The Theoretical Improvisation of (and within) Possible Worlds

THE THEORETICAL IMPROVISATION OF (AND WITHIN) POSSIBLE WORLDS MICHAEL C. GARDINER Where, for the complete expression of one’s subject, does a particular relation stop—giving way to some other not concerned in that expression? Really, universally, relations stop nowhere, and the exquisite problem of the artist is eternally but to draw, by a geometry of his own, the circle within which they shall happily appear to do so. —Henry James, preface to Roderick Hudson (8) 0.0 INTRODUCTION HIS PAPER EXPLORES THE POSSIBILITY of reading music-theoretic space as both a “site” and a “trajectory” for improvisational gesture based on Alain Badiou’s book Being and Event (hereafter BE), which articulates a set-theoretic architecture of the subject, an ontology , posited against a backdrop of pure multiplicity.1 In a generic sense, a site is a bracketed region, a situated focus or viewpoint that gains a foothold in the midst of a multiplicity (where “generic” refers to a mathematic orientation that admits aspects of the unnameable, the T 32 Perspectives of New Music unassignable, and the indiscernible into being) (BE 538, 542). A site frames elements but does not complete them, insofar as they remain open to the indiscernible. The role of the site is to assemble a representational space that will serve both as a general background, as well as the point of departure for any individual use of that space. Next, a trajectory is the moment-to-moment unfolding of a path, an improvisation , that originates within a site, but thereafter leads to unexpected flights extending beyond the site’s initial scope. Many have argued that we live in an age of synthetic philosophy and virtual reason,2 one that makes room for a multiplicity of possible worlds.3 Additionally, scientific research has shown that we live in constructed worlds of perception and cognition, worlds that can likewise be interpreted as highly synthetic and dynamic. How does this context impact ontology, specifically music-theoretic ontology? Following a philosophical overview of the site/trajectory pairing—the site as a situated focus that gains a foothold in the midst of a multiplicity, and the trajectory as the moment-to-moment unfolding of an individual, improvised path that originates within a site—this paper suggests that the principles of construction and subsequent engagement with possible worlds in the domains of philosophy, cognition, and music theory involve improvisative assemblages that lead to the formation of identity in the midst of multiplicity. (An “assemblage” demarcates the initial phases of a set-syntax in which a singular ordering of elements is not relevant, resulting in a horizon open to continuous conjugation merging content and expression.) In this scenario, music theory becomes a mode of action in a possible world that theory itself has instantiated. Which is to say, improvisative constructions result in the configuration of a site as well as the exploration of that site’s hypothetical contents, its trajectories. For Badiou, this coupled logic of site and trajectory, namely “being” and “event,” leads to the discernment of new truths.4 Following a summary of Badiou’s arguments in Being and Event in the first section of the paper, the second section aligns some technological aspects of music’s improvisational templates, as discussed by George E. Lewis and August Sheehy, with Badiou’s philosophical understanding of being-as-site and event-as-trajectory. The coupling of Being with “site” and Event with “trajectory” is true for Badiou insofar as: “Being is a category of that which constitutes any world [i.e., a site], whereas Existence is a category of appearing [i.e., a trajectory] in a determined world” (Badiou 2011, 9). (To this I would add that a trajectory, defined here as that which follows from a determined existence, constitutes both an “appearing,” and the continuation of the The Theoretical Improvisation of (and within) Possible Worlds 33 inflection of appearing; a path capable of opening into the indiscernible.) The third section of the paper examines the construction of background maps in neural populations as exemplars of site formation in the field of perception and offers a reading of music theory modeled upon the embodiment of Badiou’s ontology and its relation to the...