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14-note Fokker blocks

🔗Gene Ward Smith <gwsmith@svpal.org>

10/1/2005 2:37:24 PM

I've uploaded a zip file for some of these. None of the scales turned
out to be epimorphic, though presumably less interesting ones could be
found which are. However, one set, based on 2048/2025 and 2048/1875
strikes me as quite interesting. I called this series "diaddim", after
"diaschismic" and "double diminished third". It is interesting from
the point of view of marvel tempering. 256/225 serves as an 8/7 in
marvel, and is at an angle of 10.9 degrees from 2048/2025 and 19.1
from 2048/1875, and between them. The product of 2048/2025 and
2048/1875 is only 3 degrees from 256/225. As a result, the Fokker
blocks are long in the 256/225 direction, and there are relatively a
lot of tetrads; the scales feature four otonal and four utonal
tetrads, which isn't bad. The fullest harmonies are from diaddim2 and
its inverse diaddim3, which have
six of each kind of triad.