Atonal Transformational Voice-Leading in Webern’s Op.27 #3
[1.] One had something to say. What did one say? Ideas. [But] how have ideas been formulated according to musical laws? …
[2.] Presentation of a musical idea: what is one to understand by that? The presentation of an idea by means of notes. …
[3.] The highest principle in all presentation of an idea is the law of comprehensibility. Clearly this must be the supreme law 1
In his “Path to New Music” lectures, Webern distills, exposes, and elevates ad summum four terms which he situates in a dialectical relationship. 2 Hence, ideas, formulation according to musical laws, presentation by means of notes, 3 and absolute conformity to the principle of comprehensibility, form the substructural quadrality of Webern’s compositional language. Migrating them to our present work: Op.27 #3’s idea, accordingly, consists of a rhythmicised unfolding of Webern’s 12-tone Nomos. 4 The presentation of this idea is athematic 5 (as I hear it), however, it is clearly partitioned in five variations. 6 The variation’s structural divisions are demarcated by ritardandi and changes in tempo, while also involving sudden changes in the textural interplay of legato or quasi-legato lines (albeit in short constellations of notes), staccato articulations (both single notes and chords, thus also highlighting the work’s pointillistic nature), and chordal resonance reposes (as in the sustained trichords and tetrachords in mm.24-42; 56-66). I will focus my analysis on precisely this latter third feature. Applying an analytical apparatus similar to Joseph Strauss (pages 107-110), I will present and argue the logical coherence of Op.27 #3’s trichordal transformational voice leading.
The first sustained chord in the piece occurs in mm. 24. From there on until mm. 42, all other sustained trichords sound simultaneously with either another note above or below the held chords, or with an appoggiatura-like note which is held throughout the sustained chord’s duration (as in mm. 34; 38). I think it is important to decide whether to treat these pitches as ornamental to the sustained resonances, or as an integral and active participant in their construction and subsequent unfolding. In my voice-leading schematization (Fig.2 and 3), I have excluded them entirely, since, in all cases, I hear them as belonging to another melodic line. In fact, starting with mm. 24, I hear the first clearly distinguished two-voiced polyphonic texture of the piece: Where the first voice is the composed-out 7 stream of sustained resonances (mm. 24-42), while the second voice is the legato or staccato melodic line that unravels simultaneously with it. In the whole piece, there are only two occurrences—in mm. 37 and 41—where Webern verticalizes both voices into a tetrachord. However, as Fig.1 illustrates below, I would argue that the tetrachords appearing in mm. 37 and 41, are only rhythmically displaced variations on the gestures which precede both tetrachords a few measures earlier.
Fig. 1: Verticalization of two tetrachords, formed by rhythmically displacing an appoggiatura figure in the preceding measures. 8 (Webern, Variations Op.27 #3, mm. 34; 37; 38-39; 41)
Having thus established the clear independence of the sustained trichordal resonances, in Fig.2 we can proceed with rhythmically abstracting and schematizing them in one over-arching gesture. What is meaningfully revealed by this enumeration, is their membership to the the same set class 3-5 (016), which is a further motivation for unearthing their voice mappings into one another.
Fig. 2: Schematization and enumeration of the sustained trichords. (Webern, Variations Op.27 #3, mm. 24-42)
Fig. 3, below, illustrates the pitch class counterpoint that results from the transpositional and inversional operations. I believe it would be fruitless to go further layers down in the analysis, by considering separately only the transpositions or inversions that result 9, because what matters—and is clearly heard,—are only the trichords’ relationships in immediate sequence.
Fig. 3: Transformational voice leading (Webern, Variations Op.27 #3, mm. 24-42)
It is significant to observe how Webern has essentially limited the movement of the voices to either harmonic planing, or to outer-voice inversional exchanges. No other movement occurs in the passage. This willful limitation in choice, however, not only guarantees the passage’s coherence and comprehensibility, 10 thus rendering a long-range progression audible, but it can also serve the pianist in making meaningful choices about the chord’s voicings.
Once the passage in mm. 24-42,—which is also the movement’s third variation,— sets up this voice-leading precedent, let us turn to the concluding “Wieder Ruhig” section in mm. 56-66 —which is also the movement’s final variation and the Nomos’ recapitulation,—to see if Webern employs a similar voice leading strategy. The crucial difference between the two passages, one immediately discovers, is the interplay between sustained trichords and their staccato companions. Although my intention thus far has only aimed at analyzing the voice leading transformations that occur between the sustained resonances, as it will be shown below in Fig. 4 and 5, it is crucial to include both types of chords into the following schematization. Hence, Fig.4 rhythmically abstracts and schematizes them in one over-arching gesture, while Fig.5 illustrates the pitch class counterpoint that results from the transpositional and inversional operations:
Fig. 4: Schematization and enumeration of the sustained and staccato trichords (Webern, Variations Op.27 #3, mm. 56-66)
Fig. 5: Transformational voice leading (Webern, Variations Op.27 #3, mm. 56-66)
What Webern does with this passage becomes utterly transparent once we present the chords according to their set-class memberships. The sustained/staccato articulations, exchange places among (014) and (016) chords, however, the voice leading between the chords does not deviate at all from the outer-voice inversional exchanges illustrated earlier in Fig.3. Consequently, it is logical to deduce that Webern first composed this passage by separately looking after the (016) and (014) chord progressions and their abiding to only one type of pitch-class voice leading movement; And only in a second moment, did he set in motion the playful articulation exchanges. Op.27’s late Webern, therefore, is quite different from his earlier self as presented by Strauss’ analysis ( pages 107-110). Whereas formerly he favored more pitch-class counterpoint motion variety, in Op.27 #3, he pursues stricter, more austere voice movements. Certainly, part of the reason for this change, is to be found in the formulation 11 of the 12-tone Nomos. However, the intentionality and strictness that results from the voice leading schema, implies that Webern was actively involved with more than blindly following the row’s arbitrary caprices.
Schoenberg, Arnold. (1975) ‘New Music, Outmoded Music, Style and Idea’, in Style and Idea. Berkeley and Los Angeles: University of california Press.
Straus, Joseph N. (2005) Introduction to Post-Tonal Theory, 3rd edition New Jersey: Pearson Education
Webern, Anton. (1963) The Path to the New Music. Bryn Mawr, Pennsylvania: Theodore Presser Co.