Week 4 - Reading Summary (embodied)

 Capozucca, A. & Fermani, M. (2019). Make music visible, play mathematics. Bridges Conference Proceedings, p. 647-650.

Presenting my posts for this week in a little different order and starting with my reading summary as I am not finished playing with my art just yet!

I found that I had to do some embodied learning myself to fully understand this article, so I am offering it to you as well by embedding some videos for your aural enjoyment!

This article, stemming from Bridges 2019 conference proceedings, describes a 5 part workshop done with music and math teachers with the aim of "making maths audible as well as visible, and...use this geometrical method to foster a new approach towards music theory where to show how music could be effectively displayed" (p. 647).

I did attempt a bit of a trig review to get through the "Things We Need to Know Before We Get Started" and did some scribbling (that may or may not be correct) before deciding to trust the authors that the trig would help determine the triangles later discussed in the paper.

Here is a quick video of the musical knowledge from the "Things We Need to Know" section:

The paper describes the 5 sections of the workshop, each that had a "minds-on activity, a hands-on activity, and a consolidation" (p. 648). Not each of the 3 parts of each section was explicitly described.

I'll describe the first 3 sections with videos.

Section 1 - Do they play nice?

In the first section of the workshop, participants were each given a BoomWhacker (BW) (percussive tube played by striking it on the hand or other place on the body) corresponding to one of the notes on the chromatic scale. They moved around the room to meet with other participants and played their BoomWhackers together. In the consolidation, participants discussed which notes were pleasant when played together. These notes were described in how far apart they are on the chromatic circle.

Here are some videos that demonstrate how these intervals sound:

Plus and minus 3 - minor 3rd, major 6th

Plus and minus 4 - major 3rd, minor 6th

Plus and minus 5 - perfect 4th and perfect 5th

Plus and minus 6 - augmented 4th/diminished 5th

Section 2 - Build up the triangles

During the second section of the workshop, participants worked with the chromatic circle and lengths of straws to map out the 'pleasant' intervals and build chords (3 or more notes played together) from these. They looked at triangles formed by the notes of the chords and specifically the four triangles that were fully inscribed inside the chromatic circle. Chords and triangles were classified (triangles with the use of the Law of Sines).

Major and minor chords

Diminished and augmented chords

Section 3 - What happens if?

In this third section of the workshop, participants were asked to move or otherwise manipulate the triangles of the 4 chords to see the effects on the chords.

Rotating a triangle around the chromatic circle (major chord)

Section 4 - It's time to play

In the fourth section, participants chose songs from a list and examined them for the geometry in the chords. They also played and sang the songs together.

Section 5 - It's time to compose

In the final section of the workshop, participants used the discovered traingles/chords to make their own compositions, what the authors "a tasty dish for the ears and eyes by using suitable ingredients (notes0, proper tools BW or other instruments) and some geometric recipes" (p. 650).

Conclusion

The authors found that the format of workshops of this collaborative type allow for conversations about the connections between math and music and propose that this can be extended to other interdisciplinary endeavours and across age levels. They suggest that both disciplines of math and music (or whatever combination of subjects) "can gain mutual benefit from this approach" (p. 650).