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Godzilla-Miracle common notation

🔗Gene Ward Smith <gwsmith@svpal.org>

4/23/2005 4:51:40 PM

Godzilla/Semaphore/Hemifourths is the 7-limit temperament which splits
a sharp fourth in half, getting a combination 8/7 and 7/6 which it
uses as a generator. Even numbers of generator steps give 5-limit
meantone, so we tend to get a good 5-limit and a somewhat cheezy
7-limit. Not only is 19 7 and 9 limit poptimal, so is 81, so we can
use an excellent 5-limit meantone tuning. It can also be called 19&24,
and has {49/48, 81/80} as a comma basis.

If we stretch a secor by a little over a factor of two (or a ratio of
6:13 to be precise about it) we get a corresponding godzilla
generator. Along the lines of the meantone notation for 36-et, this
gives a correspondence between miralcle and godzilla, and hence to a
subset of miracle with even numbers of generator steps and meantone.
Notations designed for miracle can be used for godzilla, and vice
versa. This doesn't do much for the 7-limit aspect of godzilla, but of
course the 5-limit part is meantone and moves nicely over to miracle.

Here is a table giving generators from -10 to 10, and detemperings
using godzilla, 7-limit miracle, and 11-limit miracle respectively.

-10:15/16 49/48 45/44
-9: 15/14 35/32 12/11
-8: 5/4 7/6 7/6
-7: 10/7 5/4 5/4
-6: 5/3 4/3 4/3
-5: 20/21 10/7 10/7
-4: 9/8 32/21 32/21
-3: 9/7 49/30 18/11
-2: 3/2 7/4 7/4
-1: 7/4 15/8 15/8
0: 1 1 1
1: 7/6 15/14 15/14
2: 4/3 8/7 8/7
3: 14/9 49/40 11/9
4: 9/5 21/16 21/16
5: 21/10 7/5 7/5
6: 6/5 3/2 3/2
7: 7/5 8/5 8/5
8: 8/5 12/7 12/7
9: 28/15 64/35 11/6
10:32/15 49/25 49/25