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Journal articles

The Inconstancy of Music

Abstract : 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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Contributor : Florence Levé Connect in order to contact the contributor
Submitted on : Wednesday, August 11, 2021 - 4:41:12 PM
Last modification on : Thursday, April 7, 2022 - 1:58:26 PM


  • HAL Id : hal-03319124, version 1


Florence Levé, Gianluca Micchi, Jean-Paul Allouche. The Inconstancy of Music. Journal of Mathematics and Music, Taylor & Francis, In press. ⟨hal-03319124⟩



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