|Genre Categories||;; ; ;|
|Work Title||Squaring the Circle|
|Year/Date of CompositionY/D of Comp.||2000|
|Composer Time PeriodComp. Period||Modern|
|Instrumentation||alto saxophone, baritone saxophone, piano|
Program Note: In classical Greek mathematics, three problems in particular influenced the course geometry subsequently took. The challenges facing ancient mathematicians included doubling the cube, trisecting an angle and squaring the circle. It was not until 1882 that the last and most famous problem was shown to be impossible, with Lindemann's proof that pi is transcendental. The problem involves, essentially, constructing a square equal in area to a given circle.
Dante's Divine Comedy ends with a reference to this impossible task to illustrate how it is impossible for a time-based, finite human mind to imagine the eternal. It strikes me as parallel to my own concerns in composition with trying to represent timelessness inside the bounds of a time-based medium - a hopeless task, but one in which the attempt yields interesting results. Squaring the Circle is so named because it represents this aesthetic thread, which runs through most of my music.
The composition was begun during a reading of The Divine Comedy. Reflecting on the way that the timeless landscapes of Hell, Purgatory and Heaven are temporarily imbued with time by the presence and movement of the human figure of Dante, I imagined a melodic strand running through a static musical landscape. Applying a maxim of Brian Eno - "Go to an extreme, come part way back" - I went about composing music which subtly suggests this notion rather than embodying it in a clear, direct manner - the concepts informed the music, but the composition was primarily concerned with intuitive choices of pitches and rhythms.
Nevertheless, several aspects of slowing and stopping time are explored in the work. Resolution and cadence are avoided as devices which cause an excess of forward direction. Instead, vertical harmony and the suspension of instability are favoured for their static qualities.
One way time is distorted is in the use of inexorable processes (like those of Tom Johnson), in which expectation is stifled by impersonal system. This results in the listener "chunking" the material, which alters the sense of time passing. Process passages are essentially nonlinear, as there is little hierarchy. Motion results from unchanging principles, and is not perceived as progression.
Constantly present is the use of functional harmony – such as chord progressions Bach would have used to lead directly through a passage – compressed into single sonorities, as if time has been frozen and extended.