Stasis as a Style Type in the Works of Elliott Carter

Introduction

Among the many contrasting characters Elliott Carter explores in his music from about 1950 onward is a sense of stasis. Passages that feature this "stasis" character, identifiable by its texture comprising long-sustained notes, inhabit a grand scale of time and evoke a state of transcendence. Some instances of stasis, where it is combined with other textures to create something new, seem especially suited for topical analysis. While a theoretical framework for topical analysis is relatively well established for eighteenth- and nineteenth-century music, it is less so for more recent music. This study aims to begin building the framework for performing such an analysis of Carter's music by reviewing the theory and conducting a corpus study of selected works. Robert Hatten's definition of topic seems especially applicable to analyses of relatively recent music.¹ Implied in his definition is a requirement that a topic be first identified as a familiar style type. With this in mind, the selected works are examined for frequency of occurrences of this static texture. Two compositions are selected for formal and harmonic analysis to further identify distinctive features associated with stasis in Carter's music. The findings show some similarities between the passages beyond texture. In both cases, stasis articulates the formal proportions of the works in terms of their Golden Sections. In addition, during these passages, there is overall harmonic movement from asymmetry to symmetry. A common transformation from 4–Z15 (0146) to 4–22 (0247) is found to mark the ends of main sections in the passages. These findings suggest a path for further study to possibly identify stasis as an interopus style type within the context of Carter's works and as potentially being topical in the broader discourse of twentieth-century music.

Stasis As Texture

Stasis in Carter's music is characterized by long-sustained notes (or long durations of rests) and often accompanies, or is contrasted against, more kinetic musical gestures.² In some cases, it becomes the dominant texture of a substantial section of a composition, and is often marked by soft dynamics and a slow tempo. During these serene moments, the music can take on a meditative, otherworldly character, evoking a state of transcendence—a respite from the busy realm of terrestrial conflicts—until the listener is jostled back into the intense contrast of energetic ideas that characterizes much of Carter's music.

Stasis As A Topic

Overview

It may be possible to interpret this static texture in Carter's music as topical in certain contexts. How to approach this in practice is by no means clear, but an initial step might involve what Michael Klein describes as abductive leaps in forming an intertext for an uncoded sign.³ Before continuing with a discussion of stasis in Carter's music, some general concerns with regard to the analysis of topics in twentieth-century music must be addressed. Firstly, there is the evolutionary nature of the definition of musical topics in general. By this I mean the very definition of topos, which can be seen to evolve with each study. For example, one use of the word topic can be synonymous with style or type, while another may be conditional upon meeting additional criteria. These discrepancies may complicate discussion beyond a fundamental level. On the other hand, this may be unavoidable, or even desirable, and each perspective can still be pursued within the context of its own definitions. Secondly, there is the issue of public and private meanings as they relate to topics; analytical methods for the eighteenth century may not work well for the nineteenth century onward, due to the notion that composers' expressions become increasingly private. This problem may potentially be overcome in part through pointing out that there may not be a clear distinction between public and private meanings. The plausibility of private meaning itself can also be called into question. Thirdly, a method must be devised for forming an intertext. Finally, it may not be possible to discuss topics in the context of a single composer's oeuvre. It may still be possible to consider stasis as an interopus style type within the works of Elliott Carter. The utility of this distinction would perhaps ultimately depend upon how it might help to clarify the theoretical framework.

Evolving Definitions

Topic theory inherently draws attention to the difficulty, if not the implausibility of pinning down the meaning of a sign among a range of intertexts under continual evolution. As Klein notes, "an intertext begins by pointing to meaning and ends by scattering meaning."⁴ This is reflected in the evolution of musical topoi through substantially different definitions that have emerged in the relatively short period since Leonard Ratner's seminal work in 1980.⁵

Ratner defines topics as "characteristic figures" and "subjects for musical discourse" that include types and styles [italics in the original].⁶ For Ratner, types are "fully worked-out pieces," including a variety of eighteenth-century dances. Styles involve "figures and progressions within a piece." While a thorough discussion of the diverse definitions of topics is beyond the scope of this study, it may be worth comparing Ratner's definition of topics to Robert Hatten's in the Oxford Handbook of Topic Theory.⁷ Hatten defines topic as "a familiar style type with easily recognizable musical features," noting "a familiar style type only becomes topical when it is imported [italics in the original] into different contexts." By "style type," Hatten seems not to be referring to Ratner's definition of "fully worked-out" types, but more generally to what he designates as style, or "figures and progressions within a piece," with the caveat that it be "familiar" in order to have topical potential. Another important requirement for a style type to be considered topical according to this definition is that its features be "easily recognizable."

I will mostly be working with Hatten's “familiar style type [italics added] with easily recognizable musical features,” as it relates to his definition of topic in part. In doing so, I aim to conduct preliminary work toward identifying stasis in Carter's music as such a style type, so that it may be possible, with further study, for it to be discussed in a topical context.

Public vs. Private Codes

In considering the possibility of a familiar style type in the context of twentieth-century music, there is first the question of plausibility. In view of the relatively well-established style types of the eighteenth century, would it be feasible to identify style types in twentieth-century compositions? Moreover, would it make sense to think of a familiar style type in the context of a single composer's oeuvre in the twentieth century as we do eighteenth-century style types?

