Computing with Chord Spaces

The number of solutions involved in many algorithmic composition problems is too large to be tractable without simplification. Given this, it is critical that composition algorithms be able to move through different levels of abstraction while maintaining a well-organized solution space. In this paper we present the following contributions: (1) extended formalizations and proofs needed to implement the chord spaces defined by Tymoczko [11] and Callender et al. [2], (2) a generalized framework for moving between levels of abstraction using quotient spaces that can easily be integrated with existing algorithmic composition algorithms, and (3) an application of both to voiceleading assignment.