Symmetries by Syrynx


Since I was a very young child, I've been fascinated-- perhaps even obsessed-- by various forms of symmetry:

1. Exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center of an axis. 2. A relationship of characteristic correspondence, equivalence, or identity among constituents of an entity or between different entities: the narrative symmetry of the novel. 3. Beauty as a result of balance or harmonious arrangement.

--The American Heritage Dictionary of the English Language, Third Edition. Copyright © 1992 by Houghton Mifflin Company


The symmetry of tiled graphics in accordance with the first definition is evident at a glance. The symmetry of musical canons in accordance with the second definition is, perhaps, not so obvious. Douglas R. Hofstadter's succinct explanation of the form not only clarifies the "identity among constituents" of a canon, but inspired my own attempts to compose canons:

The idea of a canon is that one single theme is played against itself. This is done by having "copies" of the theme played by the various participating voices. But there are many ways to do this. The most straightforward of all canons is the round, such as "Three Blind Mice", "Row, Row, Row Your Boat", or "Frère Jacques". Here, the theme enters in the first voice and, after a fixed time-delay, a "copy" of it enters, in precisely the same key. After the same fixed time-delay in the second voice, the third voice enters carrying the theme, and so on.

--Douglas R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid. Copyright © 1979 by Basic Books, Inc.

The canons I offer here are all "the most straightforward of all canons"-- I have not yet progressed to the more sophisticated transformations of the theme used by Bach (and detailed by Hofstadter). In fact, I have deliberately refrained from listening to Bach; I want to hear what I can compose without his direct influence, before making the inevitable comparisons.

Whether any of the music or graphics presented here meet the third definition is for you to decide.

~ Tile Territory ~ Canon Corner ~
~ Animation Alley ~ Mixed Media ~

Copyright by Syrynx