We are confronted with additional complications: starting in the nineteenth century, Western art music seems to require competency in increasingly private codes for interpretation. For example, Janice Dickensheets includes regional dialects and relatively private "surface languages" in her thesaurus of Romantic topoi.⁸

On the other hand, the possibility of private rules for language has been dismissed outright. In exploring the paradox in Ludwig Wittgenstein's private language argument, Saul Kripke observes that, while denying a "'private model' of rule following," Wittgenstein "agrees with the sceptic that the attempt to imagine the sensations of others on the model of my own is ultimately unintelligible," leaving only a provisional possibility for a communal system of language, with no room for "private models."⁹ If such a model is implausible, then so is any distinction between public and private meanings.

Even in granting the possibility of private musical codes, a clear distinction between public and private musical discourse seems untenable. Kofi Agawu posits that this "public-private" dichotomy can be eroded in eighteenth- and nineteenth-century music.¹⁰ Noting that Romantic music "prefers a break with the outside world by entering into private biographical realms in which the cryptic sign holds the key to meaning in the musical work," Agawu observes that a semiotic interpretation of Romantic music is only possible after undermining its "public-private opposition" with Classic music. In working to obscure this distinction, he points out that it is possible to interpret the music of Classic composers as containing private meaning.¹¹ As an example, he points to the use of private jokes in Haydn's string quartets. Among the Romantics, Agawu points to contradictions in Schumann, Liszt and Wagner with their "outgoing" expressions of internal discourse, further blurring the line between notions of public and private meanings.

Stasis As A Style Type?

With the erosion of a clear distinction between public and private musical codes, making the leap necessary in order to identify a topic in the context of a single composer’s oeuvre would seem plausible. Similarly, if musical topics can be discussed in the context of eighteenth- and nineteenth-century music without issue in terms of a public-private dichotomy, this would seem to be the case for twentieth-century music as well. In the context of stasis in Carter's music then, a topical analysis could start with abducting an intertext as a code for interpreting a possible topic associated with this texture; distinguishing whether this code is public or private may not be possible. As an initial step in this process, it would seem plausible to proceed toward establishing stasis as a style type, according to the definition above, even within the context of a single composer's works in the twentieth century.

Stasis as a texture is readily identifiable as a familiar musical feature in Carter's music. As an initial step to support this observation, I conducted a corpus study of 26 pieces Carter wrote between 1984 and 1995 with the aim of discovering how frequently the composer employed static textures. I found that many of the pieces do indeed feature substantial sections, or entire movements, in which this texture is a dominant characteristic.

To refine the definition of stasis as it applies to Carter's music, I conducted a comparative analysis of two works from the corpus, and found that sections in which a static texture predominates mark important proportional boundaries within the compositions. I further found that there is a common transformation of the harmonic materials that occurs during these passages. These findings help to furnish details of the "recognizable musical features" of stasis.

In terms of my overall methodology, if this texture can be established as a familiar style type in Carter's music, it could be interpreted as being imported into a new context to become topical in two pieces in the corpus in particular: Fragment No. 1, and the "Adagio sereno" of String Quartet No. 5. At the same time, if the importation of stasis into this new context could be interpreted as being topical in Fragment No. 1, written in 1994, the analogous tropological interaction in String Quartet No. 5, written the following year, would decrease in creativity because it would have been “less strikingly new” by then.¹² This notion of creativity as developed by Hatten will be discussed later in this study in relation to my analysis of the "Adagio sereno."

A Corpus Study Of Works Between 1984 And 1995

Fragment No. 1 (1994) and String Quartet No. 5 (1995) "Adagio sereno"

In selecting a range for a corpus study of Carter's works, I begin with two compositions, which feature extended passages with a uniform texture of stasis combined with a uniform texture of string harmonics throughout, Fragment No. 1 for string quartet and the "Adagio sereno" of String Quartet No. 5—the likely candidates for topical analysis mentioned above. Carter's earlier string quartets also feature passages with a uniform texture of stasis, with some of the voices reaching the upper register and sometimes playing string harmonics, but never in all of the voices at the same time. The combination of stasis with a uniform texture of string harmonics in these two works was a logical, yet strikingly new development in his compositional style; prior to these pieces, composed a year apart in 1994 and 1995 respectively, Carter had never combined these textures in this way.

Provisionally, this may be viewed as an importation of this potential style type of stasis into a new textural context of uniform string harmonics. This importation would seem to work metaphorically to further elevate the transcendental quality associated with stasis in Carter's music. The height in register and the distinct textural quality of string harmonics transports the "Adagio sereno" of String Quartet No. 5 a figurative distance away from the registral and textural domains of the other sections of the composition (with the exception of the "Lento espressivo" movement with respect to stasis, as it also features tranquillo as a dominant texture, but without harmonics). Similarly, the use of harmonics throughout Fragment No. 1 makes the piece stand out among Carter's works.

Stasis in Carter's Music Between 1984 and 1995

To establish a framework for topical analysis of these two pieces, I set the corpus window from 1984, ten years before Fragment No. 1 was written, through 1995, when String Quartet No. 5 was composed. Table 1 lists the 26 compositions counted in the corpus (the Brass Quintet was written in 1974 and revised in 1993).¹³ While not meant as an exhaustive list of its occurrences in the corpus, measure numbers are provided for each piece as examples of where stasis can be found. As this is a provisional step in the study, the process of identifying stasis is somewhat informal; the results may contain inconsistencies. A clear segmentation of stasis can at times prove problematic in music that features simultaneous development of contrasting ideas. In Carter's music, there are typically multiple streams of characters in continual development, one of them usually being some form of stasis.¹⁴ This static texture tends to play a subordinate role to more active textures, which makes for a dramatic effect when it comes to the fore, especially as a uniform texture in an extended passage. Even when it is not featured as a dominant texture, the frequency with which these long-sustained notes occur supports a case for the familiarity of this texture within the corpus.

