### Ring Theory Application to Musical Tones Compositions

Received: 26 May 2023     Accepted: 27 June 2023     Published: 6 September 2023
Abstract

This paper critically analyzed the idea of using musical tones and mathematical techniques to composed a beautiful, listenable musical sound. observed the tone behavior and connection between mathematical concepts (such as rings) and musical notes. The twelve, (12), musical notes were used for the composition, which formed a ring with addition, +, and multiplication, *, operations, such that additive semigroup and multiplicative group forms a commutative group and semigroup respectively. This was done as a specific technique for the composition of music in which, with the aid of mathematical matrix developed, an equal importance is given to all twelve musical tones in the chromatic scale. The ring theorem is a branch of mathematics that is applicable to music composition, contrary to what people might think, as shown by a practical demonstration of mathematical techniques applied to the twelve musical tones that produced a good sound when played on the keyboard, one of the fundamental musical instruments used for translation of keys to sound. There were some claims that had supporting evidence as a prove that, mathematics is one of the tools for music composition. The research is a prove that, ring theory which is an aspect of mathematics that can be used to formulate music using the twelve musical notes, the behaviors and sound produced attested to the fact that mathematics is musical friendly.

 Published in International Journal of Theoretical and Applied Mathematics (Volume 9, Issue 1) DOI 10.11648/j.ijtam.20230901.12 Page(s) 6-9 Creative Commons This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. Copyright Copyright © The Author(s), 2023. Published by Science Publishing Group
Keywords

Abstract Algebra, Ring Theory, Music, Musical Notes, Mathematics, Musical Notes Composition, Group Theory

References
 [1] Rasika Bhalero. The twelve-tone method of composition. Available online: htpp://sites.maths.washington.edu/~morrow/336_15/papers/rasika pdf [2] Samuel Hwere Tsor, et. al. application of Group Theory to Musical Notes, African Journal of Mathematics and Statistics Studies. Vol. 1, Issue 1, pp. 10-20. [3] Robert Morris. Mathematics and the twelve-tone system: past, present and future. Perspectives of New Music. 45 (2) (2007), 76-107. [4] Weibel Charles A. (2013), The K-book: An introduction to algebraic K-theory. Graduate Studies in Mathematics, Vol. 145, Providence, RI: Americal Mathematical Society, ISBN: 978-0-8218-9132-2. [5] Biljana, J. and Tatjana A., (2018), Application of Mathematics in Music Combinatorics and Twelve-tone Music, ISTRAZIVANJE MATHEMATICKOG OBRAZOVANJA, Vol. X, Broj 19, 11-16. [6] Olorunsola, S. A, Olaosebikan, T. E. and Adebayo, K. J., (2014), On application of Modified Lagrange Multipliers in both Equality and Inequality Constraints, International Organization of Scientific Research Journal of Mathematics. Vol. 10, Issue 3. [7] Ohio Department of Education. (2022, August 8). Fine Arts Standards. Retrieved from https://education.ohio.gov/Topics/Learning-in-Ohio/Fine-Arts/Fine-Arts-Standards [8] Ohio Department of Education. (2022, June). Fine Arts: Music. Ohio’s Learning Standards. Retrieved from https://education.ohio.gov/getattachment/Topics/Learning-in-Ohio/FineArts/Fine-Arts-Standards/FA_Music_June22-Final-DRAFT.pdf.aspx?lang=en-US [9] Gelb, R. E. (2021). Mathematicians and music: Implications for understanding the role of affect in mathematical thinking. Columbia University, 1 (1), 1-152. [10] Bobis, J. & Still, K. (2023). The Integration of Mathematics and Music in the Primary School Classroom. Research Gate, 1 (1), 712-719. [11] Silva A., Bernardino Lopes J., Costa C. (2021) Doing math with music - Instrumental orchestration. In A. Reis, J. Barroso, J. B. Lopes, T. Mikropoulos, & C. W. Fan (Eds.), Technology and innovation in learning, teaching and education. TECH-EDU 2020. Communications in Computer and Information Science, vol 1384. Springer, Cham. https://doi.org/10.1007/978-3- 030-73988-1_8 [12] Ndemo, Z., & Mtetwa, D. (2021). Mathematics education undergraduates’ personal definitions of the notion of angle of contiguity in Kinematics. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6 (2), 111-127. https://doi.org/10. 23917/jramathedu.v6i2.11130 [13] Svahn, J., & Bowden, H. M. (2021). Interactional and epistemic challenges in students’ help-seeking in sessions of mathematical homework support: presenting the problem. Classroom Discourse, 12 (3), 193-213. https://doi.org/10.1080/19463014.2019.1686998 [14] Mishiwo, M. (2021). Effect of mathematics method course on pre-service teachers’ knowledge of content and teaching fractions. British Journal of Education, 9 (7), 1-13. [15] Kelly, G. J., & Takao, A. (2002). Epistemic levels in argument: An analysis of university oceanography students’ use of evidence in writing. Science Education, 86 (3), 314-342. https://doi.org/10.1002/ sce.10024
• APA Style

