geometria situs (2009-10)
‘Geometria situs’ is the Latin term adopted for the study of the geometry of place. This field of mathematics has become known as topology. It deals with the spatial properties of an object that remain constant when undergoing deformations such as compression or stretching, but not by cutting or gluing. Some objects may be deformed into each other; the classic example is a coffee cup and a donut, both of which feature a single hole. Topology is also referred to as flat sheet geometry. In geometria situs, all players operate independently of each other. They each have a series of pages, each of which contains a single sustained sound that undergoes gradual changes of timbre and dynamic. The conductor cues these changes at irregularly spaced time points. Players choose when to start each page, so the material is stretched and compressed depending on its placement in the piece, such that the same material might be differently structured (or deformed) on each hearing. So for example, if a change of mute position for a trombonist is timed between two closely-spaced cues given by the conductor, the change of sound will be correspondingly fast. The same change might take much longer were it to coincide with more widely spaced cues.
The piece develops my interest in modular and open forms, especially the series #[unassigned] which I worked on from 2000-9. Since completing this project, I have worked with similar material, but explored other ways of structuring the interface that connects modules (typically a short section of differentiated sounds, or a single sustained sound), often incorporating local decisions made by the performers. In the series divisions which could be autonomous but that comprise the whole (2009- ) the constituent pieces use the same score format: single pages containing sound events spread across a variable duration of between 40” – 1’20” which may be reordered by the players. In either/or (2008-9) players’ actions are individually governed by assessing the activity of other players at specified time points: logic gates instruct them either to play a sound, or not.
geometria situs explores similar ground and is also partly a response to the orchestral music of Christian Wolff, which I had been researching for a book chapter at the time of composition. I was particularly struck by the range of strategies Wolff adopts for giving freedom to the players. When planning the piece, I wanted to create a situation where players had some autonomy, and in particular where choices they make have an effect on the shape of the piece. This is not a normal orchestral situation; it is closer to a series of parallel solos.
geometria situs was commissioned by Südwestrundfunk for the Donaueschinger Musiktage 2010. It was first performed by James Saunders and the SWR Sinfonieorchester at the Donaueschinger Musiktage on 17 October 2010.