Decompositions of nil sums of roots of unity. An adaptation of “Sommes nulles de racines de l'unité”

DOI10.1080/17459737.2018.1453951zbMath1395.00021OpenAlexW2809242446MaRDI QIDQ5374500

Emmanuel Amiot

Publication date: 14 September 2018

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

Full work available at URL: https://doi.org/10.1080/17459737.2018.1453951

zbMATH Keywords

decompositionpolynomialspolygonroots of unityirreducibilitybalanceperfect balance

Mathematics Subject Classification ID

Galois theory (11R32) Mathematics and music (00A65)

Related Items (5)

Introduction to the special issue on perfect balance and the discrete Fourier transform ⋮ Exploring the space of perfectly balanced rhythms and scales ⋮ Perfect balance and circularly rich words ⋮ Harmonic qualities in Debussy's “Les sons et les parfums tournent dans l'air du soir” ⋮ GeneralizedTonnetzeandZeitnetze, and the topology of music concepts

Uses Software

• OEIS

Cites Work

• Music through Fourier space. Discrete Fourier transform in music theory
• Generating bracelets with fixed content
• On vanishing sums of roots of unity.
• Perfect Balance: A Novel Principle for the Construction of Musical Scales and Meters
• On Vanishing Sums of Distinct Roots of Unity
• Exploring the space of perfectly balanced rhythms and scales

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