Advances and Applications in Discrete Mathematics
Volume 17, Issue 1, Pages 49 - 112
(January 2016) http://dx.doi.org/10.17654/DM017010049 |
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MATHEMATICAL ANALYSIS OF MELODIES: SYMMETRY
Fumio Hazama
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Abstract: A plane graph, called an M-graph, is attached to every melody. The main purpose of the paper is to obtain a complete classification of melodies of arbitrary length whose M-graphs have lines of symmetry. A crucial role is played by a matrix pencil, attached to the set of those melodies, whose fiber at a point is revealed to hide a twelve-tone row composed by Webern. |
Keywords and phrases: symmetry of graphs, matrix pencils. |
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