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«Volume 17, Number 2, July 2011 Copyright © 2011 Society for Music Theory A Tonal Revolution in Fifths and Semitones: Aaron Copland’s Quiet City ...»

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Volume 17, Number 2, July 2011

Copyright © 2011 Society for Music Theory

A Tonal Revolution in Fifths and Semitones: Aaron Copland’s

Quiet City

David J. Heetderks

NOTE: The examples for the (text-only) PDF version of this item are available online at:


KEYWORDS: Copland, Quiet City, Tonnetz, centricity, neo-tonal, geometric, symmetry, pitch space, pattern completion,


ABSTRACT: Tonal ambiguity in Aaron Copland’s Quiet City, a feature frequently noted by critics, results from a radical reorganization of the constituent elements of tonality. Many sections of the work eschew triads and, in lieu of tonal progressions and key centers, the work shifts between referential collections and emphasizes pitches through salience. This paper creates a perfect fifth/semitone Tonnetz to model two of Quiet City’s most notable features: motives built from pentatonic subsets and semitonal shifts. The Tonnetz reveals isomorphisms between melodic motives and characteristic shifts between pitch-class collections, and it shows that climactic sections feature dramatic reversals of motion. Pattern completion—a voice-leading technique in which a missing note from a collection established as normative sounds conspicuously—articulates points of arrival and confirms central pitches. This analysis shows that Quiet City transforms the relations among the constituent elements of tonality in order to further explore the potential of the tonal system, an avowed aesthetic goal of Copland’s.

Received September 2010 [1] A number of pieces written in the first half of the twentieth century sound tonal while also containing decidedly modern elements. The label “neo-tonal” or “centric” is often applied to such works, which include music by Britten, Prokofiev, Shostakovich, Stravinsky during his neoclassical period, and others. Zimmerman (2002) and Silberman (2006) point out that readings of neo-tonal music often combine techniques of both tonal and post-tonal analysis, an approach that opens the question of precisely which elements of the tonal idiom are applicable to the work under discussion. (1) Such readings also raise a related question of whether a single mode of analysis can apply to an entire composition, or whether we must jettison the assumption of stylistic unity and find the best possible method for each individual section. (2) Aaron Copland’s Quiet City (1940) raises similar questions for analysts. The work has a consonant musical surface yet often strips away many markers of

common-practice tonality. This paper offers a hearing of Quiet City that is oriented toward two of its most salient features:

1 of 13 motives built from pentatonic subsets and semitonal shifts. An ic1/ic5 Tonnetz models the pitch-class collections that generate musical material in the work and motion between them. Completion of normative sets and salience conditions serve to define central pitches. In addition, motion within the Tonnetz shows a large-scale coherence within the work’s pitch organization, and provides an example of Copland’s expansion of tonal techniques.

[2] Critics faced with the task of describing the pitch structure of Aaron Copland’s compositions often resort to the explanation that it is tonally ambiguous. For example, Wilfrid Mellers (2000) states that many of Copland’s Twelve Poems of Emily Dickinson can be heard either as tonal or as in one of the diatonic modes. In his analysis of Copland’s Sextet, Daniel Mathers (1989, 56–57) identifies a “tonal axis”—that is, a dichotomy between two competing tonal centers—between the lower tonic and upper dominant. Howard Pollack (1999, 384) states that the violin part in the second movement of Copland’s Violin Sonata suggests different keys with each melodic turn, and suggests that Copland learned how to write such a melodic line in part by studying the music of Stravinsky. He also remarks that the ending of Copland’s concert work Quiet City can be heard in either C major or F major. Copland wrote Quiet City for trumpet, English horn, and strings in 1940, a year after he wrote incidental music for a play called The Quiet City by Irwin Shaw. (3) The concert work recycles many themes from the incidental music, and Pollack (Pollack 1999) speculates that the close relationship allows a programmatic reading of

the tonal ambiguity of the concert work’s ending:

