Writings

Various scholars such as Lewin, Straus, Childs, Gollin, and others have attempted to extend the neo-Riemannian transformations P, R, and L first defined for triads to other trichords and larger set classes. However, no theorist has yet explored the shared structure that underlies the diverse transformations they discuss: each involves the inversion of a set class around a symmetrical subset. A family of contextual inversions thus exists that includes a wide variety of operations described in the theoretical literature as well as many others not yet discussed.

This generalized family of common-tone preserving contextual inversions can be defined as follows: Jx is any contextual inversion wherein the pitch classes of a symmetrical subset with cardinality N-x invert onto themselves, where N is the cardinality of the original set and x is the number of set class members that invert onto new pitch classes. After presenting a system of nomenclature for this new family and data regarding the possible J-inversions and their inherent voice-leading distances, this theoretical framework will be applied to the music of Ellen Taaffe Zwilich, whose recent Quintet (2011) provides an excellent case study. In that work, three different of the five possible J1 and J2 transformations on [012479] play significant roles in the work’s musical surface and large-scale structure. By examining Zwilich’s use of the generalized J-inversion in the Quintet and highlighting that family’s unique aspects, I will demonstrate its relevance for theorists and composers alike.

Though few fragments of musical notation from Ancient Greece survive, contemporary descriptions and theoretical discussions agree that such music relied on three tetrachords—known as the diatonic, chromatic, and enharmonic genera—from which scales were derived.  The diatonic genus includes a half-step followed by two whole-steps and is the foundation for the major/minor modal system upon which Western art and popular music has been based for centuries.  The chromatic (two semitones plus a minor third) and the enharmonic (two quarter-tones and a major third) also can be used to build seven-note scales, yet those collections fell out of favor after the time of the Ancient Greeks.  While the diatonic has been thoroughly covered in the theoretical literature, the collections built on the other genera have not received nearly as much attention.  My research attempts to rectify that situation by applying to the other two Greek genera criteria previously discussed in relation to the diatonic.  By examining the scales of all three Greek genera through a variety of approaches, I hope to stimulate renewed interest in the chromatic and enharmonic as both important historical artifacts and viable compositional resources. 

Writings on Ellen Taaffe Zwilich’s music focus on three main elements: organic melodic development, continuous variation, and orchestration. Though the first two of these issues are of prime importance, the last has been discussed most frequently in the existing literature, and none of the existing studies offer any clear insight into how Zwilich creates the unified, yet unpredictable structures that characterize her style.  Her idiosyncratic construction of strongly directional, yet varied lines is rarely explored and remains little understood.

The present study will examine the ways Zwilich employs two groups of characteristic transformations to create, disrupt, and ultimately resolve pitch processes: retrograde inversional chains (or RICHes) and the neo-Riemannian L, P, R, and S.  Such transformations are often constructed as chains, which Zwilich then interrupts, diverts, or dissolves to build forward motion and increase continuity.  Using examples from across her career, this paper will show how Zwilich’s distinctive melodies often appear to strive toward a goal, encounter obstacles and detours, and eventually reach a satisfying conclusion.  The transformational approach taken here thus will not only offer a technical account of the pitch organization of Zwilich’s distinctive melodies, but also provide a basis for dramatic interpretation.

The three main themes from Ellen Taaffe Zwilich’s Concerto Grosso (1985) all exhibit a tripartite structure wherein each element is developed using a unique strategy: an object-based approach in which an identifiable melodic pattern is transformed using various means, a process-based approach whereby a limited set of operations are applied to diverse objects, and a combination-based strategy involving a limited number of static objects being placed into a particular structural position. While each of the three thematic elements and their related developmental strategies transverse rich analytical territory, this paper will focus on Zwilich’s treatment of first such element: the opening six-note motive, which in fact is treated with both object- and process-based approaches.

Zwilich’s use of that main motive (a member of set class 6-14 or 013458) is largely based on a contextual inversion labelled J, wherein a symmetrical subset whose cardinality is one less than that of the original set is preserved while the remaining pitch inverts around the fixed subset. That transformation plays three vital roles allowing Zwilich to apply both object- and process-based developmental strategies to the main motive. First, J-related pairs of 6-14s are a significant surface feature of the work. Second, any such a pair of J-related 6-14s forms the septachord 7-Z37 [0134578], which serves as a source set for other pitch material. Lastly, Zwilich incorporates a process-based approach by applying J to set classes other than 6-14 (including those of differing cardinalities). Those three uses of J thus connect disparate motive forms into a rich network of associations, giving the work a striking organicism and natural ease that belies the sophisticated developmental strategies at work.

Gyorgy Ligeti’s Arc-en-Ciel from the Etudes pour Piano synthesizes a number of sophisticated rhythmic processes into a subtle and highly personalized temporal language.  Through the use of techniques including polymeter, polyrhythm, implied meter, and rhythmic pivots, Ligeti deftly introduces, prolongs, and resolves rhythmic dissonance to create a deeply moving musical expression.  Clarifying some often confused rhythmic terms and introducing new phrases sets up a strong foundation to study Ligeti’s manipulation of music’s temporal aspect in greater detail.  Drawing on analyses of both the musical surface and deeper rhythmic frameworks, this paper will examine the above techniques to show how Ligeti incorporates them into a unique and meaningful language.