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Journal of Mathematics and Music
Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance
Volume 1, 2007 - Issue 2: The legacy of John Clough in mathematical music theory
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Editorial

The legacy of John Clough in mathematical music theory

Pages 73-78 | Published online: 01 Aug 2007

References

  • Clough , J. , Douthett , J. , Ramanathan , N. and Rowell , L. 1993 . Ancient Indian scales and recent diatonic theory . Music Theory Spectrum , 15 : 36 – 58 .
  • Clough , J. 1957 . The leading tone in direct chromaticism . Journal of Music Theory , 1 : 2 – 21 .
  • Hellegouarch , Y. 1983 . Gammes naturelles . Publication de l'A.P.M.E.P. , 53 : 127 – 158 .
  • Hellegouarch , Y. 1987 . A la recherche de l'arithmétique qui se cache dans la musique . Gazette des mathématiciens , 33 : 71 – 80 .
  • Hellegouarch , Y. , 1999 , Gammes naturelles . Gazette des mathématiciens , 81 , 25 – 39 ; 82, 13–25 .
  • Clough , J. 1970 . TEMPO: A composer's programming language . Perspectives of New Music , 9 : 113 – 125 .
  • Clough. , J. 1965 . Pitch-set equivalence and inclusion: A comment on Forte's theory of set-complexes . Journal of Music Theory , 9 : 163 – 171 .
  • Clough , J. 1983 . Profiling pitch-class sets by means of the exclusion relation . Journal of Music Theory , 27 : 181 – 201 .
  • Clough , J. and Douthett , J. 1991 . Maximally even sets . Journal of Music Theory , 35 : 93 – 173 .
  • Douthett , J. and Krantz , R. 1996 . Energy extremes and spin configurations for the one-dimensional antiferromagnetic Ising model with arbitrary-range interaction . Journal of Mathematical Physics , 37 : 3334 – 3353 .
  • Quinn , I. , 2004 , A unified theory of chord quality in equal temperaments . PhD dissertation, University of Rochester .
  • Douthett , J. and Krantz , R. , forthcoming , Maximally even sets and configurations: Common threads in mathematics, physics, and music . Journal of Combinatorial Optimization , doi: 10.1007/s10878-006-9041-5 .
  • Clough , J. 1979 . Aspects of diatonic sets . Journal of Music Theory , 23 : 45 – 61 .
  • Clough , J. 1979 . 1980, Diatonic interval cycles and transformational structures . Perspectives of New Music , 18 : 461 – 482 .
  • Clough , J. and Myerson , G. 1985 . Variety and multiplicity in diatonic sets . Journal of Music Theory , 29 : 249 – 270 .
  • Clough , J. and Myerson , G. 1986 . Musical scales and the generalized circle of fifths . The American Mathematical Monthly , 93 : 695 – 701 .
  • Carey , N. and Clampitt , D. 1996 . Self-similar pitch structures, their duals, and rhythmic analogues . Perspectives of New Music , 34 ( 2 ) : 62 – 87 .
  • Carey , N. and Clampitt , D. 1989 . Aspects of well-formed scales . Music Theory Spectrum , 11 : 187 – 206 .
  • Carey , N. and Clampitt , D. 1996 . Regions: A theory of tonal spaces in early medieval treatises . Journal of Music Theory , 40 : 113 – 147 .
  • Agmon , E. 1996 . Coherent tone systems: A study in the theory of diatonicism . Journal of Music Theory , 40 : 39 – 59 .
  • Carey , N. , 2004 , Well-formed scales and the Stern-Brocot tree . Talk given 10 January at the Joint Mathematics Meetings of the American Mathematical Society and the Mathematical Association of America, Phoenix.
  • Vicinanza , D. , 2005 , Paths on the Stern-Brocot tree and winding numbers of modes . Proceedings of the ICMC , Barcelona.
  • Cafagna , V. and Noll , T. , 2003 , Algebraic investigations into enharmonic identification and temperament . In G. Di Maio and C. di Lorenzo , Proceedings of the 3rd International Conference on Understanding and Creating Music , Caserta.
  • Sós , V.T. 1958 . On the distribution mod 1 of the sequence nα. Annals of the University of Science, Budapest Eötvös . Sect Math , I : 127 – 134 .
  • Clough , J. 1989 . Review of David Lewin's Generalized Musical Intervals and Transformations . Music Theory Spectrum , 11 : 226 – 231 .
  • Lewin , D. 1987 . Generalized Musical Intervals and Transformations , New Haven, CT : Yale University Press .
  • Clough , J. 1998 . A rudimentary model for contextual transposition and inversion . Journal of Music Theory , 42 : 297 – 307 .
  • Douthett , J. , Hyde , M. and Smith , C. forthcoming , Music Theory and Mathematics: Chords, Collections, and Transformations ( Rochester, , NY : University of Rochester Press ).
  • Morse , M. and Hedlund , G. A. 1938 . Symbolic dynamics . American Journal of Mathematics , 60 : 815 – 866 .
  • Morse , M. and Hedlund , G. A. 1940 . Symbolic dynamics II: Sturmian trajectories . American Journal of Mathematics , 62 : 1 – 42 .
  • Chemillier , M. and Truchet , C. 2003 . Computation of words satisfying the ‘rhythmic oddity property’ (after Simha Arom's works) . Information Processing Letter , 86 : 255 – 261 .
  • Noll , T. , 2007 , Algebraic combinatorics of words and scales . Talk given 20 May, at the First International Conference of the Society for Mathematics and Computation in Music, National Institute for Music Research, Berlin .
  • Dominguez , M. , Clampitt , D. and Noll , T. , 2007 , WF scales, ME sets, and Christoffel words . Talk given 20 May at the First International Conference of the Society for Mathematics and Computation in Music, National Institute for Music Research, Berlin .
  • Allouche , J.-P. , 2007 , Sturmian sequences: a mathematical promenade . Talk given 13 May, at the Helmholtz Workshop, Klang und Ton, at Hermann von Helmholtz-Zentrum für Kulturtechnik, Humboldt University, Berlin .

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