Gesture Homology for Counterpoint
The purpose of this chapter is to review our contrapuntal model such that the group-theoretical contrapuntal symmetries are reinterpreted in the framework of topology, where continuity can be addressed. In particular, we shall interpret the set of intervals as being a topological category. We shall then develop a theory of hypergestures in such a category and investigate the first singular homology group associated with hypergestures. It will turn out that the above conditions defining contrapuntal symmetries can be restated in terms of topology and its associated homology of hypergestures.
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