Whether one considers the final pitch an unresolved dominant or a more restful tonic, the work ends on a hesitant note; like Shaw’s play, the music raises more questions than it answers. (332) [3] The ending of Quiet City is reduced in Figure 1. A solo trumpet reprises the main theme of the work—Copland called it a portrait of David Mellnikoff, one of the characters from Shaw’s play—against a C pedal (Copland and Perlis 1984, 287). If we were to assume a preference for hearing a diatonic collection as indicating either a major or minor scale, we would hear the passage in F major and conclude that the work ends on the dominant harmony. (4) The trumpet uses pitches from the F-major scale, save for one note. A B occurs in the middle of the trumpet solo nine measures after rehearsal 16, as if the instrument were feinting toward the C-major scale, but in the following measure the trumpet reverts to using B. There is little other strong support for hearing the passage in F major; moreover, Copland’s use of diatonic modes in other compositions renders tenuous the assumption that the tonic can be determined simply from the scale used in a passage.

Position assertion—that is, the use of music-rhetorical devices and formal placement to establish a tonic—favors hearing the passage in C (Harrison 1994, 75–90). The trumpet begins and ends on this note, the strings hold it throughout, and the note is the last one heard in the composition. Other than repeated C’s, the final two notes are G 4 and C 4, played by the English horn three measures after rehearsal 17. These two notes could suggest the root and fifth of a tonic sonority. Other indicators of C major are likewise spare: B, its leading tone, appears for only a fleeting moment, as does E, the tonic triad’s third. As Pollack suggested, interpreting the ending according to tonal norms yields conflicting conclusions. (5) Such an interpretation also does little to reveal relationships among the work’s constituent parts, and does not address ways in which most of the work eschews pitch constructions reminiscent of common-practice tonality in favor of others.

[4] Building on the work of Stephen Brown (1999, 80–141) and others, my analysis uses an ic1/ic5 Tonnetz, shown in Figure 2, to model pitch-related events in Quiet City. (6) Both individual motives and motion between referential collections are represented spatially within this network. The primary referential collection in the work is the pentatonic collection; this is expressed on the horizontal axis as a multiplication by five of a generating perfect fifth. (7) A semitone generates the vertical axis; it represents marked semitone shifts that occur throughout the composition. Brown defines a number of operations within the Tonnetz; the most important for the present study is T(x,y), which moves an object x spaces to the right and y spaces up (Brown 1999, 14). This paper will informally express T operations as horizontal or vertical steps on the Tonnetz; for example, moving from C to G is equivalent to making one rightward step. The dotted paths in Figure 2 show that, in equal temperament, the network “twists” upon itself so that the E at the top right corner links directly by one rightward step to the first B in the second row, and the D at the right edge of the second row links directly by one rightward step to the A in the third row. These direct links could be represented in three-dimensional space by placing the pitches along a helix. In addition, the F in the bottom row links directly to the D in the top row, so that the two points in the path marked with the symbol “α” connect by one horizontal step. (8) The vertical axis twists upon itself in a similar fashion, but this feature of the 2 of 13 network does not play a major structural role in Quiet City, so it is not represented. The twist at the α symbol could be represented in three-dimensional space by connecting the ends of the helix to form a torus.

