>>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?