12 note, 225/224 planar temperament scales

These are, of course, expressed in terms of the 72-et. They have three step sizes, which are 2, 5, and 7 in the 72-et, so this is closely related to Miracle, as one would expect. They are sorted in terms of number of edges (consonant intervals) and then connectivity.

[0, 5, 12, 19, 21, 28, 35, 42, 49, 51, 58, 65]
[5, 7, 7, 2, 7, 7, 7, 7, 2, 7, 7, 7]
edges 34 connectivity 4

[0, 5, 12, 19, 21, 28, 35, 42, 49, 56, 58, 65]
[5, 7, 7, 2, 7, 7, 7, 7, 7, 2, 7, 7]
edges 34 connectivity 4

[0, 5, 12, 14, 21, 28, 35, 42, 49, 51, 58, 65]
[5, 7, 2, 7, 7, 7, 7, 7, 2, 7, 7, 7]
edges 33 connectivity 4

[0, 5, 12, 19, 26, 28, 35, 42, 49, 51, 58, 65]
[5, 7, 7, 7, 2, 7, 7, 7, 2, 7, 7, 7]
edges 33 connectivity 3

[0, 5, 7, 14, 21, 28, 35, 42, 49, 56, 63, 65]
[5, 2, 7, 7, 7, 7, 7, 7, 7, 7, 2, 7]
edges 32 connectivity 5

[0, 5, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70]
[5, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2]
edges 32 connectivity 5

[0, 5, 7, 14, 21, 28, 35, 42, 44, 51, 58, 65]
[5, 2, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7]
edges 32 connectivity 4

[0, 5, 7, 14, 21, 28, 35, 42, 49, 51, 58, 65]
[5, 2, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7]
edges 32 connectivity 4

[0, 5, 7, 14, 21, 28, 35, 42, 49, 56, 58, 65]
[5, 2, 7, 7, 7, 7, 7, 7, 7, 2, 7, 7]
edges 32 connectivity 4

[0, 5, 12, 14, 21, 28, 35, 42, 44, 51, 58, 65]
[5, 7, 2, 7, 7, 7, 7, 2, 7, 7, 7, 7]
edges 32 connectivity 4

[0, 5, 12, 14, 21, 28, 35, 42, 49, 56, 58, 65]
[5, 7, 2, 7, 7, 7, 7, 7, 7, 2, 7, 7]
edges 32 connectivity 4

[0, 5, 12, 19, 21, 28, 35, 42, 44, 51, 58, 65]
[5, 7, 7, 2, 7, 7, 7, 2, 7, 7, 7, 7]
edges 32 connectivity 3

[0, 5, 12, 14, 21, 28, 35, 42, 49, 56, 63, 65]
[5, 7, 2, 7, 7, 7, 7, 7, 7, 7, 2, 7]
edges 31 connectivity 4

[0, 5, 7, 14, 21, 28, 35, 37, 44, 51, 58, 65]
[5, 2, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7]
edges 31 connectivity 4

[0, 5, 12, 14, 21, 28, 35, 37, 44, 51, 58, 65]
[5, 7, 2, 7, 7, 7, 2, 7, 7, 7, 7, 7]
edges 30 connectivity 3

[0, 5, 7, 14, 21, 28, 30, 37, 44, 51, 58, 65]
[5, 2, 7, 7, 7, 2, 7, 7, 7, 7, 7, 7]
edges 30 connectivity 3

[0, 5, 12, 19, 26, 28, 35, 42, 44, 51, 58, 65]
[5, 7, 7, 7, 2, 7, 7, 2, 7, 7, 7, 7]
edges 29 connectivity 2

[0, 5, 7, 14, 21, 23, 30, 37, 44, 51, 58, 65]
[5, 2, 7, 7, 2, 7, 7, 7, 7, 7, 7, 7]
edges 29 connectivity 2

[0, 5, 12, 19, 21, 28, 35, 37, 44, 51, 58, 65]
[5, 7, 7, 2, 7, 7, 2, 7, 7, 7, 7, 7]
edges 28 connectivity 3

[0, 5, 7, 9, 16, 23, 30, 37, 44, 51, 58, 65]
[5, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7]
edges 28 connectivity 1

[0, 5, 7, 14, 16, 23, 30, 37, 44, 51, 58, 65]
[5, 2, 7, 2, 7, 7, 7, 7, 7, 7, 7, 7]
edges 28 connectivity 1

