Metodo

International Studies in Phenomenology and Philosophy

Series | Book | Chapter

226963

A categorical generalization of Klumpenhouwer networks

Alexandre PopoffAndrée C. Ehresmann Moreno Andreatta

pp. 303-314

Abstract

This article proposes a functorial framework for generalizing some constructions of transformational theory. We focus on Klumpenhouwer Networks for which we propose a categorical generalization via the concept of set-valued poly-K-nets (henceforth PK-nets). After explaining why K-nets are special cases of these category-based transformational networks, we provide several examples of the musical relevance of PK-nets as well as morphisms between them. We also show how to construct new PK-nets by using some topos-theoretical constructions.

Publication details

Published in:

Collins Tom, Meredith David, Volk Anja (2015) Mathematics and computation in music: 5th international conference, MCM 2015, London, UK, June 22-25, 2015. Dordrecht, Springer.

Pages: 303-314

DOI: 10.1007/978-3-319-20603-5_31

Full citation:

Popoff Alexandre, Ehresmann Andrée C., Andreatta Moreno (2015) „A categorical generalization of Klumpenhouwer networks“, In: T. Collins, D. Meredith & A. Volk (eds.), Mathematics and computation in music, Dordrecht, Springer, 303–314.