John Link - The Composition of Elliott Carter's Night Fantasies
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The Composition of Elliott Carter's Night Fantasies [*]

by John F. Link
William Paterson University
┬ęCopyright 1994, 2000 by John F. Link

Elliott Carter's sketches provide a rich documentary record of the working methods of one of the great composers of the last hundred years. The present article is a study of the sketches for one of Carter's most fascinating and important compositions–Night Fantasies, for solo piano, completed in 1980. By examining the sketches it is possible to trace the basic outline of Carter's compositional process from his first thoughts about the piece to the finished score, and to witness the development of harmonic and rhythmic ideas that became the foundation of his compositional practice throughout the 1980s and into the 1990s.

***

Carter's sketches for Night Fantasies, along with most of the sketches for his other works, are housed at the Paul Sacher Foundation in Basel, Switzerland. According to the Sacher Foundation catalog, there are 1001 pages of sketches for Night Fantasies. In addition, there are autographs of a draft version of the entire score (marked "Night Fantasies [/] Final Sketch"), a pencil fair copy on velum (marked "1st complete edition, April 14, 1980 correct[ed] April 21,"), and a blueprint on heavy cardboard of mm. 1-197 of the velum fair copy (marked "Early draft of 1st Part") containing various emendations, mostly dynamics.

The majority of the sketches are made on sheets of 24-stave paper, ca. 13 x 21 inches. Carter usually tore each sheet in half producing two sheets, 13 x 10 inches with 24 staves on both recto and verso of each sheet. There are also 72 sheets of sketches on 8 1/2 x 11 inch unlined paper, usually containing tempo modulations or other rhythmic notations.

Carter composed Night Fantasies between November, 1978 and April, 1980. He dated about half of the sketches, either by hand or with an adjustable date stamp. Most of the dated sketches are grouped in folders, one for each month from November, 1978 to November, 1979. A single folder contains sketches for December, 1979 and January, 1980. The remainder of the dated sketches are in a folder labeled "Dated Sketches (dates from different months on each page)." These are most often collections of several sheets which Carter grouped by subject and stapled together.[1] The undated sketches are divided into two folders which are labeled "Undated Sketches on King Brand 24-stave paper," and "Undated Sketches (24 stave paper with no brand name)."[2]

***

In his preface to the score, Carter describes Night Fantasies as "a piano piece of continuously changing moods, suggesting the fleeting thoughts and feelings that pass through the mind during a period of wakefulness at night."[3] In order to realize this conception, Carter decided to write a piece made up of many short, contrasting episodes. The large-scale rhythmic development is guided by a polyrhythm consisting of two streams of slow periodic pulsations. In the faster stream pulsations occur once about every five and one-half seconds; in the slower stream there is a pulsation about every seven seconds. The two streams coincide only on the downbeat of m. 3, and again on the last notes of the piece, twenty minutes later, forming a polyrhythm of 216:175 which is present throughout, renotated in a variety of different meters and tempi. The polyrhythm serves as a kind of formal and rhythmic skeleton, marking important moments of transition or arrival, and generating a wide variety of faster rhythmic patterns that occupy the musical surface.[4]

Harmonically, Night Fantasies is based on a collection of twelve-note "all-interval" chords, in which each of the twelve pitch classes and, between consecutive notes, each of the eleven intervals occurs exactly once.[5] Carter treats these chords – each of which spans five and one-half octaves – as a repertoire of harmonic possibilities. Each one contributes to a variety of different harmonic events, while maintaining its own unique spatial arrangement of pitches distributed across the entire range of the keyboard.

The large-scale harmonic and rhythmic design of Night Fantasies can be observed in the opening measures (see Example 1).

The rhythm of this passage is guided by the two streams of the underlying polyrhythm. In the faster stream pulsations (marked by short articulations) recur every 35 sixteenths. In the slower stream pulsations recur every 27 quintuplet eighths, marking each successive onset of a repeated iambic pattern of 9 + 18 quintuplet eighths. Harmonically, the passage is based on an all-interval chord (mm. 3-8), together with its inversion (mm. 8-11). The chords are connected by their four common tones – F#1, F3, C#5, and C7 (see example 2).

Example 2 - All-interval chord and its inversion
from mm. 1-11 of Night Fantasies.

