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?
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