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
(Webern: 17; emphasis added)
In his “Path to New Music” lectures, Webern distills, exposes, and elevates ad summum four terms which he situates in a dialectical relationship. Hence, ideas, formulation according to musical laws, presentation by means of notes, 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. The presentation of this idea is athematic (as I hear it), however, it is clearly partitioned in five variations. 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 (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 (Ex.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 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 Ex.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.
Example 1: Verticalization of two tetrachords, formed by rhythmically displacing an appoggiatura figure in the preceding measures. (Webern, Variations Op.27 #3, mm. 34; 37; 38-39; 41)
Having thus established the clear independence of the sustained trichordal resonances, in Ex.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.
Example 2: Schematization and enumeration of the sustained trichords. (Webern, Variations Op.27 #3, mm. 24-42)
Ex. 3, therefore, 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, because what matters—and is clearly heard,—are only the trichords’ relationships in immediate sequence.
Example 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 (Webern: 22), 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 Ex. 4 and 5, it is crucial to include both types of chords into the following schematization. Hence, Ex.4 rhythmically abstracts and schematizes them in one over-arching gesture, while Ex.5 illustrates the pitch class counterpoint that results from the transpositional and inversional operations:
Example 4: Schematization and enumeration of the sustained and staccato trichords (Webern, Variations Op.27 #3, mm. 56-66)
Example 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 Ex.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 (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  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.
 Webern’s syntactic choices ambiguously wrap-up these terms in a complicated relationship. Everything is further compounded whether one decides to etymologically excavate the differences between formulation and presentation of an idea, which could mark an important hermeneutical distinction between the two. Lastly, the English translation of Idee, Gedanke, and Einfall, as simply Idea, is a complication in itself which, again, I am completely avoiding.
 Contrast this to Schoenberg’s broader formulation in “New Music, Outmoded Music…”:
“In its most common meaning, the term idea is used as a synonym for theme, melody, phrase, or motive. I myself consider the totality of a piece as the idea: the idea which its creator wanted to present (Schoenberg: 122-123).”
 cf. “ I read in Plato that ‘Nomos’ (law) is also the word for ‘melody.’ Now, the melody the soprano soloist sings in
my piece as the introduction (recitative) may be the law (Nomos) for all that follows! As with Goethe’s ‘primeval plant’ with this model, and the key to it, one can straightway invent plants ad infinitum . . . Isn’t that the meaning of our law of the row, at its deepest? … In my case; nothing happens any more unless it’s agreed on in advance according to this ‘ melody‘! It’s the law, truly the ‘Nomos!’ But agreed on in advance on the basis of canon!” (Webern: 63, et passim).
 cf. “But now I can invent more freely; everything has a deeper unity. Only now is it possible to compose in free
fantasy, adhering to nothing except the row. To put it quite paradoxically, only through these unprecedented fetters has complete freedom become possible.” (Webern: 55-56)
 cf. “Examining the development of variation technique one has direct access to serial technique. Relationship to
theme or row is quite analogous. But Schoenberg once said: the row is more and less than a variation-theme. More, because the whole is more strictly tied to the row; less, because the row gives fewer possibilities of variation than the theme.” (Webern: 58)
 That is, composed over a long stretch of time as one unified gesture, without any reference to J.N.Strauss use of
the same term in (103-106).
 An interesting argument could be made about the transformation of an appoggiatura into a suspension.
 As does Strauss in pg. 107-108
 Here I am distinguishing between the formulation of the Nomos and the set of pitch relationships which can
potentially result from it, and its presentation as it concretely occurs in the piece through its rhythmicisation, row transpositional choices, articulations, and textures. Also, cf. with footnote nr.1.
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.