Academic journal article Music Theory Online

Metaphors in Motion: Agents and Representation in Transformational Analysis

Academic journal article Music Theory Online

Metaphors in Motion: Agents and Representation in Transformational Analysis

Article excerpt

[1.1] Readers of David Lewin's transformational theories may sense a tension between his very dynamic conception of music and the static diagrams he presents. He describes analysis performatively, in terms of an actor or agent who moves through a transformational "space" via distinctive "gestures," but this conceptualization is difficult to convey on the printed page.(1) In the last few years, other scholars have begun to explore the possibilities of computer animation for highlighting the dynamic and spatial qualities of transformations.(2) Many of these analyses retain the abstract graph-theoretic diagrams that are typical of Lewin's static analyses, but add objects moving in time with recordings, thus achieving some sense of spatiality and performative gesture.

[1.2] At the same time, however, these improved representations highlight some basic questions about transformational conceptualizations of music that, because they were not so apparent in static analyses, have not been critically examined. Both in language and in visual representation, transformational theory invokes numerous mental models that are not always consistent. As animations become more representational and realistic, these underlying models become more obvious, as do their different conceptual schemas. It seems to be a good moment, then, to examine the language and graphics used in the foundational documents of transformational analysis in order to ensure that the symbol systems of new graphics will neither contradict nor overwhelm the theory's essential perspective.

[1.3] Inspiration for this type of detailed meta-level attention to the underlying conceptualization of a musical analysis could come from work done in the field of music cognition, particularly from those studies that focus on the use of metaphor as a means of elucidating underlying conceptualizations of music. Through this sort of attention to the details of language used for transformational theory specifically, general assumptions of the discipline can be revealed and possibly questioned. Once this groundwork has been covered, the opportunity arises to use these underlying conceptualizations in the creation of new graphic analyses that have the potential for deeper and more meaningful communication of information than the original graphs.

[1.4] Transformational theory uses many of the same metaphors and underlying concepts as other theories of music, but also contains unique elements. For a computer animation of a transformational analysis to be effective and well-situated, these elements must be analyzed and questioned. My analysis will examine two texts considered fundamental to transformational theory: Lewin's Generalized Musical Intervals and Transformations (Lewin 1987; henceforth, GMIT) and his analysis of Stockhausen's Klavierstück III in Musical Form and Transformation (Lewin 1993; henceforth, MFT), which is set up as a how-to manual for completing a transformational analysis. The two sources in combination will present most of the key issues in the language of transformational theory.(3)

Categories and transformations

[2.1] The most general concept used in transformational theory, and one common to most theories of music, concerns the nature of music itself. Contrary to the phenomenological position, where music is conceptualized only through an individual's subjective experience, most music theories use a language which conceptualizes music in terms of concrete objects.(4) This could be as simple as conceptualizing music as a series of objectively discriminate sounds, or it could entail more complex systems that classify musical events in different ways: pitches, members of scales, durations, and so forth. The advantage to this conceptual turn is that it allows theorists to describe relationships among these discrete objects.

[2.2] The grouping of objects into more complex systems based on the relationships among them demonstrates the cognitive process of categorization, which is a common way of organizing and understanding knowledge about the world. …

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