The Principle of Opposition - Functional Transformations and Octatonality in Selected Works by

In an interview with Crumb, Paul Steenhuisen commented that he felt a duality present in Crumb’s music, something he equated to “a polarity of light and dark, of life- affirming and deathly forces.”41

Crumb affirmed this observation and replied, “There are opposites like that, yes. I’ve always liked music that had the quality of presenting

opposites.”42

This opposition is present on many different levels in Crumb’s music. At the most superficial level, even the titles of his pieces suggest this preoccupation. In

Black Angels, movements are titled “Devil-music” and “God-music,” or in Makrokosmos

IIthe self-reflexive title “Twin Suns (Doppelgänger aus der Ewigkeit)” hints at an oppositional duality. Edward Pearsall describes “several structural paradigms that engender goal-direction in Crumb’s music. These paradigms are dialectical in nature:

Steenhuisen, “George Crumb,” 112.

equilibrium and disequilibrium, stasis and motion, and closure and continuity.”43 In particular, Pearsall situates symmetrical and asymmetrical pitch collections as opposing pairs because of the dialectic in which “asymmetry resists symmetry, while symmetry seeks to overcome asymmetry.”44

Resulting from this oppositional battle, Pearsall suggests, “Motion in this case is brought about through an interplay of contrasting ideas.”45

Such interplay between contrasting ideas is highlighted in Night of the Four

Moons (see Figure 2.19). Composed as “an artistic response to an external event,” the

work symbolizes Crumb’s “rather ambivalent feelings vis-à-vis Apollo 11.”46 This ambivalence, and perhaps disappointment, regarding the decreasing mystery of Earth’s opposing partner is reflected in the text of the first movement: La luna está muerta,

muerta. The farewell music shown in Figure 2.19, which alludes to Mahler’s “Der

Abschied” from Das Lied von der Erde and Haydn’s “Farewell” Symphony No. 45, “is

Crumb’s Das Lied von den Mond, a regretful farewell to the poetic and mystical qualities long associated with the moon, forever altered in 1969 by our arrival on the lunar

Edward Pearsall, “Dialectical Relations Among Pitch Structures in the Music of George Crumb,” in George Crumb & The Alchemy of Sound: Essays on His Music, ed. Steven Bruns, Ofer Ben- Amots, and Michael D. Grace (Colorado Springs: Colorado College Music Press, 2005), 58.

Ibid., 63.

Ibid., 65.

surface.”47

Not only does this intertextual connection highlight opposition in Crumb’s music but, also the intra-opus opposition between the white-note “Musica Mundana” {7902} tetrachord, which is played on stage and the primarily black-note “Musica Humana” D5

collection, which is played off stage.

Opposition is highlighted in both the objects and the transformational processes found in “Litany of the Galactic Bells” (see Figure 2.20). The piece begins with the right hand playing three hexachords belonging to WT2 while the left hand plays grace-note

Steven Bruns, “Les Adieux: Haydn, Mahler, and George Crumb’s Night of the Four Moons,” in George Crumb & The Alchemy of Sound, 125.

hexachords belonging to WT1. Following a four-second pause, the registral arrangement of collections is reversed and the right-hand pitches outline WT1 and the left-hand pitches outline WT2. In addition, the transformation of one hexachord to the next within each three-note segment is reversed: the first hexachord is transposed up by six semitones and then down by two semitones while the fourth hexachord is transposed down by six semitones and then up by two semitones.48

A similar grace-note technique, which also exhibits the principle of opposition, is found in Crumb’s “Music of the Starry Night” from Music for a Summer Evening (see Figure 2.21). In the program notes Crumb states:

As Bass argues, this figure references the chordal progression which opens the coronation scene from Mussorgsky’s Boris Godunov (see “Pitch Structure,” 354–57).The relationship of these whole-tone hexachords to the major-minor seventh tetrachords of Boris Godunov may seem tenuous; however, the style of a left-hand grace-note chord leading to a right-hand sustained chord is a familiar technique found in Crumb’s music. In “Primeval Sounds” Crumb opened with minor chord alternations which comprised members either of an octatonic or a mode-4 collection (see Figure 2.12). The resultant hexachord was the inversion of the Petrushka chord (see Figure 2.14). This stylistic grace-note figure also appears in “Music of the Starry Night” from