***

Because of their central role in Night Fantasies, it will be helpful to review the basic properties of all-interval chords. Their number and nomenclature vary somewhat in the literature; I will follow Bauer-Mengelberg and Ferentz, notating them as strings of eleven intervals, these being the intervals between consecutive pitches of a given all-interval chord. The operations P (the identity operation), I (inversion), and R (retrogression) are defined in the usual way. There is also an operation Q which may be thought of as exchanging the segment of an all-interval chord that precedes the interval 6 with the segment that follows it (see example 3).[6] These operations may be compounded, and all are commutative, that is IR = RI; IRQ = IQR; and so on.

Example 3 - Operations on an all-interval chord

P = 7423198E65T
R = T56E8913247
I = 58T9E341672
Q = 5T67423198E
IR = RI = 276143E9T85 etc.

The all-interval chords Carter eventually decided to use in Night Fantasies are all RI-invariant, which means that the RI form of a given chord is equal to the chord itself.[7] All such chords have a tritone in the central order position number six, and complementary intervals occupying complementary order positions (see example 4).

Example 4 - The RI-invariant all-interval chord
from the beginning of Night Fantasies.

Also of interest to Carter scholarship are the QI-invariant all-interval chords, in which a central tritone is flanked by a five-interval "wing" on either side. Complementary intervals occupy the same order position in each "wing" (see Example 5)

Example 5 - A QI-invariant all-interval chord.

In most of his works since Night Fantasies, Carter has preferred to use all-interval chords of the QI-invariant type.

The starting point of Carter's harmonic investigations for Night Fantasies was the printout of 1,928 all-interval chords made available by Bauer-Mengelberg and Ferentz in connection with their article.[8] His method seems to have been simply to go through the list manually, looking for chords with particular characteristics, and to write them out in music notation, beginning on an arbitrary pitch, as he found them.[9]

The earliest table of all-interval chords among the Night Fantasies sketches is a group of five sheets of King Brand staff paper stapled together (1/79, no. 7). There are two date stamps, JAN 02 1979 on 1r, and JAN 12 1979 on 3r. 4r contains the handwritten date "Jan 14, 1978," which is probably an error on Carter's part, of the type one often makes near the beginning of a new year. The table contains 23 all-interval chords arranged in systems of four measures each.[10] Each measure corresponds to one of the four forms of a given chord – P, R, I, and RI – in which Carter initially was interested. An 8 1/2 x 11 salmon-colored sheet, which was originally attached to these pages, contains the same 23 all-interval chords written as numbers indicating strings of intervals, with "T" substituting for the number 10 and "E" substituting for 11.[11]

Carter apparently chose the chords on these tables because they contain segments that form instances of the all-interval tetrachord [0,1,4,6]. On the staff paper table each twelve-note chord is written out beginning on A1, and the segmental [0,1,4,6]s are circled in red pencil. Also indicated are instances, both segmental and non-segmental, of the all-trichord hexachord [0,1,2,4,7,8].[12] Though his initial interest seems to have been in particular subsets of the twelve-note chords, Carter was already taking note of the symmetries inherent in some of them. Chords number 1, 2, 3, 7, 9, and 10 are QI-invariant, which Carter notes on the salmon-colored page by writing the intervals after the central tritone below their complements, as in example 6.

Example 6 - Carter's notation of QI-invariant all-interval chord no. 1
on the salmon-colored chart from January, 1979.

1a827E96
4T513

Carter also notes the symmetry of the QI-invariant chords by writing the intervals of chord 1a vertically from low to high in the margin of the first staff paper page of the chord table and drawing lines connecting complementary intervals. Chords 12-23 on the table are RI-invariant, and Carter has drawn lines on the salmon-colored page connecting complementary intervals on all twelve of these chords.

Carter made a second copy of his initial table of 23 all-interval chords on January 22, 1979 (1/79, no. 23). He transposed the chords to begin on F#1, and partitioned the pitches of each one into various groupings: pairs of six-note chords formed by taking every other note, triples of four-note chords formed by taking every third note, and so on. On this table Carter gives pride of place to the RI-invariant chords: numbers 12-22 appear on page 1r and number 23, which appears on page 3r, is connected to the others by an arrow. Page 2r contains chords number 1-7 (except for number 5 which does not appear) and page 3r contains chords 8-11.

