Two more 72-et 7-tone scales

(1)

0-7-23-30-42-49-65

This has a 5-limit approximation

1--16/15--5/4--4/3--3/2--8/5--15/8

Consonant 9-odd-limit intervals not derivable from this are all follow from 225/224~1; this is, therefore, a 225/224 planar temperament scale. They are

16/15--5/4 (7/6)
16/15--3/2 (7/5)
16/15--15/8 (7/4)
5/4--8/5 (9/7)
4/3--15/8 (7/5)
8/5--15/8 (7/6)

(2)

0-14-23-26-35-49-58

This has a 7-limit approximation

1--8/7--5/4--9/7--7/5--8/5--7/4

11-limit consonances not deriveable from this use the commas 225/224,
385/384, 441/440 and 540/539; this is therefore emphatically a 72-et scale, and not a linear or planar temperament scale in an et version.

The additional intervals are

8/7--5/4 (12/11, from 385/384)
8/7--7/5 (11/9, from 441/440)
5/4--7/5 (9/8, from 225/224)
5/4--8/5 (9/7, from 225/224)
9/7--7/5 (12/11, from 540/539)
8/5--7/4 (12/11, from 385/384)

Of course the 12/11 is more consonant when taken as 11/6 or 11/3, just as 9/8 we all know to sound much smoother as 9/4 or 9/2.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> (1)
>
> 0-7-23-30-42-49-65
>
> This has a 5-limit approximation
>
> 1--16/15--5/4--4/3--3/2--8/5--15/8
>
> Consonant 9-odd-limit intervals not derivable from this are all
follow from 225/224~1; this is, therefore, a 225/224 planar
temperament scale. They are
>
> 16/15--5/4 (7/6)
> 16/15--3/2 (7/5)
> 16/15--15/8 (7/4)
> 5/4--8/5 (9/7)
> 4/3--15/8 (7/5)
> 8/5--15/8 (7/6)
>
>
> (2)
>
> 0-14-23-26-35-49-58
>
> This has a 7-limit approximation
>
> 1--8/7--5/4--9/7--7/5--8/5--7/4
>
> 11-limit consonances not deriveable from this use the commas
225/224,
> 385/384, 441/440 and 540/539; this is therefore emphatically a 72-
et scale, and not a linear or planar temperament scale in an et
version.
>
> The additional intervals are
>
> 8/7--5/4 (12/11, from 385/384)
> 8/7--7/5 (11/9, from 441/440)
> 5/4--7/5 (9/8, from 225/224)
> 5/4--8/5 (9/7, from 225/224)
> 9/7--7/5 (12/11, from 540/539)
> 8/5--7/4 (12/11, from 385/384)
>
> Of course the 12/11 is more consonant when taken as 11/6 or 11/3,
just as 9/8 we all know to sound much smoother as 9/4 or 9/2.

Cool!