# BY DEGREES (2020)

Instrumentation: small ensemble

Around the time of this work, I had been assigned the task of writing a piece that examined different kinds of notation, was immersed in the probabilistic procedures Iannis Xenakis used to compose Achorripsis, and was harbouring a desire to return to the so-called ‘modular’ notation I used in Variations mostly because of how fun it was to use.

As I thought of ways I could serve all of these interest in a single piece, I not entirely unexpectedly found my way to those ‘chose-your-own-adventure’ books for ideas while looking for guidance, and can report proudly that though I expected to come across easily ridiculable stuff that might nevertheless provide me with a bit of clarity on the kinds of things I could expect from my notation I in fact stumbled my way into a genre replete with innovators and movements and shovel-loads of imagination. Research has made it difficult to determine exactly how, but I somehow ended up sitting with a copy of Raymond Queneau’s Exercises in Style for an hour or so and this fired my own imagination to the point that I was able to start devising the basis of a notational system.

## The overarching design of the piece serves as a means of attempting to answer the question of what varying the amount of control a composer allows themselves over the realisation of their music has on the end result. My idea was that to the left of my score, notation would be at its most inflexible, requiring the least creative input from performers, and the inverse true on the opposite side. Subsequent research showed the idea of ‘control’ over notation to be a far more complex and imprecise concept than I had appreciated (thinking about a hypothetical notation that requires zero input from performers helps to illustrate the problem—what would such a notation look like? How detailed and complex would it need to be? Is there really a way to quantify the amount of input given to a piece by a performer, or indeed in any given moment? Is it possible to have no control over the realisation of a piece, and what would be the role of a ‘composer’ in such a case?), but there is a general trend throughout the piece of me loosening control and requiring more input from performers to determine the sounds produced.

## There’s a lot of maths here. The thing below is Xenakis’ starting point for Achorripsis.

## Check out the commentary for the maths, but a Poisson distribution (a type of probability) determines how many ‘events’ take place in each cell. Or, put another way, density is the parameter given the highest hierarchical position in the piece’s structure (would it not be a cool idea to run with this idea and consider what would happen if you took any parameter other than pitch, harmony or rhythm and made it the basis of a piece, you ask? It would—might I direct you to my Parametric Study). I noted that I could simply steal this idea, but still I needed ways of formalising and controlling the following parameters:

##

## Pitch

## Duration

## Modularity—simply, the relationships between cells. Does a cell begin immediately after the one preceding it has ended, do you move on to it when some other event happens, etc.