Publication Cover
Journal of Mathematics and Music
Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance
Volume 18, 2024 - Issue 1
120
Views
0
CrossRef citations to date
0
Altmetric
Articles

Musical stylistic analysis: a study of intervallic transition graphs via persistent homology

ORCID Icon, ORCID Icon &
Pages 89-108 | Received 29 Apr 2022, Accepted 30 Jun 2023, Published online: 10 Aug 2023

References

  • Alcalá-Alvarez, Alberto, and Pablo Padilla-Longoria. 2023. “A Framework for Topological Music Analysis (TMA).” To Appear in Journal of Mathematics and Music 1–23 https://arxiv.org/abs/2204.09744 DOI: 10.1080/17459737.2023.2219994
  • Atienza, Nieves, Rocio Gonzalez-Díaz, and Manuel Soriano-Trigueros. 2020. “On the Stability of Persistent Entropy and New Summary Functions for Topological Data Analysis.” Pattern Recognition 107(1):107509. https://doi.org/10.1080/17459737.2023.2219994.
  • Attali, Dominique, André Lieutier, and David Salinas. 2013. “Vietoris-Rips Complexes also Provide Topologically Correct Reconstructions of Sampled Shapes.” In 27th Annual Symposium on Computational Geometry, 46. Paris, France: Association for Computing Machinery.
  • Berge, Claude. 1973. “Graphs and Hypergraphs.” North-Holland Publishing Company. https://books.google.com.ph/books/about/Graphs_and_Hypergraphs.html?id=X32GlVfqXjsC&redir_esc=y
  • Bergomi, Mattia Giuseppe. 2015. “Dynamical and Topological Tools for (Modern) Music Analysis.” Ph.D. thesis, Università degli Studi di Milano; Université Pierre et Marie Curie.
  • Bergomi, Mattia G., and Adriano Baratè. 2020. “Homological Persistence in Time Series: An Application to Music Classification.” Journal of Mathematics and Music 14 (2): 204–221. https://doi.org/10.1080/17459737.2020.1786745.
  • Carlsson, Gunnar. 2009. “Topology and Data.” Bulletin of the American Mathematical Society 46 (2): 255–308. https://doi.org/10.1090/S0273-0979-09-01249-X.
  • Chartrand, G., L. Lesniak, and P. Zhang. 2016. Graphs & Digraphs. Discrete Mathematics and Its Applications Series, New York: CRC Press, Taylor & Francis Group: New York. https://books.google.com.mx/books?id=vkQwjgEACAAJ.
  • Diestel, Reinhard. 2017. Graph Theory. Vol. 173, 5th ed. Berlin, Germany: Springer Verlag.
  • Edelsbrunner, Herbert, and John Harer. 2008. “Persistent Homology–a Survey.” Discrete & Computational Geometry – DCG 453 (26): 257–282.
  • Edelsbrunner, Herbert, and Hubert Wagner. 2018. “Topological Data Analysis with Bregman Divergences.” Journal of Computational Geometry 9 (2): 67–86. https://doi.org/10.4230/LIPIcs.SoCG.2017.39
  • Eerola, Tuomas, and Petri Toiviainen. 2004. “MIDI Toolbox: MATLAB Tools for Music Research.” Department of Music, University of Jyväskylä.
  • Grant, Ben, Francis Knights, Pablo Padilla, and Dan Tidhar. 2022. “Network-theoretic Analysis and the Exploration of Stylistic Development in Haydn's String Quartets.” Journal of Mathematics and Music 16 (1): 18–28. https://doi.org/10.1080/17459737.2020.1825844.
  • Hatcher, Allen. 2005. Algebraic Topology. Cambridge: Cambridge University Press.
  • Horak, Danijela, Slobodan Maletić, and Milan Rajković. 2009. “Persistent Homology of Complex Networks.” Journal of Statistical Mechanics: Theory and Experiment 2009 (03): P03034. https://doi.org/10.1088/1742-5468/2009/03/P03034.
  • Jolliffe, I. T. 1986. Principal Component Analysis. New York, NY: Springer Verlag.
  • Knights, Francis, Mateo Rodríguez, and Pablo Padilla. 2022. “O Splendor Gloriae: Taverner Or Tye?.” Early Music 49 (4): 565–577. https://doi.org/10.1093/em/caab072.
  • Knights, Francis, Mateo Rodríguez, Pablo Padilla, and Dan Tidhar. 2019. “The Importance of Silence in Stylistic Classification in Music.” Computer Music Journal 43 (2–3): 9–14. https://doi.org/10.1162/comj_e_00515.
  • Liu, Jen-Yu, Shyh-Kang Jeng, and Yi-Hsuan Yang. 2016. “Applying Topological Persistence in Convolutional Neural Network for Music Audio Signals.” arXiv preprint arXiv:1608.07373.
  • Mazzola, Guerino. 2012. The Topos of Music: Geometric Logic of Concepts, Theory, and Performance. Basel: Birkhäuser.
  • Meredith, David. 2016. Computational Music Analysis. Vol. 62, Cham: Springer.
  • Merelli, Emanuela, Marco Piangerelli, Matteo Rucco, and Daniele Toller. 2016. “A Topological Approach for Multivariate Time Series Characterization: The Epileptic Brain.” 12. https://doi.org/10.4108/eai.3-12-2015.2262525.
  • Munkres, James R. 2018. Elements of Algebraic Topology. CRC press.
  • Otter, Nina, Mason A. Porter, Ulrike Tillmann, Peter Grindrod, and Heather A. Harrington. 2017. “A Roadmap for the Computation of Persistent Homology.” EPJ Data Science 6 (1): 1–38. https://doi.org/10.1140/epjds/s13688-017-0109-5.
  • Padilla, Pablo, Francis Knights, Adrián Tonatiuh Ruiz, and Dan Tidhar. 2017. “Identification and Evolution of Musical Style I: Hierarchical Transition Networks and Their Modular Structure.” In Mathematics and Computation in Music, 259–278. Springer International Publishing, Springer, Cham.
  • Parncutt, Richard. 1994. “A Perceptual Model of Pulse Salience and Metrical Accent in Musical Rhythms.” Music Perception 11 (4): 409–464. https://doi.org/10.2307/40285633.
  • Petri, Giovanni, Martina Scolamiero, Irene Donato, and Francesco Vaccarino. 2013. “Topological Strata of Weighted Complex Networks.” PLoS ONE 8 (6): e66506. https://doi.org/10.1371/journal.pone.0066506.
  • Rosen, Charles. 1997. The Classical Style: Haydn, Mozart, Beethoven. New York: WW Norton & Company.
  • Rucco, Matteo, Filippo Castiglione, Emanuela Merelli, and Marco Pettini. 2016. “Characterisation of the Idiotypic Immune Network Through Persistent Entropy.” In Proceedings of ECCS 2014, 117–128. Cham: Springer.
  • Rucco, Matteo, Rocio Gonzalez-Diaz, Maria-Jose Jimenez, Nieves Atienza, Cristina Cristalli, Enrico Concettoni, Andrea Ferrante, and Emanuela Merelli. 2017. “A New Topological Entropy-based Approach for Measuring Similarities Among Piecewise Linear Functions.” Signal Processing 134:130–138. https://doi.org/10.1016/j.sigpro.2016.12.006.
  • Zomorodian, Afra. 2010. “Fast Construction of the Vietoris-Rips Complex.” Computers & Graphics 34 (3): 263–271. Shape Modelling International (SMI) Conference 2010. https://doi.org/10.1016/j.cag.2010.03.007.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.