source file: m1404.txt Date: Mon, 4 May 1998 05:14:58 -0500 Subject: Optimal Integer Ratios for 12et From: "Benjamin Tubb" For those who might be interested, the following info was determined within the "constraint" of using a divisor of 2048 or less. Its usefullness is in being able to compare cents to ratios and vice versa for tuning evaluations and applications in such programs as "Pitch Palette" . A simple BASIC program was used to tackle these optimisations with a "brute force" approach, inelegant but effective . Integer Ratio Equivalents to 12et Tunings within a tolerance of .001 of a Cent: Cents Ratio ----- ----- 0000 1/1 0100 1080/1019 0200 575/512 0300 1217/1023 0400 2580/2047 0500 1366/1023 0600 2896/2047 0700 3068/2047 0800 813/512 0900 1721/1023 1000 1825/1024 1100 3867/2048 1200 2/1 Does anyone know what the physical "tolerance" of the human ear is to pitch/frequency/cents variations with the range of MIDI note (0-127) frequencies from 8.175 Hz to 12543.853? ------------- Benjamin Tubb AIM: brtubb brtubb@cybertron.com http://home.cybertron.com/~brtubb "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"