# Michael Edwards

# HOTPO

## Programme Note

Hinting at something a little more coarse, the title *HOTPO* is in fact a
completely innocent reference to the *Collatz Conjecture*. This mathematical
proposition, also known by other names, refers to a succession of numbers called
the *hailstone sequence* (or *wondrous numbers*), because their values usually
ascend and descend like hailstones in a cloud.

Though the mathematical proof of the conjecture is complex, the proposition is
very simple: Take any positive whole number; if it is even, divide it by two; if
it is odd, multiply it by three and add one (hence the acronym *Half Or Three
Plus One*: *HOTPO*); repeat the process with the result and you will find that
no matter which number begins the process, you will always, given enough
iterations, reach the number one.

The algorithm is easy to programme and experiment with; plus it produces rather nice images when given different starting numbers and plotted over various iterations. I used the algorithm in this piece to generate section lengths and repeated structures from nine basic rhythm sequences, hence my sequence was 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1. The piece alternates sections opposing mixed materials (odd section numbers) with obsessively repeated material (even). The numbers are also used for the generation of the sound files triggered during the performance. Despite the rather abstract nature of the generative procedure, the results of the algorithms were developed intuitively and the piece as a whole arises out of and proceeds through a maelstrom of events fitting to the imagery of a hailstorm.