This article introduces a workshop based on interdisciplinary and interactive activities. Through these activities, the relationship between mathematics and music becomes visible. This approach encourages music teachers to adopt a geometric approach for their students to learn music theory.
It begins by discussing the historical perspective on this relationship, emphasizing the role of counting, ratios, and mathematics in music theory. The article challenges the notion of connecting the creative art of music with the logical framework of mathematics, asserting that music goes beyond mere notes and beats to encompass the creation process. By involving students in hands-on, multisensorial activities, educators can demonstrate the parallel application of complementary viewpoints in mathematics and music.
This workshop is based on chromatic scale and chromatic scale circles (If we put these 12 notes evenly distributed around a circle, we obtain what is called “chromatic circle”). The workshop is divided into five sections. Each section follows a three-part pedagogical model: a minds-on activity, a hands-on activity, and a consolidation. Participants begin by using straws, scissors, tape, and a chromatic circle to create segments representing pleasant intervals in music. They then build triangles with these segments, discovering that specific triangles perfectly inscribed in the circle represent musical chords like Major, Minor, Diminished, and Augmented. Rotating and symmetrising these triangles reveal how chord shapes change while maintaining their musical essence. Finally, Participants analyze song harmonic structures and collaborate to compose harmonic pieces using geometric chords.
The workshop aims to change mindsets towards mathematics and music, fostering creativity and problem-solving skills through interdisciplinary exploration and experimentation.
Stops:
I never thought about putting a whole scale in a circle when I used to learn saxophone. When I read this article, I was amazed that harmonic scales can be represented by triangles. I think this is a brilliant example of combining maths and music because of the aesthetics embedded in it. I think it would be great if the workshop allowed participants to bring an instrument they are good at to complete this activity!
Question:
What other ways are there to connect maths and music? If you're having a hard time coming up with an example, you can also make some suggestions for the workshops described in this article.
Hi Stelios
ReplyDeleteThanks for sharing this interdisciplinary approach in math and music. Actually, I'm not very skilled in music, but I came across an article that introduced me to the idea of creating music using mathematics. Although the music terminologies, like chromatic scale and chromatic scale circles, are often too complex for me, I can share a short video that explains the simple concept of creating melodies using circular ratios. In this technique, the right hand represents the main melody, while the left hand represents the chords, resulting in a song based on the digits of pi.
https://www.youtube.com/watch?v=vpwurbd-L4U
ReplyDeleteHi Stelios
Thank you for sharing your thoughts in relation to mathematics and music. Same as you, I am also amazed by the fact that harmonic series can be formed by different types of triangles through arranging all the notes in a circle. Your stop foster me the further exploration of the variation of geometric shapes in the creations of chord and here's what I find. Aside from triangle, quadrilaterals can be used to form tetrachords, such as major and minor 7th. Tetrachords is also related to heptagons but with upper structure triads. Furthermore, heptagons also represents the most commonly used scales and modes.
https://www.youtube.com/watch?v=ZWzwb4BumIk
Encouraging participants to bring instruments not only enriches their experience by fostering authenticity but also facilitates a more genuine application of mathematics. The synergy between musical expression and mathematical principles becomes evident as participants actively engage with their instruments, creating a dynamic link between theory and practice. This dual benefit enhances the overall learning journey, offering a unique platform for participants to apply mathematical concepts in a real-world context. By intertwining the realms of music and mathematics, the experience becomes a harmonious blend, allowing participants to explore the beauty of both disciplines in an authentic and interconnected manner, resulting in a more profound and enriching educational encounter.
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