Stasis takes on several different guises in Carter's music. At times these long-held notes are marked with soft dynamics, as in Fragment No. 1 (1994) and String Quartet No. 5 (1995), mentioned above, as well as in mm. 50–64 of Esprit Rude/Esprit Doux (1984) and mm. 431–63 of String Quartet No. 4 (1986). During the Tranquillo of Violin Concerto (1990) "slowly rising and falling waves of sound" in the orchestra accompany the "dramatic recitative" of the solo violin, marked espressivo, cantabile (m. 217).¹⁵ During mm. 225–45 of Penthode (1985) the long notes themselves are marked espressivo with a dynamic range of pp to fff, eventually leading to a climactic crescendo in mm. 264–77, creating a substantially different effect from the softer variety mentioned above. In Canon for 4 (1984) the slow texture is marked tranquillo and is dominant in approximately three-quarters of the piece, but smoothly transitions back and forth to and from faster textures, thus carrying with it considerable momentum.

Given the variety of forms stasis can take, it may prove helpful to develop a set of axes with which to identify these forms. One of the axes could be that of uniformity—whether stasis is presented as a uniform texture, or if it is combined with others. Another could be dynamics—whether the static texture is performed loudly or softly, or whether it is evenly balanced with other textures. If stasis is identified as a uniform texture, it could be interpreted as being dominant, whether it is performed loudly or softly. Conversely, if it is on the other end of the uniformity scale, and is played softly relative to other textures, it could be interpreted as playing a supportive role.

Yet another axis with which to identify the variety of forms stasis can take could be that of tempo. For example, starting in m. 151 of the Violin Concerto, a quiet stasis takes over the textural domain of the music after a crescendo to ff in the winds and brass sections. The violin begins a solo of long-held notes, marked p tranquillo, yet the fast tempo of the opening continues, at Impulsivo 𝅘𝅥=155. The shorter duration of the held notes in the orchestral accompaniment and the return to the fast music shortly thereafter provide momentum relative to the Tranquillo section (m. 213) that follows, marked 𝅗𝅥=52+, where the pulse slows to half the tempo and the orchestral accompaniment holds much longer notes—the "slowly rising and falling waves of sound" mentioned above—for a noticeably different effect.¹⁶

Since Carter's music often dramatizes contrasting characters in continual development and the resultant textures often rapidly and smoothly transition along these multiple dimensions, I find it useful to identify instances where the texture is relatively stable as a starting point for discussion. In my comparative analysis below, I select two compositions that feature such instances of stasis, in the uniform, quiet and slow points on the axes described above.

Esprit Rude/Esprit Doux (1984) and String Quartet No. 5 (1995)

To establish a basis for a study of the role of stasis in Carter's works, I selected two compositions from my corpus—one from the beginning, the other from the end—that feature similar varieties of the texture: Esprit Rude/Esprit Doux (1984), and String Quartet No. 5 (1995). In the former piece, stasis is prominent in the tranquillo section (mm. 50–64) and in the latter, during the "Adagio sereno" movement (mm. 251–81).

As will be detailed below in my analysis, I find certain syntactical commonalities between the passages. The onset of stasis occurs near the Golden Mean of each composition, and there is overall harmonic movement from asymmetry to symmetry. Additionally, I find within each of these sections similar transformations involving two tetrachordal set classes. These transformations work on instances of the all-interval tetrachord (AIT) 4–Z15 (0146), resulting in instances of 4–22 (0247) that mark the ends of main segments in the passages.

As my findings emphasize similarities between these compositions, I omit certain details that might otherwise be significant to an analysis of a piece on its own. For example, the other all-interval tetrachord (AIT) 4–Z29 (0137), while known to play a significant role in Carter's compositions, as is the case in the "Adagio sereno," is not emphasized in my analysis, since it is not featured in the tranquillo.¹⁷

Esprit Rude/Esprit Doux (1984)

Overall Form

Esprit Rude/Esprit Doux is a duo for flute and clarinet written in 1984 for Pierre Boulez's 60th birthday.¹⁸ It is a short piece approximately 5 minutes in duration, with a vibrant and playful character that contrasts rough and smooth textures, as indicated by its title (Rough Breathing/Smooth Breathing). The form is outlined by a long-range polyrhythmic cycle, with a duration of approximately 4 minutes and 40 seconds.¹⁹ A short introduction of 5 measures is followed by a full iteration of the polyrhythmic cycle.²⁰

The piece features a tranquillo section (mm. 50–64) during which the rapid rhythmic textures of the previous measures give way to stasis. As John Link observes, the pulsations of the long-range polyrhythm, related by a ratio of 21:25, are presented here in isolation.²¹ The pulses that begin the section in each of the voices in mm. 50–51 bracket the Golden Section (0.618...) of the cycle, at 15/25 (0.6) for the clarinet and 13/21 (0.619...) for the flute, thus locating the tranquillo just after the Golden Section of the composition. As will be shown later, this is also the case for the "Adagio sereno" of String Quartet No. 5 (1995) and looks to be the case for at least several other pieces.²²

Mm. 50–64, Tranquillo

External listening: Carter, Esprit rude / Esprit doux — from the tranquillo (YouTube) ↗

The tranquillo is a particularly clear example of stasis in Carter's music. While the slow texture is foreshadowed by utterances of long-held notes in the music that precedes the section, the tranquillo passage is clearly demarcated and contrasted against the rest of the piece by intensely fluid music that erupts in a rapidly accented marcato figure, just before an abrupt transition to stasis. This texture is uninterrupted for about 14 measures thereafter, roughly one minute of music, at a tempo of 𝅘𝅥=60–63.

