A model for tonal progressions of seventh chords. Issue 1 (2nd January 2023)

• Record Type: Journal Article
• Authors: Marohnić, Luka
• Is Part Of: Journal of mathematics and music. Volume 17:Issue 1(2023)
• Page Start: 78
• Page End: 99
• Publication Date: 2023-01-02
• Subjects: seventh chord -- harmony -- voice leading -- line of fifths -- parsimony -- chord progression -- graph theory -- shortest-path algorithm -- pitch spelling; 00A65 -- 05C90 -- 94C15; Music theory -- Periodicals; Music -- Mathematical models -- Periodicals; Music -- Mathematics -- Periodicals; 781.2
• DOI: 10.1080/17459737.2021.1928311
• Languages: English
• ISSNs: 1745-9737

Abstract

Abstract : In this paper, we propose a model for idealized diatonic and chromatic voice leadings between seventh chords and study its computational aspects. The model provides a mathematical formalization of the concept of tonal seventh chord realizations including augmented sixth chords. Certain contrapuntal aspects, such as preparation and resolution of certain dissonant intervals, are taken into account. Possible applications of the model are discussed using a graph-theoretic approach. In particular, we present an algorithm for generating concrete voicings from sequences of seventh-chord symbols.