase in activity and intensity, from faint pp iterations in the mm. 3- 9 (becoming silent in the second last line of the verse) to the surging dynamic contours of the close of the section.


Example 4: Marimba in Bar 15

Section Two (mm. 16 - 22)

The first line of the second stanza is a short vocal solo, where the harmonic source pitch classes B, B, and F# are used with the B emphasized by its duration. Its first occurrence is the opening note of the solo, where it is the longest note of the solo, and both occurrences of B are accented, the second in connection with accented D- naturals of a clearly exposed M3rd. The duration values in the vocal line in this section range from triplet sixteenths to dotted-quarters (the broadest range in the piece). Though there doesn't seem to be any correlation between the use of harmonic source pitch classes and their length there is a traceable pattern, at least from the perspective of the trichords, where consecutive harmonic source pitch classes are grouped by similar durational values.


Example 5: "Insomnia" mm. 16 - 17

The marimba and viola join the vocal line in the second stanza and they remain together however dying out in their activity toward the end of the verse. The marimba starts with a horizontal "included" trichord (B b -B-C) followed by the insistent "overlapping" dyad D#-B, anticipated in m. 15 (see Example 5) now in conflict with the B-D of the voice in m.16. This dyad is similarly emphasized in the viola through bars seventeen and eighteen with a further conflict with a B-F fifth in the violin in m. 18.

Although the polyrhythmic lines are dropped for most of this section it returns significantly in the piccolo and violin against the central phase of the text, "a mirror on which to dwell.". Here the piccolo is offset from the previous pulse by 15.3 quarter-notes while the violin is offset by 15.1 quarter-notes. The resultant discrepancy is equal to one quintuplet sixteenth, the base unit of measurement in the violin pulse, assumedly for the purpose of more favorable surface rhythmic tensions. With the re-introduction of the polyrhythm the dynamic level drops from the mf-ff range in mm. 16 - 19 to the pp-ppp range that dominated in part one.

An "included" semitone dyad (G-G#) pervades the pp-ppp section in the polyrhythm in the piccolo and violin in bars twenty and twenty-one. It recurs with the B-B ostinato in the piccolo in m. 21 and is seen later in the G-G# oscillations in the viola in m. twenty-two. These dyads are aurally significant as they comprise the only activity in these lines. A very important diad is developed in the vocal part this section. The "excluded" dyad D-E which was focused in the lower register in the parenthesis of the text mm. 8-9 is again emphasized in m. 20 ("so wrap up") with the E by itself having appeared at the very center of the key thematic phrase of the text in m.19 ("a mirror on which to dwell"). Carter's manipulation of interval quality becomes very clear in this pivotal passage where the (01,2,) melodic groups of the central hexachord (m. 19) give way to interlocking (0,1,4) groups ("dwell, so wrap up care") and return to descending (0,1,2) groups ("in a cobweb and drop") and give way to the descending and ascending thirds which link the second and third verses.



Example 6: "Insomnia" Vocal Line mm. 16 - 22


Section Three

The text of this verse does offers a number of opportunities for representing the imagery of the poem quite literally in the music. Schiff identifies the word painting of the line where left is always right in bars twenty-three and twenty-four where Carter uses A and F for "left" followed by F and A for "right". This however is part of a larger intervallic symmetry beginning with the B natural on "-ed" of "inverted" and ending with the D "real-" of "really" in which, starting in the middle with the A natural of "right", the order of the preceding intervals is presented backwards with their direction reversed (ascending instead of descending, descending instead of ascending). A more obvious example of word painting precedes this development however in the descending thirds for "drop it down a well," and, in the midst of the developing intervallic symmetries, the repetition of the word "where" at the beginning of four successive phrases. There is a hint here that Carter is using the hexachord here as a point of departure; three of the four "where's" - including the first and last - are sung on the F# and G natural of the referential hexachord.

The polyrhythm in this section continues in the violin and viola in mm. 22-25 and then shifts back to the piccolo and violin. The polyrhythm actually overlaps in m. 25 - the last note played by the viola being extended by two quintuplet sixteenths to cover the violin when it picks up the polyrhythm. The piccolo overlaps the violin when it resumes its polyrhythm, however by doing so it enters a whole eighth note early. Once the violin resumes the articulation of the polyrhythm in bar twenty-five the viola continues it role in sustained notes.