A harmonic analysis of these measures reveals an overall progression from asymmetry to symmetry. This is shaped by a succession of intervals in the counterpoint between the two voices, as well as by a transformation of pitch-class collections, namely instances of 4–Z15 (0146) to 5–35 (02479), the latter containing subsets 4–23 (0257) and 4–22 (0247).

First six interval classesSecond sequence to the end

ics = interval classes

pcis = pitch-class intervals (from low to high)

From Variation to Similarity

I begin my analysis by looking at the interval classes between the two voices. Example 1 is a reduction of the tranquillo passage that shows the sequence of interval classes. I included the ordered pitch-class intervals measured from low to high pitches in parentheses in the example, when their integers differed from those of the interval classes. For instance, in mm. 57–58, ic5 is accompanied by (7) to indicate the ordered pitch-class interval, which in this instance corresponds to a perfect fifth.

Example 1 shows that all six interval classes are introduced one by one, starting at the beginning of the passage, from ic6 in m. 51 to ic1 in m. 58, where a minor-second is formed in the upper register, between F₆ in the flute and E₆ in the clarinet (sounding pitch). The completion of the statement of the full set of interval classes is demarcated by a breath in the clarinet part, indicated by a comma in m. 59, a particularly salient feature of the passage.

The ic1 here serves as a bridge to another succession of interval classes that ends in m. 63 with an ic2. Here, a major 23rd sounds between F♯₃ in the chalumeau register of the clarinet and a high G♯₆ in the flute. The second statement follows ic⟨1, 4, 6, 3, 5, 2⟩. The beginnings and endings of each sequence of the six interval classes are indicated in the example by vertical lines and arrows above where the interval classes are shown. The passage concludes with two similar intervals, both instances of ic5, the latter of which is also a perfect fifth. This final interval of the tranquillo provides a sense of resolution, if only momentarily, before the music quickly returns to the intensely fast textures that dominate the music preceding the stasis section.

From Asymmetry to Symmetry

In addition to the sequence of interval classes, Example 1 shows the formation of set classes in the passage. Two instances of (0146) at the beginning of the section are also demarcated with a breath indicated by a comma, this time in the flute part in m. 56. The ic2 sounded here does not belong to either collection. However, each note in the C–B♭ dyad belongs to different instances of (0146), [G, A, C, C♯] and [E, F, G♯, B♭] respectively, that bookend the interval class. In m. 61, the G♯₆ in the flute completes the exposition of the two instances of the set class. This completion is emphasized both by the pitch being the highest in the tranquillo section and by the simultaneous decrescendi to pianissimo on the downbeat in both voices. The high G♯ is also an aurally salient detail, although the notated decrescendi to pp may be less perceptible in performance because of the difficulty of sustaining such soft dynamics in these registers.

Turning to the end of the tranquillo passage in Example 1, the last five intervals in the counterpoint form two overlapping instances of (0257), shown below and above the system, and one instance of (0247), shown below. The two instances of (0257) have three notes in common, as do the last two tetrachords in the example. The first two of the three tetrachords, [F♯, G♯, B, C♯] and [C♯, D♯, F♯, G♯] form an instance of (02479). The last two tetrachords of the example, [C♯, D♯, F♯, G♯] and [D♯, F♯, G♯, A♯] form another instance of the pentachord.

The relatively frequent occurrence of ic5 in the pentatonic set class (02479) and its subset (0257) can be heard in the counterpoint toward the end of the tranquillo, which offers a sense of stability—especially with a perfect fifth marking the end of the passage. Furthermore (02479) is a symmetrical collection, in contrast to the asymmetric AIT (0146) with its maximally varied interval vector 111111. Ic6 in mm. 61–62 serves as a pivot from asymmetric to symmetrical set classes (Example 2). In addition, the statement of the second instance of (0146) in inversion (I₅) signals a shift toward symmetry, by serving as a symmetric counterpart to the first.

Tetrachords, analytical rendering

Thus, in the tranquillo, there is overall harmonic movement from asymmetry—with a high variation of interval classes, both in the content of tetrachords and in the counterpoint at the beginning of the section—to symmetrical and relatively stable harmonies, as reflected in the pentatonic collections and the similar occurrences of interval classes at the end.

Transformation from (0146) to (0247)

In Example 2, I have labelled the transformation that takes place from the second instance of (0146) to (0247) at the end of the tranquillo as Y. The two pcsets involved in transformation Y have two pitch classes in common, 8 and 10, which are made salient in the sustained G♯₆ in the flute through the intervening harmonies and its descent to A♯₄, connecting the two tetrachords. The remaining pcs 4 and 5 of (0146) form an ic1, prominently featured as the high minor second between F₆ and E₆, as mentioned above. This interval moves "outward" to pcs 3 and 6 in (0247) which form an ic3, between the last two pitches of the clarinet, F♯₃ and D♯₄.

ic1→3Interval class 1 to interval class 3YTransformation Y

The two tetrachords in the transformation are shown in Example 3a. The ics 1, 2 and 3 mentioned above are indicated in the example. Slurs outline the interval classes and solid arrows show a proposed voice leading from the pitch classes in ic1 to those in ic3. A dotted arrow expresses a shift downward in register from B♭₅ to A♯₄. This pitch class is paired with G♯ in the ic2 dyad that the two tetrachords have in common.

