Chord Transformations in Higher Dimensional Networks

Proposes an in-depth formal framework for generalized Tonnetze, takes an algebraic approach, studies systems of k-chords in n-TET scales derived from a given k-mode through mode permutations and chord root translations, by combining key ideas of the neo-Riemannian Tonnetz theories with serial approaches to chordal structures. 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