Possible and Impossible Melody: Some Formal Aspects of Contour

  • Polansky L
  • Bassein R
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Abstract

This paper explores some formal aspects of contour, especially the mathematics of an abstract definition of contour itself. In hope of establishing a general formulation that will be of use to more specific, style- and genre-related theoretical work in contour, a "non-stylistic" approach is taken. Specific musical situations (like the equivalence classes generated by elementary transformations, or musical assumptions made by ethnomusicological contour studies) are not invoked. Further generalization of the theory of the "number of possible contours" includes the formulation of a theory of contour for asymmetrical and non-ternary contour descriptions, one we believe to be of musical interest. We assume that contour may be applied to any parameter of music, at any hierarchical level. These ideas may be used in the analysis of waveforms, melody, the sequence of pitch means in some large-scale segmentation of a piece, or any other quantifiable parameter.

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Authors

  • Larry Polansky

  • Richard Bassein

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