The geometry of musical chords

Science

Volumn 313, Issue 5783, 2006, Pages 72-74

  Tymoczko, Dmitri ^a,b  

^a PRINCETON UNIVERSITY   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; MAPPING; NUMERICAL METHODS;

DISSONANT CHORDS; GEOMETRICAL SPACES; MUSICAL CHORDS; NON-EUCLIDEAN GEOMETRY;

COMPUTATIONAL GEOMETRY;

GEOMETRY; MAPPING;

ACOUSTICS; ARTICLE; MATHEMATICAL ANALYSIS; MUSIC; PRIORITY JOURNAL; VOICE;

HUMANS; MATHEMATICS; MUSIC; PITCH PERCEPTION;

EID: 33745917405     PISSN: 00368075     EISSN: 10959203     Source Type: Journal    
DOI: 10.1126/science.1126287     Document Type: Article

References (25)

1. C. Masson, Nouveau Troité des Règies pour lo Composition de to Musique (Da Capo, New York, 1967).
2. O. Hostinský, Die Lehre von den musikalischen Klöngen (H. Dominkus, Prague, 1879).
3. D. Huron, Mus. Percept. 19, 1 (2001).
4. J. D. Heinichen, Der General-Boss in der Composition (G. Olms, New York, 1969).
5. R. Cohn, J. Mus. Theory 41, 1 (1997).
6. J. Roeder, thesis, Yale University (1984).
7. E. Agmon, Musikometrica 3, 15 (1991).
8. R. Cohn, Mus. Anal. 15, 9 (1996).
9. C. Callender, Mus. Theory Online 10 (2004) (http://mto. societymusictheory.org/issues/mto.04.10.3/mto.04.10.3.callender.pdf).
10. G. Mazzola, The Topos of Music (Birkhäuser, Boston, 2002).
11. R. Morris, Mus. Theory Spectrum 20, 175 (1998).
12. J. Douthett, P. Steinbach, J. Mus. Theory 42, 241 (1998).
13. J. Straus, Mus. Theory Spectrum 25, 305 (2003).
14. F. Attneave, R. Olson, Am. Psychol. 84, 147 (1971).
15. R. Shepard, Psychol. Rev. 89, 305 (1982).
16. See supporting material on Science Online.
17. I. Satake, Proc. Natl. Acad. Sci. U.S.A. 42, 359 (1956).
18. W. Thurston, The Geometry and Topology of Three-Manifolds (wwwi.msri.org/publications/books/gt3m).
19. ChordGeometries 1.1 (http://music.princeton.edu/~dmitri/ChordGeometries. html).
20. R. Cohn, J. Mus. Theory 35, 1 (1991).
21. W. Sethares, Tuning, Timbre, Spectrum, Scale (Springer, New York, 2005).
22. R. Cohn, 19th Cent. Mus. 22, 213 (1999).
23. B. Boretz, Perspect. New Mus. 11, 146 (1972).
24. C. Callender, I. Quinn, D. Tymoczko, paper presented at the John Clough Memorial Conference, University of Chicago, 9 July 2005.
25. Thanks to D. Biss, C. Callender, E. Camp, K. Easwaran, N. Elkies, P. Godfrey Smith, R. Hall, A. Healy, I. Quinn, N. Weiner, and M. Weisberg.