Near-just

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> --- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote:
> Absolutely not! JI includes only systems or sets of tones related by
> intervals that are defined as small-number (i.e., rational) ratios.
> This involves two concepts:

I count more than that.

> There is some point, however, at which a harmonic limit can be so
> high as to be meaningless. I think that I can safely conclude that
> you have exceeded it.

He did get up to the 19087-limit.

> 2) Ratio
>
> Any tuning in which a rational interval (no matter how small)
> vanishes is by definition a temperament, not a rational tuning.

What about a tuning where octaves are stretched, but with no commas?

> However, we could save ourselves a lot of grief by calling these low-
> error temperaments "near-just" tunings or temperaments and refraining
> from misrepresenting them as "just intonation", because, by
> definition, they aren't JI.

Which means, of course, JI is theory--which is an idea I like. It also
means that JI cannot possibly be the unique possessor of the Omnitude of
pure, powerful healing sounds. So where does that start?

> May I suggest that (taking 72-ET as a point of departure) only
> temperaments having an error less than 4 cents for all of the
> consonances being represented within the specified harmonic limit
> (and less than 2 cents for 2:3 and 3:4) be designated "near-just"?

We've got a term "wafso-just" which is like what you are proposing. When
I say "effectively just" I mean something stronger than that; within a
1/2 cent of just at least. Hence I've called 118 "effectively just" in
the 5-limit,
and 171 or the ennealimmal temperament effectively just in the 7-imit. I
also don't call something a "microtemperament" unless it gets closer to
just than 72 does--octoid or the 224-et I call microtemperaments, but I
don't yet have the courage to call them "effectively just", despite how
hard it is to find any difference.