Tuesday, April 20, 2010
A Musical Palindrome
It's no surprise that Ana is a competent, or better than competent, mathematician, having received early training in math as a toddler on Thomo and having learned to navigate a vessel through the universe. Perhaps that's why she so enjoys the music of J. S. Bach. (We are reminded of her comment that one of Bach's compositions sounded like "the engine of the galaxy.") Of course, she could enjoy the music of Bach simply because it is so surpassingly beautiful....
In particular, she treasures several recordings of Bach's Musical Offering, a famously cerebral composition in which Bach seemed to be exploring the farthest possibilities of the fugue, far beyond anything ever done by any other composer. We must admit that we have found the piece interesting, but not so compelling as to become one of our favorites. Ana, however, was profoundly affected by a video clip which illustrates the theme of the piece in a most unique, and visual, way.
We must admit she has a point about the Musical Offering. Even for the casual listener, the clip reveals the theme of The Musical Offering (shown above) in such a way that, if it isn't perfectly transparent, it can easily be appreciated for the immensely intricate and clever creation it is. Any music lover should find it as mind-bending as Ana does. It amounts to a musical palindrome, and a three-dimensional musical palindrome at that.
The clip is on a site called "Strange Paths: Physics, Computation, Philosophy," which sounds forbidding enough to put most of us off. If that weren't enough, the description of the presentation is even more dense:
"In the enigmatic Canon 1 a 2 from J. S. Bach’s 'Musical Offering' (1747) (also known as 'crab canon' or 'canon cancrizans'), the manuscript shows a single score, whose beginning joins with the end. This space is topologically equivalent to a bundle of the line segment over the circle, known as a Möbius strip. The simultaneous performance of the deeply related forward and backward paths gives appearance to two voices, whose symmetry determines a reversible evolution. A musical universe is built and then is 'unplayed' back into silence."
Do not be put off by that description! The actual performace is exhilarating. If you would like to hear and see an example of what Ana calls "brain frisks," click (or right click, to open in another window) this video clip.
(Editor's note: Ana had to look up the word "cancrizans." It's from a Latin root meaning "crab," as in "cancer," the astrological sign for which is a crab. In this case, "cancrizans" means "moving sideways," like a crab!)