Generalized tonnetze

Journal of Mathematics and Music

Volumn 5, Issue 2, 2011, Pages 117-139

  Catanzaro, Michael J ^a  

^a WAYNE STATE UNIVERSITY   (United States)

Author keywords

generalized scales; geometry of chords; N tone equal temperament; simpicial complex; space of triads; Tonnetz; torus

Indexed keywords

EID: 80053599760     PISSN: 17459737     EISSN: 17459745     Source Type: Journal    
DOI: 10.1080/17459737.2011.614448     Document Type: Article

References (17)

1. B. Hyer, Tonal Intuitions in Tristan und Isolde, PhD diss., Yale University, 1989.
2. D. Tymoczko, The geometry of musical chords, Science 313(72) (2006), pp. 72-74.
3. R. Cohn, Neo-Riemannian operations, parsimonious trichords, and their Tonnetz representations, J. Music Theory 41 (1997), pp. 1-66.
4. R. Cohn, Introduction to Neo-Riemannian theory: A survey and a historical perspective, J. Music Theory 42 (1998), pp. 167-180.
5. J. Douthett and P. Steinbach, Parsimonious graphs: A study in parsimony, contextual transformations, and modes of limited transposition, J. Music Theory 42 (1998), pp. 241-263.
6. E. Gollin, Some aspects of three-dimensional Tonnetze, J. Music Theory 42 (1998), pp. 195-205.
7. G. Mazzola,The Topos of Music. Geometric Logic of Concepts, Theory, and Performance, BirkhäuserVerlag, Berlin, 2002.
8. R.W. Peck, Klein-Bottle Tonnetze, Music Theory Online 9 (2003), pp. 1-45.
9. H. Riemann, Grosse Kompositionslehre, Der homophone Satz (Melodielehre und Harmonielehre), Spemann Publishing, Berlin & Stuttgart, 1902.
10. A. Netske, Paradigmatic Motivic Analysis, Perspectives in Mathematical and Computational Music Theory, Osnabrück Series on Music and Computation, Electronic Publishing Osnabruck, 2004, pp. 343-365.
11. G. Balzano, The group-theoretic description of 12-fold and microtonal pitch systems, Comput. Music J. 4 (1980), pp. 66-84.
12. T.M. Fiore and R. Satyendra, Generalized contextual groups, Music Theory Online 11 (2005), pp. 1-28.
13. M.J. Greenberg and J.R. Harper, Algebraic Topology: A First Course, Westview Press, New York, 1981.
14. C.A. Weibel, An Introduction to Homological Algebra, Cambridge University Press, New York, 1994.
15. A. Pressley, Elementary Differential Geometry, Springer-Verlag London Limited, London, 2001.
16. A.S. Crans, T.M. Fiore, and R. Satyendra, Musical actions of dihedral groups, Amer. Math. Monthly. 116(6) (2009), pp. 479-495.
17. B.J. McCartin, Prelude to musical geometry, College Math. J. 29 (1998), pp. 354-370.