It is common for composers to consider their work through a number of dimensions or axes; examples of which can be found in fugue technique, Whishart’s lattice model (Wishart, 2002) or more extremely, embodied throughout the methodology of 12 tone serialism (Schoenberg and Stein, 1950).
This planar thinking lends itself to the invention of various compositional techniques, on a simplistic level running variables in in retrograde fashion through to the nested recursion of the Art of Fugue (Bach, 1750) and Markov Chain compositional techniques (Roads, 2000). This is often linear, looking at a set of pitches or rhythms; interrogating and manipulating a stream of data points. From there it is only a small step to link extra information to this data. For instance, at a given time a certain note could be played at a specified volume by a given instrument (Boulez, Cage and Nattiez, 1999). Thus, in computing terms we arrive at a two-dimensional array of data, something potentially very close to a square if you were to tabulate it.
With the addition of other data and relationships comes the opportunity for higher dimensions within this array, popping an extra axis into a cube, followed by a tesseract, up until such points as it would be difficult to perceive within an audible work.
What if, rather than dealing with data points the composer was able to manipulate the dimensional space of the larger work?
Precession is an exploration of these ideas. It draws on the Pitch Volume Timbre space defined by Wishart but folds in one side of the ‘cube’ to form a pyramid space. Working from the assumption that pitch is mapped to x volume to y and timbre to z notes can be placed anywhere within the body of the pyramid. This simple translation brings a deal of creative perturbation to the system, as when any datum is near the apex of the pyramid (z axis) its potential placement within the two remaining axes (x,y) across the square base are several limited.
Where this becomes especially interesting is being able to roll the pyramid like a die within compositional space. If the view point remains fixed with x for pitch etc. any movement of the pyramid re-voices the notes therein, potentially in strikingly different ways. Thus, phrases are cast and re-cast within the rolling die of the shape causing processionary transformations of the material.
Instrument design realised in Supercollider
Visual components and data transformation in Processing
Composition and array transformations Excel
System communication OSC
Edward Wright 3/12/19
| Bibliography: |
| Bach, J.S. (2013). The Art of the Fugue & A Musical Offering. Composed c. 1740-50. Newburyport: Dover Publications. |
| Boulez, P., Cage, J. and Nattiez, J. (1999). The Boulez-Cage correspondence. Cambridge [England]: Cambridge University Press. |
| Roads, C. (2000). The computer music tutorial. Estados Unidos: The MIT Press. |
| Schoenberg, A. and Stein, L. (1985). Style and idea. First published 1950. Berkeley: University of California Press. |
| Wishart, T. (2002). On sonic art. London: Routledge. |
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