Maximal consistent sets of odds for ETs

A similar message was posted to the tuning list:

I think we are astoundingly ignorant of the rational identities
available in ETs where 3's or 5's are not included.

Who can generate a list for all the ETs up to 2000, giving for each ET
the maximal sets of mutually-consistently-approximated odd numbers up
to 35? And then give the reverse-lookup version of that list, where
each maximal set has the corresponding list of ETs after it.

So for example, if it were limited to odds up to 13,
20-tET would show 1:3:11:13 and 1:3:7:11, but not 1:3:7 (because it's
included in 1:3:7:11) and not 1:3:7:11:13 (because they are not all
mutually consistent). 11-tET would show 1:3:11 and 1:7:9:11.

Likewise, in the reverse list, 20-tET would not appear next to 1:3:7
because it has a larger consistent set containing that. It would
appear in only two places.

Remember I'm assuming a limit of 13 for these example and would really
want to go up to 35.

Sets would only be given in lowest terms, e.g. not 3:9:27 as well as
1:3:9.

--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...>
wrote:
> A similar message was posted to the tuning list:
>
> I think we are astoundingly ignorant of the rational identities
> available in ETs where 3's or 5's are not included.
>
> Who can generate a list for all the ETs up to 2000, giving for
each ET
> the maximal sets of mutually-consistently-approximated odd
numbers up
> to 35?

didn't carl write a program to do this or something very much like
it?

>>I think we are astoundingly ignorant of the rational identities
>>available in ETs where 3's or 5's are not included.

There's some truth to this.

>>Who can generate a list for all the ETs up to 2000, giving for
>>each ET the maximal sets of mutually-consistently-approximated
>>odd numbers up to 35?
>
>didn't carl write a program to do this or something very much
>like it?

Given a list of chords and an et (I could step through all ets
up to 2000, but I think 282 would be plenty enough), I can return:

() The portion of chords in the input list that are not
consistently represented (I can also return the actual failing
or passing chords, but these are often abundant) in the et.

() The identities which are present in any of the input chords
but in none of the passing chords.

() The identities which are present in any of the input chords
and in all of the failing chords.

I don't think any of this gets you just what you want, Dave...
I suppose I could add code that would create as the input list
all 17-tone subsets of the 35-limit otonality (an 18-ad), and
if none of them pass, all 16-note subsets, and so on. In many
cases there may be multiple "maximal" sets (sets of the same
card that pass). How would you like me to proceed?

-Carl

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:
> >>I think we are astoundingly ignorant of the rational identities
> >>available in ETs where 3's or 5's are not included.
>
> There's some truth to this.
>
> >>Who can generate a list for all the ETs up to 2000, giving for
> >>each ET the maximal sets of mutually-consistently-approximated
> >>odd numbers up to 35?
...
> Given a list of chords and an et (I could step through all ets
> up to 2000, but I think 282 would be plenty enough), I can return:

282-tET would do me fine and so would 19-limit, but I figure there are
others who would want more.

...
> I don't think any of this gets you just what you want, Dave...
> I suppose I could add code that would create as the input list
> all 17-tone subsets of the 35-limit otonality (an 18-ad), and
> if none of them pass, all 16-note subsets, and so on. In many
> cases there may be multiple "maximal" sets (sets of the same
> card that pass). How would you like me to proceed?

I see my meaning of "maximal" is still unclear. Cardinality isn't
relevant. There's probably a better term. Gene? It's kinda-like
saturated. What I mean by a maximal-mutually-consistent-set, is one to
which no further odds (within the 35-limit) can be added without
introducing inconsistency. An ET may have several of these which
overlap.

Please proceed however you can. Thanks. And it would be good if more
than one person did it, so results could be checked. It's beyond my
spreadsheeting I'm afraid.

>282-tET would do me fine and so would 19-limit, but I figure there are
>others who would want more.

Let them eat cake! :)

I'll go to 25 for now, to get some ASSes. Once I get my ASS-complete
chord progie going, I'll drop it to 19.

>> I don't think any of this gets you just what you want, Dave...
>> I suppose I could add code that would create as the input list
>> all 17-tone subsets of the 35-limit otonality (an 18-ad), and
>> if none of them pass, all 16-note subsets, and so on. In many
>> cases there may be multiple "maximal" sets (sets of the same
>> card that pass). How would you like me to proceed?
>
>I see my meaning of "maximal" is still unclear. Cardinality isn't
>relevant. There's probably a better term. Gene? It's kinda-like
>saturated. What I mean by a maximal-mutually-consistent-set, is one to
>which no further odds (within the 35-limit) can be added without
>introducing inconsistency. An ET may have several of these which
>overlap.

Not unclear; just wanted to be sure you knew about that last bit.
Cardinality is relevant -- you want the largest sets that are
still consistent.

>Please proceed however you can. Thanks. And it would be good if more
>than one person did it, so results could be checked. It's beyond my
>spreadsheeting I'm afraid.

I'm glad you got back to me before the work week started. I'll see
if I can fire this off tonight. No promises.

It should be easy to check the results by hand, though I'd love
a 2nd opinion... actually, I fully expect to be the 2nd opinion,
since others here can probably beat me to this.

-Carl