Friday, August 31, 2007
WHY 17 PATTERNS?
"Renaissance choral music should sound like wallpaper." -- Richard K. Winslow
At first, I thought that Winslow's quip was all wrong, reducing gloriously detailed counterpoint to flat and monotonous wall hangings. But a bit of research into wallpaper patterns or groups quickly demonstrates that wallpaper is much more than Muzac for tired eyes.
There are 17 possible wallpaper groups, which are two dimensional repetitive patterns. Wallpaper groups are more complex than frieze groups (which repeat in only one dimension) and less complex than three-dimensional crystallographic or space groups. The groups are classified according to their symmetries, and once you understand the symmetries, even the most mathematically resistant can follow the proof that there can only be 17.
If I were a more social type, I'd rush out to invite 16 other composers to join me in composing a set of 17 pieces, each one based upon one of the 17 wallpaper patterns. The patterns can be usefully extended through the choice of colors, something which immediately suggests a variety of scoring patterns in a musical translation. I don't know if they'd be better served by a vocal ensemble or by Morton Feldman's ensemble of flute/percussion/piano (with doublings). In any case, the title would have to be Why 17 Patterns?