Convexity and the well-formedness of musical objects

Aline Honingh*, Rens Bod

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


It is well known that subsets of the two-dimensional space 2 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 is hypothesised that the notion of convexity may be a covering concept of musical phenomena and possibly reflects other mathematical properties of these musical structures. Furthermore, convexity can be used in a pitch-spelling model.

Original languageEnglish
Pages (from-to)293-303
Number of pages11
JournalJournal of New Music Research
Issue number3
Publication statusPublished - 1 Nov 2005
Externally publishedYes


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