Example 3b shows the transformations between the interval classes in pitch-class space.²³ The tetrachords share a common ic2. The remaining ic1 dyad [E, F] and the resulting ic3 dyad [D♯, F♯] share inversion index I₉, which is preserved under the proposed voice leading as one pitch class moves by +1 and the other by −1.²⁴

Thus, transformation Y involves a common ic2 between (0146) and (0247), where an ic1 formed by the remaining pitches of (0146) expands in pitch-class space to become an ic3 between the remaining pitches in (0247), through outward motion of one pitch-class interval in each voice.

A set-theoretic formalization of Y can be constructed from a property of 4–Z15 (0146) described by Adrian P. Childs: in an (0146)-type AIT, the six interval classes partition into the nonoverlapping pairs 1+2, 4+5, and 3+6.²⁵ Let X be an instance of 4–Z15, let D₁(X) = {a, a + 1} denote its unique ic1 dyad, and let D₂(X) denote its unique ic2 dyad. Transformation Y can then be defined as:

In other words, Y preserves the ic2 dyad while expanding the paired ic1 by contrary semitone motion to ic3. For X = {4, 5, 8, 10}, this gives Y(X) = {3, 6, 8, 10}, the instance of 4–22 shown in Example 3. Applied across the complete T/I orbit, the rule gives a one-to-one mapping from the 24 forms of 4–Z15 to the 24 forms of 4–22. It is also compatible with transposition and inversion: Y(T_nX) = T_nY(X) and Y(I_nX) = I_nY(X).

The preserved inversion indices of these corresponding subset dyads suggest that Klumpenhouwer networks may reveal an additional relationship between the two tetrachords. The choice of network partition is motivated by the relationships between ic1 and ic2, and between ic2 and ic3, already foregrounded in the preceding voice-leading analysis. Example 3c shows strongly isographic networks, in which corresponding T- and I-arrows carry identical subscripts.²⁶ Let y₁ and y₂ denote the K-nets on pcsets [E, F, G♯, B♭] and [D♯, F♯, G♯, A♯], respectively. The K-nets y₁ and y₂ are strongly isographic under ⟨T₀⟩: corresponding T-arrows carry identical subscripts, and corresponding I-subscripts differ by 0 (mod 12).

Example 3d shows alternative K-nets that are negatively isographic under ⟨I₃⟩: corresponding T-subscripts are complementary, and corresponding I-subscripts sum to 3 (mod 12). The same node mapping can be expressed as the dual inversion I₁/I₂: one of the two corresponding dyadic subsets of y₁ maps onto its counterpart in y₂ under I₁, and the other under I₂. At the pitch-class level, I₁ maps the ic5 dyad [F, B♭] onto [G♯, D♯], while I₂ maps the ic4 dyad [E, G♯] onto [A♯, F♯].²⁷ The dual subscripts sum to 3, matching the subscript of ⟨I₃⟩.²⁸

These networks are not intended as a competing account of the voice leading proposed in Examples 3a and 3b; rather, they represent additional structural relationships between the two tetrachords by comparing transformations internal to their K-nets. The node correspondences in these K-nets imply pitch-class mappings different from the voice leading proposed above. Because this study does not pursue higher-level network relations, the analytical role of the K-nets here is limited to this supplementary comparison of internal structure, although these relationships may provide a basis for further study.

Independently of these K-net observations, transformation Y may be an identifying characteristic of a potential “stasis” style type, as similar transformations can be found in the “Adagio sereno” of String Quartet No. 5, as will be shown later in the paper.²⁹

As was seen in Example 1, the tranquillo began with ic6 and completed its first statement of all six interval classes with ic1. These two interval classes distinguish the two tetrachords in transformation Y. (0146) contains all of the interval classes, whereas (0247) does not contain ics 1 and 6. Instead it contains two instances each of ics 2 and 5, as can be seen from its interval vector, 021120. Looking at the two complete statements of the interval classes, we see that both sequences move toward ics 2 and 5. Both the interval-class sequences and transformation Y thus move from an emphasis on ics 1 and 6 toward ics 2 and 5.

As an additional detail to further support the interpretation of an overall harmonic motion toward (0247), we can identify the last four pitches in each voice as instances of the set class. These instances are [F, G♯, A♯, C] in the flute and [B, C♯, D♯, F♯] in the clarinet. Furthermore, the final eight pitches across the two parts form the pcset [F♯, G♯, A♯, B, C♯, D, D♯, E], an instance of the set class 8–22 (0123568t), the complement of (0247), which plays a similar supportive role in the Adagio. This role will also be discussed later in the paper.

Summary

The tranquillo section of Esprit Rude/Esprit Doux features stasis as the dominant texture and is located slightly after the Golden Section of the composition. The succession of interval classes and the resulting transformations in the tranquillo show an overall harmonic progression from asymmetry to symmetry. This takes the form of an overall transformation from (0146) to (02479). One transformation in particular, from the second instance of (0146) to the final (0247), is highlighted because analogous transformations occur in the “Adagio sereno” of String Quartet No. 5. This transformation can be further framed in terms of a harmonic movement from an emphasis in ics 1 and 6 to 2 and 5, which is supported by the sequence of interval classes. These details may serve as a starting point from which to begin identifying a set of distinguishing characteristics for stasis.

