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Published in:
2017 | OriginalPaper | Chapter
Local Facts, Processes, and Gestures
Authors : Guerino Mazzola, René Guitart, Jocelyn Ho, Alex Lubet, Maria Mannone, Matt Rahaim, Florian Thalmann
Published in: The Topos of Music III: Gestures
Publisher: Springer International Publishing
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In this chapter we describe the mathematical framework for the three fundamental layers of musical ontology: facts, processes, and gestures. The layer of facts is described by the theory of local and global compositions, a major topic in American Set Theory [765] and in the European school developed by the author and his collaborators [682]. The second layer is captured by the American Transformational Theory [605, 538] and, again in Europe, by the author’s theory of categorical limits (and colimits) as embedded in topos theory [714]. The third layer has been the author’s main concern in the last ten years [720, 723, 727], also paralleled by American research such as Robert S. Hatten’s work [446].