Department of Computer Science and Technology

Technical reports

On the calculation of explicit polymetres

W.F. Clocksin

March 1995, 12 pages

DOI: 10.48456/tr-360


Computer scientists take an interest in objects or events which can be counted, grouped, timed and synchronised. The computational problems involved with the interpretation and notation of musical rhythm are therefore of particular interest, as the most complex time-stamped structures yet devised by humankind are to be found in music notation. These problems are brought into focus when considering explicit polymetric notation, which is the concurrent use of different time signatures in music notation. While not in common use the notation can be used to specify complicated cross-rhythms, simple versus compound metres, and unequal note values without the need for tuplet notation. From a computational point of view, explicit polymetric notation is a means of specifying synchronisation relationships amongst multiple time-stamped streams. Human readers of explicit polymetic notation use the time signatures together with the layout of barlines and musical events as clues to determine the performance. However, if the aim is to lay out the notation (such as might be required by an automatic music notation processor), the location of barlines and musical events will be unknown, and it is necessary to calculate them given only the information conveyed by the time signatures. Similar problems arise when trying to perform the notation (i.e. animate the specification) in real-time. Some problems in the interpretation of explicit polymetric notation are identified and a solution is proposed. Two different interpretations are distinguished, and methods for their automatic calculation are given. The solution given may be applied to problems which involve the synchronisation or phase adjustment of multiple independent threads of time-stamped objects.

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BibTeX record

  author =	 {Clocksin, W.F.},
  title = 	 {{On the calculation of explicit polymetres}},
  year = 	 1995,
  month = 	 mar,
  url = 	 {},
  institution =  {University of Cambridge, Computer Laboratory},
  doi = 	 {10.48456/tr-360},
  number = 	 {UCAM-CL-TR-360}