String Quartet No. 5 (1995)

Overall Form

String Quartet No. 5, written in 1995, is a composition approximately 20 minutes in duration, commissioned for the Arditti Quartet. Carter explains in the program note that the piece is based on patterns of human behavior that mirror “our inner experience of forming, ordering, focussing, and bringing to fruition—and then dismissing—our feelings and ideas.” For Carter, these patterns are reflected in the rehearsal process of chamber music, when performers play and discuss a composition in fragments while putting together a performance.³⁰ He adds, “In this score the matter of human cooperation with its many aspects of feeling and thought was a very important consideration.” The program note offers clues to interpreting the composition, based on themes of fragmentation and cooperation as they relate to our inner experiences and to human behavior.

The string quartet as a whole spans twelve continuous sections, six of which are designated by tempo markings and associated characters, such as “Adagio sereno (𝅘𝅥=48)” (which is the fifth such character explored in the composition). The composition begins with an introduction, after which the six movements alternate with five interludes. During the interludes, Carter explains, “the players discuss in different ways what has been played and what will be played.”

As Carter notes, each player is presented in the introduction, “trying out fragments of later passages.” With this in mind, the opening measures foreshadow the stasis texture in the viola, with a long-held high G♯₆ marked pp tranquillo (m. 4) and played as a string harmonic. Similar indications in mm. 178–79 further anticipate the “Adagio sereno” character (mm. 251–81), where all four voices cooperate to articulate a unified texture of stasis with string harmonics.

As was observed earlier, an identifying characteristic of stasis as a style type could be its association with the Golden Section of a composition. The Adagio itself begins (in notated time) at around 13 1/2 minutes in a work lasting roughly 18 minutes and 45 seconds (13.5/18.75 = 0.72), well after the Golden Section. The onset of stasis, however, occurs in the preceding interlude, where it begins to interrupt the “Allegro energico” character at ca. 11 minutes 45 seconds into the piece (0.627), just after the Golden Section.³¹

"Adagio Sereno," Mm. 251–81

External score video: Elliott Carter, String Quartet No. 5 — from around m. 245 (YouTube) ↗

The “Adagio sereno” of the string quartet is another extended and uninterrupted section featuring stasis. At approximately 2 1/2 minutes, it lasts longer than the previously examined tranquillo section of Esprit Rude/Esprit Doux. The Adagio is further characterized by string harmonics throughout all four parts, offering the possibility of identifying the passage as topical. Expanding upon his definition of topic, Hatten offers:

Non-topical imports may include ... style types that are unique to a composer. However, any distinctly defined musical element that is imported will typically be marked [italics in the original] as topical by the very fact of its appearance in a new context.³²

While Hatten acknowledges a possibility that "non-topical imports may [italics added] include ... style types unique to a composer," he implicitly allows that they, along with "any [italics in the original] distinctly defined musical element," can also be topical simply by being imported into a new context. This supports my previous discussion that it may be possible to speak of style types and topics in the context of a single composer's works, based on Agawu's erosion of the distinction between private and public musical meaning, as well as on the implausibility of private language in general posited by Wittgenstein. It also significantly opens up possibilities for "any distinctly defined" texture, such as stasis, to be identified as a style type with topical potential.

Furthermore, how this musical element might be defined is not made explicit in Hatten's definition, leaving open the possibility that it can be defined in any number of ways, including historically, geographically, harmonically, texturally, or by any combination of these or other approaches. This flexibility would make this definition particularly suitable to the topical study of music for which analytical methods are not as well established, such as modernist compositions of the twentieth century.

In discussing his "axes of relationships between a topic and its new environment,” Hatten notes that the creativity of a tropological interaction can be gauged based on "the relative frequency with which similar interactions have appeared in a musical style."³³ The importation of stasis into a uniform string-harmonics context appears only once before in the corpus, in Fragment No. 1 for string quartet, written the previous year, making it a relatively creative interaction within the context of Carter's works, albeit not as creative as that which takes place in the fragment.

The above discussion of topics suggests that the importation of stasis into a string-harmonics context in the Adagio (and Fragment No. 1) can be interpreted as "creatively new" within the context of Carter's works and may be "distinctly defined" in any number of ways. This study aims to begin defining stasis in historical (within Carter's works), textural, formal, and harmonic terms by identifying similar characteristics between the Adagio and the tranquillo of Esprit Rude/Esprit Doux. In so doing, I hope to establish a framework for further study of the remaining works in the corpus, so that the texture may be considered a style type with topical potential.

Harmonic Overview of "Adagio Sereno"

As with my analysis of the tranquillo of Esprit Rude/Esprit Doux, my analysis of the Adagio focuses on compositional strategies shared between the pieces. As in the tranquillo, the overall harmony of the “Adagio sereno” moves from asymmetry to symmetry. Similarly, transformation Y, which marks the change to the final chord in the tranquillo, appears at the ends of main segments in the Adagio.

I find it useful to segment the Adagio into three main sections, divided by "breaths" or short rests in the music. Segment 1 extends from the beginning of the movement at m. 251 to the first breath on the downbeat of m. 258. The second such breath occurs at the end of the first beat of m. 275, marking the end of Segment 2. Segment 3 continues to the end of the movement, which, in addition to a transition in texture, is also marked by a brief rest before the final chord in the second violin.

