225/224-planar equal temperaments

This is a kind of generic tuning to apply to large enough (and 12
seems to be large enough) 5-limit JI scales, since they always seem to
have these relations. I ran a badness filter on the rms 225/224-planar
temperaments, treating it just like a 5-limit JI computation but using
the adjusted values for 3 and 5, and got the following list of
temperaments, where the first column is the et (to 10000), the second
the 225/224-planar val, the third column where the standard val maps
225/224 (if this is 0, the standard val and the 225/224 val are the
same in the 7-limit) and the fourth the badness measure, set to be
less than 1. From 72 and 175 we can conclude that 7-limit miracle is a
good 225/224-planar tuning, but 156 and 228 give duodecimal (mapping
[<12 19 28 34|, <0 0 -1 -2|]) with rms error 1.5 cents vs 1.64 for
miracle. Beyond that, 403, 559 and 631 work; 559 gives us two vals,
one an excellent 5-limit JI val <559 886 1298| and the other an
excellent 225/224-planar val <559 885 1297|. Since there is nothing
especially magical about the rms 225/224 tuning versus, eg, minimax
the results beyond this point are pretty meaningless, I suspect. A
kind of adaptive tuning, where the first 559 val was used for purely 5
limit chords and the second, with major thirds and fifths shifted down
a schisma, for chords involving 7 would be possible.

1 [1, 2, 2] 0 .736966
2 [2, 3, 5] 0 .743974
3 [3, 5, 7] 1 .433823
4 [4, 6, 9] -1 .665419
5 [5, 8, 12] 1 .892828
7 [7, 11, 16] -1 .637629
12 [12, 19, 28] 0 .548311
15 [15, 24, 35] 1 .977303
19 [19, 30, 44] 0 .360557
31 [31, 49, 72] 0 .857806
53 [53, 84, 123] 0 .666832
72 [72, 114, 167] 0 .522038
84 [84, 133, 195] 0 .989711
103 [103, 163, 239] 0 .939217
156 [156, 247, 362] 0 .720534
175 [175, 277, 406] 0 .741466
228 [228, 361, 529] 0 .536746
403 [403, 638, 935] 4 .411588
559 [559, 885, 1297] 4 .946951
631 [631, 999, 1464] 4 .635276
1034 [1034, 1637, 2399] 7 .896596
1593 [1593, 2522, 3696] 11 .551130
1996 [1996, 3160, 4631] 15 .989239
2224 [2224, 3521, 5160] 14 .632155
2627 [2627, 4159, 6095] 18 .805402
3817 [3817, 6043, 8856] 25 .870642
4220 [4220, 6681, 9791] 29 .567603
6444 [6444, 10202, 14951] 41 .504831
8037 [8037, 12724, 18647] 50 .945557