The connection between Western music and mathematics has been recognized since antiquity, with figures like Pythagoras, Plato, and Aristotle noting parallels. Both disciplines utilize symbolic notation and incorporate concepts like symmetry, patterns, ratios, and divisions. Musical intervals are defined by ratios of small whole numbers (e.g., octave 1:2, fifth 2:3, fourth 3:4). Mathematicians like Descartes, Kepler, and Euler studied music, while musicians utilized mathematics for analysis and composition, employing techniques such as counterpoint, crab canons, and palindromes. Mathematical principles are evident in harmony theory (simultaneous sound combinations), rhythm theory (temporal organization), and form theory (organization of musical events and proportions). This study aims to investigate the interconnections between music and mathematics as perceived by mathematicians, musicians, and teacher educators, highlighting the practical implications for teacher training and student instruction.

Recent studies demonstrate positive transfer effects from music to mathematics learning, particularly when using symbolic notation to explicitly connect musical and mathematical concepts. Studies with elementary school students showed improved mathematical and musical achievements in experimental groups after participating in multidisciplinary programs integrating music and mathematics, focusing on patterns, symmetry, and fractions. A meta-analysis by Wang et al. (2024) confirmed the significant positive impact of music integration in mathematics instruction, highlighting factors like incorporating music within math interventions, using calming and math-related music, and early-grade exposure. Music's pedagogical value lies in connecting mathematical concepts to real-world contexts, increasing student interest and motivation. This study builds upon this research by exploring the perspectives of university-level music and mathematics experts, both theorists and educators, on paralleling content areas in classroom learning.

This qualitative study employed semi-structured interviews with 16 experts: four mathematicians, four musicians, four mathematics education lecturers, and four music education lecturers. Participants were recruited from various Israeli universities and teacher training colleges. Interviews explored participants' perceptions of the connections between music and mathematics in general and from a pedagogical standpoint. The first author conducted all interviews, which were video and audio-recorded and transcribed. Data analysis used a grounded theory approach, focusing on three lenses: theory, affect, and learning opportunities. Experts' statements were categorized into these lenses and further subdivided into subcategories. Inter-coder validation was performed by the first and third authors, achieving approximately 90% agreement. The findings presented primarily utilize excerpts from four participants (Dan – mathematics educator, Mika – music educator, Adam – mathematician, and Lisa – music theorist) whose views were representative of the larger sample.

Analysis revealed seven key categories of experts' perceptions: 1) Abstract Language and Structure: Both educators and theorists recognized music and mathematics as abstract languages with similar semantic systems and formal structures. Educators emphasized communication and message transmission, while theorists focused on numerical representation and historical context (Pythagoras). 2) Freedom and Creative Thinking: Participants noted the freedom and creative thinking allowed within the structures of both disciplines. Music theorists particularly highlighted the creative potential within structured composition. 3) Beauty and Aesthetics: Beauty and aesthetics were central themes, with educators viewing them as tools for understanding and theorists connecting them to structure and rule-breaking. 4) Discovery, Wonder, and Emotions: Participants described the wonder and emotional engagement evoked by discoveries in both fields. 5) Integrating Mathematics and Music into Various Disciplines: Most participants, particularly educators, supported integrating music and mathematics with other subjects (art, literature, philosophy, science) for holistic learning. 6) Music as a Tool for Learning Mathematics: Music educators specifically highlighted music's use in teaching mathematics, particularly fractions and rhythm. 7) Mathematics as a Tool for Music Analysis and Creation: Music theorists emphasized mathematics' role in analyzing and composing music, using concepts like counterpoint and fractals. Word clouds visually represented the most frequent words used by all participants and by each group of experts, illustrating the key themes and terms discussed.

The study findings demonstrate that experts' perceptions of the connection between music and mathematics are multifaceted and influenced by their professional identity (theorist vs. educator) and discipline (mathematics vs. music). The shared themes of abstract languages, structure, beauty, and aesthetics highlight the fundamental interconnectedness of these fields. The emphasis on freedom and creative thinking, wonder, and emotions points to the importance of affective factors in learning and teaching both disciplines. The strong support for multidisciplinary integration underscores the potential of leveraging these connections for enhanced learning outcomes. The different perspectives regarding the use of music to teach mathematics and mathematics to compose music demonstrate the potential of using one field to enhance the other.

This study provides valuable insights into the diverse perspectives of experts regarding the connection between music and mathematics. Future research should involve a larger and more diverse sample, employing mixed methods to further validate the proposed model and explore practical applications in curriculum development. The findings highlight the significant potential for creating integrated learning modules that leverage the strengths of both disciplines to enhance student learning and foster 21st-century skills.

The relatively small sample size of this study limits the generalizability of the findings. Future research with larger and more diverse samples would strengthen the conclusions and provide more robust insights into the connections between music and mathematics across various populations and educational settings. The study’s focus on Israeli universities might not be fully representative of other contexts.