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Mathematical Morphology Operators for Harmonic Analysis

Isabelle Bloch
Carlos Agon
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Mathematical Morphology provides powerful tools for image processing, analysis and understanding. In this paper, we will work on how to apply these tools to analyze scores, that are image-like representations of Music. To do that, we will consider chroma rolls, a representation of scores similar to piano rolls that use chromas instead of pitches. Endowing this representation with a lattice structure, one can define Mathematical Morphology operators, and setting a group structure to the Time-Frequency plane allows us to use the notion of structuring element. We will show throughout some examples how this relates with the notion of pitch-class set and chord progressions, and we will analyze two Chopin's Nocturnes with this technique.
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Dates and versions

hal-03638362 , version 1 (12-04-2022)
hal-03638362 , version 2 (04-10-2022)



Gonzalo Romero-García, Isabelle Bloch, Carlos Agon. Mathematical Morphology Operators for Harmonic Analysis. MCM 2022 - 8th International Conference Mathematics and Computation in Music, Jun 2022, Atlanta, United States. pp.255-266, ⟨10.1007/978-3-031-07015-0_21⟩. ⟨hal-03638362v2⟩
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