Reflections on non-linearity

At present I’m about two-thirds of the way through my doctorate (with Mark Bowden at Royal Holloway, University of London) and, although the project still feels like a sprawling mass at this point, one or two key concepts have started to emerge a little. I’ve become increasingly interested in structures which follow a downward, or decreasing, shape – a ‘diminuendo’ in the more literal/non-musical translation of the word – ever since I started thinking about pieces that I love, and why I’m fascinated by them. My attention was grabbed by the following passage in Bob Snyder’s excellent book Music and Memory:

Closure that is realized through other means, as through downward motion of parametric values […] is not as precise. When we hear a falling series of values for a single parameter, we are probably not sure what the last value in the series will be—there is no specific implied final point.
Music and Memory (Snyder 2001), p. 201

This idea has found its way into a number of recent pieces; the piano part to the second movement of in negative is constructed via a simple, but rigid, algorithmic process: two sequences (one of pitch, one rhythm) are interwoven to generate a musical line:

Opening to second movement of 'in negative', piano part

This is then eroded by a second process – at first small pauses appear, and the idea seems to become a little tentative:

Piano part to 'in negative', b. 16-18

Ultimately the line decays almost entirely, revealing a slow & indistinct ground bass:

This erosion/decay is also a principal factor in the structure of scolorire, the orchestral piece I’ve been working on this year (see posts elsewhere on this subject). Here more sequences are at work, governing a gradual lengthening of sections even as a second process sees the character of the material becoming progressively less homogenous.

scolorire decay sequence

Patterns of decay in ‘scolorire’

The emphasis on over-arching technical processes has taken me from a compositional approach quite focused on the conscious composition of linear structures (devices or processes aimed at guiding the interpretive faculties of the listener) to one which, in the service of ambiguity, readily engages with non-linearity as defined by Jonathan D. Kramer:

While linear principles are in constant flux, non-linear determinations do not grow or change. Non-linear principles may be revealed gradually, but they do not develop from earlier events or tendencies. A work or section’s non-linearity is present from the beginning.
The Time of Music (Kramer 1988), p. 21

In short – in these two pieces, I’ve taken the leap from directly focusing on the way in which my music shapes expectations & develops, to the creation of a set of principles/processes by which the music ‘reveals’ itself over a span of time. (Those principles are present from the start, but take a little time to be heard due to the essentially time-bound nature of music.)

It’s been an interesting experiment, one which has changed the music I write and the way I write it. Most enjoyably, it seems to have been useful in engendering discipline & refining ideas: the initial principles have to be kept firmly in mind for the successful realisation of the musical process, and as a result cohesive solutions to other, smaller-scale, problems are never too far away.