A couple of "schismatic meantone" scales

These may have been proposed already, but I'll go ahead anyway.I came up with
two temperaments just now, both of them meantone-type (or what I once called a
"bent fifth"). But instead of the 81/80 comma being used, I used the schisma,
32805/32768, as well as the septimal schismaThe first scale is based on a
tempering of 1/8 of a schisma. The fifth is 2/10^(1/8) (two divided by the
eighth root of 10), or ~701.71079 cents. The second is based on 1/14 of a
septimal schisma. The fifth is 2/56^(1/14) (two divided by the fourteenth root
of 56), or ~702.22672 cents.A third scale, based on the geometric mean of both
intervals (the square root of the first interval times the second), has a fifth
of ~701.96875. Compare to the Pythagorean fifth (3/2), about ~701.95500 cents.
The difference is obviously quite tiny.The use of a mean could also be applied
to comma-based meantones. An example is the mean of the fifth in 1/4-comma
meantone and the fifth in 1/2-septimal comma meantone, which is the arithmetic
mean of ~696.57843� and ~688.32295�, or ~692.45069�. Ultimately the means of
many prime-number commas could be used.~Danny~

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