ON CONTEXTUAL TRANSFORMATIONS.(music)

THE PROPOUND CHANGES that David Lewin and transformational theory have engendered in our thinking about music offer analytical possibilities that have only begun to be explored. The most compelling applications of Lewin's ideas have been by Lewin himself, in the illustrative analytic commentary on excerpts and short works of Generalized Musical Intervals and Transformations, and in the full-scale analyses of Musical Form and Transformation. [1] Analytical studies by Michael Cherlin, Henry Klumpenhouwer, Edward Gollin, and Shaugn O'Donnell, among others, have drawn inspiration from Lewin in interesting and productive ways. [2] Otherwise, Lewin's ideas have been slow to yield analytic offspring of consistently commensurate quality-a reflection not of their limits but of their depths. The basic reorientation that Lewin's approach Requires--the shift of focus away from equivalence relations among individual pitch-class collections and toward transformational processes that relate them--reaches deep into the analy tic process and adds an important, distinctive dimension to such inquiries. It also inspires an expansion and redefinition of what, exactly, a transformation is.

Perhaps the most successful, and broadly suggestive, analytical results have arisen from attempts to formulate new transformations that are sensitive to particular aspects of a given musical context. Contextual transformations help establish extensive and penetrating connections among musical events that might at first seem only unremarkably related, or not related at all. This manner of understanding transformation offers powerful possibilities, with applicability that is as rich (or as limited) as the musical ideas being examined. It deserves greater critical attention, and studied consideration of the possibilities it holds and the directions it might lead.

To explore this subject I first discuss and characterize the type of contextual transformation that has appeared most frequently in Lewin's work. Then I explore alternative conceptions and new analytic possibilities.

To start, let us take a look at a portion of Lewin's analysis of Dallapiccola's "Simbolo," the first piece from Quaderno musicale di Annalibera (MFT 1-15). Example 1a displays measures 11-16 of the work, and 1b reproduces Lewin's analytic notations for that passage through the beginning of measure 16 (from Example 1.2, MFT, 5). Lewin's analysis highlights two "configurations" of the aggregate (measures 11-14) 15- 16), each with an [F.sub.3]-[G[flat].sub.4] dyad in the left hand and a series of dyads and trichords, which he explains as products of linear motion, in the right hand. The transformation from the first configuration to the second, he asserts, occurs via operation "I," defined as "inversion about [an] odd-dyad-out" (MFT, 7). In other words, the [F.sub.3]-[G[flat].sub.4] dyad--the "odd-dyad-out"--acts as a kind of inversional hinge in the transformation of the first configuration into the second. Lewin explains,

The operation I, it will be noted, was not defined as "inversion about F and F#," or as "inversion about C, followed by [T.sub.11]." It was not defined with reference to any pitch classes whatsoever. Rather, it was defined with respect to a "contextual" feature of the configuration(s) upon which it operates .... This sort of "inversion" operation differs from those defined by pitch-class centers. (MFT, 7)

In other words, to use terminology that Lewin expressly avoids early on in his analysis, the configurations realize two forms of the piece's row that are inversionally related (at [T.sub.11]I). The odd-dyad-out is an invariant ic 1 dyad between the two forms. There is no complete, unambiguous row ordering at the beginning of the piece, but we initially suspect, and eventually can confirm, that this invariant dyad occurs in the row's first two order positions. From this we may conclude that any pair of row forms [P.sub.n] and [I.sub.(n+1)] will share an initial ic 1 dyad. Indeed, that is exactly how Lewin approaches "I" later in the piece, when configurations cease to connect via odd-dyads-out, requiring him to invoke "some stronger ordering from which both types of configurations can be derived," namely the piece's tone row, and to redefine "I" as "inversion-about-thenotes-of-the-boundary-semitone" (MFT, 12-13).

Lewin's initial "I", then, recognizes a special way of configuring any two row forms [P.sub.n] and [I.sub.(n+1)] such that the initial invariant dyad is highlighted as an inversional hinge. This "I" is typical of many of the contextual transformations that Lewin defines and describes in his analyses. The configurations being associated are inversionally equivalent, and the key contextual feature that relates them, the catalyst of transformation, is a set of common tones. A survey of other contextual transformations throughout Lewin's work reveals that invariance among inversional equivalences (in pitch or pitch-class space) is almost always somehow involved.