Abstract
The problem of identifying musical styles using mathematical tools is central not only in musicology and the mathematical theory of music, but also in applications to music pattern recognition and automated music generation in a particular idiom. In this paper we propose a methodology related to the transition network approach developed by D. Cope in his Experiments on Musical Intelligence, EMI. This extension allows for the possibility of defining stylistic cells at different scales as motifs and moduli of networks at the corresponding scale. It can be applied to study recursivity aspects of music. We also outline how this methodology can be used to systematically study stylistic changes in different contexts by incorporating probabilistic and statistical tools and connections with other approaches.
Misura ciò che è misurabile, e rendi misurabile ciò che non lo è.
(Measure what is measurable, and make measurable what is not).
Attributed to Galileo Galilei.
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Notes
- 1.
Methods based on random walks provide a way of generating music fragments (see for instance (Collins and Laney 2017)).
- 2.
Not to be confused with the motifs introduced by U. Alon in the context of systems biology, which will also be used. In order to avoid confusion we employ the term structural cells for moduli of graphs.
- 3.
For instance, singular value decomposition, spectral analysis, principal component analysis, etc. See (Knights et al. 2017a). For more details on statistical methods.
- 4.
The previous histograms for pitch clases and intervals were also generated using Miditoolbox (Tolviainen and Eerola 2016).
- 5.
C# enters the mode as a leading tone, although it does not belong to it in a strict sense.
- 6.
In particular, we used Cytoscape in order to analyze the networks. This open source software has already a built in analyzer.
- 7.
The same consideration can be applied to different performers, focusing on the rhthmic aspects, rather than the melodic ones, which in principle are fixed. Of course ornamentation aspects or improvised music can also be approached using these tools.
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Padilla, P., Knights, F., Ruiz, A.T., Tidhar, D. (2017). Identification and Evolution of Musical Style I: Hierarchical Transition Networks and Their Modular Structure. In: Agustín-Aquino, O., Lluis-Puebla, E., Montiel, M. (eds) Mathematics and Computation in Music. MCM 2017. Lecture Notes in Computer Science(), vol 10527. Springer, Cham. https://doi.org/10.1007/978-3-319-71827-9_20
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