Building Topological Spaces for Musical Objects

Abstract

Abstract. The development of spatial representations of musical objects allows for a reformulation of algorithmic problems arising in musical theory, fosters novel classifications and provides new computational tools. In this paper, we show how a topological representation for n-note chords associated with the degrees of the diatonic scale and for the AllInterval Series (AIS) can be automatically built using MGS, a rule-based spatial programming language. Then, we suggest a new categorization for AIS based on their spatial construction.

Supporting Music Composition with Interactive Paper

“…These six translations can be associated with the six possible moves in the hexagonal space. Although the resulting space noticed in [16] is not a perfect Tonnetz since the axes do not represent constant semitone intervals, it still offers a powerful tool for composition.…”

The T-calculus

“…Doing so, we somehow aim at generalizing to spatiotemporal structures the notion of spatial programming that is already emerging in bioinformatics system modeling or musical structure analysis [2,3].…”

Spatial Computing in MGS

“…MGS has also been used in other application area like self-assembly [15], autonomic computing [14] or automatic music analysis [4]. "Conventional" questions still apply to "unconventional" program, and for instance, the model-checking of a small fragment of MGS is presented in [9].…”