11-limit Starling

This apparently should be the temperament with TM basis {126/125,
243/242}, which has the same tuning in the 7-limit as 126/125-planar.
Another closeby tuning is top for {126/125, 176/175}-planar, at a
distance of 0.114 cents. I proposed thrush some while back for this,
and so far no objections have been lodged. If we take all three
commas, we get the nonkleismic temperament, which like 7-limit
starling I've actually composed in.

On Fri, 16 Jan 2004 08:58:08 -0000, "Gene Ward Smith" <gwsmith@svpal.org>
wrote:

>This apparently should be the temperament with TM basis {126/125,
>243/242}, which has the same tuning in the 7-limit as 126/125-planar.
>Another closeby tuning is top for {126/125, 176/175}-planar, at a
>distance of 0.114 cents. I proposed thrush some while back for this,
>and so far no objections have been lodged. If we take all three
>commas, we get the nonkleismic temperament, which like 7-limit
>starling I've actually composed in.

243;242 is |-1 5 0 0 -2> : it's compatible with 31, 58, 62, and 89-ET.

176;175 is |4 0 -2 -1 1> : this is one of the commas of my 11-limit
extension of porcupine. Compatible starling ET's include 12, 15, 16, 31,
43, 46, 58, 73, 89.

As it turns out, DNA experiments have revealed that starlings are more
closely related to thrushes and mockingbirds than previously suspected. If
we accept this classification, it's a good argument for keeping the name
"thrush" for a temperament that has a close relationship with "starling".

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
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\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> 176;175 is |4 0 -2 -1 1> : this is one of the commas of my 11-limit
> extension of porcupine.

I would hope it would be a comma of anyone's version of porcupine, but
I could run the naming convention check on it; I've been calling this
simply "procupine" or 11-limit porcupine if we need to be precise. The
top tunings for 5-limit and 7-limit porcupine are the same; the
11-limit tuning involves less sharpening of the octave, and moves it
close to 22-equal--less than a cent away in val space.

Compatible starling ET's include 12, 15, 16, 31,
> 43, 46, 58, 73, 89.

I get 31, 58, 65, and 89 for 11-limit starling, and your list for thrush.

> As it turns out, DNA experiments have revealed that starlings are more
> closely related to thrushes and mockingbirds than previously
suspected. If
> we accept this classification, it's a good argument for keeping the name
> "thrush" for a temperament that has a close relationship with
"starling".

Thanks, Herman. I guess that settles it. :)