source file: m1406.txt Date: Tue, 5 May 1998 17:25:40 -0500 Subject: Update to Optimal Integer Ratios for 12et From: "Benjamin Tubb" 12tet Optimal Ratio Equivalents at variable Tolerance Levels =============================== (i.e. 2^((x*100)/1200) for x=0 to 12) and where of course at 0 the ratio is 1/1, and for 12 it is 2/1. All output values "curtesy" of Mathematica v3.0.1's 'Rationalize[]' function which I just "discovered" . 10^-1 Tolerance Level ---------- 1 1 2 9/8 3 6/5 4 5/4 5 4/3 6 3/2 7 3/2 8 3/2 9 5/3 10 9/5 11 17/9 10^-2 Tolerance Level ---------- 1 18/17 2 9/8 3 25/21 4 5/4 5 4/3 6 17/12 7 3/2 8 27/17 9 37/22 10 16/9 11 17/9 10^-3 Tolerance Level ---------- 1 18/17 2 55/49 3 44/37 4 34/27 5 295/221 6 41/29 7 442/295 8 27/17 9 37/22 10 57/32 11 185/98 10^-4 Tolerance Level ---------- 1 89/84 2 55/49 3 44/37 4 63/50 5 295/221 6 99/70 7 442/295 8 100/63 9 37/22 10 98/55 11 185/98 10^-5 Tolerance Level --------- 1 196/185 2 1769/1576 3 1785/1501 4 349/277 5 295/221 6 577/408 7 442/295 8 1008/635 9 3002/1785 10 1527/857 11 185/98 10^-6 Tolerance Level --------- 1 1657/1564 2 1769/1576 3 1785/1501 4 635/504 5 3544/2655 6 1393/985 7 2655/1772 8 1008/635 9 3002/1785 10 1527/857 11 2943/1559 ------------- Benjamin Tubb brtubb@cybertron.com http://home.cybertron.com/~brtubb