Reading:
Capozucca & Fermani (2019) Make music visible, and play mathematics.
Summary:
The
reading describes the procedures for conducting a workshop that intends to connect
music and geometry. The goal is to use geometry to make music theory visible,
specifically offering a “first-hand experience in developing harmonic
composition skills concerning practical geometric and aesthetic aspects”. The
authors described the step-by-step to conduct this workshop but not its
results.
Stop 1: Make Music Visible
My first stop was actually in the title of the paper because it made me remember a wonderful YouTube channel that helped me for the first time understand the complexity involved in music.
Music is not the area I have more facility to understand all details. I have the impression that I can not literally hear the variations, compositions, and complexity of a song. Classical music which all these elements are present is even harder. However, my mother-in-law is a classical piano teacher and my husband has a large knowledge and practice in the area even though is not his career. Thus, he shows me this website that helps me to finally see (and hear) the complexity of the music. I highly recommend you take a look at this YouTube channel.
Stop 2: Relationship between math and music
My second stop
was after trying to understand the author's thesis in this paper: “[...] participants
could observe how the problem-solving frameworks for two different approaches –
mathematics and music – are actually very closely related to one another”.
I stopped because even though I agree with their thesis (music and mathematics are related), I do not think their workshop was able to prove that and I also think they forced the relationship to become something artificial.
They argued that participants in the workshop would choose as “sound good” only the sounds that also make a triangle in the chromatic scale circumference. They said that you should expect that “at the end of the activity, the intervals perceived as pleasant are essentially (and culturally) those of minor third/major sixth (+3, -3), major third/minor sixth (+4, -4), perfect fourth/perfect fifth (+5, -5) and augmented fourth/diminished fifth (+6, -6)”. However, I do not think this is true.
I went to the piano and asked my husband to play all the notes. I do not think any of them “sound bad”. I can see how they should be used in different music styles/ intentions but they are pretty in different ways. I believe neither of their students identified unanimously some sounds as good or bad. By the way, the authors did not report the results of their workshop.
Thus, my problem with this activity is that it tries to prove a relationship that, even though is real, seems artificial throughout this workshop. In the big picture, my problem in trying to connect math and other areas in an artificial and superficial way is that not only cannot show their real connection but it can also discourage people from exploring deep these connections.
Question:
How can we teach students the connection between math and
other areas when these connections request understanding a high level of
mathematics or the other areas?
Thank you for sharing your insights on the workshop described in the reading. I appreciate your perspective on the potential artificiality of the relationship between math and music, as presented in the workshop. I agree that the workshop's approach may oversimplify the connection between math and music. As you mentioned, music is subjective, and personal choice plays a significant role in determining what sounds are perceived as pleasant or unpleasant. Without reported results, it's hard to assess its effectiveness. Moving forward, we should design activities that encourage deeper exploration of interdisciplinary concepts.
ReplyDeleteTo answer your question, we, as educators, can use real-life examples where mathematical concepts are applied in music, art, architecture, or nature. Designing interdisciplinary projects for students could encourage them to apply mathematical principles behind music composition, analyze the geometric patterns in art, or even the angles and proportions in architectural design. The connection between math and art can Encourage curiosity, critical thinking, and open-ended questioning to promote deeper understanding. Students can be engaged through creative projects to think creatively and critically about how mathematical concepts are applied in different contexts. By scaffolding learning experiences and providing appropriate support, we can facilitate understanding and appreciation of the connections between math and other areas, even when they involve higher-level concepts.
Thank you for sharing the Youtube channel that helped you understand the complexity in music. I like how the workshop has interdisciplinary activities that intend to make meaningful connections between mathematics and music. It is nice to see this paper being presented in Bridges 2019 conference. In my reading, I read that it was organized in Austria. I agree that it is problematic to artificially try to make connections between mathematics and music, when such connections don't form organically.
ReplyDeleteWe can teach students the connections between mathematics and other areas by organizing fun and interactive activities that allow them to experiment and make these connections by doing things.