# Precedent for triangular rhythmic series

An expanding triangular series for an integer n is 1, 2, ... , n-1, n, and a contracting triangular series for an integer n is the retrograde of the expanding triangular series for n.

By setting 1 to a unit of time, either series can be realized as a rhythm in which the rhythm's ordered series of inter-onset intervals is an expanding or contracting triangular series, measured according to this unit.

I can think of isolated examples of such a rhythmic series. But I'm wondering if there is a composer or type of music for whom/which this sort of thing is a distinctive aspect, assuming n of sufficient size (and variety) to be distinctive.

Thanks,

-Scott Murphy

## Comments

Hi Scott,

I don't know about this being characteristic for this composer, but Vineet Shende's

Throw Down or Shut Up!(2006) uses such series (both contracting and expanding, but mostly contracting) thematically. Taking a quick look, I think the longest one might be 11-10-9 ... 3-2-1. My quartet of the same name is in the process of publicizing our recording of this piece, but I can send mp3 and score directly in case that's useful.Cheers,

Daphne Leong