225:224

>>Terry Riley's "The Harp of New Albion" is beautiful (Riley manages to
>>increase the effective number of pitches per octave in this 5-limit
tuning >>by using the interval 225/128 as a convincing approximation 7/4.)

Does anybody know the best 5-limit shape for taking advantage of the
225:224 at the 7-limit? When looking for the best 7-limit shape to take
advantage of the comma in the 5-limit, I came up with...

/
/
5/3--------5/4......28/15-----
/|\ / |. / \
/ | \ / | . / \
/ 7/6--------7/4 . /
/ // \\ \ / / / . /
4/3-/---\-1/1../...112/75----
/|\/ \/| /
/ |/\ /\| /
/28/15------7/5
/ // \\ \ / //
16/15/---\-8/5 /
| / \ | /
|/ \|/
112/75-----28/25

...can anyone find a better one that's still reasonable as a scale?

>>Terry Riley's "The Harp of New Albion" is beautiful (Riley manages to
>>increase the effective number of pitches per octave in this 5-limit
tuning >>by using the interval 225/128 as a convincing approximation
7/4.)

Carl Lumma wrote,

>Does anybody know the best 5-limit shape for taking advantage of the
>225:224 at the 7-limit? When looking for the best 7-limit shape to
take
>advantage of the comma in the 5-limit, I came up with...

> /
> /
> 5/3--------5/4......28/15-----
> /|\ / |. / \
> / | \ / | . / \
> / 7/6--------7/4 . /
> / // \\ \ / / / . /
> 4/3-/---\-1/1../...112/75----
> /|\/ \/| /
> / |/\ /\| /
> /28/15------7/5
> / // \\ \ / //
> 16/15/---\-8/5 /
> | / \ | /
> |/ \|/
> 112/75-----28/25

>...can anyone find a better one that's still reasonable as a scale?

You mean among 12-tone scales, right? I see 6 consonant tetrads here
(you didn't even show one of them). That's pretty impressive! I don't
think that can be beat. Why not use 72-tET and reduce the maximum error
from almost 8 cents to under 3 cents?