Two 3136/3125 planar scales

If we take two chains of 28/25s a minor third apart, we get the following 10 note scales, in their 99, 118 and 130-et versions:

sa99 := [0, 16, 26, 32, 42, 48, 58, 64, 74, 90]
sa118 := [0, 19, 31, 38, 50, 57, 69, 76, 88, 107]
sa130 := [0, 21, 34, 42, 55, 63, 76, 84, 97, 118]

We also get these twelve note scales:

sb99 := [0, 7, 16, 26, 32, 42, 48, 58, 64, 74, 80, 90]
sb118 := [0, 8, 19, 31, 38, 50, 57, 69, 76, 88, 95, 107]
sb130 := [0, 9, 21, 34, 42, 55, 63, 76, 84, 97, 105, 118]

The ten-note scales have 20 consonant intervals and 10 triads, while the twelve-note scales have 29 intervals and 20 triads, all in the
7-limit.

>sa99 := [0, 16, 26, 32, 42, 48, 58, 64, 74, 90]
>sa118 := [0, 19, 31, 38, 50, 57, 69, 76, 88, 107]
>sa130 := [0, 21, 34, 42, 55, 63, 76, 84, 97, 118]
/.../
>The ten-note scales have 20 consonant intervals and 10 triads, while
>the twelve-note scales have 29 intervals and 20 triads, all in the
>7-limit.

This is so cool.

-Carl

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

> We also get these twelve note scales:
>
> sb99 := [0, 7, 16, 26, 32, 42, 48, 58, 64, 74, 80, 90]
> sb118 := [0, 8, 19, 31, 38, 50, 57, 69, 76, 88, 95, 107]
> sb130 := [0, 9, 21, 34, 42, 55, 63, 76, 84, 97, 105, 118]

> The ten-note scales have 20 consonant intervals and 10 triads, while the twelve-note scales have 29 intervals and 20 triads, all in the
> 7-limit.

The twelve-note scale is also h12-epimorphic.