scale derived by intersection of sets

Hello,

I am new to the list and am enjoying the info swapping and dialougue
very much.

I have developed a scale you might find neat.

It involves generating two sets of ratios (as outlined below) then
finding the intersection of the two.

In this case, the set to the right is exactly 3/2 of the set to the
left. I stopped where I have because I have not found any more common
ratios beyond this point.

1/2:1/1:2/1 3/4:3/2:3/1
2/3:1/1:3/2 1/1:3/2:9/4
3/4:1/1:4/3 9/8:3/2:2/1
4/5:1/1:5/4 6/5:3/2:15/8
5/6:1/1:6/5 5/4:3/2:9/5
6/7:1/1:7/6 9/7:3/2:7/4
7/8:1/1:8/7 21/16:3/2:12/7
8/9:1/1:9/8 4/3:3/2:27/16
9/10:1/1:10/9 27/20:3/2:5/3
10/11:1/1:11/10 15/11:3/2:33/20
11/12:1/1:12/11 33/24:3/2:18/11
12/13:1/1:13/12 18/13:3/2:13/8
13/14:1/1:14/13 39/28:3/2:21/13
14/15:1/1:15/14 7/5:3/2:45/28
15/16:1/1:16/15 45/32:3/2:8/5

The intersection of these two is:

1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 12/7 7/4 9/5 15/8 2/1

or, if you're like me, you might prefer more conventional notation:

A B C+ C#- D E F+ F#- F#++ G-- G+ G#- A

The pluses and minuses represent 15 cents each, and are a modification
to the standard 12 note equal temperament. I use this system on a
guitar I had re-fretted (more about the guitar another time.)

thanks,

Robin Perry (jinto83@hotmail.com)
2022 N. 10th St.
Phoenix, AZ 85006 USA
(602) 252-3961

Oh, by the way... is anyone living in the area of Phoenix?
I would be very interested in getting together.









______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com