Harmonic Analysis of the End of Segment 1

The harmonic analysis in Example 4 reveals transformations similar to those found in Example 2: a transformation between two instances of (0146) toward the beginning and another involving (0146) and (0247).

T₃Opening (0146) transpositionYTetrachords, analytical renderinghex.Hexachords, analytical renderingrec.End transformation, recording

Example 4a shows a transpositional relationship between the instances of (0146). As with the tranquillo, these instances occur early in the section (mm. 251–252) and establish the set class as the beginning harmony of the Adagio. The main difference is that instead of an inversional relationship that begins to shift the harmony toward symmetry in the earlier example, here the asymmetrical quality of the tetrachord is preserved.

rec.End of Segment 1, recording

The end of Segment 1 features a crescendo to piano (from pp) of 8-note and 6-note chords in m. 257, followed by a brief rest (Example 5). This can be heard as the end of a phrase. A subtle harmonic shift within the chord held at the end of this “phrase” is particularly distinctive. An analysis of this brief moment—one quarter beat at the end of m. 257—reveals an unexpected harmonic relationship with the tranquillo of Esprit Rude/Esprit Doux.

Example 4b shows a transformation between subsets (0146) and (0247) of two hexachords, 6–Z17 (012478) and 6–Z26 (013578), respectively. The first hexachord is a familiar sound in Carter's music since the 1970s and is favored by the composer for its asymmetric properties.³⁴ Transformation Y here works in a similar way to that described in Example 2. In this instance, the shared pitch classes forming ic2 are 11 and 1. The remaining two pcs 7 and 8 in (0146) forming an ic1 move to pcs 6 and 9, forming an ic3 in (0247). In the notation defined above, this instance is Y({7, 8, 11, 1}) = {6, 9, 11, 1}.

As a transformation between subsets, it is perhaps not as salient, but the tetrachords are voiced together in their respective hexachordal supersets, with (0247) especially emphasized, as the top four pitches of (013578), as indicated with a bracket in Example 4b. A hearing of the transformation is further complicated by the fact that the hexachords are sounded together as part of set class 8–16 (01235789), and emphasized only fleetingly, albeit by conspicuously placed rests, as shown in Example 5. Although the rests occupy very small fractions of the quarter note, the tempo is quite slow, at 𝅘𝅥=48, and the all-trichordal hexachord (ATH) (012478) is clearly heard during the sixteenth rest in the first violin (m. 257). The target hexachord (013578) is revealed for an even shorter duration (of 1/30 of a quarter beat), but with an accurate performance, the chord is emphasized as the last sound heard before the subsequent breath. In addition, the resulting ic3 (pcs 6 and 9) of the transformation is further emphasized as the last two pitches held by the first violin. Such fine details would perhaps go unnoticed, or not be deemed significant, if it were not for their relationship with the tranquillo as described above. A further common detail is that in each case, transformation Y involves an instance of (0247) at the end of a segment, perhaps indicating that it may play a role in a cadence-like function.

Harmonic Analysis of the End of Segment 2

rec.End of Segment 2, recording

YTransformation Y8–22 and subset tetrachordsOctachord 8–22 and subset tetrachords

The all-trichordal hexachord permeates the end of the second segment, most prominently in the outer voices, as shown in Example 6. The hexachord [B, C, E♭, F, F♯, G] in the cello line is made salient by a drop to E♭₄ in m. 270, the lowest pitch in the Adagio thus far, followed by a gradual increase in dynamics through mezzo forte to an accented forte at the end of the segment, the loudest dynamic in the Adagio to this point. This statement of the hexachord is also shown in the example as a progression from (0146) to (0156). The latter tetrachord is made especially salient with two accented perfect fifths played a half-step apart. While most of the harmonies shown in the example are asymmetrical, the cello line shows a shift toward symmetry at the end of the segment with a clear articulation of this tetrachord. The violin line is shown to outline another instance of the ATH [E, F, G♯, B♭, B♮, B♯] at the beginning of the example, indicated by a bracket above the system (mm. 269–73). Yet another instance of the hexachord [C, C♯, E, F♯, G, G♯] is formed by a group of notes emphasized by accented mezzo forte dynamics (mm. 271–72).

A similar group of accented notes, four dyads at the end of the segment (mm. 274–75) marked forte, form the complement of (0247). This octachord, 8–22 (0123568t), which is also found in the tranquillo (as noted above), contains seven 4–22 (0247)-type tetrachords as subsets, one of which is shown in parentheses in the example, [A♯, C♯, D♯, F]. While this instance of (0247) is not particularly salient, the octachord supports an interpretation of a progression toward (0247) at the end of the segment, as with the tranquillo.

Example 7 shows another instance of transformation Y, similar to those shown in Examples 2 through 4, as it occurs here between the instance of (0146) in the cello and (0247) at the end of the segment. As shown at the end of the example, ic5 is emphasized in the voicing of the octachord, between C₅ and G₅, as well as A₅ and D₆, which together form an instance of (0257). The remaining pitches correspond to the target of the transformation, (0247). In the notation defined above, this instance is Y({11, 0, 3, 5}) = {10, 1, 3, 5}. Such a transformation may not seem significant in a harmonic analysis of the string quartet on its own, but emerges as a potential identifying characteristic of stasis in the context of this comparative analysis.

