Seven connected scales

Here are the seven connected scales one gets from
(9/8)^3 * (10/9)^2 * (16/15)^2 = 2, when modes and inversions are taken as equivalent:

[9/8, 9/8, 10/9, 16/15, 9/8, 10/9, 16/15]
[1, 9/8, 81/64, 45/32, 3/2, 27/16, 15/8]
connectivity = 1

[9/8, 9/8, 10/9, 16/15, 9/8, 16/15, 10/9]
[1, 9/8, 81/64, 45/32, 3/2, 27/16, 9/5]
connectivity = 1

[9/8, 9/8, 16/15, 10/9, 9/8, 10/9, 16/15]
[1, 9/8, 81/64, 27/20, 3/2, 27/16, 15/8]
connectivity = 1

[9/8, 10/9, 9/8, 10/9, 9/8, 16/15, 16/15]
[1, 9/8, 5/4, 45/32, 25/16, 225/128, 15/8]
connectivity = 1

[9/8, 10/9, 9/8, 10/9, 16/15, 9/8, 16/15]
[1, 9/8, 5/4, 45/32, 25/16, 5/3, 15/8]
connectivity = 2

[9/8, 10/9, 9/8, 16/15, 9/8, 10/9, 16/15]
[1, 9/8, 5/4, 45/32, 3/2, 27/16, 15/8]
connectivity = 2

[9/8, 10/9, 10/9, 9/8, 16/15, 9/8, 16/15]
[1, 9/8, 5/4, 25/18, 25/16, 5/3, 15/8]
connectivity = 1

Gene, this is amazing!

-C.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> Here are the seven connected scales one gets from
> (9/8)^3 * (10/9)^2 * (16/15)^2 = 2, when modes and inversions are
taken as equivalent:
>
> [9/8, 9/8, 10/9, 16/15, 9/8, 10/9, 16/15]
> [1, 9/8, 81/64, 45/32, 3/2, 27/16, 15/8]
> connectivity = 1
>
> [9/8, 9/8, 10/9, 16/15, 9/8, 16/15, 10/9]
> [1, 9/8, 81/64, 45/32, 3/2, 27/16, 9/5]
> connectivity = 1
>
> [9/8, 9/8, 16/15, 10/9, 9/8, 10/9, 16/15]
> [1, 9/8, 81/64, 27/20, 3/2, 27/16, 15/8]
> connectivity = 1
>
> [9/8, 10/9, 9/8, 10/9, 9/8, 16/15, 16/15]
> [1, 9/8, 5/4, 45/32, 25/16, 225/128, 15/8]
> connectivity = 1
>
> [9/8, 10/9, 9/8, 10/9, 16/15, 9/8, 16/15]
> [1, 9/8, 5/4, 45/32, 25/16, 5/3, 15/8]
> connectivity = 2
>
> [9/8, 10/9, 9/8, 16/15, 9/8, 10/9, 16/15]
> [1, 9/8, 5/4, 45/32, 3/2, 27/16, 15/8]
> connectivity = 2
>
> [9/8, 10/9, 10/9, 9/8, 16/15, 9/8, 16/15]
> [1, 9/8, 5/4, 25/18, 25/16, 5/3, 15/8]
> connectivity = 1