The search for the white keys!

Dan,

You very succinctly stated what it is that
I've been looking for in my scale quest! I
don't know what the limit of notes a white
key scale should have is, but even 21 seems
large!

As an example of a scale that my program
spat out that I thought would converge
with the M thread, I was looking for a
scale of the form

LssLssLs

and got various approximations for

1/1 7/6 11/9 9/7 3/2 11/7 18/11 21/11
14/9
In 31-EDO this is very nicely 72272272.
The implies that it can be wandered up
and down the 'transposing scale tree'
(which has a better and bigger name,
horogram?)

(up)

1/1 11/9 9/7 11/7 18/11

(and down)
5 2 etc
1/1 10/9 7/6 11/9 9/7 10/7 3/2 11/7 18/11 20/11 21/11
9/8

(and continues to 14, 17 and 31 in 31-EDO, which

Despite having lots of common ingrediants,
I couldn't figure out a way that
LssLssLs could map to 72 and preserve these
identities.

Bob Valentine

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> Dan,
>
> You very succinctly stated what it is that
> I've been looking for in my scale quest! I
> don't know what the limit of notes a white
> key scale should have is, but even 21 seems
> large!

I don't think anyone would claim that any set of 21 notes could
function as a "white-key scale".

Graham Breed suggested the 7-tone neutral thirds scale, the 10-tone
MOS of the generator, and the 5-tone "septimal pentatonic" scales as
possible "white-key scales" for the MIRACLE family.
>
> As an example of a scale that my program
> spat out that I thought would converge
> with the M thread, I was looking for a
> scale of the form
>
> LssLssLs
>
> and got various approximations for
>
> 1/1 7/6 11/9 9/7 3/2 11/7 18/11 21/11
> 14/9
> In 31-EDO this is very nicely 72272272.
> The implies that it can be wandered up
> and down the 'transposing scale tree'
> (which has a better and bigger name,
> horogram?)

Yup. The generator of this scale is 13/31 oct. or approximately a 7:9.
>
> Despite having lots of common ingrediants,
> I couldn't figure out a way that
> LssLssLs could map to 72 and preserve these
> identities.
>
You must be making use of some of 31-tET's unison vectors that are
not quite unisons in 72-tET. I'm sure we could figure this out if we
wanted to (do you want to?).

I wrote:
> --- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

> > In 31-EDO this is very nicely 72272272.
> > The implies that it can be wandered up
> > and down the 'transposing scale tree'
> > (which has a better and bigger name,
> > horogram?)
>
> Yup. The generator of this scale is 13/31 oct. or approximately a
7:9.

Sorry -- that should be 11/31 oct.