348
Views
17
CrossRef citations to date
0
Altmetric
Original Articles

Musical Actions of Dihedral Groups

, &
Pages 479-495 | Published online: 31 Jan 2018

REFERENCES

  • M. Babbitt, Twelve-tone invariants as compositional determinants, The Musical Quarterly 46 (1960) 246–259.
  • J. Baez, This week's finds in mathematical physics (Week 234) (2006), available at http://math.ucr.edu/home/baez/week234.html.
  • A. Childs, Moving beyond neo-Riemannian triads: Exploring a transformational model for seventh chords, Journal of Music Theory 42 (1998) 181–194.
  • R. Cohn, Dramatization of hypermetric conflicts in the Scherzo of Beethoven's Ninth Symphony, 19th-century Music 15 (1992) 22–40.
  • R. Cohn, Introduction to neo-Riemannian theory: A survey and a historical perspective. Journal of Music Theory 42 (1998) 167–180.
  • R. Cohn, Neo-Riemannian operations, parsimonious trichords, and their Tonnetz representations, Journal of Music Theory 41 (1997) 1–66.
  • R. Cohn, Properties and generability of transpositionally invariant sets. Journal of Music Theoty 35 (1991) 1–32.
  • J. Douthett and P. Steinbach, Parsimonious graphs: A study in parsimony, contextual transformations, and modes of limited transposition, Journal of Music Theory 42 (1998) 241–263.
  • T. M. Fiore, 2007 Chicago REU lectures on mathematical music theory, available at http://www.math.uchicago.edu/~fiore/.
  • T. M. Fiore and R. Satyendra, Generalized contextual groups, Music Theory Online 11 (2005); available at http://mto.societymusictheory.org.
  • A. Forte, The Structure of Atonal Music, Yale University Press, New Haven, 1977.
  • E. Gollin, Some aspects of three-dimensional Tonnetze, Journal of Music Theory 42 (1998) 195–206.
  • J. Hook, Uniform triadic transformations, Journal of Music Theory 46 (2002) 57–126.
  • J. Hook, Uniform Triadic Transformations, Ph.D. dissertation, Indiana University, Bloomington, IN, 2002.
  • B. Hyer, Reimag(in)ing Riemann, Journal of Music Theory 39 (1995) 101–138.
  • D. Lewin, A formal theory of generalized tonal functions, Journal of Music Theory 26 (1982) 32–60.
  • D. Lewin, Generalized Musical Intervals and Transformations, Yale University Press, New Haven, 1987.
  • B. J. McCartin, Prelude to musical geometry, College Math. J. 29 (1998) 354–370.
  • R. Morris, Composition with Pitch-Classes: A Theory of Compositional Design, Yale University Press, New Haven, 1988.
  • J. Rahn, Basic Atonal Theory, Schirmer, New York, 1980.
  • H. Riemann, Ideen zu einer ‘Lehre von den Tonvorstellungen’, Jahrbuch der Musikbibliothek Peters 21/22 (1914/15) 1–26.
  • H. Riemann, Ideas for a study “on the imagination of tone” (trans. R. W. Wason and E. W. Marvin), Journal of Music Theory 36 (1992) 81–117.
  • J. J. Rotman, An Introduction to the Theory of Groups, 4th ed., Graduate Texts in Mathematics, vol. 148, Springer-Verlag, New York, 1995.
  • D. Waller, Some combinatorial aspects of the musical chords, The Mathematical Gazette 62 (1978) 12–15.
  • R. W. Wason and E. W. Marvin, Riemann's “Ideen zu einer ‘Lehre von den Tonvorstellungen’”: An annotated translation, Journal of Music Theory 36 (1992) 69–79.

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.