Musical Composition and Gestural Diagrams

Abstract

By an adjoint functor argument, we reinterpret categorical gestures as being “continuous diagrams” with values in topological categories, which we therefore call “gestural diagrams”. This allows to view traditional transformational diagrams as canonical restrictions of gestural diagrams and to reinterpret musical gesture theory in a natural way as a topological extension of transformational theory. We apply these tools to extend the concept of a musical score to a “processual diagrammatic score”. Such a score not only captures the result of a compositional effort but also the poietic process and its underlying gestures. These conceptual extensions can be modeled on the level of denotators and forms so that an implementation for the Rubato Composer software becomes feasible. Recent developments in this software enable the definition of affine transformations using finger gesture input on trackpads. Once such gestures are abstracted in a transformational processual diagram we introduce a Bruhat decomposition argument for $\text{SL}_2(\Bbb{Z})$ to reconstruct canonical gestural diagrams. Based on this model, we suggest new ways of graphical software interaction that facilitate dynamic navigation and intervention in the composition’s history.