I recently wrote a little article about English Change Ringing, English Country Dance, and Mystical Minimalism.
Before you read it, please listen to this recording of church bells in Oxford. It's supposed to be in the article, and somehow isn't, yet is essential to an understanding of my comparison between the bells and the music of Glass, Pärt, and Moody.
After you've listened to the bells, you can read the article. To experience the full effect, please listen to/watch the recordings that are mentioned therein. I'd love your responses here. Thanks!
~ Sørina
1 comment:
Wonderful article!
I first learned about change ringing at math camp in Amherst, Mass., through a talk given by a woman mathematician (Susan Landau?) who did bell ringing as a hobby. That was the same summer that I first discovered contra dancing, which I still love. Both of these activities have deep mathematical connections related to combinatorics and group theory.
In change ringing, the set of bells is rung in a series of "rows" or permutations, starting with "rounds" (a portion of a sequential, descending scale) and then changing a wee bit for each subsequent permutation. A "permutation" is a rearrangement of a set which uses each element in the set precisely once (e.g., 123456 or 214365). So each "row" in change ringing would consist of all the bells being run in some predetermined sequence. Due to the nature of bells, each bell can only change position by at most one slot from row to row. So change ringing involves swapping the order of one or more pairs of bells from row to row, either as directed by a conductor or according to a predetermined rule.
In true change ringing, each possible permutation can only be used once and they must all be rung. So that leads to the question of how many possible permutations there are of a group of n bells. The answer is n! or n-factorial (= n * n-1 * n-2 * ... * 1). For a set of 7 bells, that's 5040. (I wanted to use an exclamation point at the end of that sentence, but you might have misconstrued my meaning.) Ringing 5000 or more changes is known as a "peal," and it takes about 3 hours.
There are some links to resources on the group theory of change ringing here.
Try playing around with this change ringing Java Applet to learn more.
Here are some resources on the connection between contra dancing and mathematics:
Contra Dances, Matrices, and Groups
Mattresses, Contra Dancing and Quilts
Another "Holy Minimalist" I recently discovered is the Slovak composer Vladimír Godár. (There are some samples of his music at that link.)
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