It seems to me there are two conditions it would make sense to put on something intended as an odd-limit temperament:

(1) Weak condition--no element of the tonality diamond is allowed to be a unison

(2) Strong condition--all elements of the tonality diamond are distinct

Clearly (2)==>(1); in the 5-limit case, (1) excludes 6/5, 5/4, 4/3 and 3/2; and (2) also excludes 25/24 and 16/15, leaving 27/25 to be king of funkiness.

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

> (1) Weak condition--no element of the tonality diamond is allowed to be a unison (exluding 1/1) > > (2) Strong condition--all elements of the tonality diamond are distinct (including 1/1)

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote: > It seems to me there are two conditions it would make sense to put on something intended as an odd-limit temperament: > > (1) Weak condition--no element of the tonality diamond is allowed to be a unison

Fine. Then we won't need a lower bound on g anymore, will we? > > (2) Strong condition--all elements of the tonality diamond are distinct

That would make me cry, as it excludes twintone in the 7-limit.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote: > --- In tuning-math@y..., "paulerlich" <paul@s...> wrote: > > > That would make me cry, as it excludes twintone in the 7-limit. > > That occurred to me also; I think the strong condition is too strong, but I see no problem with the weak condition.

I agree. but we'd like to know when the strong condition applies to a temperament. This is shown as "unique" in Graham Breed's output, as in all elements of the diamond are represented by a unique interval in the temperament.