# Relational poly-Klumpenhouwer networks for transformational and voice-leading analysis

@article{Popoff2018RelationalPN, title={Relational poly-Klumpenhouwer networks for transformational and voice-leading analysis}, author={Alexandre Popoff and Moreno Andreatta and Andr{\'e}e C. Ehresmann}, journal={Journal of Mathematics and Music}, year={2018}, volume={12}, pages={35 - 55} }

In the field of transformational music theory, which emphasizes the possible transformations between musical objects, Klumpenhouwer networks (K-nets) constitute a useful framework with connections in both group theory and graph theory. Recent attempts at formalizing K-nets in their most general form have evidenced a deeper connection with category theory. These formalizations use diagrams in sets, i.e. functors where is often a small category, providing a general framework for the known group…

## 8 Citations

Groupoids and Wreath Products of Musical Transformations: A Categorical Approach from poly-Klumpenhouwer Networks

- Computer ScienceMCM
- 2019

This work proposes a new groupoid-based approach to transformational music theory, in which transformations of PK-nets are considered rather than ordinary sets of musical objects.

On the use of relational presheaves in transformational music theory

- MathematicsJournal of Mathematics and Music
- 2020

Traditional transformational music theory describes transformations between musical elements as functions between sets and studies their subsequent algebraic properties and their use for music…

Composing (with) automorphisms in the colored Cube Dance: an interactive tool for musical chord transformation

- Mathematics
- 2022

The ‘colored Cube Dance’ is an extension of Douthett’s and Steinbach’s Cube Dance graph, related to a monoid of binary relations defined on the set of major, minor, and augmented triads. This…

From Music to Mathematics and Backwards: Introducing Algebra, Topology and Category Theory into Computational Musicology

- Art
- 2018

Despite a long historical relationship between mathematics and music, the interest of mathematicians is a recent phenomenon. In contrast to statistical methods and signal-based approaches currently…

Meter networks: a categorical framework for metrical analysis

- MathematicsJournal of Mathematics and Music
- 2020

A framework based on category theory which unifies the simultaneous consideration of timepoints, metrical relations, and meter inclusion founded on the category Rel of sets and binary relations is developed.

The Tonnetz Environment: A Web Platform for Computer-aided "Mathemusical" Learning and Research

- Computer ScienceCSEDU
- 2021

The Tonnetz web environment is described and some of the possible applications developed within a pedagogical workshop on mathematics and music that has been conceived for high-school students and is aimed at enhancing "mathemusical" learning processes.

Statistical analysis of songs by composers of the Romantic era: A comparison of F. Schubert and his contemporaries

- Computer ScienceRevista Música Hodie
- 2021

The study investigates musical compositions via quantification using mathematical methods based on Franz Schubert's song cycle Die Winterreise, Robert Schumann’s song cycle Myrthen, and on works by other composers to allow finding objective criteria for describing his work in comparison with the works of other Composers.

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