7 and 10 note Magic scales

These are 7-connected scales in the Magic temperament
[5 1 12 25 -5 -10]. They are presented in terms of the 41-et, but are generic 7-limit Magic scales. It is striking that in both the 7 and 10 note cases, there is a non-MOS scale with the same connectivity as the MOS scale.

7 notes

[0, 11, 13, 24, 26, 37, 39]
[11, 2, 11, 2, 11, 2, 2] 2

[0, 11, 13, 15, 26, 37, 39]
[11, 2, 2, 11, 11, 2, 2] 2

[0, 11, 13, 24, 26, 28, 30]
[11, 2, 11, 2, 2, 2, 11] 1

10 notes

[0, 9, 11, 13, 22, 24, 26, 35, 37, 39]
[9, 2, 2, 9, 2, 2, 9, 2, 2, 2] 4

[0, 9, 11, 13, 15, 24, 26, 35, 37, 39]
[9, 2, 2, 2, 9, 2, 9, 2, 2, 2] 4

[0, 9, 11, 13, 15, 24, 26, 28, 30, 32]
[9, 2, 2, 2, 9, 2, 2, 2, 2, 9] 3

[0, 9, 11, 13, 22, 24, 26, 28, 30, 39]
[9, 2, 2, 9, 2, 2, 2, 2, 9, 2] 3

[0, 9, 11, 13, 22, 24, 26, 28, 30, 32]
[9, 2, 2, 9, 2, 2, 2, 2, 2, 9] 2

[0, 9, 11, 13, 15, 17, 19, 28, 30, 39]
[9, 2, 2, 2, 2, 2, 9, 2, 9, 2] 2

[0, 9, 11, 13, 15, 17, 19, 21, 23, 32]
[9, 2, 2, 2, 2, 2, 2, 2, 9, 9] 2

[0, 9, 11, 13, 15, 17, 19, 21, 30, 39]
[9, 2, 2, 2, 2, 2, 2, 9, 9, 2] 1

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

> These are 7-connected scales in the Magic temperament
> [5 1 12 25 -5 -10]. They are presented in terms of the 41-et, but
>are generic 7-limit Magic scales. It is striking that in both the 7
>and 10 note cases, there is a non-MOS scale with the same
>connectivity as the MOS scale.

This would be very striking if the 7- and 10-tone scales are really
intended to be used for 7-limit harmony. I thought we really had to
go to 13 notes. Anyway, I'd like to see lattices -- repeating ones to
show the cylidricality of Magic. Maybe I should make some myself --
someone please remind me sometime.