An algebra for periodic rhythms and scales

DOI10.1080/17459737.2011.640469zbMath1264.00016OpenAlexW2102254957MaRDI QIDQ4922583

William A. Sethares, Emmanuel Amiot

Publication date: 30 May 2013

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

Full work available at URL: https://doi.org/10.1080/17459737.2011.640469

zbMATH Keywords

scalestilingsDFTFourierscale matrixhomometryscale vectorLewincirculating matricesFLIDlinear combination of scalesperiodic rhythmsum of scalesZ-relation

Mathematics Subject Classification ID

Mathematics and music (00A65)

Related Items (8)

Applications of DFT to the Theory of Twentieth-Century Harmony ⋮ The S-canon and the multi-S-canon: an introduction ⋮ The discrete Fourier transform of distributions ⋮ Exploring the space of perfectly balanced rhythms and scales ⋮ Symbolic dynamical scales: modes, orbitals, and transversals ⋮ LR property of non-well-formed scales ⋮ Entropy of Fourier coefficients of periodic musical objects ⋮ Symbolic structures in music theory and composition, binary keyboards, and the Thue–Morse shift

Cites Work

• Unnamed Item
• Enhancing sparsity by reweighted \(\ell _{1}\) minimization
• Phase retrieval
• Projection pursuit
• Z-relation and homometry in musical distributions
• Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
• Time-frequency localization operators: a geometric phase space approach
• Matching pursuits with time-frequency dictionaries

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