Instrumentation

Four Like Saxophones (SSSS,AAAA,TTTT, or BBBB)​

​

Program Note

Collatzeral Branches is a proof of concept for a repeatable process to derive music from the mathematical series produced by the Collatz Conjecture. Yet unproven to be infinite, the Collatz Conjecture produces numerical rows that, for all known whole positive integers, inevitably simplifies to a repeating pattern. By selecting any number, one can produce a predetermined row of numbers that can then be filtered through rulesets to produce whole musical rows.

In Collatzeral Branches, elements of the series are reflected in their arrangement, using four identical voices to highlight the unique qualities of each row and their similarities to each other. However, each row inevitably returns to a repeating pattern, their paths including and comprising other entire rows; whatever choices are made, there is only one result for each row. Therefore, this process serves as an exercise of the composer’s agency solely in creating interest and cohesion between these rows through arrangement.

​

Recording:

​

​

​

​

​

​

​