Chord Transformations in Higher-Dimensional Networks

Rafael Cubarsi

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English

Chapman & Hall/CRC
26 June 2025

Theory of music & musicology; Algebra; Number theory; Applied mathematics

Chord Transformations in Higher-Dimensional Networks proposes an in-depth formal framework for generalized Tonnetze. It takes an algebraic approach and studies systems of k-chords in n-TET scales derived from a given k-mode (array of step intervals) through mode permutations and chord root translations, by combining key ideas of the neo-Riemannian Tonnetz theories with serial approaches to chordal structures. In particular, it provides the generalization of the neo-Riemannian P, R, L transformations via the notion of ‘drift’ operator, which is the main novelty of the approach. At the same time, the book is thorough in building the formal framework covering many moments and details, with special attention to trichords and tetrachords, which allow the geometric visualization of their structure helping to understand the more abstract transformations in higher-dimensional networks.

Features

Chord transformations are explained from a new approach, by considering the chord as a two-component entity (root and mode), which is simpler than that of the neo-Riemannian theory The chords transformations presented can be easily converted to computational algorithms to deal with higher-dimensional Tonnetze Presents the study of chords with a scope that goes from scratch up to higher levels, about to develop research works

By: Rafael Cubarsi
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
ISBN: 9781032982908
ISBN 10: 103298290X
Pages: 130
Publication Date: 26 June 2025
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Forthcoming

Rafael Cubarsi, mathematician and physicist by training, received his PhD from the Astronomy Department of the Universitat de Barcelona in 1988 with a dissertation on Chandrasekhar Stellar Systems. He developed and conducted research at the Universitat Aut`onoma de Barcelona and Universitat Polit`ectica de Catalunya, where he used to teach, and has more than 70 published papers in peer-reviewed journals to his credit. His research focused on the fields of Astronomy & Astrophysics and Mathematical Biology. Recently his interest is centered on Mathematical Theory of Music.