Saturday, September 07, 2024

Interplay between music and mathematics in the eyes of the beholder: focusing on differing types of expertise

Libby Azaryahu,
Ido Ariel &
Roza Leikin

Humanities and Social Sciences Communications volume 11, Article number: 1153 (2024)

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Article
Open access

Published: 07 September 2024


Abstract



This study explored the unique connections between music and mathematics as perceived by four groups of experts: professional mathematicians and musicians, as well as teacher educators in these two fields. Using 2 × 2 study design, we studied four groups of participants, comprising theorists and educators from various Israeli universities. During semi-structured interviews, the study participants were asked about their views on the connections between mathematics and music. This study proposes a model of experts’ conceptions of the connection between mathematics and music, which is of descriptive and explanatory power. that reveals differences between the four groups of experts. Theoreticians in both disciplines highlighted Mathematics as a key tool for music analysis and creation. Musical educators emphasized the role of music as a tool for learning mathematics. All the study participants, independently of the field of their expertise, value structure, beauty, sense of wonder, freedom and creative thinking as characteristics of both fields. Additionally, all the experts hold conceptions of the importance of integrating music and mathematics into various discipline. This study opened new doors for future research wherein utilization of experts’ insights to craft integrated study modules of music and mathematics can be explored, a pursuit that carries substantial significance.




Introduction



The connection between Western music and mathematics has been recognized since the days of Pythagoras, Plato and Aristotle, who wrote about the overlap and parallels between the two disciplines. Both disciplines – music and mathematics – are expressed through the use of representative language and symbolic notation (Papadopoulos 2002). Mathematical concepts such as symmetry, patterns, ratio, and division are expressed in music. In music, intervals, rhythm, duration, speed, and many musical concepts are naturally represented by numbers (Bamberger and Disessa 2003). For example, the intervals between harmonic notes in music are determined by ratios of small whole numbers. When plucking two strings of the same length, the ratio between their lengths is 1:1, resulting in identical and harmonious sounds (sounds that blend well together). Moreover, differing ratios of string lengths will produce various harmonic intervals, such as the octave (string ratio of 1:2), the fifth (2:3), and the fourth (3:4).

Music was a subject of research among mathematicians such as Descartes, Kepler, and Euler, and on the other hand musicians were attracted to the possibilities inherent in the science of mathematics for analyzing works and composing (Wollenberg 2003). Compositional methods that draw inspiration from mathematical ideas included, among others, counterpoint (a second voice that appears simultaneously with the first voice in a polyphonic texture), a crab canon (the second voice is an imitation of the first voice in reverse), or a palindrome (a section that can be played from beginning to end and from end to beginning, in mathematics y = −x), and geometric designs of musical melodies (for example reflective symmetry, where a melody repeats itself in a mirrored fashion). In addition, mathematical images in Western music are expressed musically in the theory of harmony, the theory of rhythm, and the theory of forms. The theory of harmony reveals a fundamental regularity in how sounds are combined simultaneously, how they relate to one another, and how they are distributed over time. The theory of rhythm refers to how the sounds are organized in time and the continuation relationships between them. And finally, the theory of forms addresses how musical events are organized and the proportions created between musical parts (Douthett 2008; Johnson 2008; Rothstein 2006). In light thereof, the current study aims to uncover the profound interconnections between the disciplines, as perceived by mathematicians, musicians, and educators in teacher training programs. By adopting a wholistic perspective, this research seeks to highlight the practical relevance of these interdisciplinary connections both in training teachers and instructing students.

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https://www.nature.com/articles/s41599-024-03631-z


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