Formalized Music: Thought and Mathematics in Composition

Formalized Music: Thought and Mathematics in Composition

Formalized Music: Thought and Mathematics in Composition

Formalized Music: Thought and Mathematics in Composition

Excerpt

The formalization that I attempted in trying to reconstruct part of the musical edifice ex nihilo has not used, for want of time or of capacity, the most advanced aspects of philosophical and scientific thought. But the escalade is started and others will certainly enlarge and extend the new thesis. This book is addressed to a hybrid public, but interdisciplinary hybridization frequently produces superb specimens.

I could sum up twenty years of personal efforts by the progressive filling in of the following Table of Coherences. My musical, architectural, and visual works are the chips of this mosaic. It is like a net whose variable lattices capture fugitive virtualities and entwine them in a multitude of ways. This table, in fact, sums up the true coherences of the successive chronological chapters of this book. The chapters stemmed from monographs, which tried as much as possible to avoid overlapping.

But the profound lesson of such a table of coherences is that any theory or solution given on one level can be assigned to the solution of problems on another level. Thus the solutions in macrocomposition on the Families level (programmed stochastic mechanisms) can engender simpler and more powerful new perspectives in the shaping of microsounds than the usual trigonometric (periodic) functions can. Therefore, in considering clouds of points and their distribution over a pressure-time plane, we can bypass the heavy harmonic analyses and syntheses and create sounds that have never before existed. Only then will sound synthesis by computers and digital-to-analogue converters find its true position, free of the rooted but ineffectual tradition of electronic, concrete, and instrumental music that makes use of Fourier synthesis despite the failure of this theory. Hence, in this book, questions having to do mainly with orchestral sounds (which are more diversified and more manageable) find a rich and immediate application as soon as they are transferred to the Microsound level in the pressuretime space. All music is thus automatically homogenized and unified.

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