Abstract

Previous abstract Back to issue content Next abstract
Symmetry: Culture and Science
Volume 35, Number 4, pages 519-528 (2024)
https://doi.org/10.26830/symmetry_2024_4_519

SYMMETRY IN MUSICAL SPACES

S. P. Kathryn Lee1, C. H. Raymond Ooi2, Ita Wang3

1 University of Malaya: Creative Arts Faculty, Kuala Lumpur, Malaysia;
Email: kathrynleesp@yahoo.com

2 University of Malaya: Creative Arts Faculty, Kuala Lumpur, Malaysia;
Email: rooi@um.edu.my

3 University of Malaya: Creative Arts Faculty, Kuala Lumpur, Malaysia;
Email: wangita@um.edu.my

Abstract: An analysis of symmetry was applied to the Bach Violin Chaconne (BWV 1004, c.1720) and modern Piano Chaconne by Sofia Gubaidulina (c.1962). Excerpts from musical contours may appear in symmetrical forms (1Apagyi, 1989,5 Donnini, 1986, 9Morgan, 1998 & 10Voloshinov, 1996) and more interestingly as recontextualized form (Hanninen,2003)6. This study explores the drawing of music in symmetry by an illustrative pitch height (y-axis) against time (x-axis) topology.

References:
Altschuler, E., Phillips, A. (2015) The sound of topology; 2D manifolds in Bach, The Musical Times, 1569(1933), 57-64.

Altschuler, E.L. (2005) Were Bach's Toccata and Fugue BWV 565 and the Ciacconia from BWV1004 Lute Pieces? The Musical Times, 146(1893), 77-86. https://doi.org/10.2307/30044126

Apagyi, M. (1989) Symmetries in Music Teaching, Computers Math. Applic. 17(4-6), 671-695. https://doi.org/10.1016/B978-0-08-037237-2.50048-9

Brumbeloe, J. (2000) Patterns and performance choices in selected perpetual-motion movements by J.S. Bach, Theory and Practise, 25,1-25.

Donnini, R. (1986) The visualization of music: Symmetry and asymmetry, Comp. and Mathematics, with Appls., 12B (1/2), 435-463. https://doi.org/10.1016/B978-0-08-033986-3.50035-5

Evans, B. (1992) Number as form and content; A composer's path of inquiry, Leonardo 25, Visual mathematics: Special Double Issue, 303-311. https://doi.org/10.2307/1575855

Haek, J. (2008) Residue cycles of Fibonacci series modulo m as tools for serial composition, Perspectives of New Music, 46(2), 33-58. https://doi.org/10.1353/pnm.2008.0001

Hanninen, D. (2003) Theory of recontextualization in music: Analyzing phenomenal transformations of repetition, Music Theory Spectrum, 25(1), 59-97. https://doi.org/10.1525/mts.2003.25.1.59

Irving, D. (2007) Bach unaccompanied, Early Music, 35(4), 661-663. https://doi.org/10.1093/em/cam074

Klapuri, A., Davy, M. (2006) Signal Processing Methods for Music Transcription, Springer Science +Business Media LLC. https://doi.org/10.1007/0-387-32845-9

McWhinnie, H.J. (1987) A review of selected research on the golden section hypothesis, Visual Arts Research, 13(1), 73-84.

Morgan, R.P. (1998) Symmetrical form and common-practice tonality, Music TheorySpectrum, 20(1), 1- 47. https://doi.org/10.2307/746155

Pierce, J.C. (1951) The Fibonacci series, The Scientific Monthly, 73(4),224-228.

Powell, N.W. (1979) Fibonacci and the golden mean: Rabbits, rumbas and rondeaux, Journal of Music Theory 23(2), 227-273. https://doi.org/10.2307/843726

Smith, D.E. (1927) Esthetics and mathematics, The Mathematics Teacher, 20(8), 419-428. https://doi.org/10.5951/MT.20.8.0419

Stakhov, A.P. (1989) The golden section in the measurement theory, Computers Math, Applic. 17(4-45), 613-638. https://doi.org/10.1016/B978-0-08-037237-2.50045-3

Stakhov, A.P. (2006) Fundamentals of a new kind of mathematics based on the golden section, Chaos, Solitons and Fractals, 27, 1124-1146. https://doi.org/10.1016/j.chaos.2005.05.008

Voloshinov, A. (1996) Symmetry as a superprinciple of science and art, Leonardo, 29(2), 109-113. https://doi.org/10.2307/1576340

Previous abstract Back to issue content Next abstract