T6 T−2 T−6 WT1 WT2 WT2 WT1 T2

In its overall style, Summer Evening might be described as either more or less atonal, or more or less tonal. The more overtly tonal passages can be defined in terms of the basic polarity Fs/ds minor (or, enharmonically, Gb/eb minor). This (most traditional) polarity … is stated once again in “Music of the Starry Night,” with the quotation of passages from Bach’s ds minor fugue (Well-Tempered

a) p. 18, s. 1 b) p. 18, s. 1 c) p. 19, s. 2

Oct2 Oct1 Oct2 Oct2 Oct1 Oct2 Oct2 Oct1 Oct2 F0 F1 F3 F0 F1 F3 F0 F1 F3

T−5 T2 T−5 T2 T−5 T2

Oct2 Oct1 Oct2 Oct2 Oct1 Oct2 F0 F1 F3 F0 F1 F3

T−5 T2 T−5 T2

F4 F5 F1 F0 F5 F3 d) p. 24, s. 2–p. 25, s. 1 e) p. 25, s. 1

Oct1 Oct3 Oct1 Oct2 Oct3 Oct2 T−5 T2 T5 T−2

Clavier, book II) and a concluding “Song of Reconciliation” in Gb (overlaid by an intermittently resounding “Five-fold Galactic Bells” in Fs).49

This polarity occupies a significant portion of “Music of the Starry Night” and separates the structure of the movement into two parts: the first part contains the quotations of Bach’s fugue and the second part consists of the “Song of Reconciliation.” Although Crumb mentions a polarity between a major key and its relative minor key, polarity is also present within the transformational structure of the bell-like figures.50 The transformations of these figures within the first section of “Starry Night” remain

unchanged, featuring a T−5 to T2 pattern (see Figure 2.21a–c). This corresponds with the Ds-minor fugue quotations in this section.51 In the opposing second section, characterized by the Gb “Song of Reconciliation” and Fs “Galactic Bells,” the transformational scheme is altered for the final version of the grace-note figure (see Figure 2.21e). Instead of conforming to the established T−5 to T2 pattern, the indices of transposition are inverted to a T5 to T−2 pattern.

In “Litany,” defining the opposite whole-tone collection was relatively simple since there are only two distinct whole-tone collections; however, in “Starry Night” each hexachord could belong to either an octatonic collection or Messiaen’s fourth mode, which is indicated below the staff. There is always an intersection of four pitch classes between two octatonic collections: the intersection of Oct2 and Oct1 is {0369} while the

Crumb, program notes to Music for a Summer Evening (Makrokosmos III), in George Crumb & The Alchemy of Sound, 311.

These bell-like figures are reminiscent of the first three chords from “Litany of the Galactic Bells” (cf. Figure 2.20).

intersection of Oct2 and Oct3 is {258B}. Therefore, considering pc intersection, both Oct1 and Oct3 are equally opposite Oct2. This battle with opposition, and the symmetry which this opposition represents, is played out in the music. The first three progressions, shown in Figure 2.21a–c, are firmly entrenched in an Oct2–Oct1–Oct2 pattern. The first

progression of the opposing section transposes the original progression, which was framed by Oct2, and is comprised of the opposing collections to Oct2 (see Figure 2.21d). The final progression of the piece is the polar version of the first progression: instead of proceeding to Oct1, Oct3 is utilized, which changes the transformational schema (see Figure 2.21e). This reversal corresponds with the key-area polarity between the sections. The interpretation of each chord as a subset of Messiaen’s fourth mode does not reflect a similar oppositional pattern.52 Therefore, the preference to choose the octatonic reading over the mode-4 reading rests upon the two-fold assumption that both opposition and symmetry are essential characteristics of Crumb’s music.

The principle of opposition is evident in the progressions from “Come Lovely” (see Figure 2.6 and Figure 2.18).53 The tonal reading hinted at a tonic-dominant-tonic

The number of intersecting pitch classes between mode-4 collections depends on how far a collection is from another. For example, F0 shares six pitch classes with its immediate neighbours F1 and F5, while sharing only four pitch classes with F2, F3 and F4. Following the same criteria of determining an opposite as with the octatonic collection above, it would appear then that F2, F3, and F4 are all equally opposite. The reading of the first three progressions (F0–F1–F3) would result in a less symmetrical interpretation than the octatonic reading. Instead of “object–opposite–object,” the progression would be read as “object–neighbour–opposite.”

Robert Cook has pointed out that opposition is an important principle in other sections of “Come Lovely” in “Emerson’s Compensation and a Whitman Song by Crumb,” 6th

European Music Analysis Conference, Freiburg, Germany, 2007 and in an adaptation of this paper in “Crumb’s Apparition

opposition for the first three chords and the octatonic reading mimics this with an Oct1-Oct3-Oct1, Oct3-Oct2-Oct3, or Oct2-Oct1-Oct2 progression in the respective

iterations. Following the fourth chord, the fifth, sixth, and seventh chords cycle through each octatonic collection. An alternate segmentation of this chord progression also highlights the opposition within the progression. The segment from the third to fifth chords, as well as the segment from the fourth to sixth chords of each progression, exhibits the same type of polarity.

In document Functional Transformations and Octatonality in Selected Works by George Crumb (Page 51-58)