What Do Equations Sound Like on the Piano?
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Episode Show Notes
Description
Let’s make equations musical. Instead of visualizing equations on a graph, let’s listen to them on the piano, merging all our math and music knowledge. You can make two-dimensional x-y math equations audible – or sonify them – by translating the x-values to time and the y-values to the keys of a piano. If you can’t play them on the piano yourself, we can use the free web app Chordinates! by Pios Labs to do it instead. Listen to the sound of coordinates, linear equations, polynomials, trigonometric functions, and random distributions of notes on the piano, and analyze their patterns. Then take the audio review quiz at the end, complete with extended creative and technical challenges. Got your own reactions to this episode? Would love to hear your thoughts.
Equations referenced:
- y = x
- y = 2x
- y = 5x
- y = -2x
- Linear equation, minor scale
- Linear equation, chromatic scale
- y = x2
- y = (1/10)x2
- y = (-1/4)x2 + 20, free rhythm
- y = -(1/100)x3 - (1/5)x2 + 3x + 3, free rhythm
- y = sin(x), free rhythm
- y = 16sin(x), free rhythm
- y = 16sin(x) + 12, free rhythm
- y = 16sin(x) + 12, steady rhythm
- y = 5tan((1/2)x), free rhythm
- y = 5tan((1/2)x), steady rhythm
- Square wave, amplitude = 2, offset = 2, major 3rd harmony
- y = uniform random distribution, from -23 to 28
- y = uniform random distribution, from -10 to 10
- y = normal random distribution, mean = 0, SD = 5,
- y = normal random distribution, mean = -8, SD = 5
- y = normal random distribution, mean = -8, SD = 2
- y = 5sin((1/2)(x - 4)) - 5
- y = -2x - 20
- y = -x
- y = -0.08(x - 8)(x + 16)
- y = 6sgn(cos(x)) - 5
- y = -0.01x3 - 0.2x2 + 3x + 3
Music credits (All under Creative Commons 0 Licenses):
Related Links
- Chordinates!: A free web toy for listening to equations as music, by Pios Labs.
- Coordinate plane: Example from Desmos.
- HCI Beyond the GUI: Book by Dr. Philip Kortum.
- Google Books Ngram Viewer: Data about the popularity of the words "sonify" and "sonification" in published books.
Subscribe and leave episode reviews wherever you get your podcasts. Support Pios Labs with regular donations on Patreon or by buying a copy of the reference book Engineer's Guide to Improv and Art Games by Pius Wong. You'll also be supporting educational tools and projects like Chordinates! or The Calculator Gator. Thanks to our donors and listeners for making the show possible. The K12 Engineering Education Podcast is a production of Pios Labs.