Automatic Exercise Generation for Exploring Connections between Mathematics and Music
Mathematics and Music are closely connected and their multifaceted relationship has been explored since ancient times. Pythagoras was one of the first who discovered and formalized one of those connections by studying the arithmetic of musical intervals, expressing them by numerical ratios and relat...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-04-01
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| Series: | Open Education Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/edu-2022-0183 |
| _version_ | 1827953118105567232 |
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| author | Brito Irene Almeida José João Machado Gaspar J. |
| author_facet | Brito Irene Almeida José João Machado Gaspar J. |
| author_sort | Brito Irene |
| collection | DOAJ |
| description | Mathematics and Music are closely connected and their multifaceted relationship has been explored since ancient times. Pythagoras was one of the first who discovered and formalized one of those connections by studying the arithmetic of musical intervals, expressing them by numerical ratios and relating ratios to consonance/dissonance notions, being the Pythagorean tuning and scale based on arithmetic principles. Another interesting link between Mathematics and Music is the geometric approach to musical composition. Geometric patterns are present in different musical style compositions and some composing techniques, such as the 12-tone technique, use geometric transformations, involving also applications of modular arithmetic and set theory to Music. The aim of this work is to present existing relations between Mathematics and Music and to propose automatic exercise generation for exploring and studying those relations. The exercises are generated using the system MVGEN and the LaTeX package MusiXTeX. The generation process and the automatically generated exercises can be used for creating learning and assessment materials for education in Mathematics and Music, linking Science and Art. |
| first_indexed | 2024-04-09T14:07:54Z |
| format | Article |
| id | doaj.art-b076873f5ddc42a2a05585f549d2d673 |
| institution | Directory Open Access Journal |
| issn | 2544-7831 |
| language | English |
| last_indexed | 2024-04-09T14:07:54Z |
| publishDate | 2023-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Education Studies |
| spelling | doaj.art-b076873f5ddc42a2a05585f549d2d6732023-05-06T15:58:55ZengDe GruyterOpen Education Studies2544-78312023-04-0151pp. 1510.1515/edu-2022-0183Automatic Exercise Generation for Exploring Connections between Mathematics and MusicBrito Irene0Almeida José João1Machado Gaspar J.2Departamento de Matemática e Centro de Matemática, Universidade do Minho, 4800Guimarães, PortugalDepartamento de Informática, Algoritmi, Universidade do Minho, 4710Braga, PortugalDepartamento de Matemática e Centro de Matemática, Universidade do Minho, 4800Guimarães, PortugalMathematics and Music are closely connected and their multifaceted relationship has been explored since ancient times. Pythagoras was one of the first who discovered and formalized one of those connections by studying the arithmetic of musical intervals, expressing them by numerical ratios and relating ratios to consonance/dissonance notions, being the Pythagorean tuning and scale based on arithmetic principles. Another interesting link between Mathematics and Music is the geometric approach to musical composition. Geometric patterns are present in different musical style compositions and some composing techniques, such as the 12-tone technique, use geometric transformations, involving also applications of modular arithmetic and set theory to Music. The aim of this work is to present existing relations between Mathematics and Music and to propose automatic exercise generation for exploring and studying those relations. The exercises are generated using the system MVGEN and the LaTeX package MusiXTeX. The generation process and the automatically generated exercises can be used for creating learning and assessment materials for education in Mathematics and Music, linking Science and Art.https://doi.org/10.1515/edu-2022-0183mathematicsmusicsteamautomatic exercise generationmultiple-choice question |
| spellingShingle | Brito Irene Almeida José João Machado Gaspar J. Automatic Exercise Generation for Exploring Connections between Mathematics and Music Open Education Studies mathematics music steam automatic exercise generation multiple-choice question |
| title | Automatic Exercise Generation for Exploring Connections between Mathematics and Music |
| title_full | Automatic Exercise Generation for Exploring Connections between Mathematics and Music |
| title_fullStr | Automatic Exercise Generation for Exploring Connections between Mathematics and Music |
| title_full_unstemmed | Automatic Exercise Generation for Exploring Connections between Mathematics and Music |
| title_short | Automatic Exercise Generation for Exploring Connections between Mathematics and Music |
| title_sort | automatic exercise generation for exploring connections between mathematics and music |
| topic | mathematics music steam automatic exercise generation multiple-choice question |
| url | https://doi.org/10.1515/edu-2022-0183 |
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