11-limit holey scales 2

This time the hole is around [0, 1/2, 1/2, 1/2].

Shell 1 radius^2 = 2
g1 := {5, 7, 11, 15, 21, 33, 35, 55, 77, 77/3, 35/3, 55/3}

Ball scale 8 notes
[1, 35/33, 7/6, 5/4, 14/11, 15/11, 3/2, 35/22, 5/3, 7/4, 20/11, 21/11]

Shell 2 radius^2 = 4
{3, 9, 45, 63, 99, 105, 165, 231, 11/3, 5/3, 7/3, 385/3, 385/9,
77/9, 55/9, 35/9}

Ball scale 28 notes
[1, 36/35, 22/21, 16/15, 11/10, 8/7, 33/28, 6/5, 11/9, 44/35, 9/7,
4/3, 48/35, 88/63, 99/70, 22/15, 3/2, 32/21, 11/7, 8/5, 33/20,
176/105, 12/7, 16/9, 9/5, 11/6, 66/35, 88/45]

Shell 3 radius^2 = 6
{1, 25, 27, 49, 121, 385, 55/7, 35/11, 77/5, 25/3, 105/11, 385/27,
121/3, 231/5, 49/3, 165/7}

Ball scale 44 notes
[1, 36/35, 22/21, 16/15, 12/11, 11/10, 8/7, 121/105, 33/28, 6/5, 11/9,
44/35, 9/7, 33/25, 4/3, 66/49, 48/35, 11/8, 88/63, 7/5, 99/70, 10/7,
16/11, 22/15, 3/2, 32/21, 54/35, 11/7, 8/5, 44/27, 33/20, 176/105,
12/7, 121/70, 44/25, 16/9, 88/49, 9/5, 64/35, 11/6, 28/15, 66/35,
40/21, 88/45]

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> Ball scale 8 notes
12 notes
> [1, 35/33, 7/6, 5/4, 14/11, 15/11, 3/2, 35/22, 5/3, 7/4, 20/11, 21/11]

This hole scale is interesting. Scala tells me it is permutation
epimorphic, via <12 21 31 37 41|, and it certainly does more than dip
its toe into the 11-limit.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
>
> > Ball scale 8 notes
> 12 notes
> > [1, 35/33, 7/6, 5/4, 14/11, 15/11, 3/2, 35/22, 5/3, 7/4, 20/11, 21/11]
>
> This hole scale is interesting. Scala tells me it is permutation
> epimorphic, via <12 21 31 37 41|, and it certainly does more than dip
> its toe into the 11-limit.

It can be analyzed as the union of two disjoint CPS. The first is a
hexany; the {1,5,7,11} CPS of products taken two at a time, transposed
up by 3. The second is the {5,7,9,11} CPS of products taken two at a time.