Convexity and the well-formedness of musical objects

@article{Honingh2005ConvexityAT,
  title={Convexity and the well-formedness of musical objects},
  author={Aline K. Honingh and Rens Bod},
  journal={Journal of New Music Research},
  year={2005},
  volume={34},
  pages={293 - 303}
}
Abstract It is well known that subsets of the two-dimensional space ℤ2 can represent prominent musical and music-theoretical objects such as scales, chords and chord vocabularies. It has been noted that the major and minor diatonic scale form convex subsets in this space. This triggers the question whether convexity is a more widespread concept in music. This article systematically investigates the convexity for a number of musical phenomena including scales, chords and (harmonic) reduction. It… 

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