[5] Many stretches of Quiet City can be represented as filling up horizontal spans within the Tonnetz. (9) The opening five measures of the piece, shown in Figure 3, provide an example. The passage fills the span {B F C G D}, and the opening three measures repeat a motivic dyad C-F, which represents two horizontally adjacent notes in the Tonnetz. Brackets in the reduction show appearances of this C-F dyad: the violas state it melodically, the violins repeat it vertically in measure 2, and the violins repeat it again melodically two octaves higher over measures 2–3. It is the pentatonic collection itself and the C-F dyad that are highlighted in the opening; no specific pitch emerges as central. A perfect fourth or fifth might suggest the root and fifth of a tonic sonority, but after the statements of the C-F dyad, the centricity of either pitch is undercut by the ’celli, which descend from F 3 to B 2. The centricity of B is then undermined when the ’celli descend to G 2 in measure 5 and form a perfect fourth with the English horn’s C 4. The opening measures are also notable for their avoidance of stating triads: the violas state an [025] trichord C-F-D in measures 1–3, and form a vertical instance of the same trichord with the violins when they reach their last note. The ’celli imitate the same trichord a fifth lower, with octave displacement, over measures 3–4. (10) [6] Brown (1999, 6) suggests that an analyst take into account the proclivity for associating the x-axis with time and the y-axis with vertical sonorities when deciding on an orientation of a dual interval space, or DIS. (11) I have chosen instead to use the axes of the Tonnetz to highlight a qualitative difference between different types of intervals in Quiet City. Motion by ic5 in Quiet City is common and also generates harmonic collections. Motion by ic1, by contrast, is comparatively rare, and occurs exclusively between events separated in time. (12) Thus, vertical motion suggests salience, markedness, or even effort. In order to keep in mind the qualitative difference between the types of intervals in Quiet City, it might be helpful to imagine the helical arrangement of pitch classes as if they were placed on the surface of a mountain, as depicted in Figure 4a. Horizontal motion consists of walking around its perimeter, while vertical motion requires the effort of pushing against gravity and stepping upward or downward. Figures 4b and 4c show two marked semitone motions that occur in the first section of Quiet City (from the beginning to rehearsal 3). Both involve salient parts within the texture that transform significant [025] trichords into [015] trichords. Figure 4b shows the inflection of the trichord C-F-D, which the violas introduce in the first three measures. Four measures after rehearsal 2, the strings and English horn play a brief interlude to the trumpet solo. Its uppermost line, played by the first violins, lowers the final note of the trichord by semitone to transform it to C-F-D. Figure 4c shows a chromatic inflection that takes place in the trumpet solo. The solo begins one measure after rehearsal 1 by alternating between C and B. Given the exclusive use of the pentatonic collection thus far in the composition, a continuation to G, the note enclosed in parentheses, is expected. Eight measures after rehearsal 8, the middle note is inflected to create C-B -G. In the score, a unique legato articulation mark on the B in the trumpet part provides a phenomenal accent to highlight the fact that the note is unexpected.

[7] The Tonnetz admits to multiple possible pathways between pitches. For example, a “downward” step is equivalent to five “rightward” steps. (13) My analysis follows the law of the shortest way—that is, a preference for motion involving the least number of steps—and prefers to find paths that minimize vertical motion. (14) This is not to say that any Tonnetz analysis must provide only one possible path between any two of its members. Gollin (2000, 99–102) shows that a network defined by a closed mathematical group can still allow for multiple pathways between members, and there may be times when exploring alternate concepts of distance opened up by different pathways is analytically appropriate.

[8] Within normative collections, central pitches assert themselves through salience and through the process of pattern completion. This is a voice-leading technique that Joseph Straus (1982) found in Stravinsky’s music; it occurs when a missing pitch from a collection established as normative sounds prominently in order to create a sense of arrival and define formal boundaries. (15) Pattern completion creates arrivals on the pitches F and C in the first appearance of the trumpet’s main theme (one measure after rehearsal 1). Figure 5 shows an animated Tonnetz analysis (Flash plugin required) of this passage. A dotted box around the horizontal span {B F C G D} indicates the five-note collection undergoing completion. A solid box encloses notes that have prominently sounded. The animation shows that within the first phrase, the trumpet effects a vertical motion of a single pitch on the Tonnetz through chromatic inflection. The rest of the phrase sounds the remaining 3 of 13 notes of the pentatonic collection except for F. At the end of the phrase, F sounds as a long-held pitch to complete the collection. The pitch C marks the end of the second phrase in a similar manner. (The second phrase also contains a rapid arpeggio. Because it gives the effect of a sweeping gesture, rather than a series of discrete pitches, I have not included it in my analysis.) These two arrival pitches—F and C—are a retrograde of the C-F dyad established as motivic at the work’s opening.

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