Publication Cover
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
908
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

Enharmonic systems: A theory of key signatures, enharmonic equivalence and diatonicism

Pages 99-120 | Received 16 Aug 2006, Published online: 01 Aug 2007

References

  • Clough , J. and Douthett , J. , 1991 , Maximally even sets . Journal of Music Theory , 35 , 93 – 173 .
  • Byrd , D. , 2006 , Extremes of conventional music notation . Available online at : http://www.informatics.indiana.edu/donbyrd/CMNExtremes.htm (accessed 8 May 2007) .
  • Temperley , D. , 2000 , The line of fifths . Music Analysis , 19 , 289 – 319 .
  • Riemann , H. , 1992 . Ideen zur einer ‘Lehre von den Tonvorstellungen’, R. Wason and E. West Marvin (Transl) . Journal of Music Theory , 36 , 69 – 117 (original work published 1915) .
  • Lewin , D. 1987 . Generalized Musical Intervals and Transformations , New Haven, CT : Yale University Press .
  • Hook , J. , Signature transformations . In : J. Douthett , M. Hyde , and C. Smith Music Theory and Mathematics: Chords, Collections, and Transformations Rochester, NY : University of Rochester Press (to appear) .
  • Tymoczko , D. , 2005 , Voice leadings as generalized key signatures . Music Theory Online ,. 11 ( 4 ).
  • Blackwood , E. 1985 . The Structure of Recognizable Diatonic Tunings , Princeton, NJ : Princeton University Press .
  • Sethares , W. , 2005 , Tuning, Timbre, Spectrum, Scale (2nd edn) ( London : Springer-Verlag ).
  • Mandelbaum , M.J. , 1961 , Multiple division of the octave and the tonal resources of 19-tone temperament. PhD dissertation, Indiana University .
  • Blackwood , E. , 1982 , Twelve Microtonal Etudes for Electronic Music Media, Op. 28 ( New York : G. Schirmer ).
  • Blackwood , E. , 1994 , Microtonal compositions . Performed by E. Blackwood, synthesizer, et al. Compact disc recording, Cedille 90000 018 .
  • Clough , J. and Myerson , G. , 1985 , Variety and multiplicity in diatonic systems . Journal of Music Theory , 29 , 249 – 270 .
  • Carey , N. and Clampitt , D. , 1989 , Aspects of well-formed scales . Music Theory Spectrum , 11 , 187 – 206 .
  • Carey , N. and Clampitt , D. , 1996 , Self-similar pitch structures, their duals, and rhythmic analogues . Perspectives of New Music , 34 ( 2 ), 62 – 87 .
  • Cohn , R. , 1997 , Neo-Riemannian operations, parsimonious trichords, and their Tonnetz representations . Journal of Music Theory , 41 , 1 – 66 .
  • Balzano , G. , 1980 , The group-theoretic description of 12-fold and microtonal pitch systems . Computer Music Journal , 4 ( 4 ), 66 – 84 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.