Week 4 Post

Capozucca, A., & Fermani, M. (2019). Make music visible, play mathematics. In Proceedings of the Bridges 2019 Conference (pp. 647–650). Bridges Organization.

Introduction

The article Make Music Visible, Play Mathematics by Andrea Capozucca and Marco Fermani presents an interdisciplinary, hands-on workshop that connects mathematics and music through geometry, with the goal of making mathematics audible and music visible through playful, multisensory learning experiences. The authors argue that music and mathematics share deep structural relationships that go beyond counting and ratios, and that these connections become especially clear when musical harmony is explored visually and spatially. Using the chromatic scale arranged as a circle, where the twelve notes are evenly spaced and musical intervals correspond to angles, the workshop provides a concrete geometric framework for understanding music theory.

The workshop follows a five-part discovery-based structure that emphasizes active participation. Participants first explore which musical intervals sound pleasant through embodied listening activities, then construct geometric segments and triangles representing these intervals using simple materials. Through this process, they discover that only four types of triangles can be perfectly inscribed in the chromatic circle, corresponding to the four fundamental chord types: major, minor, diminished, and augmented. By rotating and reflecting these triangles within the circle, participants experience musical transposition and transformation, learning that geometric rotation preserves a chord’s identity while symmetry changes it.

In the later stages, participants apply their geometric understanding to analyze the harmonic structure of familiar songs and collaboratively compose original music using geometric “recipes.” The authors conclude that this inquiry-based, playful approach increases engagement, confidence, and creativity in both mathematics and music learning. They argue that such interdisciplinary workshops support open-ended problem solving, authentic collaboration, and positive attitudes toward learning, and that geometry can function as a shared language that allows mathematics and music to mutually enrich one another across educational contexts.

Reflection

This article is illustrative but not comprehensive; it is a short piece that offers a glimpse into how mathematics and music can be meaningfully connected through geometry and hands-on learning. While it does not aim to fully map the theoretical foundations of either discipline, it succeeds in opening a creative window into interdisciplinary thinking and shows how mathematical ideas can be experienced in ways that are intuitive, sensory, and playful.

One point that made me stop while reading was the authors’ statement that “mathematics is about structure and pattern.” I really appreciate this way of describing mathematics because it captures what feels most fundamental about the subject. I think this is exactly why mathematics can serve as a root for so many different areas and be investigated across disciplines. In basic terms, much of the work we do in mathematics, science, and even the arts involves identifying patterns, finding ways to describe those patterns clearly and systematically, and then creating or building something new based on them. Seen from this perspective, mathematics is not just a school subject but a way of organizing and making sense of the world.

The connection the article builds between music and mathematics is also especially interesting, particularly the idea that “music is the sensation of counting without being aware you were counting.” This insight resonated with me, although I also think music goes beyond counting alone. Sound itself can be understood numerically through properties such as frequency measured in hertz, even if I have not formally studied music from this perspective. Still, the idea that musical elements like chords can be analyzed mathematically—just as the authors do through geometric representations—suggests a rich and enjoyable way to explore music. This approach makes me curious about how much musical structure, including chord types and harmony, might be better understood by uncovering the patterns and numbers behind what we hear.

Overall, it has brought me insight into a way to analyze art. I think it invites a broader view of mathematics as a deeply human and artistic activity rather than a purely technical or procedural one. By using geometry to explore musical harmony, the authors show how mathematics can function as a creative language for interpreting sound, beauty, and structure. Mathematics here is not presented as a set of rules to be memorized, but as a way of seeing, shaping, and creating meaning—much like art and music themselves. I guess that’s why many artworks can be demonstrated mathematically.

Question

Do you have any experience investigating a form of art—such as music, visual art, or dance—through mathematics, or noticing mathematical patterns while creating or experiencing art?