104edo and dual uses

104edo is an excellent magic temperament tuning if you use the flat major third it provides, and an excellent diaschismic tuning if you use the sharp major third. Can anyone think of a way in which this fact and similar facts for other equal divisions could be made useful?

On Fri, Dec 10, 2010 at 9:45 PM, genewardsmith
<genewardsmith@...> wrote:
>
> 104edo is an excellent magic temperament tuning if you use the flat major third it provides, and an excellent diaschismic tuning if you use the sharp major third. Can anyone think of a way in which this fact and similar facts for other equal divisions could be made useful?

I've come across similar tunings a lot, but never thought to write any
of them down. Although, I sometimes like tunings with really high
error (like 26edo as a meantone), because of the characteristic flavor
they provide. In light of this, 59edo makes for an obvious example of
a tuning that doubles as a near-optimal porcupine and an interestingly
flat "infra-meantone," as Margo Schulter once put it.

Are there any tunings in which one minor third provides for a good
meantone, and another minor third provides for a good porcupine, and
the difference is split more reasonably than with 59-tet?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Are there any tunings in which one minor third provides for a good
> meantone, and another minor third provides for a good porcupine, and
> the difference is split more reasonably than with 59-tet?

I'm not sure what minor thirds have to do with it, but <293 466 669| works well as a porcupine tuning, and <293 463 680| as a meantone tuning, where "well" of course is defined as aside from the fact that it has nearly 300 notes in an octave. Another possibility is <212 337 491| and <212 335 492|.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> I'm not sure what minor thirds have to do with it, but <293 466 669| works well as a porcupine tuning, and <293 463 680| as a meantone tuning, where "well" of course is defined as aside from the fact that it has nearly 300 notes in an octave. Another possibility is <212 337 491| and <212 335 492|.
>

Sorry, this should have been <293 466 679|. One "use" for such a thing is that it can be used to map meantone to porcupine and vice-versa, so that, for instance, porcupine could be bizarrely notated in standard meantone notation. I've thought about how to use it for composition, but it doesn't seem too easy to get that to work. If someone else wants to try, I'll all in favor.