We celebrate 3.14, PI day, with some selections of mathematics, music, and visualization…
Sometimes the results resemble scores, sometimes toys, and sometimes – more rarely – real musical instruments. But part of why I love computing as a window into music is its ability to visualize music’s mathematical beauty.
I happened across this image from Flickr. It’s a chalk pattern on pavement for a children’s game (I’m not actually sure what game). But the math-compelled photographer found in it musical, harmonic intervals. I’ll have to sketch a little Processing and Pd design that plays with this idea. I put it here because someone out there might be inspired to do the same, and this is just ambiguous enough that it could easily lead in dozens of wildly-divergent paths.
I know some of my own students are literally on a beach for spring break and the nerd elite is busy partying in Austin, but, uh, maybe someone out there will file this away for later.
The photographer explains the math:
Also not sure what this game is called, but it contains some interesting mathematical properties. Can you see the oblong numbers (2,6,12,20,30…) in this representation?
Per Mathgym:
Readers who are familiar with the theory of music will recognise the list of oblongs as the intervals in decreasing order of consonance: Octave (1:2), Perfect Fifth (2:3), Perfect Fourth (3:4), Major Third (4:5), Minor Third (5:6), etc. It is Pythagoras who is credited with discovering this mathematical relationship between music and numbers.
This discovery, that the pitch of a note is related to the length of the string which produced it, is credited as being the spark which ignited Pythagoras’ imagination and philosophy. It allowed Pythagoras a glimpse of a whole new order in the Universe, one governed by intellect and logic and capable of the sublimest of pleasures. And a glimpse was all that he needed.
With this discovery, Pythagoras and the Pythagoreans set in train a way of investigation which has proved to be one of the most productive ideas in human history – that mathematics can be used to unravel the mysteries of the Universe.
Now, after those deep thoughts, who’s worked an appetite for some PI pie?