An important milestone in the composition of Night Fantasies was Carter's decision to use RI-invariant all-interval chords exclusively. The motivation for this choice may have been Carter's discovery of the Q operation, which is documented on a table of all-interval chords typed on the same 8 1/2 x 11 salmon-colored paper used for the first table, 1/79, no. 1. (The new table is UnKB, no. 74.) The new table begins with chords 1-11, which are separated from the chords that follow by a row of lower-case "x"s. The table continues with chords 12-23. Now, however, Carter has indicated that chord 21 is the Q form of chord 12 and that the ten new chords, which he has added and numbered 24-33, are the Q forms of numbers 13-23.[13] Several additional chords, numbered 14a, and 34-40, appear below number 33.

At this point Carter decided to abandon the all-interval chords which are not RI-invariant, and to regroup the others in pairs, related by the Q operation. He wrote out the results in music notation, again starting each chord on F#1 (UnKB, no. 84). On this table Carter has circled chord number 25 in light blue pencil and marked it "source," identifying for the first time his interest in the chord that became the basis for the opening of Night Fantasies, and a central referential sonority throughout the composition. He also added two new chords, numbers 41 and 42. Carter next recopied the table onto a single page, beginning with number 25, which is again circled in light blue pencil (DDM, no. 6, p. 1r). Each all-interval chord together with its inversion is assigned a single catalog number, and each prime/inversion pair is followed by its Q-related forms. The table is date stamped FEB 18 1979, and contains two new chords, numbers 43 and 44.

Clearly by the end of February Carter had formulated many of his ideas about the all-interval chords he wanted to use, and how best to organize them. But his repertory was to undergo several subsequent transformations before it took on its final form. Carter made two significant tables of all-interval chords on April 8th. They seem to have been motivated by the desire to expand the pool of chords used in the piece. Carter produced the first table by returning to the Bauer-Mengelberg and Ferentz list, this time looking specifically for RI-invariant chords. When he found one, he checked to see if it was already on the table from February 18th. If not, he added it to the new table, otherwise he omitted it. (The new table is 4/79, no. 6.)

The second April 8th chord table is a re-copied and re-ordered version of the first. It lists chords 45-98, and there are sketches of additional chords, numbered 99-103, which are crossed out. This table was clearly meant as a continuation of the one from February 18th, which lists chords 12-44.[14] At this point Carter had found all 88 of the RI-invariant all-interval chords on which the harmony of Night Fantasies is based. They are numbers 12-98, plus number 14a.[15]

Carter's listing of all-interval chords did not reach its final state until almost three months later, when he decided to reorganize the chords and to renumber them from 1-88. This final listing, which was still in Carter's possession in the mid-1990s, is dated June 25, 1979. To facilitate the transition from the old to the new numbering, Carter compiled a concordance on July 3rd, which made it possible to look up the old number of a chord and find its new number (Sketches on unlined paper, no. 2). The concordance also documents Carter's awareness that all 88 of the all-interval chords are generated by only four hexachords – [0,1,2,3,4,5], [0,1,3,4,5,8], [0,2,3,4,5,7], and [0,2,4,5,7,9] – which are Carter's hexachords number 4, 3, 5, and 6, respectively. On the July 3rd concordance these hexachord numbers are indicated in light green pencil, and the bottom of the page, in the same light green pencil, Carter has written "change in numbering of all interval chords."

In Carter's final ordering, all-interval chords are grouped according to their similarities (see example 7).

Example 7 - The first four chords of Carter's final all-interval chord chart for Night Fantasies.

1) 274316E985T (T589E613472)
2) 134726T589E (E985T627431)
3) 274916E385T (T583E619472)
4) 194726T583E (E385T627491)

As was mentioned earlier, each chord together with its inversion is assigned a single catalog number. The numbering also pairs chords that are related by the Q operation: chord number 2 is the Q form of the second version (in parentheses) of chord number 1. Finally, note that chords 1 and 3 are related by Andrew Mead's "exchange three and nine" operation (call it Ø) by which the order positions of the intervals three and nine are exchanged (see note 6). All 88 of the chords on Carter's final table are thus arranged: the first of each group might be called "prime," the second is the Q form, the third is the Ø form, and the fourth is the QØ form. Of all the operations on RI-invariant all-interval chords described by various theorists, only the M5/M7 operation is not reflected in Carter's numbering.

