No man's land between sensi and squares

Tutim was asking about ~9/7 generators that fall between 5\14 and
4\11, and if there was any temperament name associated with that
region, especially around 9\25 or so. A quick look at the wiki leaves
me scratching my head.

The only named temperament I can find in this area at all is "Sidi,"
which is really high error. The best I could do is this

http://x31eq.com/cgi-bin/rt.cgi?ets=14_25&limit=11

Ehhhhhhhh, not that great. Anyone see any brilliant subgroups that
might make this range make sense?

A few problems are that this is the range where there's no clear
dominant mapping for 2 generators (right between 13/8 and 18/11 and
5/3). You might thus expect that 55/54 would be good here, since it
equates 5/3 and 18/11, but if you put in 55/54 and 245/243 you get
pretty abysmal results

http://x31eq.com/cgi-bin/uv.cgi?uvs=55/54+245/243

Any ideas?

-Mike

Mike wrote:

> A few problems are that this is the range where there's no clear
> dominant mapping for 2 generators (right between 13/8 and 18/11 and
> 5/3). You might thus expect that 55/54 would be good here, since it
> equates 5/3 and 18/11, but if you put in 55/54 and 245/243 you get
> pretty abysmal results

First of all, what's wrong with squares?

Okay, there's supermajor temperament which requires as many as 80 tones in
an octave to start making sense:
http://xenharmonic.wikispaces.com/Ragismic+microtemperaments#Supermajor

Then there's the one which I was calling fasum (meaning "far from
supermajor's accuracy"):
http://x31eq.com/cgi-bin/rt.cgi?ets=53%2C14p&limit=2.3.5.13

Then there's hedgehog which does use a 9/7-like generator but you need to
have a half-octave period.

If I allow more mistuning, there's the 5-limit unison vector of ||43 -33
4>>. The temperament could possibly be extended to higher limits but it's
probably something else than you want anyway.

If I allow significantly more complexity, there's the one of ||91 51 -74>>
but do we want to go as far as that? It doesn't seem to be particularly "in
tune" to make it worth it. The same goes for ||102 -79 10>>.

Petr

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Tutim was asking about ~9/7 generators that fall between 5\14 and
> 4\11, and if there was any temperament name associated with that
> region, especially around 9\25 or so. A quick look at the wiki leaves
> me scratching my head.
>
> The only named temperament I can find in this area at all is "Sidi,"
> which is really high error. The best I could do is this
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=14_25&limit=11
>
> Ehhhhhhhh, not that great. Anyone see any brilliant subgroups that
> might make this range make sense?
>
> A few problems are that this is the range where there's no clear
> dominant mapping for 2 generators (right between 13/8 and 18/11 and
> 5/3). You might thus expect that 55/54 would be good here, since it
> equates 5/3 and 18/11, but if you put in 55/54 and 245/243 you get
> pretty abysmal results
>
> http://x31eq.com/cgi-bin/uv.cgi?uvs=55/54+245/243
>
> Any ideas?
>
> -Mike
>

Recently I asked about the generator of 9/7 tempered down by 1/3 of the unidecimal comma, between 429.225 cents, which in this particular range and has moments of symmetry at 11 and 14, and was told "squares". There's also an MOS at 25 and I tried 1/4 and
1/2-unidecimal comma versions as well, the 1/4 comma version jibing with 9°of 25.

In what way is this different?

On 4/10/2012 1:26 AM, Mike Battaglia wrote:
> Tutim was asking about ~9/7 generators that fall between 5\14 and
> 4\11, and if there was any temperament name associated with that
> region, especially around 9\25 or so. A quick look at the wiki leaves
> me scratching my head.

It doesn't look like there's much in that range. 14c&53, maybe 14c&39 or 14c&25e.