112 as a two-faced tuning

Or in this case maybe a three-faced tuning.

112edo has a second best fifth which has been mentioned as a meantone
fifth (between 31 and 81, close to 1/4-comma) and a best fifth about
the same amount sharp as the meantone fifth is flat. It also has two
usable 7's. It shares its near-pure major third, deriving from 28, with
56, 84, 140, 224 and 364. The major third we don't want to mess with,
but we can get interesting results with three out of the four choices
for sharp/flat fifths and 7s.

fifth sharp, 7 sharp: this supports shrutar, the 22&46 temperamet.

fifth sharp, 7 flat: this supports (contortedly) superkleismic, the
41&56 temperament, and anything else you might want to use 56 for.

fifth flat, 7 flat: this is, of course, for septimal meantone and not
much else, but it's an excellent meantone tuning.

Was it not I who asked for a Sagittal notation for this one as distinct from
224?

Oz.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 12 Mart 2007 Pazartesi 23:44
Subject: [tuning] 112 as a two-faced tuning

> Or in this case maybe a three-faced tuning.
>
> 112edo has a second best fifth which has been mentioned as a meantone
> fifth (between 31 and 81, close to 1/4-comma) and a best fifth about
> the same amount sharp as the meantone fifth is flat. It also has two
> usable 7's. It shares its near-pure major third, deriving from 28, with
> 56, 84, 140, 224 and 364. The major third we don't want to mess with,
> but we can get interesting results with three out of the four choices
> for sharp/flat fifths and 7s.
>
> fifth sharp, 7 sharp: this supports shrutar, the 22&46 temperamet.
>
> fifth sharp, 7 flat: this supports (contortedly) superkleismic, the
> 41&56 temperament, and anything else you might want to use 56 for.
>
> fifth flat, 7 flat: this is, of course, for septimal meantone and not
> much else, but it's an excellent meantone tuning.
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Was it not I who asked for a Sagittal notation for this one as
distinct from
> 224?
>
> Oz.

Indeed it was, and I gave you a notation for 112 in Scala with narrow
fifths:
/tuning/topicId_67957.html#68019
with the following lines added to the sag_et.par file:

n 112 65
~|( /|) (|) /|\ (|\ (N( /N\

In that message please ignore my mention of a Scala bug (inasmuch as
Manuel promptly fixed it).

I also mentioned a wide-fifth (superpythagorean) notation, which I
gave here:
/tuning/topicId_67957.html#68102
It's not as simple, nor as good, as the meantone one, but I think you
weren't interested in wide fifths anyway. In order to try that one
out in Scala, you'd have to replace the narrow-fifth lines with the
wide-fifth ones, so you could use only one at a time.

--George

It is an excellent notation too. If only there was a way to implement 112 on
an actual acoustic instrument...

Oz.

----- Original Message -----
From: "George D. Secor" <gdsecor@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 13 Mart 2007 Sal� 19:59
Subject: [tuning] Re: 112 as a two-faced tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Was it not I who asked for a Sagittal notation for this one as
> distinct from
> > 224?
> >
> > Oz.
>
> Indeed it was, and I gave you a notation for 112 in Scala with narrow
> fifths:
> /tuning/topicId_67957.html#68019
> with the following lines added to the sag_et.par file:
>
> n 112 65
> ~|( /|) (|) /|\ (|\ (N( /N\
>
> In that message please ignore my mention of a Scala bug (inasmuch as
> Manuel promptly fixed it).
>
> I also mentioned a wide-fifth (superpythagorean) notation, which I
> gave here:
> /tuning/topicId_67957.html#68102
> It's not as simple, nor as good, as the meantone one, but I think you
> weren't interested in wide fifths anyway. In order to try that one
> out in Scala, you'd have to replace the narrow-fifth lines with the
> wide-fifth ones, so you could use only one at a time.
>
> --George
>
>