11-limit holey scales 1

By these I mean scales of ball type, centered on holes of the lattice
where 9,5,7, and 11 generate an A4 sublattice. Here are scales
centered on [-2/5, 3/10, 3/10, 3/10]

Shell 1 radius^2 = 8/5
{|1 0 0 0>, |0 1 0 0>, |-1 0 1 0>, |-1 0 0 1>,
|0 0 1 0>, |0 0 0 0>, |-1 1 0 0>, |0 0 0 1>}

8 note ball
[1, 7/6, 5/4, 11/8, 3/2, 5/3, 7/4, 11/6]

Shell 2 radius^2 = 18/5
{|1 0 1 0>, |1 0 0 0>, |1 0 0 1>, |1 1 0 0>, |-1 0 1 1>,
|2 0 0 0>, |-1 1 1 0>, |-1 1 0 1>, |0 1 0 0>, |-1 0 1 0>,
|-10 0 1>, |0 0 1 0>, |0 0 0 0>, |-2 0 0 1>, |-1 1 0 0>,
|-2 0 11>, |-2 0 1 0>, |0 0 0 1>, |-2 1 0 0>, |-2 1 0 1>, |-2 1 1 0>,
|-1 0 0 0>}

22 note ball
[1, 33/32, 77/72, 10/9, 9/8, 55/48, 7/6, 11/9, 5/4, 21/16, 4/3, 11/8,
35/24, 3/2, 55/36, 14/9, 77/48, 5/3, 7/4, 11/6, 15/8, 35/18]

22 note ball, miracle reduced
[-21, -19, -15, -14, -13, -8, -7, -6, -4, -2, -1, 0, 1, 2, 3, 4, 6, 7,
9, 12, 15, 21]

Shell 3 radius^2 = 28/5
{|1 1 0 -1>, |1 0 1 0>, |1 0 0 0>, |1 0 0 1>, |-1 -1 1 1>,
|1 1 0 0>, |-1 1 -1 1>, |-1 1 1 -1>, |-1 0 1 1>, |1 -1 0 1>,
|0 -1 0 1>, |-3 0 1 1>, |0 1 -1 0>, |2 0 0 0>, |-1 1 1 0>,
|-11 0 1>, |-3 1 0 1>, |1 -1 1 0>, |-3 1 1 0>, |0 1 0 0>,
|0 -1 1 1>, |0 -1 1 0>, |-1 0 1 0>, |-1 0 0 1>, |0 0 1 0>,
|0 0 0 0>, |-2 0 0 1>, |0 0 1 1>, |0 0 1 -1>, |-1 1 0 0>, |-2 0 1 1>,
|-2 0 1 0>, |1 0 -1 1>, |0 1 0 -1>, |0 1 -1 1>, |0 1 1 0>, |0 1 1 -1>,
|0 1 0 1>, |1 0 1 -1>, |0 0 0 1>, |-2 1 0 0>, |-2 1 0 1>,
|-2 1 1 0>, |1 1 -1 0>, |-1 0 0 0>, |0 0 -1 1>}

46 note ball
[1, 55/54, 33/32, 21/20, 35/33, 77/72, 15/14, 35/32, 11/10, 10/9, 9/8,
55/48, 7/6, 33/28, 77/64, 11/9, 5/4, 14/11, 77/60, 35/27, 55/42,
21/16, 4/3, 15/11, 11/8, 7/5, 77/54, 10/7, 35/24, 3/2, 55/36, 14/9,
11/7, 35/22, 77/48, 33/20, 5/3, 55/32, 7/4, 20/11, 11/6, 15/8, 21/11,
77/40, 35/18, 55/28]

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

> Shell 1 radius^2 = 8/5
> {|1 0 0 0>, |0 1 0 0>, |-1 0 1 0>, |-1 0 0 1>,
> |0 0 1 0>, |0 0 0 0>, |-1 1 0 0>, |0 0 0 1>}
>
> 8 note ball
> [1, 7/6, 5/4, 11/8, 3/2, 5/3, 7/4, 11/6]

This can be characterized as [3,5,7,11] union 3*[3,5,7,11].