Chord Transformations in Higher-Dimensional Networks-finelybook

Chord Transformations in Higher-Dimensional Networks

Author: Rafael Cubarsi

Publisher finelybook 出版社:‏ ‎ Chapman and Hall/CRC

Edition 版本:‏ 1st edition

Publication Date 出版日期:‏ 2025-06-26

Language 语言: English

Print Length 页数: 130 pages

ISBN-10: 103298290X

ISBN-13: 9781032982908

Book Description

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

About the Author

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.

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Chord Transformations in Higher-Dimensional Networks