579
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

In Search of Universal Properties of Musical Scales

&
Pages 81-89 | Published online: 31 Mar 2011

References

  • Agmon , E. 1989 . A mathematical model of the diatonic system . Journal of Music Theory , 33 ( 1 ) : 1 – 25 .
  • Ball , P. 2008 . Facing the music . Nature , 453 : 160 – 162 .
  • Balzano , G. J. 1980 . A group theoretical description of 12-fold and microtonal pitch systems . Computer Music Journal , 4 ( 4 ) : 66 – 84 .
  • Browne , R. 1981 . Tonal implications of the diatonic set . Theory Only , 5 : 3 – 21 .
  • Burns , E. 1999 . “ Intervals, scales and tuning ” . In Psychology of Music , 2nd ed. , Edited by: Deutsch , D . 215 – 264 . New York : Academic Press .
  • Carey , N. and Clampitt , D. 1989 . Aspects of well-formed scales . Music Theory Spectrum , 11 ( 2 ) : 187 – 206 .
  • Clough , J. and Douthett , J. 1991 . Maximally even sets . Journal of Music Theory , 35 : 93 – 173 .
  • Clough , J. and Myerson , G. 1985 . Variety and multiplicity in diatonic systems . Journal of Music Theory , 29 ( 2 ) : 249 – 270 .
  • Drabkin , William . 2011 . Scale . Grove Music Online. Oxford Music Online , Retrieved 28 January 2011 from http://www.oxfordmusiconline.com/subscriber/article/grove/music/24691
  • Ellis , C. J. 1965 . Pre-instrumental scales . Ethnomusicology , 9 ( 2 ) : 126 – 137 .
  • Euler , L. 1739/1865 . Tentamen novae theoriae musicae . Musique mathématique , pp. i–vii, 1–215). Paris
  • Fokker , A. D. 1949 . Just Intonation , The Hague : Martinus Nijhoff .
  • Fokker , A. D. Unison vectors and periodicity blocks in the three-dimensional (3-5-7) harmonic lattice of notes . Proceedings of Koninklijke Nederlandsche Akademie van Wetenschappen .
  • Gärdenfors , P. and Williams , M. A. Reasoning about categories in conceptual spaces . Proceedings of the Fourteenth International Joint Conference of Artificial Intelligence . Seattle, WA, USA. pp. 385 – 392 .
  • Honingh , A. K. 2006 . The origin and well-formedness of tonal pitch structures , the Netherlands : University of Amsterdam . (PhD thesis)
  • Honingh , A. K. and Bod , R. 2005 . Convexity and the well-formedness of musical objects . Journal of New Music Research , 34 ( 3 ) : 293 – 303 .
  • Jaeger , G. 2009 . “ Natural color categories are convex sets ” . Key note lecture at the Amsterdam Colloquium 2009. Retrieved from http://www2.sfs.uni-tuebingen.de/jaeger/publications/convPca.pdf
  • Lindley , M. and Turner-Smith , R. 1993 . Mathematical Models of Musical Scales: A New Approach , Bonn : Verlag für systematische Musikwissenschaft .
  • Lloyd , J. E. 2004 . “ Quickhull3d ” . Retrieved from http://people.cs.ubc.ca/∼lloyd/java/doc/quickhull3d/quickhull3d/QuickHull3D.html
  • Longuet-Higgins , H. C. 1962a . Letter to a musical friend . Music Review , 23 : 244 – 248 .
  • Longuet-Higgins , H. C. 1962b . Second letter to a musical friend . Music Review , 23 : 271 – 280 .
  • Nettl , B. 1956 . “ Scale and melody ” . In Music in Primitive Culture , 45 – 60 . Cambridge : Harvard University Press .
  • Riemann , H. 1914 . Ideen zu einer Lehre von den Tonvorstellungen . Jahrbuch der Musikbibliothek Peters , 21/22 : 1 – 26 .
  • Sachs , C. 1962 . The Wellsprings of Music , The Hague : Martinus Nijhoff .
  • Scala Archive . 2010 . Retrieved July 2010 from http://www. huygens-fokker.org/docs/scales.zip (version 74)
  • Scale . 2011 . The Oxford Dictionary of Music , 2nd ed. rev. Edited by: Kennedy , M. Retrieved 28 January 2011 from http://www.oxfordmusiconline.com/subscriber/article/opr/t237/e8999
  • Schneider , A. 2001 . Sound, pitch, and scale: From ‘tone measurements’ to sonological analysis in ethnomusicology . Ethnomusicology , 45 ( 3 ) : 489 – 519 .
  • Scholes , P. , Nagley , J. and Temperley , N. 2011 . “ Scale ” . In The Oxford Companion to Music Edited by: Latham , A. Retrieved 28 January 2011 from http://www.oxfordmusic online.com/subscriber/article/opr/t114/e5921
  • Sethares , W. A. 1999 . Tuning, Timbre, Spectrum, Scale , 2nd ed. , Berlin : Springer .
  • Von Helmholtz , H. 1863/1954 . On the Sensations of Tone , 2nd English ed. , New York : Dover .

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.