Endlessly Rising Canon

2007-10-08T20:42:47Z

This post will serve two purposes. The first is to subtly notify the world that I’ve finally finished GÃ¶del, Escher, Bach: An Eternal Golden Braid. OK, so maybe I’ve blown the subtle part. While I found the book very interesting, enlightening even, it was hard to get through all 700 or so pages before I found something else to read. It just didn’t hold my attention. Every few months, I’d pick it up again. After years of episodic reading, I read the last page in the wee hours of Sunday.

The second purpose is to note an odd bit of synchronicity. This morning, I stumbled upon an example of a striking audio illusion that I had seen mentioned toward the end of GÃ¶del, Escher, Bach only a few days ago.

You can find an even more striking example at the Wikipedia article on Shepard tones.

Canon 5 of Bach’s Musikalisches Opfer is an example of a spiral canon which ends a tone higher than it starts. The canon can then be played at that higher pitch and end one tone higher yet again. This could be done ad infinitum leading to ever higher pitches, though we would eventually be unable to hear the music.

Hofstadter suggests that this audio illusion could transform Bach’s canon into a piece which would only sound as though it were ever rising.

Interestingly, GÃ¶del, Escher, Bach itself takes the form of an endlessly rising prose canon which I suppose means that I’m not finished reading yet.

Green Oasis

Endlessly Rising Canon