Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorem
After presenting the general framework of `mathemusical' dynamics, we focus on one music-theoretical problem concerning a special case of homometry theory applied to music composition, namely Milton Babbitt's hexachordal theorem. We briefly discuss some historical aspects of homometric str...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212114 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorem. Moreno Andreatta, Corentin Guichaoua and Nicolas Juillet. SIGMA 20 (2024), 009, 19 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862663560152219648 |
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| author | Andreatta, Moreno Guichaoua, Corentin Juillet, Nicolas |
| author_facet | Andreatta, Moreno Guichaoua, Corentin Juillet, Nicolas |
| citation_txt | Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorem. Moreno Andreatta, Corentin Guichaoua and Nicolas Juillet. SIGMA 20 (2024), 009, 19 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | After presenting the general framework of `mathemusical' dynamics, we focus on one music-theoretical problem concerning a special case of homometry theory applied to music composition, namely Milton Babbitt's hexachordal theorem. We briefly discuss some historical aspects of homometric structures and their ramifications in crystallography, spectral analysis, and music composition via the construction of rhythmic canons tiling the integer line. We then present the probabilistic generalization of Babbitt's result, which we recently introduced in a paper entitled ''New hexachordal theorems in metric spaces with probability measure'' and illustrate the new approach with original constructions and examples.
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| first_indexed | 2026-03-16T06:39:46Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212114 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T06:39:46Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Andreatta, Moreno Guichaoua, Corentin Juillet, Nicolas 2026-01-28T13:57:23Z 2024 Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorem. Moreno Andreatta, Corentin Guichaoua and Nicolas Juillet. SIGMA 20 (2024), 009, 19 pages 1815-0659 2020 Mathematics Subject Classification: 00A65; 28A75; 05C12; 60D05 https://nasplib.isofts.kiev.ua/handle/123456789/212114 https://doi.org/10.3842/SIGMA.2024.009 After presenting the general framework of `mathemusical' dynamics, we focus on one music-theoretical problem concerning a special case of homometry theory applied to music composition, namely Milton Babbitt's hexachordal theorem. We briefly discuss some historical aspects of homometric structures and their ramifications in crystallography, spectral analysis, and music composition via the construction of rhythmic canons tiling the integer line. We then present the probabilistic generalization of Babbitt's result, which we recently introduced in a paper entitled ''New hexachordal theorems in metric spaces with probability measure'' and illustrate the new approach with original constructions and examples. The authors wish to thank the editors of this special issue for their invitation to celebrate Jean-Pierre Bourguignon’s 75th birthday through a paper centered around some aspects of contemporary ‘mathemusical’ research. We are particularly grateful to the anonymous referees for their careful reading of the manuscript and their valuable criticisms that helped us to improve many aspects of the present article. Many thanks to the colleagues at IRMA-University of Strasbourg and IRCAM-Sorbonne University for all the discussions that contributed to clarifying some of the ideas developed in this article. This research is partially supported by the Interdisciplinary Thematic Institute CREAA, as part of the ITI 2021-2028 program of the Université de Strasbourg, the CNRS, and the Inserm (funded by IdEx Unistra ANR-10-IDEX-0002, and by SFRI-STRAT’US ANR-20-SFRI-0012 under the French Investments for the Future Program). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorem Article published earlier |
| spellingShingle | Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorem Andreatta, Moreno Guichaoua, Corentin Juillet, Nicolas |
| title | Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorem |
| title_full | Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorem |
| title_fullStr | Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorem |
| title_full_unstemmed | Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorem |
| title_short | Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorem |
| title_sort | taking music seriously: on the dynamics of 'mathemusical' research with a focus on hexachordal theorem |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212114 |
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