GeneralizedTonnetzeandZeitnetze, and the topology of music concepts

DOI10.1080/17459737.2020.1725667zbMath1466.00023OpenAlexW3009738483MaRDI QIDQ4993920

Jason Yust

Publication date: 11 June 2021

Published in: Journal of Mathematics and Music (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17459737.2020.1725667

zbMATH Keywords

geometryFourier transformtopologyTonnetzvoice leading

Mathematics Subject Classification ID

Relations with algebraic geometry and topology (11F23) Combinatorics and topology in relation with holomorphic dynamical systems (37F20) Mathematics and music (00A65)

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Cites Work

• Music through Fourier space. Discrete Fourier transform in music theory
• Interval content vs. DFT
• Probing questions about keys: tonal distributions through the DFT
• Applications of DFT to the Theory of Twentieth-Century Harmony
• Spelled Heptachords
• Tonal Scales and Minimal Simple Pitch Class Cycles
• Mazzola’s Model of Fuxian Counterpoint
• Generalized Voice-Leading Spaces
• GeneralizedTonnetze
• Structural properties of Euclidean rhythms
• David Lewin and maximally even sets
• Fourier Phase and Pitch-Class Sum
• A Topological Approach of Musical Relationships
• The Torii of Phases
• Computation and Visualization of Musical Structures in Chord-Based Simplicial Complexes
• Decompositions of nil sums of roots of unity. An adaptation of “Sommes nulles de racines de l'unité”
• Exploring the space of perfectly balanced rhythms and scales
• Harmonic qualities in Debussy's “Les sons et les parfums tournent dans l'air du soir”
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