×

When virtual reality helps fathom mathemusical hyperdimensional models. (English) Zbl 1495.00011

Montiel, Mariana (ed.) et al., Mathematics and computation in music. 8th international conference, MCM 2022, Atlanta, GA, USA, June 21–24, 2022. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13267, 86-98 (2022).
Summary: Mathemusicians have always produced models for understanding, analyzing or computing music. We are used to visualize some of them on paper, in a theater or on a computer screen.
Even if they refer to multidimensional spaces (3D-4D), while displaying these models on a computer screen the viewer ends up with a 2D picture, or a movie.
Planar projection limits the perception, nowadays, in the era of virtual reality, we propose tools and solutions to better apprehend these models and give the viewer an improved immersive experience.
Taking advantage of methods used in air traffic simulations, we are developing techniques that we will apply to existing mathemusical visualizations, beginning with Tonnetze and Hyperspheres.
We herewith introduce two recently revealed mathemusical models that we have created:
2D: The Shadow Tonnetz, our latest extension of the Tonnetz that keeps trace of a harmonic path.
4D: The Entangled Hyperspheres, a combination of two Planet-4D models that enables us to visualize microtonal music.
The images in this paper are extracted from immersive virtual reality world; during MCM we intend to presented the movies with adapted 3D equipment.
All videos including virtual ones will be available on www.mathemusic.net.
For the entire collection see [Zbl 1492.00048].

MSC:

00A65 Mathematics and music

Software:

Planet-4D; Tonnetz
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Baroin, G.; Agon, C.; Andreatta, M.; Assayag, G.; Amiot, E.; Bresson, J.; Mandereau, J., The planet-4D model: an original hypersymmetric music space based on graph theory, Mathematics and Computation in Music, 326-329 (2011), Heidelberg: Springer, Heidelberg · Zbl 1321.00079 · doi:10.1007/978-3-642-21590-2_25
[2] Baroin, G., de Gérando, S.: Sons et représentation visuelle en hyperespace: l’hypersphère des spectres, Les Cahiers de l’Institut International pour l’Innovation, la Création Artistique et la Recherche, 3icar éditions (2012)
[3] Baroin, G.; Calvet, A.; Montiel, M.; Gomez-Martin, F.; Agustín-Aquino, OA, Visualizing temperaments: squaring the circle?, Mathematics and Computation in Music, 333-337 (2019), Cham: Springer, Cham · Zbl 1456.00059 · doi:10.1007/978-3-030-21392-3_27
[4] Baroin, G.: Music Mathematic and 4D, keynote during Virtuality Experience, Buenos Aires/Paris 04 December 2020. www.virtuality.io)
[5] Sherman, W., et al.: Understanding Virtual Reality: Interface, Application, and Design, 2nd edn. Elsevier Science (2018)
[6] Dohy, D., Mora-Camino, F., Mykoniatis, G., Raoul, J.-L.: Air traffic complexity through local covariance in the context of large areas of operations. In: 9th International Conference on Experiments/Process/System Modeling/Simulation/Optimization, Athens, Greece, July 2021 ⟨hal-03313081⟩ (2021)
[7] Baroin, G.: Drone simulations in virtual environment. Neometsys NMS Lab. www.neometsys.fr
[8] Baroin, G., Khannanov, I.: The Shadow-Tonnetz: visualizing speed and weight within harmonic progressions. In: Conference: 10th European Music Analysis Conference (Euromac 10), Moscow, Pre-Proceedings (2022)
[9] Andretta, M.: On group-theoretical methods applied to music: some compositional and implementational aspects. Perspectives in Mathematical Music Theory (2004) · Zbl 1114.00304
[10] Seress, H., Baroin, G.: De l’Hypersphère au Spinnen Tonnetz: propositions d’adaptation pour les modèles triadiques. Musimédiane, no. 11 (2019). https://www.musimediane.com/11seressbaroin/
[11] Andreatta, M.; Baroin, G.; Kapoula, Z.; Vernet, M., An introduction on formal and computational models in popular music analysis and generation, Aesthetics and Neuroscience, 257-269 (2016), Cham: Springer, Cham · doi:10.1007/978-3-319-46233-2_16
[12] Albini, G.; Antonini, S.; Chew, E.; Childs, A.; Chuan, C-H, Hamiltonian cycles in the topological dual of the Tonnetz, Mathematics and Computation in Music, 1-10 (2009), Heidelberg: Springer, Heidelberg · Zbl 1247.00015 · doi:10.1007/978-3-642-02394-1_1
[13] Baroin, G., de Gérando, S.: The Entangled Hyperspheres, an innovative approach to visualize microtonal music. Les Cahiers de l’Institut International pour l’Innovation, la Création Artistique et la Recherche, icareditions (2022, to appear)
[14] de Gérando, S.: Music from «le Labyrinthe du Temps», Performances since 2020
[15] Jedrzejewski, F.: Ivan Wyschnegradsky et la musique microtonale. Musique, musicologie et arts de la scène. Université de Paris 1 Panthéon-Sorbonne (2000)
[16] Bigo, L., de Gérando, S.: Invention algorithmique du matériau compositionnel: les séries tous intervalles dans une octave et en zigzag (STIOZ), les séries tous intervalles imbriqués dans une série micro-intervallique (STISMI), Rapport de recherche, icarEditions (2017)
[17] Villena-Taranilla, R.; Tirado-Olivares, S.; Cózar-Gutiérrez, R.; González-Calero, J., Effects of virtual reality on learning outcomes in K-6 education: a meta-analysis, Educ. Res. Rev., 35, 100434 (2022) · doi:10.1016/j.edurev.2022.100434
[18] Cohn, R., Weitzmann’s regions, my cycles, and douthett’s dancing cubes, Music Theory Spectr., 22, 1, 89-103 (2000) · doi:10.2307/745854
[19] Douthett, J.; Steinbach, P., Parsimonious graphs: a study in parsimony contextual transformations, and modes of limited transposition, J. Music Theory, 42, 2, 241-265 (1998) · doi:10.2307/843877
[20] Mazzola, G.: The topos of music: Birkhäuser Basel (2005)
[21] Amiot, E.; Yust, J.; Wild, J.; Burgoyne, JA, The Torii of phases, Mathematics and Computation in Music, 1-18 (2013), Heidelberg: Springer, Heidelberg · Zbl 1270.00023 · doi:10.1007/978-3-642-39357-0_1
[22] Yust, J., Generalized Tonnetze and Zeitnetze, and the topology of music concepts, J. Math. Music, 14, 170-203 (2020) · Zbl 1466.00023 · doi:10.1080/17459737.2020.1725667
[23] Tymoczko, D., A Geometry of Music. Oxford Studies in Music Theory (2011), Oxford: Oxford University Press, Oxford
[24] Chew, E.; Anagnostopoulou, C.; Ferrand, M.; Smaill, A., The spiral array: an algorithm for determining key boundaries, Music and Artificial Intelligence, 18-31 (2002), Heidelberg: Springer, Heidelberg · doi:10.1007/3-540-45722-4_4
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.