source file: m1415.txt Date: Wed, 13 May 1998 23:38:41 -0500 Subject: Integer Ratios for 12tet Semitones at Variable Error Tolerance Levels From: "Benjamin Tubb" For reference and interest to some who may not otherwise have the means to conveniently have access to such data, the following is provided. Anyone interested in any special tables of cents/ratios, feel free to contact me in private email. I'm fortunately using Mathematica. Integer Ratios for 12tet Semitones for Various Error Tolerances Error Tolerance Levels Cents 10^-2 10^-3 10^-4 10^-5 1 0 - 1 18 18 89 196 _100 -- -- -- --- 17 17 84 185 9 55 55 1769 _200 - -- -- ---- 8 49 49 1576 25 44 44 1785 _300 -- -- -- ---- 21 37 37 1501 5 34 63 349 _400 - -- -- --- 4 27 50 277 4 295 295 295 _500 - --- --- --- 3 221 221 221 17 41 99 577 _600 -- -- -- --- 12 29 70 408 3 442 442 442 _700 - --- --- --- 2 295 295 295 27 27 100 1008 _800 -- -- --- ---- 17 17 63 635 37 37 37 3002 _900 -- -- -- ---- 22 22 22 1785 16 57 98 1527 1000 -- -- -- ---- 9 32 55 857 17 185 185 185 1100 -- --- --- --- 9 98 98 98 2 1200 - 1 For general info, the following 10-^5 error tolerance used for the cents range 0-1 in increments of 0.1 cent is shown for which the error level is just small enough to distinguish each value to a different integer ratio. Cents 10^-5 1 0 - 1 17313 0.1 ----- 17312 8657 0.2 ---- 8656 5771 0.3 ---- 5770 4329 0.4 ---- 4328 3463 0.5 ---- 3462 2886 0.6 ---- 2885 2474 0.7 ---- 2473 2165 0.8 ---- 2164 1924 0.9 ---- 1923 1732 1. ---- 1731 ------------- Benjamin Tubb AIM: brtubb brtubb@cybertron.com http://home.cybertron.com/~brtubb/theory.html "Music creates order out of chaos; for rhythm imposes unanimity upon the divergent, melody imposes continuity upon the disjoin- ted, and harmony imposes compatibility upon the incongruous." - Yehudi Menuhin, from "Theme and Variations"