Morphisms of Generalized Interval Systems and PR-Groups
Abstract
We begin the development of a categorical perspective on the theory of generalized interval systems (GIS's). Morphisms of GIS's allow the analyst to move between multiple interval systems and connect transformational networks. We expand the analytical reach of the Sub Dual Group Theorem of Fiore--Noll (2011) and the generalized contextual group of Fiore--Satyendra (2005) by combining them with a theory of GIS morphisms. Concrete examples include an analysis of Schoenberg, String Quartet in D minor, op. 7, and simply transitive covers of the octatonic set. This work also lays the foundation for a transformational study of Lawvere--Tierney upgrades in the topos of triads of Noll (2005).
Keywords
Cite
@article{arxiv.1204.5531,
title = {Morphisms of Generalized Interval Systems and PR-Groups},
author = {Thomas M. Fiore and Thomas Noll and Ramon Satyendra},
journal= {arXiv preprint arXiv:1204.5531},
year = {2013}
}
Comments
35 pages. Revised paper, and added new material: permutations, new network in Figure 10, more systems in Section 4, and more. Retypeset Summary Network with measure numbers