Whats this structure?

The way I produced MOS scales was to divide the overall period (octave for instance) into two chunks and continue dividing it so that it always has two step sizes.

So... for instance

31 =
20 11 =
9 11 11 =
9 9 2 9 2 = 3L2s
7 2 7 2 2 7 2 2 = 3L5s
5 2 2 5 2 2 2 5 2 2 2 = 3L8s
3 2 2 2 3 2 2 2 2 3 2 2 2 2 = 3L11s
1 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 14L3s

Now, with a "chromatic" scale (and I'm not really sure that 1 is really a melodic interval rather than an ornament...) one can work
back and find other melodic structures (for instance 5 4 5 4 5 4 4)
or harmonic structures (septimal minor sevenths, neutral neutral seventh, etc).

Despite all this talk, 9 9 2 9 2 was really the start of the exploration.

I assume there was a generator I implicitely used to get here and that this has a name and history. What is it?

--- In tuning@yahoogroups.com, "bobvalentine1" <bob.valentine@...> wrote:

> I assume there was a generator I implicitely used to get here and that this has a name and history. What is it?

11\31 is a generator for squares temperament:

http://xenharmonic.wikispaces.com/Meantone+family#Squares

--- In tuning@yahoogroups.com, "bobvalentine1" <bob.valentine@...>
> I assume there was a generator I implicitely used to get here and
> that this has a name and history. What is it?

You can discern that from the first division you did, from 31 to 20 and 11. Your generator is either the 20 or the 11 (octave inversions of each other, so both produce the same scale). The name for this temperament is either Sentinel (named for the piece Jacob Barton wrote in it, the first documented instance of its use) or Squares (I think).

Generally, any time you use this process of successive divisions, your very first division gives you your generator.

HTH.

-Igs