Publication Cover
Journal of Mathematics and Music
Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance
Volume 8, 2014 - Issue 1
149
Views
0
CrossRef citations to date
0
Altmetric
Articles

Constructing an optimal circulating temperament based on a set of musical requirements

Pages 25-39 | Received 28 Jun 2011, Accepted 17 Sep 2013, Published online: 18 Feb 2014

References

  • Amiot, E. 2009. “Discrete Fourier Transform and Bach's Good Temperament.” Music Theory Online 15 (2). http://www.mtosmt.org/issues/mto.09.15.2/mto.09.15.2.amiot.html
  • Barnes, J. 1979. “Bach's Keyboard Temperament.” Early Music 7 (2): 236–249. doi: 10.1093/earlyj/7.2.236
  • Bavington, P. 2007. Clavichord Tuning and Maintenance. London: Keyword Press.
  • Benson, D. 2007. Music: A Mathematical Offering. Cambridge: Cambridge University Press.
  • Duffin, R.W.. 2000. “Why I Hate Vallotti (or is it Young?).” Historical Performance, 1 (online). http://music.case.edu/ rwd/Vallotti/T1/page1.html
  • Duffin, R.W.. 2007. How Equal Temperament Ruined Harmony: And Why You Should Care. London: W. W. Norton & Company, Ltd.
  • Goldstein, A. 1977. “Optimal Temperament.” SIAM Review 19 (3): 554–562. doi: 10.1137/1019077
  • Hall, D. 1973. “The Objective Measurement of Goodness-of-Fit for Tunings and Temperaments.” Journal of Music Theory 17 (2): 274–290. doi: 10.2307/843344
  • Jencka, D. 2005. “Tempering Bach's Temperament.” Early Music 33 (3): 545–548. doi: 10.1093/em/cah134
  • Jencka, D. 2006. “The Tuning Script form Bach's Well Tempered Clavier: A Possible 1/18th PC Interpretation.” Accessed March 25, 2011. http://bachtuning.jencka.com/essay.htm
  • Kellner, H.A. 1977. “Eine Rekonstruktion der wohltemperierten Stimmung von Johann Sebastian Bach [A reconstruction of the well-tempered tuning of Johann Sebastian Bach].” Das Musikinstrument 26 (1): 34–35.
  • Lehman, B. 2005a. “Bach's Extraordinary Temperament: Our Rosetta Stone–1.” Early Music 33 (1): 3–23. doi: 10.1093/em/cah037
  • Lehman, B. 2005b. “Bach's Extraordinary Temperament: Our Rosetta Stone–2.” Early Music 33 (2): 211–231. doi: 10.1093/em/cah067
  • Lindley, M. 1987. “Stimmung und Temperatur.” In Geschichte der Musiktheorie, edited by F. Zaminer, Vol. 6, 109–332. Darmstadt: Wissenschaftliche Buchgesellschaft.
  • Milne, A.J., W. A. Sethares, R. Laney, and D. B. Sharp. 2011. “Modelling the Similarity of Pitch Collections with Expectation Tensors.” Journal of Mathematics and Music 5 (1): 1–20. doi: 10.1080/17459737.2011.573678
  • O'Donnell, J. 2006. “Bach's Temperament, Occam's Razor, and the Neidhardt Factor.” Early Music 34 (4): 625–634. doi: 10.1093/em/cal101
  • Plomp, R., and W. Levelt. 1965. “Tonal Consonance and Critical Bandwidth.” Journal of the Acoustical Society of America 38 (4): 548–560. doi: 10.1121/1.1909741
  • Polansky, L., D. Rockmore, K. Johnson, and D. Repetto. 2008. “A Mathematical Model for Optimal Tuning Systems.” SFI Working Papers, Santa Fe, NM.
  • Sankey, J., and W. A. Sethares. 1997. “A Consonance-based Approach to the Harpsichord Tuning of Domenico Scarlatti.” Journal of the Acoustical Society of America 101 (4): 2332–2337. doi: 10.1121/1.418212
  • Sethares, W. 1993. “Local Consonance and the Relationship Between Timbre and Scale.” Journal of the Acoustical Society of America 94 (3): 1218–1228. doi: 10.1121/1.408175
  • Sethares, W. 1994. “Adaptive Tunings for Musical Scales.” Journal of the Acoustical Society of America 96 (1): 10–18. doi: 10.1121/1.410471

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.