Visualization of low dimensional structure in Tonal Pitch Space

International Computer Music Conference, ICMC 2005

Volumn , Issue , 2005, Pages

  Burgoyne, J Ashley ^a   Saul, Lawrence K ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTERS;

COMPLEX STRUCTURE; DISTANCE FUNCTIONS; LOW DIMENSIONAL STRUCTURE; MUSIC THEORY; NONLINEAR TECHNIQUES; STATISTICAL TECHNIQUES; TOROIDAL STRUCTURES;

COMPUTER MUSIC;

EID: 84923884458     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (12)

1. E. Chew, "Towards a mathematical model of tonality", Ph. D. dissertation, Massachusetts Institute of Technology, Cambridge, MA, 2000.
2. -, "Thinking out of the grid and inside the spiral: Geometric interpretations of and comparisons with the spiral array model", University of Southern California, Tech. Rep. 03-002, 2003.
3. J. D. Heinichen, General-Bass in der Composition, Dresden, 1728.
4. C. L. Krumhansl, Cognitive Foundations of Musical Pitch. New York: Oxford University Press, 1990.
5. C. L. Krumhansl and E. J. Kessler, "Tracing the dynamic changes in perceived tonal organisation in a spatial representation of musical keys", Psychological Review, vol. 89, pp. 334-368, 1982.
6. F. Lerdahl, Tonal Pitch Space. New York: Oxford University Press, 2001.
7. F. Lerdahl and R. Jackendoff, A Generative Theory of Tonal Music. Cambridge, MA: MIT Press, 1983.
8. G. Mazzola, The Topos of Music. Basel: Birkhauser, 2003.
9. T. Noll and J. Garbers, "Harmonic path analysis", in Perspectives of Mathematical and Computational Music Theory, G. Mazzola, T. Noll, and E. Luis-Puebla, Eds. Osnabrück: epOs-Music, 2004.
10. L. K. Saul, K. Q. Weinberger, F. Sha, J. Ham, and D. D. Lee, "Spectral methods for dimensionality reduction", in Semi-Supervised Learning, O. Chappelle, B. Schölkopf, and A. Zien, Eds. Cambridge, MA: MIT Press, in press.
11. D. Temperley, The Cognition of Basic Musical Structures. Cambridge, MA: MIT Press, 2001.
12. G. Weber, Versuch einer geordeneten Theorie der Tonsetzkunst. Mainz: B. Schotts Söhne, 1821-24.