source file: m1531.txt Date: Sun, 20 Sep 1998 13:34:12 PDT Subject: scale derived by intersection of sets From: "Robin Perry" 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