13-limit hexany hole ball scales

There is a hole around [0,1/2,1/2,1/2,1/2] of radius sqrt(2) which
gives the {5,7,11,13} CPS, or hexany. Here are the first few shells
and corresponding ball scales.

Shell 1 radius sqrt(2)
{65/64, 143/128, 35/32, 77/64, 91/64, 55/32}

Scale 6 notes
[1, 13/11, 14/11, 13/10, 7/5, 91/55]

Shell 2 radius sqrt(3)
{21/16, 33/32, 39/32, 91/48, 143/96, 77/48, 429/256, 1001/768,
715/384, 165/128, 195/128, 55/48, 65/48, 455/384, 35/24, 231/128,
273/256, 105/64, 385/384, 15/8}

Scale 26 notes
[1, 66/65, 21/20, 14/13, 11/10, 44/39, 7/6, 77/65, 6/5, 33/26, 77/60,
84/65, 4/3, 7/5, 56/39, 22/15, 3/2, 308/195, 21/13, 33/20, 22/13,
231/130, 11/6, 24/13, 28/15, 77/39]

Shell 3 radius 2
{11/8, 99/64, 117/64, 715/576, 385/288, 455/288, 1001/576, 455/256,
63/32, 715/512, 1001/512, 45/32, 385/256, 5/4, 7/4, 13/8}

Scale 42 notes
[1, 66/65, 21/20, 14/13, 11/10, 44/39, 7/6, 77/65, 6/5, 11/9, 16/13,
33/26, 77/60, 84/65, 154/117, 4/3, 88/65, 11/8, 18/13, 7/5, 56/39,
22/15, 77/52,3/2, 99/65, 14/9, 308/195, 8/5, 21/13, 33/20, 22/13,
77/45, 112/65, 7/4, 231/130, 9/5, 11/6, 24/13, 28/15, 77/40, 126/65,
77/39]

Shell 4 radius sqrt(6)
{35/18, 91/72, 169/128, 1001/640, 5005/4608, 49/32, 121/64, 715/448,
693/512, 819/512, 1287/1024, 25/16, 315/256, 585/512, 495/256,
385/208, 455/352, 77/72, 9/8, 143/72, 65/36, 55/36}

Scale 64 notes
[1, 91/88, 28/27, 455/432, 35/33, 13/12, 12/11, 195/176, 10/9,
455/396,7/6, 13/11, 105/88, 65/54, 40/33, 39/32, 364/297, 5/4,
455/363, 91/72, 14/11,169/132, 35/27, 21/16, 130/99, 4/3, 65/48,
15/11, 91/66, 140/99, 13/9, 35/24, 65/44, 40/27, 49/33, 3/2, 50/33,
91/60, 455/297, 65/42, 273/176, 14/9, 52/33, 35/22, 13/8, 5/3, 91/54,
56/33, 455/264, 7/4, 520/297, 39/22, 70/39, 65/36, 20/11, 11/6,
182/99, 15/8, 560/297, 91/48, 21/11, 52/27, 35/18, 65/33]

The second scale could reasonably be tempered in "Harry", the 58&72
temperament, with TM basis {243/242, 351/350, 364/363, 441/440}, and
mapping [<2 4 7 7 9 11|, <0 -6 -17 -10 -15 -26|]. 130 equal is a good
tuning for this.

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

> Shell 2 radius sqrt(3)
> {21/16, 33/32, 39/32, 91/48, 143/96, 77/48, 429/256, 1001/768,
> 715/384, 165/128, 195/128, 55/48, 65/48, 455/384, 35/24, 231/128,
> 273/256, 105/64, 385/384, 15/8}
>
> Scale 26 notes
> [1, 66/65, 21/20, 14/13, 11/10, 44/39, 7/6, 77/65, 6/5, 33/26, 77/60,
> 84/65, 4/3, 7/5, 56/39, 22/15, 3/2, 308/195, 21/13, 33/20, 22/13,
> 231/130, 11/6, 24/13, 28/15, 77/39]

> The second scale could reasonably be tempered in "Harry", the 58&72
> temperament, with TM basis {243/242, 351/350, 364/363, 441/440}, and
> mapping [<2 4 7 7 9 11|, <0 -6 -17 -10 -15 -26|]. 130 equal is a good
> tuning for this.

If we add the useful 7-limit comma 3136/3125 to the above TM basis for
Harry, we get the 13-limit TM basis for 130-et, incidentally.