[0, 5, 12, 14, 21, 28, 30, 37, 44, 51, 58, 65]
[5, 7, 2, 7, 7, 2, 7, 7, 7, 7, 7, 7]
edges 27 connectivity 2

[0, 5, 12, 14, 16, 23, 30, 37, 44, 51, 58, 65]
[5, 7, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7]
edges 24 connectivity 1

[0, 5, 12, 14, 21, 23, 30, 37, 44, 51, 58, 65]
[5, 7, 2, 7, 2, 7, 7, 7, 7, 7, 7, 7]
edges 24 connectivity 1

[0, 5, 12, 19, 21, 28, 30, 37, 44, 51, 58, 65]
[5, 7, 7, 2, 7, 2, 7, 7, 7, 7, 7, 7]
edges 23 connectivity 2

[0, 5, 12, 19, 26, 28, 35, 37, 44, 51, 58, 65]
[5, 7, 7, 7, 2, 7, 2, 7, 7, 7, 7, 7]
edges 23 connectivity 1

[0, 5, 12, 19, 26, 33, 35, 42, 44, 51, 58, 65]
[5, 7, 7, 7, 7, 2, 7, 2, 7, 7, 7, 7]
edges 23 connectivity 1

[0, 5, 12, 19, 21, 23, 30, 37, 44, 51, 58, 65]
[5, 7, 7, 2, 2, 7, 7, 7, 7, 7, 7, 7]
edges 21 connectivity 1

[0, 5, 12, 19, 26, 28, 30, 37, 44, 51, 58, 65]
[5, 7, 7, 7, 2, 2, 7, 7, 7, 7, 7, 7]
edges 19 connectivity 1

[0, 5, 12, 19, 26, 33, 35, 37, 44, 51, 58, 65]
[5, 7, 7, 7, 7, 2, 2, 7, 7, 7, 7, 7]
edges 18 connectivity 1

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> These are, of course, expressed in terms of the 72-et. They have
>three step sizes, which are 2, 5, and 7 in the 72-et, so this is
>closely related to Miracle, as one would expect. They are sorted in
>terms of number of edges (consonant intervals) and then connectivity.

I think Dave Keenan gave a "tetrachordal" example of one of these.
Dave?

