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Generalized diatonic scales
12 references·5 citing·22 second hop
Generalized diatonic scales (2008)Generalized diatonic scalesMusical intervals and special linear transformations (2007)Musical intervals and special…David Lewin and maximally even sets (2007)David Lewin and maximally eve…Coherence and sameness in well-formed and pairwise well-formed scales (2007)Coherence and sameness in wel…On Coherence and Sameness, and the Evaluation of Scale Candidacy Claims (2002)On Coherence and Sameness, an…Self-Similar Pitch Structures, Their Duals, and Rhythmic Analogues (1996)Self-Similar Pitch Structures…La loi de la pansonorité (1996)La loi de la pansonoritéMaximally Even Sets (1991)Maximally Even SetsAspects of Well-Formed Scales (1989)Aspects of Well-Formed ScalesA Mathematical Model of the Diatonic System (1989)A Mathematical Model of the D…Musical Scales and the Generalized Circle of Fifths (1986)Musical Scales and the Genera…Variety and Multiplicity in Diatonic Systems (1985)Variety and Multiplicity in D…The Group-Theoretic Description of 12-Fold and Microtonal Pitch Systems (1980)The Group-Theoretic Descripti…On the divisions of the octave in generalized Pythagorean scales and their bidimensional representation (2023)On the divisions of the octav…Xenakis’ Sieve Theory (2022)Xenakis’ Sieve TheoryAn alternative approach to generalized Pythagorean scales. Generation and properties derived in the frequency domain (2020)An alternative approach to ge…Mathematics and group theory in music (2014)Mathematics and group theory …Pseudo-diatonic Scales (2009)Pseudo-diatonic ScalesGeneralized Musical Intervals and Transformations (1988)Applications of DFT to the Theory of Twentieth-Century Harmony (2015)Exploring the space of perfectly balanced rhythms and scales (2017)Steve Reich’s Signature Rhythm and an Introduction to Rhythmic Qualities (2020)Tuning, Timbre, Spectrum, Scale (1998)Bridging scale theory and geometrical approaches to harmony: the voice-leading duality between complementary chords (2016)Axiomatic scale theory (2020)Musical pitch quantization as an eigenvalue problem (2020)Tonal implications of the diatonic set (1981)Modes, the Height-Width Duality, and Handschin’s Tone Character (2011)Meter and Grouping in African Music: A View from Music Theory (2000)A Platonic Model of Funky Rhythms (2016)The Geometry of Musical Rhythm (2016)Perceptual-cognitive universals as reflections of the world (1994)Perceptual-cognitive universals as reflections of the world (2001)The Evolution of Language (2010)Scales, Sets, and Interval Cycles: A Taxonomy (1999)Music theory and mathematics (2002)Spelled Heptachords (2011)Scale Networks and Debussy (2004)The distance geometry of music (2008)Sensitive Interval Property for Scales as Words in the Free Group F2 (2011)
this work references cited by second hop

References

  • 1991Maximally Even Sets203 cited
  • 1980The Group-Theoretic Description of 12-Fold and Microtonal Pitch Systems195 cited
  • 1989Aspects of Well-Formed Scales170 cited
  • 1985Variety and Multiplicity in Diatonic Systems166 cited
  • 1986Musical Scales and the Generalized Circle of Fifths80 cited
  • 1989A Mathematical Model of the Diatonic System74 cited
  • 1996Self-Similar Pitch Structures, Their Duals, and Rhythmic Analogues57 cited
  • 2007David Lewin and maximally even sets46 cited
  • 2007Musical intervals and special linear transformations29 cited
  • 2007Coherence and sameness in well-formed and pairwise well-formed scales24 cited
  • 1996La loi de la pansonorité21 cited
  • 2002On Coherence and Sameness, and the Evaluation of Scale Candidacy Claims16 cited

Cited by

  • 2020An alternative approach to generalized Pythagorean scales. Generation and properties derived in the frequency domain5 cited
  • 2014Mathematics and group theory in music5 cited
  • 2023On the divisions of the octave in generalized Pythagorean scales and their bidimensional representation4 cited

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2022
Xenakis’ Sieve Theory
3 cited
  • 2009Pseudo-diatonic Scales3 cited