Gene, what do you get as a reduced basis for my decatonic scale?

Looking at the most compact lattice arrangement, it appears that

(64/63, 50/49, 49/48) should win, though 225/224 could replace 63/64

without too much damage, and 28/27 and 25/24, while both weak

replacements for 49/48, are almost equally good in that role.

How about that reduced-basis-for-good-ETs request?

--- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:

> Gene, what do you get as a reduced basis for my decatonic scale?

I'm afraid I get <25/24, 28/27, 49/48>, which seems reasonable to me,

if not to you. Why did you expect 64/63 or even 225/224, given that

they clearly have a higher Tenney height?

> How about that reduced-basis-for-good-ETs request?

I'm afraid I've forgotten you made one. Would the idea be to do for

other ets what I just did for 10? Do you only want them in the 7-

limit?

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

> --- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:

>

> > Gene, what do you get as a reduced basis for my decatonic scale?

>

> I'm afraid I get <25/24, 28/27, 49/48>, which seems reasonable to

me,

> if not to you. Why did you expect 64/63 or even 225/224, given that

> they clearly have a higher Tenney height?

Sorry, Gene, I was thinking in terms of commatic vs. chromatic again,

and you weren't. Of course, the reduced basis stuff we've been

talking about has no provision for such distinctions. For me, my

decatonic scale is MOS or altered-MOS by nature, so should be

associated with two commatic UVs and only one chromatic one. The

three you gave are all chromatic -- meaning none of them are tempered

out in my decatonic scale.

> > How about that reduced-basis-for-good-ETs request?

>

> I'm afraid I've forgotten you made one. Would the idea be to do for

> other ets what I just did for 10? Do you only want them in the 7-

> limit?

That would be great.