optimal meantone revisited 2

Dave Keenan wrote:
>>I propose the following weighting formula, given a (non octave equivalent)
>>ratio a:b>>Max( 6/Max(a,b), (a*b)/30) )

I wrote:

>If we take 1/(odd limit) to represent this for 5->limit intervals considered in octave-invariant >terms, the
>meantone tunings ordered by mean dissonance are, >from best to worst,
>Meantone Size of Fifth Average error/limit
>1/4-comma 696.58 0.956
>Golden 696.21 1.021
>31-equal 696.77 1.025
>7/26-comma 696.16 1.029
>50-equal 696.00 1.059
>2/7-comma 695.81 1.092
>LucyTuning 695.49 1.149
>2/9-comma 697.18 1.168
>3/14-comma 697.35 1.229
>1/3-comma 694.79 1.274
>19-equal 694.74 1.303
>1/5-comma 697.65 1.338
>43-equal 697.67 1.346
>55-equal 698.18 1.526
>1/6-comma 698.37 1.593
>12-equal 700.00 2.172
>26-equal 692.31 2.706
>Pythagorean 701.96 2.868

Using RMS error instead, we get
Meantone Size of 5th RMS error/limit
63/250-comma 696.54 1.206
1/4-comma 696.58 1.207
31-equal 696.77 1.215
Golden meantone 696.21 1.222
7/26-comma 696.16 1.227
50-equal 696.00 1.250
2/9-comma 697.18 1.268
2/7-comma 695.81 1.285
3/14-comma 697.35 1.303
LucyTuning 695.49 1.363
1/5-comma 697.65 1.385
43-equal 697.67 1.391
55-equal 698.18 1.568
1/3-comma 694.79 1.609
19-equal 694.74 1.629
1/6-comma 698.37 1.644
12-equal 700.00 2.429
26-equal 692.31 2.842
Pythagorean 701.96 3.512

The RMS-optimal (inverse-limit-weighted) tuning, 63/250-comma meantone, would appear in second place on the first table, with a mean error/limit of 0.963. It is indistinguishable from that table's first-place tuning, 1/4-comma meantone.