Non-meantone temperaments with meantone generators

Ozan might be interested in these, so I'm posting a little about it
here. The idea is, if you want a temperament with good approximations
(which Ozan wants for fourths and fifths at least) and also a meantone
fifth, you can use a temperament where a generator, or some fraction
thereof, is a meantone fourth or fifth.

For instance, the 19&159 temperament, which can also be called 140&159
or 19&140, uses the flat meantone fifth (close to 19-et) of 140 or 159
as a generator. This can be regarded as a tempered version of 112/75,
which is 224/225 down from a pure fifth. It tempers out the kleisma
among other things, and isn't too bad. It has MOS of size 64 and 83,
which might work for Ozan's purposes.

Another example is the 31&224 temperament. Here the generator is a
60/49, which is half of the excellent meantone fifth of 112. Again,
the temperament isn't too bad. The MOS sizes here are 69 and 100.

Can we have the cent values of these too Gene?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 12:22
Subject: [tuning] Non-meantone temperaments with meantone generators

> Ozan might be interested in these, so I'm posting a little about it
> here. The idea is, if you want a temperament with good approximations
> (which Ozan wants for fourths and fifths at least) and also a meantone
> fifth, you can use a temperament where a generator, or some fraction
> thereof, is a meantone fourth or fifth.
>
> For instance, the 19&159 temperament, which can also be called 140&159
> or 19&140, uses the flat meantone fifth (close to 19-et) of 140 or 159
> as a generator. This can be regarded as a tempered version of 112/75,
> which is 224/225 down from a pure fifth. It tempers out the kleisma
> among other things, and isn't too bad. It has MOS of size 64 and 83,
> which might work for Ozan's purposes.
>
> Another example is the 31&224 temperament. Here the generator is a
> 60/49, which is half of the excellent meantone fifth of 112. Again,
> the temperament isn't too bad. The MOS sizes here are 69 and 100.
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Can we have the cent values of these too Gene?

I think I gave Scala files for these already, in my posting on the
"twofifths" and "toof" scales.