THE ALL-TRICHORD HEXACHORD: COMPOSITIONAL STRATEGIES IN ELLIOTT CARTER'S CON LEGGEREZZA PENSOSA AND GRA AND A FOLIO OF ORIGINAL COMPOSITIONS

Submitted by Marguerite Maree Boland, BA (Hons)

A thesis and folio submittedI in total fulfilment of the requirements for the degree of Master of Arts

School of Arts and Media Faculty of Humanities

La Trobe University Bundoora, Victoria 3083 Australia

December 1999

I This version of the dissertation varies slightly for the submitted version. Minor corrections to expression and typographical errors were made in March 2006. No substance of the dissertation has been altered, and all amendments have been footnoted. Contents

Summary iv Statement of Authorship v Glossary vi

1. Defining an Analytical Approach to Carter's Pitch Organisation 1 1.1. Unifying Harmonies: Some Analytical Considerations 1 1.2. Aspects of Carter's Compositional Aesthetic 10 1.3. Strategies for Pitch Organisation 15 Interval sets 16 'Key Chords' and intervallic saturation 18 1.4. Carter's use of the All-Trichord Hexachord as 'Key Chord' 22

2. Functions of the All-Trichord Hexachord in Con Leggerezza Pensosa 30 2.1. Formal Design: The ATH in the Context of Textural/Rhythmic Structures 32 Slow sections 32 Active sections 33 Continuity between and within textural blocks 36 2.2. The ATH at Points of Sonic Cohesion 46 The ATH and interval sets 47 The ATH as chordal sonority- an analysis of S2 51 The ATH as melodic force- an analysis of S3 59 2.3. The Role of Aggregate Formation in 'Degrees of Cohesion' 67 Aggregate formation at S-2 boundaries 67 The ATH and aggregate formation in A-2 71 2.4. Dissolution of the ATH: the last 20 bars of Con Leggerezza Pensosa 74 Construction of individual lines 77 Climax and cadence of CLP 81 2.5. Conclusion: The ATH and its Interaction with Multiple Structures 83

3. All-Trichord Hexachord Saturation in Gra 87 3.1. Formal Design and Character-types in Gra 89 3.2. The 'Field of Operation' in the Opening Passage 92 Principles of interaction between character-types 92 The use of pitch and intervallic materials of the ATH 93 3.3. Expansion of the Legato Character-type 94 Phrase shape and dramatic unfolding 94 Trichordal partitions of the ATH 100 3.4. ATH-Invariant Features in the Closing Passage 103 3.5. Contrasting 'Patterns of Action' 106 Invariant and trichordal patterns 107 The ATH and its complement 110

Conclusion 113

Appendix A: Con Leggerezza Pensosa bars 68-75: Aggregates and ATH forms 116

Appendix B: Annotated Score: Con Leggerezza Pensosa 117

Appendix C: Annotated Score: Gra 126

Bibliography 131

iv

Summary

This submission includes a thesis and a composition folio of five chamber pieces.

The central objective of the thesis is to develop a way of understanding Elliott Carter’s approach to pitch organisation and in particular his use of the All-Trichord Hexachord (ATH) in Con Leggerezza Pensosa for clarinet, violin and violoncello and Gra for solo clarinet. The thesis argues that the pitch organisation in Carter’s music is not the result of the application of a single pitch system, but rather that it flows from a general compositional aesthetic in which pitch, rhythm and texture combine to create varying degrees of sonic cohesion.

The analysis of Con Leggerezza Pensosa segments the piece according to a number of main textural ideas and associated harmonic materials. It illustrates how the ATH creates a clear harmonic focus in maximally cohesive textures and then recedes or vanishes in textures where musical streams are more differentiated. This fluctuation in degrees of cohesion and contrast is the key to understanding Carter’s use of the ATH.

In contrast to Con Leggerezza Pensosa, Gra uses the ATH as a single source for the entire pitch material in the piece. Although the ATH is used differently in Gra, the subsequent study consolidates the analytical approach to pitch developed above. It is argued that choice of set succession, registral distribution, partitioning and large-scale disposition of pitch class sets are still determined by the interaction of pitch, rhythmic and textural structures. As in Con Leggerezza Pensosa, the analysis of Gra illustrates how the overall musical syntax is based on varying degrees of cohesion and contrast. v

Statement of Authorship

"Except where reference is made in the text of the thesis, this thesis contains no material published elsewhere or extracted in whole or in part from a thesis by which I have qualified for or been awarded another degree or diploma.

No other person's work has been used without due acknowledgement in the main text of the thesis.

This thesis has not been submitted for the award of any degree or diploma in any other tertiary institution."

