The distance geometry of deep rhythms and scales

Proceedings of the 17th Canadian Conference on Computational Geometry, CCCG 2005

Volumn , Issue , 2005, Pages 163-166

  Demaine, Erik D ^a   Gomez Martin, Francisco ^b   Meijer, Henk ^c   Rappaport, David ^c   Taslakian, Perouz ^d   Toussaint, Godfried T ^d   Winograd, Terry ^e   Wood, David R ^f  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^c QUEEN S UNIVERSITY   (Canada)

^d MCGILL UNIVERSITY   (Canada)

^e Stanford University   (United States)

^f UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ONE DIMENSIONAL;

DISTANCE GEOMETRY; K POINTS; UNSOLVED PROBLEMS;

COMPUTATIONAL GEOMETRY;

EID: 34848897081     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (10)

1. J. Clough, N. Engebretsen, and J. Kochavi. Scales, sets, and interval cycles: A taxonomy. Music Theory Spectrum, 21(1):74-104, Spring 1999.
2. P. Erdos. Distances with specified multiplicities. American Mathematical Monthly, 96:447, 1989.
3. C. Gamer. Deep scales and difference sets in equal-tempered systems. In Proceedings of the 2nd Annual Conference of the American Society of University Composers, pp. 113-122, 1967.
4. C. Gamer. Some combinational resources of equal-tempered systems. J. Music Theory, 11:32-59, 1967.
5. T. A. Johnson. Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing, 2003.
6. I. Palásti. A distance problem of P. Erdos with some further restrictions. Discr. Math., 76(2):155-156, 1989.
7. G. T. Toussaint. Algorithmic, geometric, and combinatorial problems in computational music theory. In Proceedings of the 10th Encuentros de Geometria Computacional, pp. 101-107, Sevilla, Spain, June 2003.
8. G. T. Toussaint. Classification and phylogenetic analysis of African ternary rhythm timelines. In Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science, pp. 25-36, Granada, Spain, July 2003.
9. G. T. Toussaint. Computational geometric aspects of musical rhythm. In Abstracts of the 14th Annual Fall Workshop on Computational Geometry, pp. 47-48, Cambridge, MA, November 2004.
10. T. Winograd. An analysis of the properties of 'deep' scales in a t-tone system. May 17, 1966. Term paper for music theory course at Colorado College.