Insanely low complexity temperament in the 2.9/7.11/7 subgroup

http://x31eq.com/cgi-bin/rt.cgi?ets=14_3&limit=2_9%2F7_11%2F7

This tempers out 51/49 and is in the 2.9/7.11/7 subgroup, which is
built around 7:9:11 triads instead of 4:5:6 triads. It makes possible
9/7-11/9-9/7 chords that span an octave. That's about as efficient as
a temperament could ever hope to get.

I happened upon it after lots and lots of meditation in "Uncle"
temperament, ultimately realizing that the blend of 4:5:6 and 7:9:11
was what I enjoyed about it so much. It's supported by 11, 14, 17, 20,
etc equal. 11 and 17 are special in that they extend this to the
2.7.9.11 subgroup; one good temperament for this subgroup is
machine[6], which splits the generator in half and tempers out 64/63
as well. Machine could also be said to be 2-superpyth, using the
nomenclature for subtemperaments I laid out on tuning-math recently.

Graham complexity of 2... unbelievable!

-Mike

The temperament looks interesting, although I still think that the 2D version of Bohlen-Pierce (which tempers out 245/243) is unbeatable.
Next I'd put the one you were referring to; then the one with the 11/8-like generator; and then probably my "triharmonic" system where the period is 4/1 and the generator is the 9th root of 32/5.

Petr

On Sat, Aug 27, 2011 at 6:36 AM, Petr Parízek <petrparizek2000@...> wrote:
>
> The temperament looks interesting, although I still think that the 2D
> version of Bohlen-Pierce (which tempers out 245/243) is unbeatable.

Unbeatable from what standpoint, comma pumps? Scale-wise it doesn't do too well.

> Next I'd put the one you were referring to;

I think machine should probably be ahead of it, just because the
2.7.9.11 subgroup is a little nicer than 2.9/7.11/7:

http://x31eq.com/cgi-bin/rt.cgi?ets=11_17&limit=2.7.9.11

-Mike

--- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@...> wrote:
>
> The temperament looks interesting, although I still think that the 2D
> version of Bohlen-Pierce (which tempers out 245/243) is unbeatable.
> Next I'd put the one you were referring to; then the one with the 11/8-like
> generator; and then probably my "triharmonic" system where the period is 4/1
> and the generator is the 9th root of 32/5.

I think a lot of the subgroup temperaments on the Chromatic Pairs page are extremely kick-ass.

    Indeed, it DOES form a chain if root * 9/7 * 11/7 * 9/7 (apx. 7/7 9/7 11/7 14/7 22/7...)....great for chained triads!   Just for grins, there is also a 12/7 in there...so you could make a nifty 7/7 9/7 11/7 12/7 14/7 chord. 
    Maybe a bit large for my tastes but, so far as a tuning that's very strong up to 9-odd-limit (IE 7/7, 9/7, 12/7, 14/7)....I doubt it can get much better than this! :-D

>"Graham complexity of 2... unbelievable!"
  Indeed, numerically, this looks VERY impressive.  I'm going to need to try composing in it...