Date: 21 December 1999

Marguerite Boland vi

GLOSSARY Terms and Notational Conventions

The terminology used in this thesis conforms to the definitions provided by Robert Morris in his text Class Notes for Atonal Music Theory (Lebanon, NH: Frog Peak Music 1991) as do the abbreviations. However, the notational conventions deviate from Morris' notations. The table below lists the term, its abbreviation and an example of its notation as used in this thesis. Set class names and notation have been taken from Allen Forte's The Structure of Atonal Music (New Haven: Yale University Press, 1973).

Term Abbreviation Example of Notation pitch C, F# pitch class pc 0-9, 10=t, 11=e pitch class set pcset T7I [0,1,4,6] where 0=C set class OR set type 4-Z15[0146] OR [0146] interval i 0-9, 10=t, 11=e interval class ic 0-6 interval set i-set {e,9,7} unordered interval class set ic-set {1,3,5} unordered directed interval +7, -2 compound interval 1+, 8+

Chapter One

Defining an Analytical Approach to Carter's Pitch Organisation

1.1 Unifying Harmonies: Some Analytical Considerations

Of the many interesting elements to be studied in Elliott Carter's music, his harmonic procedures and pitch organisation remain the most mystifying. Studies dealing with pitch structure seem to raise as many questions as they answer and perhaps for this reason are in need of continued investigation. This study aims to investigate the role of the All-Trichord Hexachord as a unifying harmonic element in Con Leggerezza Pensosa and Gra and Carter's use of this set in the large-scale pitch designs and continuities of these pieces.

Elliott Carter's approach to harmony has provided a challenge to pitch class set analysis for some time. As far back as 1960 in a symposium at Princeton University, Carter was asked if his music had a harmonic plan. His answer provides a good starting point for discussion of some of the compositional principles and analytical difficulties of his music. He explained:

“A chord, a vertical group of pitches either simultaneously sounded or arpeggiated, like a motif, is a combination to be more or less clearly remembered and related to previous and future chords heard in the same work. Whether the composer is conscious of it or not, a field of operation with its principles of motion and of interaction is stated or suggested at the beginning of any work. The field may be tonal, employ traditional harmony, or it may be unrelated to traditional harmony, as my music seems to be nowadays, in which case I feel it imperative to establish clearly, near the beginning, the principles upon which the composition moves. Once this field of operation is established, its possibilities are explored, interesting new aspects of it are revealed, patterns of action of contrasting types emerge as the work goes along. A work whose world is not clearly defined loses a great deal of possible power and interest; (...) In my First String Quartet, I did use a "key" four-note chord, one of the two four-note groups, that joins all the two-note pairs, thus allowing for the total range of interval qualities that still can be referred back to a basic chord-sound. This chord is not used at every moment in the work but occurs frequently enough, especially in important places, to function, I hope, as a formative factor.”1 (Underlines mine)

1 Else Stone and Kurt Stone, eds., The Writings of Elliott Carter (Bloomington: Indiana University Press 1977) 204-205. (Hereafter WEC) 2

In this quotation Carter suggests that his compositions are conceived with a harmonic plan in mind, although the specific nature of such a pre-compositional plan in relation to pitch design remains unclear. He does tell us that a chord or a motif may appear at the beginning of a piece (in an obvious fashion) such that it can be "more of less clearly remembered". Furthermore, this collection of pitches, expressed vertically or horizontally, seems to have considerable influence on the entire composition: it is to be "related to previous and future chords"; it is "to function (...) as a formative factor"; it is part of the composition's "field of operation"; and it is meant to provide a "clearly defined" sound world for the piece. The role of such a collection of notes, or "key chord" as Carter refers to it, is clearly very significant.2 Carter gives us some small clues as to how this significant collection might be arranged in the First String Quartet: "It is presented in various kinds of part-writing and interval combination, the number of notes increased and diminished in it, in ways familiar to you all. The chord (...) is also used both in many intervallic inversions and in total inversion."3 These clues, while pointing the analyst in a particular direction, are extremely general and ambiguous. What we fail to gain from these comments is a more precise understanding of how the "key chord" might function in a structural way in Carter's pitch organisation.

In attempting to address the question of "how it is done"4, the analyst is faced with a number of difficulties. Firstly, the term "key chord" proves to be a problematic description of what Carter is referring to. Secondly, the process of segmenting the musical surface in order to identify and compare sets presents specific difficulties in

Carter's music. We will proceed by discussing each of these problems in more detail.

