Re: 7 and 9

> Subject: Re: 7 and 9 limit theory
>
> --- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
> >
> > Can any neutral third composers can comment on
> > creating a clear 5-limit music with 6:5 and 5:4 mapped to the
> > same note?
> >
> > Bob Valentine
>
> Daniel Wolf has remarked on this list (it's in a footnote in my
> paper) how he feels the Thai 7-tET music has 5-limit implications,
> which are reflected better by the Thai vocalists than by the fixed-
> pitch instruments that accompany them.
>

Okay, light bulb time for me, although it probably raises more
questions than answers.

I take it you are saying is that consistency rather than
uniqueness is the important factor in whether a given tuning
supports a given limit? Consistency is basically a measure for
the clarity of the context?

So assuming I had a tuning where

best_3/2 * best_4/5 = best_6/5 = best_5/4

and probably a few other similar identities, then I would
have a five-limit scale with non-unique 5/4 and 6/5. I assume
you have such identities in 22-equal which allow you to say
that the 7/5 and 10/7 are clear even though they are not unique.

For some reason, I have my doubts about this light bulb... if
I look at it that way, 12 is consistent for 7-limit. Perhaps it
is...

Bob Valentine

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

> I take it you are saying is that consistency rather than
> uniqueness is the important factor in whether a given tuning
> supports a given limit?

It can be, but it's not a hard-and-fast rule. Clearly, 5-tET doesn't
support 9-limit . . . meanwhile, 1200-tET can support limits way
beyond its consistency limit.

> For some reason, I have my doubts about this light bulb... if
> I look at it that way, 12 is consistent for 7-limit. Perhaps it
> is...

Sure . . . that's how John deLaubenfels can do his 7-limit retunings
of 12-tET MIDI files.