Music + Math: Symmetry

We love Patterns We love it when things fall into place when the last piece of the puzzle fits in when a piece of [music] returns triumphantly to the Tonic But we also love to be surprised. We'd love to see the rules get broken for the pattern to shift beneath our feet For the puzzle to refuse to fit together until we look at it from a new angle This tension between Pattern and surprise keeps our ears pricked up it gives us enough to hold on to but keeps us on our toes in both Mathematics and music a classic kind of Pattern comes from symmetry We say something is symmetric when there is some way we can transform it that keeps it the same We look about the same if you flip our image in a mirror But some of our more distant relatives look the same if you rotate them repeating patterns like these intricate Moorish mosaics from the Alhambra in Spain Stay the same if we shift them over or if we rotate them The Dodecahedron one of plato's favorite things stays the same if we rotate it There are symmetries in higher dimensions as well like this four-dimensional hypercube The mathematician Emmy nutter discovered that many of the laws of physics are actually symmetries of the universe There's another kind of symmetry in mathematics Fractals are things that look the same when we [zoom] in on them where each part looks like a smaller version of the [hole] They show up in all sorts of places including ferns coastlines and this broccoli my daughter brought home from the grocery store [even] [simple] Mathematics can make fractals take this triangle of Honeycomb and put ones on the outside Fill in each cell with the sum of the two numbers above it one plus one equals two One plus two equals three and so on now color the odd numbers black and the even numbers white what do we get if We continue the pattern and zoom out We see [a] triangle made of three triangles and each one is a smaller version of the original perhaps the most famous fractal is the Mandelbrot set Zooming in on different areas reveals endless variety, but always with a smaller copy of the entire set hiding deep inside it A Musical fractal is a piece where the theme harmonizes with a slowed down version of itself? That way the small-scale structure of the piece is Repeated at a larger grander scale Johann Sebastian bach love to play [with] symmetry in His [fugues] the theme is repeated many times in different forms in The fugue we're going to perform tonight listen for this theme in the horn Now listen for the upside down version of it in the second trumpet The slowed down version it in the first trumpet And the extremely slow down version in the Tuba Now let's hear how he puts it all together complete with a great visual of this view you you you

Channel: Santa Fe Institute

Views: 391,365

Keywords: Music And Mathematics

Id: V5tUM5aLHPA

Length: 8min 8sec (488 seconds)

Published: Fri Feb 28 2014