The term "key chord", lacking any formal definition, can conjure up associations with other terms such as key area (in the tonal sense), key motive, source chord (used by

2The idea of a unifying chord or collection as the basis of a composition is of course not unique to Carter but rather a common technique in post-tonal music. 3WEC, 205. 4Allen Edwards, Flawed Words and Stubborn Sounds: a conversation with Elliott Carter (New York: Norton 1971) 67n. This quotation is taken from a note in Allen Edward's book where he justifies asking Carter detailed technical questions as follows: "Such technical questions as here follow are of practical value not only to performers, composers and music students, but equally to listeners whose spontaneous esthetic grasp of contemporary music is already strong enough to lead to a curiosity about 'how it is done'." 3

David Schiff)5, which also resembles the term source set (used to refer to an ordered aggregate or a partitioned aggregate, as discussed in Donald Martino's "The Source Set and Its Aggregate Formations").6 All these terms contain assumptions about the organisational principles of the pitch material in a composition. However none of them seem to apply adequately to the later atonal compositions of Elliott Carter. Reference to the tonal system (needless to say) has no relevance, since this music is 'unrelated to traditional harmony' (see quotation above). Principles of 12-tone composition such as combinatoriality, array formations or linear aggregate ordering are not present. It would seem that the assumptions contained in the choice of terminology could easily confuse the direction of a pitch analysis of Carter's music. Jonathan Bernard discusses some analyses of the opening of the First String Quartet that seem to have been misled by the above quotation.7 These analyses assume that the key chord functions on some level as a generative set to which all other notes in the piece can be related, thereby creating a unified musical language. As a starting point this may seem reasonable, however in practice it proves difficult to substantiate.8 Neither of these analyses can identify set relations that are all generated by a single collection nor that illuminate more general principles of pitch structure and musical syntax at work in the piece. While Carter's term key chord contains the dangerous associations mentioned above, this study will adopt the term and develop a definition of its functions within the organisational principles that underlie Carter's method of working with pitch.

Some functions of the key chord mentioned in the above quotation, such as its referential function and its importance in defining the opening sonority of a piece, can be easily identified in many of Carter's smaller chamber pieces. The example below is of the opening of Scrivo in Vento for solo flute (1991). The boxed phrases in example 1.1 are

5David Schiff, The Music of Elliott Carter (London: Eulenburg 1983) 64. 6 Donald Martino, “The Source Set and Its Aggregate Formations”, Journal of Music Theory 5 (1961): 224-273. 7Jonathan Bernard, “Problems of Pitch Structure in Elliott Carter’s First and Second String Quartets”, Journal of Music Theory 37.2 (1993): 231-266. He notes that analysts have "sought to construe from [Carter's] comments— particularly the ones pertaining to pitch structure— a basis for some sort of consistent syntax". He points out problems with two such analyses, by Carlton Gamer and David Schiff respectively, of the opening of the First String Quartet. 8 Bernard (1994), 232-4 4 built up of one or both of the All-Interval tetrachords, 4-z15[0146] and 4-z29[0137], the key chords for this piece. The opening phrase presents a long gesture articulating T6I [0,1,4,6].9 This phrase is followed by some faster, contrasting material. The next phrase returns to the opening D and continues with a slow, drawn out gesture that contains three embedded all-interval tetrachords: Te [0,1,3,7] is articulated by the long notes in the phrase; T6I [0,1,3,7] is embedded in the middle of the phrase, initiated by the two triplet-quavers and the third embedded tetrachord (D,F,F#,C or T6I[0,1,4,6]) is a repeat of the pitches of phrase one held in the same register. A third phrase of similar sustained notes follows, this time the pitches present a straight unfolding of To [0,1,4,6]. The third phrase starts on an E. The same E appeared in bar 7 as a single long note that seemed out of context in its surroundings. With the return of this E in bar 14, the lonely E of bar 7 can be heard as a foreshadowing of the To [0,1,4,6] statement.

This example illustrates how the sound of the all-interval tetrachords is established not only by repetition but also by using registrally fixed pitches, giving the key chords a strong pitch identity in the opening bars. The key chords return in various guises throughout the rest of the piece. However they also return specifically at the same transposition levels and registral placement as in the opening, functioning explicitly as a referential sonority.

Despite some clear illustrations of how the key chord is used to establish the opening sonority of a piece, it remains difficult to define the role of this collection in the large- scale pitch organisation. Jonathan Bernard, in his article "Problems of Pitch Structure in Elliott Carter's First and Second String Quartets", remarks that "(t)he descriptions offered by Carter, though tantalising, seem to be either insufficient in themselves (...) or not susceptible of generalisation that would take in more than a limited number of isolated configurations."10

9 See Glossary for notational conventions used in this paper. 10Bernard (1993), 232.