MATHEMATICAL ANALYSIS OF MELODIES: SYMMETRY
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.
symmetry of graphs, matrix pencils.
