Building generalized neo-Riemannian groups of musical transformations as extensions

Journal of Mathematics and Music

Volumn 7, Issue 1, 2013, Pages 55-72

  Popoff, Alexandre ^a  

^a not available   (France)

Author keywords

2 cocycles; contextual transformations; group action; group extensions; neo Riemannian theory; rhythm; time span; transformation theory

Indexed keywords

EID: 84877746354     PISSN: 17459737     EISSN: 17459745     Source Type: Journal    
DOI: 10.1080/17459737.2013.768712     Document Type: Article

References (32)

1. Lewin D. Generalized musical intervals and transformations. New Haven, CT:Yale University Press; 1987.
2. Cohn R. An introduction to Neo-Riemannian theory: a survey and historical perspective. J. Music Theory. 1998;42:167-180.
3. Cohn R. Maximally smooth cycles, hexatonic systems, and the analysis of Late-Romantic triadic progressions. Music Anal. 1996;15:9-40.
4. Cohn R. Neo-Riemannian operations, parsimonious trichords, and their Tonnetz representations. J. Music Theory. 41:1-66.
5. Capuzzo G. Neo-Riemannian theory and the analysis of Pop-Rock music. Music Theory Spectr. 2004;26:177-200.
6. Douthett J. Flip-flop circles and their groups. In: Douthett J, Hyde M, and Smith C, editors. Music theory and mathematics: chords, collections, and transformations, Eastman studies in music. Rochester, NY: University of Rochester Press; 2008. p. 23-49.
7. Straus JN. Contextual-inversion spaces. J. Music Theory 2011;55:43-89.
8. Childs AP.Moving beyond neo-Riemannian triads: exploring a transformational model for seventh chords. J. Music Theory. 1998;42:181-193.
9. Gollin E. Some aspects of three-dimensional Tonnetze. J. Music Theory. 1998;42:195-206.
10. Fiore TM, Satyendra R. Generalized contextual groups. Music Theory Online. 2005;11(3).
11. Hook J. Uniform triadic transformation. J. Music Theory. 2002;46:57-126.
12. Hook J. Signature transformations. In: Douthett J, Hyde M, and Smith C, editors. Music theory and mathematics: chords, collections, and transformations, Eastman studies in music. Rochester, NY: University of Rochester Press, 2008. p. 137-161.
13. Peck R. Wreath products in transformational music theory. Perspect. New Music. 2009;47:193-211.
14. Peck R. Imaginary transformations. J. Math. Music. 2010;4:157-171.
15. Rotman JJ. An introduction to the theory of groups. NewYork, Berlin, Heidelberg: Springer-Verlag; 1995.
16. Robinson DJS. A course in the theory of groups. NewYork, Berlin, Heidelberg: Springer-Verlag; 1996
17. Hall M. Jr. The theory of groups. 2nd ed.American Mathematical Society. Providence (RI):AMSChelsea Publishing; 1999.
18. Brown KS. Cohomology of groups. NewYork, Berlin, Heidelberg: Springer-Verlag; 1982.
19. Baez J. This week's finds-week 234 [Internet]. 2006 June [cited 2012 May]. Available from: http://math.ucr. edu/home/baez/week234.html.
20. Sternberg J. Conceptualizing music through mathematics and the generalized interval system [Internet]. 2006 [cited 2012 November]. Available from: http://www.math.uchicago.edu/∼may/VIGRE/VIGRE2006/PAPERS/Sternberg. pdf.
21. Hempel CE. Metacyclic groups. Commun. Algebra 2007;28:3865-3897.
22. Lewin D. Musical form and transformation: four analytic essays. New Haven, CT:Yale University Press; 1993.
23. Kochavi J. Some structural features of contextually-defined inversion operators. J. Music Theory. 1998;42:307-320.
24. Crans AS, Fiore TM, Satyendra R. Musical actions of dihedral groups. Amer. Math. Monthly. 2009;116:479-495.
25. Fiore TM, Noll T. Commuting groups and the topos of triads. In: Agon C, Andreatta M, Assayag G, Amiot E, Bresson J, Mandereau J, editors. Mathematics and computation in music, Third International Conference, MCM 2011. Springer Lecture Notes in Artificial Intelligence, 6726; 2011. p. 69-83.
26. Ellis G, Kholodna I. Computing second cohomology of finite groups with trivial coefficients. Homol. Homotopy Appl. 1999;1:163-168.
27. Morris RD. Composition with pitch classes. New Haven, CT:Yale University Press; 1987.
28. Hook J. Rhythm in the music of Messiaen: an algebraic study and an application in the Turangalila Symphony. Music Theory Spectr. 1998;20:97-120.
29. Agmon E. Musical durations as mathematical intervals: some implications for the theory and analysis of rhythm. Music Anal. 1997;16:45-75.
30. Amiot E, SetharesWA. An algebra for periodic rhythms and scales. J. Math. Music. 2011;5:149-169.
31. Kim SL. Rhythmic development in the motivic process of Brahms's chamberworks [PhD dissertation]. Santa Barbara (CA): University of California; 2003.
32. Baumslag G, Solitar D. Some two-generator one-relator non-Hopfian groups. Bull. Am. Math. Soc. 1962;68: 199-201.