Honing, H. (2001) From time to time: The representation of timing and tempo. Computer Music Journal, 35(3), 50-61.


The first half of this paper reviews existing representations of timing and tempo as used in computational models of music cognition and in programming languages for music. They are presented in a formal way, their differences are discussed and some refinements are proposed. The second half of the paper introduces an alternative representation and model for time transformation, named timing functions (TIFs), that differs in two aspects from earlier proposals. First, timing is seen as a combination of a tempo component (expressing the change of rate over a fragment of music, such as rubato), and a timing (or time-shift) component that describes how events are timed (e.g., early or late) with respect to this tempo description. Second, timing can be specified in relation to the temporal structure (e.g., position in the phrase or bar) and global tempo.

Full paper (pdf).