The various tables of all-interval chords and their relatively unambiguous chronology are of great help in studying the Night Fantasies sketches. Whenever the old numbering of chords appears on a sketch, it must have been written before late June or early July, 1979. Sketches on which the new numbering appears must have been either written or renumbered after that point. There are many sketches on which the old numbers are crossed out and the new ones added. These sketches also provide clues as to which materials from early in the compositional process Carter thought important enough to revisit after July. For example, the sketches from January, 1979 are mainly taken up with documenting the various subsets of the original collection of 23 all-interval chords. Of more than a dozen such tables, all of which were written using the old numbers, only one has the new numbers added (1/79, no. 34). This sketch is primarily an investigation of the subsets of chord number 1 (new numbering), the chord that begins Night Fantasies, which Carter marked "source" on the sketches from the middle of February.

***

The development of a repertory of all-interval chords was not the only focus of Carter's attention during the early stages of his work on Night Fantasies. He also spent a considerable amount of time exploring how the chords might give rise to various kinds of smaller collections. One of Carter's earliest and most important harmonic ideas was to highlight smaller collections that feature a particular interval class. Throughout the year and a half he worked on the piece, Carter made frequent sketches marked "1/11," "2/10," "3/9," "4/8," or "5/7" indicating the interval class a given sketch is meant to highlight.[16]

Of particular interest is a sketch Carter made before the final renumbering of all-interval chords (UnKB, no. 28). The sketch is divided into five rows, each of which is labeled with an interval class and a symmetrical trichord or tetrachord associated with that interval class: [0,1,2] for interval class 1, [0,2,4] for interval class 2, [0,3,6,9] for interval class 3, [0,4,8] for interval class 4, and [0,2,5,7] for interval class 5. The first column of the table locates these set classes in all-interval chord number 1, and the second does the same for all-interval chord number 3. The remainder of the table locates other collections that prominently feature a single interval class in a variety of all-interval chords. This idea can be heard in the finished composition in the various partitions of chord number 1 that feature a particular interval class. At the beginning of the piece (shown in example 1) chord number 1 and its inversion are the background for a texture that prominently features interval class 5. When chord number 1 returns in mm. 38-39 it features interval class 4, and in mm. 439-441 it features interval class 1.

Similarly, Carter sometimes uses a single all-interval chord as the background for a contrapuntal dialog between two interval classes, as in mm. 150-156 in which interval class 2 (represented by set class [0,2,4]) and interval class 4 (represented by set class [0,4,8]) are emphasized within all-interval chord number 1.

As he explored the harmonic characteristics of his all-interval chords, Carter also made numerous short musical sketches to see how these characteristics might take shape in a variety of different piano textures and expressive contexts. These brief musical fragments were part of the dialectical process by which Carter composed Night Fantasies. The sketches document a constant give and take between the investigation of abstract properties and the exploration of how such properties can be musically realized. On the same day he compiled the February 18th table of all-interval chords, for example, Carter also wrote out the sketches excerpted in example 8 (2/79, no. 26r).

In the first excerpt (example 8a) Carter wrote out three instances of the all-trichord hexachord [0,1,2,4,7,8] drawn from all-interval chords number 13, 17, and 16 (old numbers).[17] Further down the page (example 8b) he sketched a succession of note heads from all-interval chords number 18, 32, and 33 (old numbers), again giving priority to the all-trichord hexachord. Finally, he fit the previous sketch into a polyrhythmic scheme of six quintuplet sixteenths in the right hand against five (occasionally six) sixteenths in the left (example 8c), resulting in a passage that eventually found its way almost unchanged into the finished score (mm. 33-35).[18]

Carter continued to compose a variety of individual short fragments of music throughout 1979. When he felt he had accumulated enough of them, his next task was to think about how they might be arranged to give the composition a sense of long-range continuity. At some point he began assigning a number, written and circled usually in purple pencil, to more than 70 of the fragments. Then he simply pinned them to the wall of his studio and rearranged them until he found an ordering he liked.[19]

Carter used the re-ordered fragments as a starting point for the composition of the draft score. They gave him a rough idea of what the piece would be like, but he clearly felt that more revisions were necessary. As he worked, he discarded about half of the fragments and added a great deal of other material, some from earlier sketches, some newly composed.

