Optimal Integer Ratios for 12et

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"