the 5, 3, 3 in 20-tone equal temperament

I'm going to be refretting another guitar to 20-tone equal
temperament, only this time it's going to be an 11-tone subset:

32123112113

This 5,3,3 subset was a result of combining the 5th and 6th rotation
of this 7-tone scale:

3414332

I already have a good idea of what I'm going to do, but I'd be
interested in any additional perspectives and input regarding the big
11-out-of-17-out-of-31 composite and how it relates to 20-tet (as
well as how it might best sit on the guitar, etc).

Dan Stearns
Guitarist-composer-microtonalist:
http://www.zebox.com/daniel_anthony_stearns/

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

> I already have a good idea of what I'm going to do, but I'd be
> interested in any additional perspectives and input regarding the
big
> 11-out-of-17-out-of-31 composite and how it relates to 20-tet (as
> well as how it might best sit on the guitar, etc).

i have no idea, but all four of these numbers share the neutral third
generator in common, so presumably your scales have some similarity
with a chain of neutral thirds (thus tying them in with the recent
discussion here) . . . ?

It's actually a wide major third generator in 1D and a major second,
wide major third generator in 2D.

The simplest JI interpretation would be 7:9 in the 1D and 1/(9:8:7)
in the 2D, but I personally prefer 1D and 2D interpretations based on
Fibonacci and Tribonacci constants as that seems like a more uniform
and internally consistent way to approach it.

Dan Stearns
Guitarist-composer-microtonalist:
http://www.zebox.com/daniel_anthony_stearns/

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "daniel_anthony_stearns"
> <daniel_anthony_stearns@y...> wrote:
>
> > I already have a good idea of what I'm going to do, but I'd be
> > interested in any additional perspectives and input regarding the
> big
> > 11-out-of-17-out-of-31 composite and how it relates to 20-tet (as
> > well as how it might best sit on the guitar, etc).
>
> i have no idea, but all four of these numbers share the neutral
third
> generator in common, so presumably your scales have some similarity
> with a chain of neutral thirds (thus tying them in with the recent
> discussion here) . . . ?