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 .