Re: Note of Thanks

In-Reply-To: <9q6r0u+7slf@eGroups.com>
Jacky wrote:

> Graham - wanted to ask what program you are using to evaluate the
> best match for given JI limits to ETs?

See <http://x31eq.com/temper.html>. It's mostly for linear
temperaments, which are harder to guess, but does ETs as a sideline. The
interface is still hacker-level, but I assure you that understanding the
output file is merely a fraction of what you need to get the music
realised!

Graham

--- In tuning@y..., jacky_ligon@y... wrote:

> Graham - wanted to ask what program you are using to evaluate the
> best match for given JI limits to ETs?

Hi Jacky -- I hope you didn't interpret my posting of Graham's
results as being ETs! They aren't -- they're linear temperaments /
MOS scales. Also, Graham's program may be missing some good ones
because of the "seeding" it uses. I'll let him reply, and post a more
comprehensive list, if he can.

As for matching JI limits to ETs, I believe Graham would evaluate
this similarly to the way I do, and have discussed here and on the
MakeMicroMusic list . . .

-Paul

Paul wrote:

> Hi Jacky -- I hope you didn't interpret my posting of Graham's
> results as being ETs! They aren't -- they're linear temperaments /
> MOS scales. Also, Graham's program may be missing some good ones
> because of the "seeding" it uses. I'll let him reply, and post a more
> comprehensive list, if he can.

Some temperaments will be missing, but I don't think they're important in
the lower limits. The details belong on tuning-math.

I've discovered some intervals were missing from the consonance limits.
If anybody was using the details in 13+ limits, get the updated files.
The 21 limit is especially changed, because a few ETs dropped out. These
include the 16/215 scale. You can bring it back by setting the
"consistency" cut-off to 0.53.

Okay, I've added files with a .inconsistent extension where ETs can be as
bad as 0.6 scale steps. That's
<http://x31eq.com/limit21.inconsistent> etc. This won't plug
all the gaps, because there are different ways of defining inconsistent
temperaments. But it does make a *lot* of difference. The top two
21-limit temperaments don't have a consistent ET between them!

> As for matching JI limits to ETs, I believe Graham would evaluate
> this similarly to the way I do, and have discussed here and on the
> MakeMicroMusic list . . .

The library does include a method for evaluating ETs, in order to
determine consistency. But there's nothing new to say about equal octave
divisions approximating JI.

Graham