Musical Durations as Mathematical Intervals: Some Implications for the Theory and Analysis of Rhythm

Abstract

'Where is the beginning of a piece of music? Where is the end?' I believe it was Edward T. Cone, in Musical Form and Musical Performance, who last set out to tackle this deceptively simple-minded question.' As Cone notes initially, 'some of the most important scientific discoveries have resulted from taking seriously questions that are usually assumed to be trivial'. With characteristic modesty, Cone makes it clear that his own conclusions would not amount to momentous scientific discoveries comparable to the theory of the expanding universe; he does hope, however, to 'throw some light on ... [the] problem ... [of] how to achieve valid and effective musical performance'. For many musicians and music theorists (myself included), Cone's slim volume has always meant much more than an essay on musical performance; Musical Form and Musical Performance is actually an important contribution to the theory and analysis of musical rhythm. If, in the present essay, I venture to revisit some of Cone's 'foolish questions', this is because I believe their rhythm-theoretic implications have not thus far been fully exhausted. Whether, in the end, these implications would seem momentous or not is of course not for me to say. Perhaps the King of Hearts, quoted above, has not only spoken the first and last word on the subject of performance (as Cone has wryly observed), but on the subject of rhythm as well.