Equal tempered approximations to just in

I thought I'd put together a table showing how closely the just 7-limit
intervals are approximated by equal temperaments. The octave inversions and
extensions of these intervals will be approximated just as well as the
intervals themselves.

Each ET is the smallest required to improve on the rms error of the previous
ET.

Notes per octave
Interval Ratio 12 15 19 22 27 31 68 72
Error in Cents for this ET:
perf.4th 4/3 2 -18 7 -7 -9 5 -4 2
maj.3rd 5/4 14 14 -7 -4 13 1 2 -3
min.3rd 6/5 -16 4 0 12 -5 -6 2 1
tritone 7/5 17 -23 -14 17 -5 -2 -0 1
sub.3rd 7/6 33 -27 -14 6 -0 4 -2 -0
sup.2nd 8/7 -31 9 21 -13 -9 1 -2 2
rootmeansquare 22 18 13 11 8 4 2 2


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