Temitayo Emmanuel Olaosebikan, Adesoji Adewumi Obayomi, Friday Ogoigbe Egbon. (2023). Ring Theory Application to Musical Tones Compositions. International Journal of Theoretical and Applied Mathematics, 9(1), 6-9. https://doi.org/10.11648/j.ijtam.20230901.12

ACS Style

Temitayo Emmanuel Olaosebikan; Adesoji Adewumi Obayomi; Friday Ogoigbe Egbon. Ring Theory Application to Musical Tones Compositions. Int. J. Theor. Appl. Math. 2023, 9(1), 6-9. doi: 10.11648/j.ijtam.20230901.12

AMA Style

Temitayo Emmanuel Olaosebikan, Adesoji Adewumi Obayomi, Friday Ogoigbe Egbon. Ring Theory Application to Musical Tones Compositions. Int J Theor Appl Math. 2023;9(1):6-9. doi: 10.11648/j.ijtam.20230901.12

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title = {Ring Theory Application to Musical Tones Compositions},
journal = {International Journal of Theoretical and Applied Mathematics},
volume = {9},
number = {1},
pages = {6-9},
doi = {10.11648/j.ijtam.20230901.12},
url = {https://doi.org/10.11648/j.ijtam.20230901.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20230901.12},
abstract = {This paper critically analyzed the idea of using musical tones and mathematical techniques to composed a beautiful, listenable musical sound. observed the tone behavior and connection between mathematical concepts (such as rings) and musical notes. The twelve, (12), musical notes were used for the composition, which formed a ring with addition, +, and multiplication, *, operations, such that additive semigroup and multiplicative group forms a commutative group and semigroup respectively. This was done as a specific technique for the composition of music in which, with the aid of mathematical matrix developed, an equal importance is given to all twelve musical tones in the chromatic scale. The ring theorem is a branch of mathematics that is applicable to music composition, contrary to what people might think, as shown by a practical demonstration of mathematical techniques applied to the twelve musical tones that produced a good sound when played on the keyboard, one of the fundamental musical instruments used for translation of keys to sound. There were some claims that had supporting evidence as a prove that, mathematics is one of the tools for music composition. The research is a prove that, ring theory which is an aspect of mathematics that can be used to formulate music using the twelve musical notes, the behaviors and sound produced attested to the fact that mathematics is musical friendly.},
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AB  - This paper critically analyzed the idea of using musical tones and mathematical techniques to composed a beautiful, listenable musical sound. observed the tone behavior and connection between mathematical concepts (such as rings) and musical notes. The twelve, (12), musical notes were used for the composition, which formed a ring with addition, +, and multiplication, *, operations, such that additive semigroup and multiplicative group forms a commutative group and semigroup respectively. This was done as a specific technique for the composition of music in which, with the aid of mathematical matrix developed, an equal importance is given to all twelve musical tones in the chromatic scale. The ring theorem is a branch of mathematics that is applicable to music composition, contrary to what people might think, as shown by a practical demonstration of mathematical techniques applied to the twelve musical tones that produced a good sound when played on the keyboard, one of the fundamental musical instruments used for translation of keys to sound. There were some claims that had supporting evidence as a prove that, mathematics is one of the tools for music composition. The research is a prove that, ring theory which is an aspect of mathematics that can be used to formulate music using the twelve musical notes, the behaviors and sound produced attested to the fact that mathematics is musical friendly.
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Author Information
• Department of Mathematical Sciences, School of Pure and Applied Science, Bamidele Olumilua University of Education, Science and Technology, Ikere-Ekiti, Nigeria

• Department of Mathematics, Faculty of Science, Ekiti State University, Ado-Ekiti, Nigeria

• Department of Mathematical Sciences, School of Pure and Applied Science, Bamidele Olumilua University of Education, Science and Technology, Ikere-Ekiti, Nigeria

• Sections