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Convex closure of 11-limit diamond in breed plane

🔗Gene Ward Smith <gwsmith@svpal.org>

6/1/2005 12:53:40 AM

The 11-limit version of the breed temperament takes the same generators,
a 49/40 neutral third and 10/7, and tempers them according to the
{243/242, 441/440} temperament. This is what we might call strong
microtemping, meaning it represents a considerable advance over
miracle in accuracy. It is not, however, quite nanotempering, which
the 7-limit version of this system is. By that I mean that tempering
by 2401/2400 is effectively JI, whereas in 11-limit breed we are only
close. In the rms tuning, the fifths are flat by 1.15 cents, major
thirds and 11/8s by about 2/3 of a cent and 7/4 by about 4/5 cent.
Unless 9 gets in the picture errors are therefore little more than a
cent and usually less.

Below I take the convex closure of the 11-limit diamond in the breed
plane, and detemper it to 11-limit JI. The result one might compare to
the scale the Scala archives calls partch_39 or partch_ur.

! diabree.scl
detempered convex closure of 11-limit diamond in {243/242, 441/440}
temperament plane
39
!
45/44
21/20
15/14
12/11
11/10
10/9
9/8
8/7
7/6
6/5
11/9
5/4
14/11
9/7
21/16
4/3
15/11
11/8
7/5
10/7
16/11
22/15
3/2
32/21
14/9
11/7
8/5
18/11
5/3
12/7
7/4
16/9
9/5
20/11
11/6
28/15
21/11
49/25
2