31-et triads redux

Here is the classification with the corresponding ratios, as suggested by Dave and Carl.

5-limit

[0, 8, 18]

[1, 6/5, 3/2]
[6/5, 1, 5/4]
[3/2, 5/4, 1]

7-limit

[0, 8, 16]

[1, 6/5, 10/7]
[6/5, 1, 6/5]
[10/7, 6/5, 1]

[0, 7, 15]

[1, 7/6, 7/5]
[7/6, 1, 6/5]
[7/5, 6/5, 1]

[0, 7, 13]

[1, 7/6, 4/3]
[7/6, 1, 8/7]
[4/3, 8/7, 1]

[0, 6, 16]

[1, 8/7, 10/7]
[8/7, 1, 5/4]
[10/7, 5/4, 1]

9-limit

[0, 13, 18]

[1, 4/3, 3/2]
[4/3, 1, 9/8]
[3/2, 9/8, 1]

[0, 15, 20]

[1, 7/5, 14/9]
[7/5, 1, 9/8]
[14/9, 9/8, 1]

[0, 5, 11]

[1, 9/8, 9/7]
[9/8, 1, 8/7]
[9/7, 8/7, 1]

[0, 5, 15]

[1, 9/8, 7/5]
[9/8, 1, 5/4]
[7/5, 5/4, 1]

[0, 13, 20]

[1, 4/3, 14/9]
[4/3, 1, 7/6]
[14/9, 7/6, 1]

[0, 11, 21]

[1, 9/7, 8/5]
[9/7, 1, 5/4]
[8/5, 5/4, 1]

[0, 5, 10]

[1, 9/8, 5/4]
[9/8, 1, 9/8]
[5/4, 9/8, 1]

[0, 5, 13]

[1, 9/8, 4/3]
[9/8, 1, 6/5]
[4/3, 6/5, 1]

11-limit

[0, 11, 20]

[1, 9/7, 14/9]
[9/7, 1, 11/9]
[14/9, 11/9, 1]

[0, 6, 20]

[1, 8/7, 14/9]
[8/7, 1, 11/8]
[14/9, 11/8, 1]

[0, 20, 24]

[1, 14/9, 12/7]
[14/9, 1, 11/10]
[12/7, 11/10, 1]

[0, 14, 21]

[1, 11/8, 8/5]
[11/8, 1, 7/6]
[8/5, 7/6, 1]

[0, 7, 22]

[1, 7/6, 18/11]
[7/6, 1, 7/5]
[18/11, 7/5, 1]

[0, 4, 17]

[1, 11/10, 16/11]
[11/10, 1, 4/3]
[16/11, 4/3, 1]

[0, 6, 15]

[1, 8/7, 7/5]
[8/7, 1, 11/9]
[7/5, 11/9, 1]

[0, 4, 9]

[1, 11/10, 11/9]
[11/10, 1, 9/8]
[11/9, 9/8, 1]

[0, 17, 23]

[1, 16/11, 5/3]
[16/11, 1, 8/7]
[5/3, 8/7, 1]

[0, 4, 8]

[1, 11/10, 6/5]
[11/10, 1, 11/10]
[6/5, 11/10, 1]

[0, 9, 18]

[1, 11/9, 3/2]
[11/9, 1, 11/9]
[3/2, 11/9, 1]

[0, 6, 10]

[1, 8/7, 5/4]
[8/7, 1, 11/10]
[5/4, 11/10, 1]

[0, 17, 26]

[1, 16/11, 9/5]
[16/11, 1, 11/9]
[9/5, 11/9, 1]

[0, 7, 14]

[1, 7/6, 11/8]
[7/6, 1, 7/6]
[11/8, 7/6, 1]

[0, 14, 22]

[1, 11/8, 18/11]
[11/8, 1, 6/5]
[18/11, 6/5, 1]

[0, 4, 15]

[1, 11/10, 7/5]
[11/10, 1, 9/7]
[7/5, 9/7, 1]

[0, 4, 13]

[1, 11/10, 4/3]
[11/10, 1, 11/9]
[4/3, 11/9, 1]

[0, 10, 14]

[1, 5/4, 11/8]
[5/4, 1, 11/10]
[11/8, 11/10, 1]

>Here is the classification with the corresponding ratios, as
>suggested by Dave and Carl.

Thanks again, Gene!

I don't suppose you have any way to return only the "magic"
chords?

-C.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> Here is the classification with the corresponding ratios, as
suggested by Dave and Carl.
>
> 5-limit
>
> [0, 8, 18]
>
> [1, 6/5, 3/2]
> [6/5, 1, 5/4]
> [3/2, 5/4, 1]

That's a good (compact yet readable) way of giving the ratios. Thanks!