A particularly striking example of the kind of revisions Carter made while working on the draft score involves a passage that begins in m. 432, and continues to what is arguably the climax of the entire piece in m. 473. The dramatic and continuous buildup created in these measures was the result of Carter's careful reworking of at least five purple-numbered fragments initially composed months apart.

The first part of this passage began as a series of three fragments—numbers 65, 24, and 58—written on strips of staff paper which Carter taped together to form a continuous sketch (DDM, no. 14). Example 9 gives fragment 65, the beginning of fragment 24, and the first part of fragment 58.

The music in fragment 24 (dated JUN 26 1979) begins in m. 445. The sketch was transposed down two half steps, but is otherwise identical to the version in the score. Fragment 65, on the other hand, was revised considerably to become mm. 438-445. An echo of the music in fragment 58 (dated AUG 14 1979) is heard in m. 449 of the score, but Carter rejected the rest of it in favor of fragment number 4 (dated MAR 02 1979) which contains the music found in mm. 451-453. The majority of the rest of the passage, mm. 457-470, appears on fragment number 61 (dated AUG 14 1979). New material was composed to form mm. 432-438, 448-450, 454-457, and 471-473.[20]

Example 9 also gives some idea of how Carter implemented the composition's overall rhythmic design. Although the idea of using a long-range polyrhythm preceded the composition of the purple-numbered fragments, very few of the latter were planned to fit a specific place in the polyrhythm. This approach allowed Carter maximum flexibility when it came to working out the order of the fragments for the finished piece. Only after he had a clear idea of the dramatic continuity of an extended passage did Carter decide how it would be aligned with the polyrhythmic pulsations.

Carter also had to contend with notational constraints. The accurate notation of a pulsation at a given tempo requires the use of a specific beat division.[21] When pulsations from both streams are present (as they almost always are) two different beat divisions are required. If the beat divisions Carter had used for a particular fragment did not match those required for the accurate notation of the pulsations, the fragment had to be rewritten. This was the case for fragment number 65, which Carter rewrote for the draft score by substituting the necessary sixteenths and quintuplet sixteenths for the original sixteenths and triplet eighths. Other fragments, such as number 24, were initially composed using the appropriate beat divisions, and required little or no revision.

The final stage of the composition of Night Fantasies was the preparation of the velum fair copy. Carter probably began this task before the draft score was finished due to the proximity of the first performance, which was given by Ursula Oppens at the Bath Festival in June, 1980. Oppens has said that she received the score one-third at a time,[22] and the blueprint of m. 1-197 of the fair copy, which is among the autograph materials, is probably a copy of the first installment. The fair copy was finished on April 14, 1980.

***

Carter's sketch materials contain a wealth of information about his music and his compositional methods. In the case of Night Fantasies the sketches document the development of a number of harmonic and rhythmic strategies, including the partitioning of twelve-note chords into smaller collections based on shared interval class or set class membership, and the use of long-range polyrhythms, which have become central to Carter's compositional practice in his more recent works. The sketches also provide a unique glimpse of the workings of a creative imagination that prizes both analytical abstraction and unrestrained flights of fancy, reminding us of the imaginative leap that underlies even the most well-documented structure.

Appendix:
Table of Elliott Carter's Numbering of Twelve-Note
All-Interval Chords Used in Night Fantasies

Twelve-note all-interval chords listed with a five-digit interval string are RI-invariant. They may be written out in full by adding a 6 at the end of the string, followed by the string's retrograde inversion. for example:

27431 = 27431 + 6 + E985T = 274316E985T.