The marimba's part is characterized by long notes played with tremolo from mm. 23 - 26 and rests from m. 26 through m. 31. In m. 32 the rhythmic character of both the viola and marimba changes to short, at times, accented notes with some sudden changes in dynamics. The dynamics remain in the pp-ppp range for most of the section however in m. 32 ("deep" in the text) the accents in all the instrumental parts are combined with fp expressions. Perhaps the most distinctive and significant development at this moment is in the marimba where the metered tremolo on the thematic F# (however in the lower register) of the referential hexachord crescendos, skipping to A# before slipping to G# and quietly to A natural. The closing figures in the marimba echo the A natural and surrounding tones of the referential hexachord. In the voice we notice once more the gravitation of (0,1,4) groups (E-G-E and D-BD of "is now deep and you love me") but also the closing return to the D-E relation in the E and D of the soft low tones of the closing contours.

The use of the harmonic source pitches is in fact markedly different in the second half of this final section. In the first part, mm. 23- 26 we see identifiable "included" dyads and trichords. In the second part, mm. 29 - 33, the chords become more complex and are, for the most part, "overlapping". There is a clear insistence of B and B towards the end of the piece, supported by pervasive use of F# before the hushed closing sonority on A-B-D-E# (see Example 9). The increased complexity of both the pitch material and the rhythm creates the piece's climax. Nevertheless the clarity of the section is maintained through the proliferation of salient fourths and fifths. These intervallic relationships also tie this closing section, in its prevalence of B-F#, to the E-B naturals of the opening.


Example 6: "Insomnia" Vocal Line mm. 22 - 32


Example 7: "Insomnia" mm. 31 - 32


Concluding Remarks

Thus we find that the large-scale polyrhythm in "Insomnia" supports the overall verse and thematic structure of the piece. Despite the link between the second and third verses, the verse structure  attains preeminance through the position of the vocal line throughout the piece.

In the first verse/section the moon is introduced, described, and subsequently discussed as a mirror of the insomniac, as it too does not sleep at night. This leads in the setting of lines five and six of the poem (mm. 9-15) where the parallel experience between the moon and the insomniac is explored. The vocal and polyrhythm lines in first subsection (mm. 1 - 8) are supported by fast moving melodic fragments in the marimba and viola. The last two lines of the first verse are set in mm. 9 - 13 of the second subsection, followed by a two and a half bar instrumental interlude leading into the second verse/section. The character of the viola changes in the bar nine; here it begins to play sustained dyads and the marimba is silent throughout the last two lines of the verse. This change in harmonic texture underlines the development of the verse as the insomniac moves from description to personal reflection. Another significant musical characteristic is the change in the dynamic character in the instrumental interlude at the end of the section; starting in the p-mp range at the end of bar thirteen it rises to the sf that closes the section.

The second verse/section is dominated by water imagery, both as a means of reflection and eventually of abandon. This latter element anticipates the identification of the source of the insomniac's troubles in the third verse. Though the overall musical character of this section does not have the same distinct break between the settings of its first four and last two lines as in the first section, the ongoing division of the setting of each verse into 4+2 is still subtly played out. One of the significant characteristics of this section is the absence of the polyrhythm throughout the first four lines of the verse; another is its dynamic character which picks up from the heightened intensity of the instrumental interlude that closed the first section. The dynamic character of the second section remains in mf-ff range in the voice for the first four lines of verse but retreats to a pp-p range for lines five and six.

The third, and final, verse/section plays on the inversional properties of both the mirror and the water, affirming the reversal of things from their natural order. Through the exploration of these properties (and their intensification in "the sea is now deep") it ultimately becomes clear that the insomniac's rejection by a former lover is the root of the sleeplessness. Here we may observe the 4+2 structure when the vertical complexity of the instrumental accompaniment increases towards the end of m. 27 with the setting of the fifth line of the verse. It is interesting to note that in spite of its increased harmonic complexity the dynamic character of the section is subdued in comparison to section two. This mirrors the shift from the outrage and physical action of the second verse to the self-reflection of the third; emotionally/internally (harmonically) the text is expanding while physical/external (dynamic) aspects of the text drop off.

