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Musical intervals and special linear transformations
14 references·8 citing·25 second hop
Musical intervals and special linear transformations (2007)Musical intervals and special linear tran…The topos of music: geometric logic of concepts, theory, and performance (2003)The topos of music: geometric…Scales, Sets, and Interval Cycles: A Taxonomy (1999)Scales, Sets, and Interval Cy…Tuning, Timbre, Spectrum, Scale (1998)Tuning, Timbre, Spectrum, Sca…Self-Similar Pitch Structures, Their Duals, and Rhythmic Analogues (1996)Self-Similar Pitch Structures…Maximally Even Sets (1991)Maximally Even SetsGeometrie der Töne (1990)Geometrie der TöneGeneralized Musical Intervals and Transformations (1989)Generalized Musical Intervals…Aspects of Well-Formed Scales (1989)Aspects of Well-Formed ScalesGeneralized Musical Intervals and Transformations (1988)Generalized Musical Intervals…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…Gruppen und Kategorien in der Musik (1985)Gruppen und Kategorien in der…The Group-Theoretic Description of 12-Fold and Microtonal Pitch Systems (1980)The Group-Theoretic Descripti…Aspects of Diatonic Sets (1979)Aspects of Diatonic SetsOn the divisions of the octave in generalized Pythagorean scales and their bidimensional representation (2023)On the divisions of the octav…Musical pitch quantization as an eigenvalue problem (2020)Musical pitch quantization as…Axiomatic scale theory (2020)Axiomatic scale theoryAn alternative approach to generalized Pythagorean scales. Generation and properties derived in the frequency domain (2020)An alternative approach to ge…Bridging scale theory and geometrical approaches to harmony: the voice-leading duality between complementary chords (2016)Bridging scale theory and geo…Two notions of well-formedness in the organization of musical pitch (2010)Two notions of well-formednes…Pseudo-diatonic Scales (2009)Pseudo-diatonic ScalesGeneralized diatonic scales (2008)Generalized diatonic scalesTonal implications of the diatonic set (1981)David Lewin and maximally even sets (2007)Modes, the Height-Width Duality, and Handschin’s Tone Character (2011)An algebra for periodic rhythms and scales (2011)Assessing The Tuning Of Sung Indian Classical Music. (2011)The Sound of Music: The Effect of Timbral Sound Quality in Audio Logos on Brand Personality Perception (2022)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)Generalized Voice-Leading Spaces (2008)Action and Agency Revisited (2013)Perceptual-cognitive universals as reflections of the world (1994)Perceptual-cognitive universals as reflections of the world (2001)The Evolution of Language (2010)Music theory and mathematics (2002)Scale Networks and Debussy (2004)The distance geometry of music (2008)Analyzing Musical Structure and Performance---A Statistical Approach (1999)Statistics in Musicology (2003)P aradoxes of P itch S pace (2008)Diagrams, gestures and formulae in music (2007)S cale T heory , S erial T heory and V oice L eading (2008)Categorical gestures, the diamond conjecture, Lewin's question, and the Hammerklavier Sonata (2009)Essay: In Order to Stay Asleep as Observers: The Nature and Origins of Anti-Cartesianism in Lewin'sGeneralized Musical Intervals and Transformations (2006)Mathematics and the Twelve-Tone System: Past, Present, and Future (2009)
this work references cited by second hop

References

  • 1988Generalized Musical Intervals and Transformations487 cited
  • 1998Tuning, Timbre, Spectrum, Scale205 cited
  • 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
  • 2003The topos of music: geometric logic of concepts, theory, and performance152 cited
  • 1986Musical Scales and the Generalized Circle of Fifths80 cited
  • 1990Geometrie der Töne80 cited
  • 1989Generalized Musical Intervals and Transformations72 cited
  • 1996Self-Similar Pitch Structures, Their Duals, and Rhythmic Analogues57 cited
  • 1999Scales, Sets, and Interval Cycles: A Taxonomy55 cited
  • 1979Aspects of Diatonic Sets51 cited
  • 1985Gruppen und Kategorien in der Musik35 cited

Cited by

  • 2020Axiomatic scale theory16 cited
  • 2020Musical pitch quantization as an eigenvalue problem16 cited

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2008
Generalized diatonic scales
14 cited
  • 2016Bridging scale theory and geometrical approaches to harmony: the voice-leading duality between complementary chords8 cited
  • 2010Two notions of well-formedness in the organization of musical pitch6 cited
  • 2020An alternative approach to generalized Pythagorean scales. Generation and properties derived in the frequency domain5 cited
  • 2023On the divisions of the octave in generalized Pythagorean scales and their bidimensional representation4 cited
  • 2009Pseudo-diatonic Scales3 cited