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New diagrams for circ temps

🔗Tom Dent <stringph@gmail.com>

9/9/2005 2:01:52 PM

Two sample diagrams are in the file tuningdiag1.pdf in the folder
'sphaerenklang'. One with lines connecting up the cycle of 5ths, one
without.

The axes are labelled in fractions of a Pythagorean comma. Thus, a M3
with +11/12 Pythagorean comma is 1 syntonic comma sharp. You can
create more general diagrams in cents if you want.

The diagonal dotted line is where the meantones are situated. Areas to
the West-by-North of the line have positive score according to my
proposal, areas to the East-by-South have negative score. The
motivation should be slightly clearer, as sharp keys mostly lie to the
left and flat keys to the right.

The minor third can also be seen, less obviously, on the diagrams: the
m3 becomes less pure when you go in the direction Northwest-by-North,
perpendicular to the line C-F on the Young 1 graph. Pure m3 would be
way off the scale to the South.

Compare A and Ab in Young I: the total abs. error is the same, but I
feel that Ab has slightly less tension about it.

~~~T~~~