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Journal Articles Journal of Mathematics and Music Year : 2023

The Inconstancy of Music


A melody is often described as a line of music that evolves through time and, therefore, it is possible to draw its 2D pitch-time representation as a series of points implicitly defining a curve. We introduce to computational musicology a descriptor of this music curve: the inconstancy, a function that gives information on the curve's smoothness as well as some of its topological properties. A mathematical analysis of the inconstancy of music is provided, followed by a lengthy application of inconstancy to musicological tasks. We compare the inconstancy of melodic lines with that of typical accompaniment patterns such as the Alberti bass; this analysis, together with the case study of W.A. Mozart's Variations on Ah ! vous dirai-je, maman, suggests a significant difference in the value of the inconstancy of a music line depending on its function. The inconstancy seems to be correlated also with the compositional style: the analysis on almost 10,000 musical themes of the common practice repertoire shows that Baroque music has higher inconstancy. Finally, we also define a windowed version of the inconstancy for studying longer scores and show the insights one can gain into, for example, structural analysis and cadence detection.
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Dates and versions

hal-03319124 , version 1 (11-08-2021)



Florence Levé, Gianluca Micchi, Jean-Paul Allouche. The Inconstancy of Music. Journal of Mathematics and Music, 2023, 17 (1), ⟨10.1080/17459737.2022.2068687⟩. ⟨hal-03319124⟩
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