idea for Jacky re:self-similar scales

If you are taking an octave (or some other interval) and dividing by some
proportion (in your case, Phi) to get intervals A and B, and then dividing
A by Phi again, etc., it seems we always end up weighted with small
intervals at the bottom, of course (at the top too, if we "symmetricalize"
it as Jacky has done).

What if, instead of always dividing the lower interval produced by the
proportion, we randomized the choice of which interval to divide?

Thus one might divide the octave into A and B, or let's say L and U (for
lower and upper intervals) and then divide *U* (not L) into an L and U,
(by the same proportion. . . so it's still self-similar) and then divide L
into an L and U, and then divide that L again, and then maybe divide U. .
The point is that every time you divide into an L and U, you *randomly*
decide which one to further subdivide.

Then, the "clustering" effect could end up anywhere in the octave (I think
. . .)

Of course, if you're obssessed with symmetry, you might not like this
idea.

Then again, you can always "symmetricalize" anything by turning it
upside-down and combining with itself.

Yay.

CB

***From: Christopher Bailey******************
http://music.columbia.edu/~chris
**********************************************

--- In tuning@y..., Christopher Bailey <cb202@c...> wrote:
> If you are taking an octave (or some other interval) and dividing
by some
> proportion (in your case, Phi) to get intervals A and B, and then
dividing
> A by Phi again, etc., it seems we always end up weighted with small
> intervals at the bottom, of course (at the top too, if
we "symmetricalize"
> it as Jacky has done).
>
> What if, instead of always dividing the lower interval produced by
the
> proportion, we randomized the choice of which interval to divide?
>
> Thus one might divide the octave into A and B, or let's say L and U
(for
> lower and upper intervals) and then divide *U* (not L) into an L
and U,
> (by the same proportion. . . so it's still self-similar) and then
divide L
> into an L and U, and then divide that L again, and then maybe
divide U. .
> The point is that every time you divide into an L and U, you
*randomly*
> decide which one to further subdivide.
>
> Then, the "clustering" effect could end up anywhere in the octave
(I think
> . . .)

This is a really interesting concept. I'll have to give it a try.

Two things I've tried, but not posted about are:

1. A union of three self similar "ratio-derived" scales, built
from 6/5, 5/4, and 3/2. T'was quite a huge scale with very close
pitches (not as playable with the old 12 tone keyboard to me, without
the addition of a number of extra fingers of considerable length).

2. Creating a chain of several choice interval sizes, from which a
highly asymmetrical scale is constructed, which is kind of what I
think you are getting at here.

>
> Of course, if you're obsessed with symmetry, you might not like this
> idea.

Not necessarily, but maybe a little! : )

>
> Then again, you can always "symmetricalize" anything by turning it
> upside-down and combining with itself.

Yep. Kind of neat that way!

I'll play some more with asymmetrical self similarity, and post a
couple of new ones.

Thanks for the suggestions!

Jacky Ligon