This piece, like the drawings that accompany it by the Dutch artist M.C. Escher, are at the intersection of the very best of both mathematics and art. The chaconne is not an unusual form in baroque music and there are hundreds of examples for just about every instrument or combination thereof. At its root, a chaconne is variations on a chord progression (some say that it requires a repeating bass line, but that is technically a passacaglia) and in the hands of a lesser composer, a piece that lasts sixteen minutes composed of sixty-four iterations of the same chords would be nothing more than an academic exercise, interesting but not engaging in an emotional way. Bach manages to take this to a level that is, in my opinion, unequaled in the form. He uses his art to elevate it to a journey with highs and lows and a very definite dramatic arc.

In the same way, the notebooks of M.C. Escher are filled with ways of drawing repeating patterns. He starts with fairly simple shapes as he works out his methods but then proceeds to work wonders, combining figures that on the surface look like they couldn't possibly go together. Determining what will tessellate is a matter of geometry, but that his fish look playful, his lizards and sea creatures are so vivid, and that his gargoyles are so startling is a matter of art, one of the most human of all qualities.

свернуть