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Timing in music and temporal logic.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>2007
<mark>Journal</mark>Journal of Mathematics and Music
Issue number3
Number of pages17
Pages (from-to)173-189
Publication StatusPublished
<mark>Original language</mark>English


'In-time' representations of music in which the time represented is the same time as inhabited by the agent making or using the representation are contrasted with 'out-of-time' representations. Temporal logics with a similar 'in-time' perspective, and in particular those using operators S and U for 'since' and 'until', are explored as a means of representing musical situations, with particular reference to a paradigm 'triangle-player problem'. Illustrative implementations are given in the music software Pd. New versions of the operators S and U are defined to accommodate the musically important phenomena of regularly occurring events associated with metre, and to allow representations to reflect actual timings rather than relations of temporal order. Nesting of out-of-time representations within in-time representations then becomes possible and arises naturally as a way of representing certain kinds of musical situation.

Bibliographic note

The final, definitive version of this article has been published in the Journal, Journal of Mathematics and Music, 1 (3), 2007, © Informa Plc