No.New Old
127431315T469E728
2134725T8E3672419
3274914E7T3681529
41947258T9E341672
54523E4618T97E523
619T785E3672418T9
74529E142956E8T37
813T78569241T873E
9589T119T856E3247
101T98559241673T8E
11583T11825E43796T
121T385592E4
133472127491
141274313472
14a-4791T
15385TE21794
161274937TE4
173T78127194
18187T3589T1
193254E3E872
20187T94E532
21529414E295
22149251T385
23523413T781
241432519472
253E87227431
26278E349712
273145T4ET73
28T541349172
29491721T985
3027194278E3
3143172235E4
3227134583T1
334137T187T3
34259E82E358
354197T19T78
36253E843712
37413524523E
382531421734
394195252941
402591452341
414E53214925
42235E414325
434E59245E92
44295E429E54
4545E923254E
4629E54187T9
4745E3234721
4823E5412743
4949712385TE
502179412749
51437124529E
522173413T78
533581245T13
542185331T54
55374ET54E23
562185932E45
57538ET21853
582149735812
59598ET21859
6021437374ET
614791T278E9
622E3583145T
634731T45T19
642E9583E278
65479E24ET79
662E97435218
67473E254E29
682E3743T187
694ET735TE83
7037TE438ET5
714ET795TE89
723521834127
735TE834137T
7438ET5259E8
755TE8941352
763412725314
7754E2341952
7832E4525914
7954E29538ET
803T18721497
8145T134197T
8231T54253E8
8345T1945E32
843E27823E54
85592E4479E2
864E2952E974
874E235598ET
88532E421437
89-4731T
90-2E958
91-43172
92-27134
93-473E2
94-2E374
95-4E592
96-295E4
97-4E235
98-532E4

IntervalsNewOld
127431448
127491650
13472214
13T78852
142956E8T37 -7
143252442
149252241
1825E43796T -11
187T31833
187T92046
19472424
19T78635
19T856E3247 -9
1T3851222
1T9851029
214376088
214975880
217345238
217945015
218535457
218595659
235E44231
23E544884
253143876
253E83682
259144078
259E83474
271343292
271943017
27431125
27491313
276143E9T85 -4
278E32630
278E92861
295E44496
29E544644
2E3586234
2E3746894
2E9586490
2E9746686
3145T2762
315T469E728 -1
31T548254
3254E1945
325E79T8164 -5
32E457856
341277672
347211347
352187266
358125358
374ET5560
37TE47016
385TE1549
38ET57470
3T1878068
3T7811723
3E2788464
3E8722519
413523775
4137T3373
419523977
4197T3581
431723191
437125136
4523E537
4529E751
45T138153
45T198363
45E324783
45E924543
4731T6389
473E26793
4791T6114T
479E26585
491722928
497124926
4E2358797
4E2958621
4E5324120
4E5924395
4E7T3681529 -3
4ET736927
4ET797165
523412340
529412139
532E48898
538ET5779
54E237755
54E297967
569241T873E -8
583T11132
589T1918
592E48512
598ET5987
5T8E3672419 -2
5TE837369
5TE897571
5E3672418T9 -6

List of Works Cited

Bauer-Mengelberg, Stefan and Melvin Ferentz. "On Eleven-Interval Twelve-Tone Rows," Perspectives of New Music 3, no. 2 (1965): 93-103.

Boros, James. "Some Properties of the All-Triad Hexachord," In Theory Only 11, no. 6 (September 1990): 19-41.

Carter, Elliott. Night Fantasies. New York: Associated Music Publishers, 1982.

Cohen, David. "A Re-examination of All-interval Rows," Proceedings of the American Society of University Composers 7, no. 8 (1972-73): 73-74.

Link, John F. "Long-Range Polyrhythms in Elliott Carter's Recent Music," Ph.D. diss., City University of New York, 1994.

Mead, Andrew. "Twelve-Tone Composition and the Music of Elliott Carter." In Concert Music, Rock, and Jazz Since 1945: Essays and Analytic Studies, ed. Elizabeth West Marvin and Richard Hermann, 67-102. Rochester, NY: University of Rochester Press, 1995.

Morris, Robert and Daniel Starr. "The Structure of All-Interval Series," Journal of Music Theory 18, no. 2 (Fall 1974): 364-389.

Schiff, David. The Music of Elliott Carter. New York: Da Capo Press, 1983. Revised second edition, Ithaca, NY: Cornell University Press, 1998.

________. "Elliott Carter's Harvest Home," Tempo 167 (December 1988), 2-13.