Harmonic Analysis of the End of Segment 3

Alternating symmetry/asymmetry of tetrachords and hexachordSet-class simultaneities, analytical renderingrec.End of the Adagio, recording

The end of Segment 3 does not contain any instances of transformation Y, but is remarkable for its alternation of symmetric and asymmetric harmonies, with an overall emphasis on symmetry. In Example 8, I show the set classes as they occur in the music as simultaneities and label them “S” for symmetric or “A” for asymmetric. Held notes are shown in parentheses as they occur in subsequent simultaneities and pizzicati (in the lower register) are shown as stemless noteheads without parentheses.

The left-hand pizzicato by the cello on D₃ in m. 278 interrupts the consistent texture of the movement (save the short tenuto dyad in the first violin in m. 257, as was seen in Example 5) and signals the end of the Adagio. The pizzicati foreshadow the dominant texture of the "Capriccioso" movement, which follows the subsequent interlude. A symmetric set class (0167) is sustained above the pizzicato note, and in the subsequent simultaneities the harmony oscillates between asymmetric and symmetric tetrachords, including the two all-interval collections (0146) and (0137). The viola and second violin follow in articulating the pizzicato texture, while the long-sustained chords thin out to a major third (m. 280) and eventually to a single note, E₆ (m. 281), which is held in the final measure by the first violin. The analysis shows the final bowed note of the viola (B♭₄ in m. 279) and the five subsequent pizzicato notes forming 6–20 (014589), an all-combinatorial collection, further signaling a shift toward symmetry at the end of the movement. The pizzicato notes of violin 2, immediately following the viola, outline overlapping instances of the two AITs. Four-note pizzicato chords in the cello and viola follow (with the viola repeatedly strumming its tetrachord, articulating an intermediate texture between stasis and pizzicato), followed by an accented fortissimo four-note chord played arco by violin 2: the final chord of the movement, the symmetric collection (0134). Two more chords follow at the beginning of the subsequent interlude (m. 282), the latter articulating another symmetric collection before the music abruptly transitions to a faster texture of flowing notes. With an overall emphasis on symmetry during these measures, the Adagio can thus be interpreted as tracing a harmonic movement from asymmetry to symmetry, from the instances of (0146) at the beginning of the movement to the symmetric harmonies at the end.

Conclusion And Further Considerations

Stasis as a Style Type

Similarities between the tranquillo section of Esprit Rude/Esprit Doux and the “Adagio sereno” of String Quartet No. 5 offer a starting point for identifying distinctive features that can be used to define stasis as an interopus style type within the works of Elliott Carter. The onset of stasis occurs near the Golden Mean of each composition. In addition, the harmonies during these passages move from asymmetry to symmetry in both works. A further detail involving a specific transformation, designated here as “Y,” articulates the end of the tranquillo as well as the ends of main segments in the Adagio. Although some instances of Y are subtly emphasized or appear as subsets of larger collections, these relationships, together with the other similarities identified above, suggest an avenue for further analysis within and beyond the corpus in order to gauge whether topical interpretations of Carter’s use of stasis are plausible.

Paths for Further Study

There is an unresolved question of whether an interopus style type within a single composer’s works can participate meaningfully in topical troping. With the erosion of the distinction between private and public meanings of music and with the application of a flexible definition of topic, it would seem so. Allowing for this possibility may prove especially useful in identifying topics in music after the nineteenth century. For example, in the program note to Fragment No. 1, Carter explains that the piece is composed in memory of his good friend and colleague, David Huntley.³⁵ Carter further notes that “this short work uses harmonics for the strings throughout, which, I hope, give a poignant character to my musical message.” It seems possible to relate this stated expression of commemoration and poignancy to the interaction of stasis with string harmonics in the piece. As with the “Adagio sereno,” the registral height and distinct textural quality of string harmonics in the fragment enhance the meditative quality of stasis, providing an added sense of “distance.” Similarly, in the program note to Remembrance (1988), which features stasis throughout, Carter commemorates Paul Fromm, further associating the texture with commemoration.

Further analyses of works within and beyond the corpus are needed to determine whether the relationships identified in this study recur and to identify additional possible relationships. The corpus could also be expanded beyond Carter's works to see whether a topical interpretation of stasis might be possible in the broader discourse of twentieth-century music. Around the period covered by the corpus, several compositions featuring textures similar to stasis come to mind as possible starting points for further study. Lachenmann's String Quartet No. 3, Grido (2001) and Mario Lavista's Reflejos de la noche for string quartet (1984) both feature static textures with string harmonics. Outside of a string-quartet context, György Ligeti's Atmosphères (1961) could provide another reference point for setting the range of a corpus beyond Carter's works. Such an expanded corpus may reveal a selection of pieces that feature textures similar to that analyzed here. This may help to identify, with some specificity, a potential style type or topic shaping a broader musical discourse in the twentieth century. These avenues could help to clarify possible expressive meanings in music that can sometimes seem abstract and enrich our interpretations of what it might aim to communicate.

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———. Esprit Rude/Esprit Doux. Program note. New York: Boosey & Hawkes, 1984.

———. Fragment No. 1. Program note. New York: Boosey & Hawkes, 1994.

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———. Esprit Rude/Esprit Doux. New York: Boosey & Hawkes, 1984.

———. Fragment No. 1. New York: Boosey & Hawkes, 1994.

———. Penthode. New York: Boosey & Hawkes, 1985.

———. String Quartet No. 4. New York: Boosey & Hawkes, 1986.

———. String Quartet No. 5. New York: Boosey & Hawkes, 1998.

———. Three Occasions for Orchestra. New York: Boosey & Hawkes, 1992.

———. Violin Concerto. New York: Boosey & Hawkes, 1990.