A hexachord of harmonic source pitch classes F#, G, G#, B b , B, C is used quite freely throughout the piece. It is the prevalence of these pitch classes primarily through a number of vertical dyads and trichords which ties the instrumental parts in with the initial statement of the vocal line. Thus, by connecting the parts initially, Carter is able to treat them independently for rest of the piece. Nevertheless, on account of the dominance of the harmonic source pitch classes in both parts, the listener still perceives them as linked. While the analysis of this hexachord of harmonic source pitch classes does not uncover a complete compositional syntax its extensive and prominent use enables it to function as a harmonic reference for the piece.

The combined effect of the polyrhythm, harmonic source pitches, and verse-level activity is one of overall cohesiveness through which Carter weaves his own reading of the poem which is the key to understanding the piece.



Bernard, Jonathan W. "The Evolution of Elliott Carter's Rhythmic Practice" Perspectives of New Music 26 (1988): 164-203.

Bernard, Jonathan W. "Problems of Pitch Structure in Elliott Carter's First and Second String Quartets" Journal of Music Theory 37 (1993): 231-66.

Bernard, Jonathan W. "Spatial Sets in Recent Music of Elliott Carter" Music Analysis 2:1 (1983): 5-34.

Carter, Elliott. A Mirror on Which to Dwell. New York, N. Y.: Associated Music Publishers, 1977.

Carter, Elliott. The Vocal Works (1975-1981) Bridge Records, 1989.

Edwards, Allen. Flawed Words and Stubborn Sounds: A Conversation with Elliott Carter. New York: W. W. Norton Company Inc, 1971.

Harvey, David I. H. The Later Music of Elliott Carter: A Study in Music Theory and Analysis. New York: Garland Publishing, Inc, 1989.

Holliger, Heinz. "Conversation with Elliott Carter" Sonus 14:2 (1994): 5-12.

Link, John. "The Composition of Carter's Night Fantasies" Sonus 14:2 (1994) 67-89.

Mead, Andres "The Role of Octave Equivalence in Carter's Recent Music" Sonus 14:2 (1994): 13-37.

Rosen, Charles. The Musical Languages of Elliott Carter. Washington, D.C.: Library of Congress Music Division, 1984.

Schiff, David. The Music of Elliott Carter. Ithaca, N. Y.: Cornell University Press, 1998.

Shreffler, Anne. "Elliott Carter and his America" Sonus 14:2 (1994): 38-66.

Uno, Yayoi "The Tempo-Span GIS as a Measure of Continuity in Elliott Carter's Eight Pieces for Four Timpani," Integral 10 (1996): 51-91.

Zimmerman, Robert. "The Poetics of Polyrhythm in Elliott Carter's Anaphora" Sonus 19:1 (1998): 67-85.

1. The author would like to acknowledge the extensive support and guidance provided by David Lidov in the research and writing of this paper.

2. Schwartz, Lloyd. "Elliott Carter and American Poetry" in A Mirror on Which to Dwell New York: Associated Music Publishers, 1977, p. 12. He also offered the following summary of Carter's style in the Bishop, Ashbery, and Lowell song cycles. " Vocal lines move in and out of melody much more abruptly than operative recitative - they're neither Wagnerian swellings into aria nor Schoenbergian sprechstimme but something stranger not only between recitative and aria but also between recitative and speech. The notes themselves evoke speech inflections, yet they can soar suddenly into high-flying operatic lyricism. Rangy coloratura alternate unpredictably with leaping declamation - it's like Bellini and Wagner at the same time." (Schwartz p. 11)

3. "Insomnia" from THE COMPLETE POEMS:1927-1979 by Elizabeth Bishop. Copyright © 1979, 1983 by Alice Helen Methfessel. Reprinted by permission of Farrar, Strauss and Giroux, LLC.

4. Schiff, David The Music of Elliott Carter Ithaca, New York: Cornell University Press,1998 pg. 176.

5. Flawed Words and Stubborn Sounds is a record of interviews with Carter collected by Allen Edwards and published in 1971. In it Carter discusses the role of large scale polyrhythms in his work: "One of the things I became interested in over the last ten years was an attempt to give the feeling of both smaller and larger-scale rhythmic periods. One way was to set out large-scale rhythmic patterns before writing the music which would then become the important stress points of the piece, or section of a piece. These patterns or cycles were then subdivided in several degrees down to the smallest level of the rhythmic structure relating the detail to the whole" (p 111)