>
> [0, 5, 12, 19, 21, 28, 35, 42, 49, 51, 58, 65]
> [5, 7, 7, 2, 7, 7, 7, 7, 2, 7, 7, 7]
> edges 34 connectivity 4
>
> [0, 5, 12, 19, 21, 28, 35, 42, 49, 56, 58, 65]
> [5, 7, 7, 2, 7, 7, 7, 7, 7, 2, 7, 7]
> edges 34 connectivity 4
>
> [0, 5, 12, 14, 21, 28, 35, 42, 49, 51, 58, 65]
> [5, 7, 2, 7, 7, 7, 7, 7, 2, 7, 7, 7]
> edges 33 connectivity 4
>
> [0, 5, 12, 19, 26, 28, 35, 42, 49, 51, 58, 65]
> [5, 7, 7, 7, 2, 7, 7, 7, 2, 7, 7, 7]
> edges 33 connectivity 3
>
> [0, 5, 7, 14, 21, 28, 35, 42, 49, 56, 63, 65]
> [5, 2, 7, 7, 7, 7, 7, 7, 7, 7, 2, 7]
> edges 32 connectivity 5
>
> [0, 5, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70]
> [5, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2]
> edges 32 connectivity 5
>
> [0, 5, 7, 14, 21, 28, 35, 42, 44, 51, 58, 65]
> [5, 2, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7]
> edges 32 connectivity 4
>
> [0, 5, 7, 14, 21, 28, 35, 42, 49, 51, 58, 65]
> [5, 2, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7]
> edges 32 connectivity 4
>
> [0, 5, 7, 14, 21, 28, 35, 42, 49, 56, 58, 65]
> [5, 2, 7, 7, 7, 7, 7, 7, 7, 2, 7, 7]
> edges 32 connectivity 4
>
> [0, 5, 12, 14, 21, 28, 35, 42, 44, 51, 58, 65]
> [5, 7, 2, 7, 7, 7, 7, 2, 7, 7, 7, 7]
> edges 32 connectivity 4
>
> [0, 5, 12, 14, 21, 28, 35, 42, 49, 56, 58, 65]
> [5, 7, 2, 7, 7, 7, 7, 7, 7, 2, 7, 7]
> edges 32 connectivity 4
>
> [0, 5, 12, 19, 21, 28, 35, 42, 44, 51, 58, 65]
> [5, 7, 7, 2, 7, 7, 7, 2, 7, 7, 7, 7]
> edges 32 connectivity 3
>
> [0, 5, 12, 14, 21, 28, 35, 42, 49, 56, 63, 65]
> [5, 7, 2, 7, 7, 7, 7, 7, 7, 7, 2, 7]
> edges 31 connectivity 4
>
> [0, 5, 7, 14, 21, 28, 35, 37, 44, 51, 58, 65]
> [5, 2, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7]
> edges 31 connectivity 4
>
> [0, 5, 12, 14, 21, 28, 35, 37, 44, 51, 58, 65]
> [5, 7, 2, 7, 7, 7, 2, 7, 7, 7, 7, 7]
> edges 30 connectivity 3
>
> [0, 5, 7, 14, 21, 28, 30, 37, 44, 51, 58, 65]
> [5, 2, 7, 7, 7, 2, 7, 7, 7, 7, 7, 7]
> edges 30 connectivity 3
>
> [0, 5, 12, 19, 26, 28, 35, 42, 44, 51, 58, 65]
> [5, 7, 7, 7, 2, 7, 7, 2, 7, 7, 7, 7]
> edges 29 connectivity 2
>
> [0, 5, 7, 14, 21, 23, 30, 37, 44, 51, 58, 65]
> [5, 2, 7, 7, 2, 7, 7, 7, 7, 7, 7, 7]
> edges 29 connectivity 2
>
> [0, 5, 12, 19, 21, 28, 35, 37, 44, 51, 58, 65]
> [5, 7, 7, 2, 7, 7, 2, 7, 7, 7, 7, 7]
> edges 28 connectivity 3
>
> [0, 5, 7, 9, 16, 23, 30, 37, 44, 51, 58, 65]
> [5, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7]
> edges 28 connectivity 1
>
> [0, 5, 7, 14, 16, 23, 30, 37, 44, 51, 58, 65]
> [5, 2, 7, 2, 7, 7, 7, 7, 7, 7, 7, 7]
> edges 28 connectivity 1
>
> [0, 5, 12, 14, 21, 28, 30, 37, 44, 51, 58, 65]
> [5, 7, 2, 7, 7, 2, 7, 7, 7, 7, 7, 7]
> edges 27 connectivity 2
>
> [0, 5, 12, 14, 16, 23, 30, 37, 44, 51, 58, 65]
> [5, 7, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7]
> edges 24 connectivity 1
>
> [0, 5, 12, 14, 21, 23, 30, 37, 44, 51, 58, 65]
> [5, 7, 2, 7, 2, 7, 7, 7, 7, 7, 7, 7]
> edges 24 connectivity 1
>
> [0, 5, 12, 19, 21, 28, 30, 37, 44, 51, 58, 65]
> [5, 7, 7, 2, 7, 2, 7, 7, 7, 7, 7, 7]
> edges 23 connectivity 2
>
> [0, 5, 12, 19, 26, 28, 35, 37, 44, 51, 58, 65]
> [5, 7, 7, 7, 2, 7, 2, 7, 7, 7, 7, 7]
> edges 23 connectivity 1
>
> [0, 5, 12, 19, 26, 33, 35, 42, 44, 51, 58, 65]
> [5, 7, 7, 7, 7, 2, 7, 2, 7, 7, 7, 7]
> edges 23 connectivity 1
>
> [0, 5, 12, 19, 21, 23, 30, 37, 44, 51, 58, 65]
> [5, 7, 7, 2, 2, 7, 7, 7, 7, 7, 7, 7]
> edges 21 connectivity 1
>
> [0, 5, 12, 19, 26, 28, 30, 37, 44, 51, 58, 65]
> [5, 7, 7, 7, 2, 2, 7, 7, 7, 7, 7, 7]
> edges 19 connectivity 1
>
> [0, 5, 12, 19, 26, 33, 35, 37, 44, 51, 58, 65]
> [5, 7, 7, 7, 7, 2, 2, 7, 7, 7, 7, 7]
> edges 18 connectivity 1