On Reading Timbre and Tempo from the Score

Typically, a musical score alludes only briefly to the ways in which timbre and tempo vary through the piece, leaving it to the performer to answer the question of how to interpret those elements in detail. If a musical piece is programmed with a computer, timbre and tempo must be specified throughout the piece. This leaves us with the problem of how to program tempo and timbre if we are given a musical score. We describe here some systematic techniques for reading timbre and tempo from a musical score. The basic idea is to associate an algebraic structure to our score, and, by associating certain parameters to that algebraic structure, derive the timbre and tempo of the piece. Our first approach is to associate a consonance structure to the score, and reflect that in the timbre and tempo of the piece. This is what we do in sections 2-5 and section 7. Here, our approach relates to the problem of tuning the notes of our piece in a consistent way. A second approach is to reflect higher dimensional arrows implied by temporal subdivisions of the piece. This is what we do in section 6. In section 8 we mention a third crude approach, where we just count through the notes of a piece successively, so our notes are indexed by elements of an interval in Z, which we reflect in the timbre of our piece using a function.