"Universal" temperament comparison

I dusted off my ancient list of 45 7-limit temperaments, and
calculated n times the rms [period, generator] for n = 152, 176, 198,
217, 224, and 270. This can give a quick idea how well these are going
to work for the various temperaments in question. The absolute error,
of course, is obtained by dividing by n, and we have more leeway on
relative error for the less complex, smaller error systems. Naturally,
if the period does not come out an integer the division is no good for
the temperament at all. Everything seems to work reasonably well for
dominant sevenths, not much of a surprise given how close the optimal
generator is to a pure fifth. 152 doesn't seem particularly terrific
for Paul's favorite systems judging by this, but it does a bang-up job
for amity, superpythagorean and godzilla (old hemifourths.)

Decimal
[4, 2, 2, -6, -8, -1]
152 [76.00000000, 31.54284989]
176 [88.00000000, 36.52329988]
198 [99.00000000, 41.08871236]
217 [108.5000000, 45.03156860]
224 [112.0000000, 46.48419984]
270 [135.0000000, 56.03006231]

Dominant seventh
[1, 4, -2, 4, -6, -16]
152 [152.0000000, 63.05137618]
176 [176.0000000, 73.00685663]
198 [198.0000000, 82.13271371]
217 [217.0000000, 90.01413573]
224 [224.0000000, 92.91781753]
270 [270.0000000, 111.9991551]

Diminished
[4, 4, 4, -3, -5, -2]
152 [38.00000000, 10.85510619]
176 [44.00000000, 12.56907033]
198 [49.50000000, 14.14020412]
217 [54.25000000, 15.49709239]
224 [56.00000000, 15.99699860]
270 [67.50000000, 19.28209652]

Blackwood
[0, 5, 0, 8, 0, -14]
152 [30.40000000, 11.47767914]
176 [35.20000000, 13.28994427]
198 [39.60000000, 14.95118731]
217 [43.40000000, 16.38589720]
224 [44.80000000, 16.91447453]
270 [54.00000000, 20.38798269]

Augie
[3, 0, 6, -7, 1, 14]
152 [50.66666666, 13.96622756]
176 [58.66666666, 16.17142139]
198 [65.99999999, 18.19284906]
217 [72.33333333, 19.93862751]
224 [74.66666666, 20.58180904]
270 [89.99999999, 24.80843054]

Pajara
[2, -4, -4, -11, -12, 2]
152 [76.00000000, 13.78314845]
176 [88.00000000, 15.95943505]
198 [99.00000000, 17.95436443]
217 [108.5000000, 19.67725799]
224 [112.0000000, 20.31200825]
270 [135.0000000, 24.48322423]

Hexadecimal
[1, -3, 5, -7, 5, 20]
152 [152.0000000, 66.73951631]
176 [176.0000000, 77.27733468]
198 [198.0000000, 86.93700151]
217 [217.0000000, 95.27944105]
224 [224.0000000, 98.35297140]
270 [270.0000000, 118.5504566]

Negri
[4, -3, 2, -14, -8, 13]
152 [152.0000000, 15.89271413]
176 [176.0000000, 18.40209004]
198 [198.0000000, 20.70235130]
217 [217.0000000, 22.68894057]
224 [224.0000000, 23.42084188]
270 [270.0000000, 28.23047905]

Kleismic
[6, 5, 3, -6, -12, -7]
152 [152.0000000, 40.11078010]
176 [176.0000000, 46.44406117]
198 [198.0000000, 52.24956882]
217 [217.0000000, 57.26341633]
224 [224.0000000, 59.11062331]
270 [270.0000000, 71.24941202]

Augmented
[3, 0, -6, -7, -18, -14]
152 [50.66666666, 11.23795078]
176 [58.66666666, 13.01236407]
198 [65.99999999, 14.63890957]
217 [72.33333333, 16.04365342]
224 [74.66666666, 16.56119063]
270 [89.99999999, 19.96214942]

Godzilla
[2, 8, 1, 8, -4, -20]
152 [152.0000000, 32.01402620]
176 [176.0000000, 37.06887244]
198 [198.0000000, 41.70248149]
217 [217.0000000, 45.70423477]
224 [224.0000000, 47.17856492]
270 [270.0000000, 56.86702022]

Meantone
[1, 4, 10, 4, 13, 12]
152 [152.0000000, 63.75792406]
176 [176.0000000, 73.82496470]
198 [198.0000000, 83.05308529]
217 [217.0000000, 91.02282579]
224 [224.0000000, 93.95904598]
270 [270.0000000, 113.2542072]

Injera
[2, 8, 8, 8, 7, -4]
152 [76.00000000, 11.86246326]
176 [88.00000000, 13.73548378]
198 [99.00000000, 15.45241925]
217 [108.5000000, 16.93522716]
224 [112.0000000, 17.48152481]
270 [135.0000000, 21.07148080]

Doublewide
[8, 6, 6, -9, -13, -3]
152 [76.00000000, 34.75589340]
176 [88.00000000, 40.24366604]
198 [99.00000000, 45.27412429]
217 [108.5000000, 49.61861097]
224 [112.0000000, 51.21921132]
270 [135.0000000, 61.73744222]

Porcupine
[3, 5, -6, 1, -18, -28]
152 [152.0000000, 20.56785647]
176 [176.0000000, 23.81541276]
198 [198.0000000, 26.79233935]
217 [217.0000000, 29.36332141]
224 [224.0000000, 30.31052532]
270 [270.0000000, 36.53500820]

Superpythagorean
[1, 9, -2, 12, -6, -30]
152 [152.0000000, 62.01792291]
176 [176.0000000, 71.81022652]
198 [198.0000000, 80.78650484]
217 [217.0000000, 88.53874520]
224 [224.0000000, 91.39483376]
270 [270.0000000, 110.1634157]

Muggles
[5, 1, -7, -10, -25, -19]
152 [152.0000000, 47.83438480]
176 [176.0000000, 55.38718240]
198 [198.0000000, 62.31058020]
217 [217.0000000, 68.28987830]
224 [224.0000000, 70.49277760]
270 [270.0000000, 84.96897300]

Beatles
[2, -9, -4, -19, -12, 16]
152 [152.0000000, 45.13235052]
176 [176.0000000, 52.25851113]
198 [198.0000000, 58.79082502]
217 [217.0000000, 64.43236884]
224 [224.0000000, 66.51083235]
270 [270.0000000, 80.16930685]

Flattone
[1, 4, -9, 4, -17, -32]
152 [152.0000000, 64.16223012]
176 [176.0000000, 74.29310856]
198 [198.0000000, 83.57974713]
217 [217.0000000, 91.60002590]
224 [224.0000000, 94.55486544]
270 [270.0000000, 113.9723824]

Magic
[5, 1, 12, -10, 5, 25]
152 [152.0000000, 48.19748333]
176 [176.0000000, 55.80761227]
198 [198.0000000, 62.78356381]
217 [217.0000000, 68.80824922]
224 [224.0000000, 71.02787017]
270 [270.0000000, 85.61395065]

Myna
[10, 9, 7, -9, -17, -9]
152 [152.0000000, 39.26051969]
176 [176.0000000, 45.45954912]
198 [198.0000000, 51.14199275]
217 [217.0000000, 56.04955772]
224 [224.0000000, 57.85760796]
270 [270.0000000, 69.73908103]

Semisixths
[7, 9, 13, -2, 1, 5]
152 [152.0000000, 56.19191550]
176 [176.0000000, 65.06432321]
198 [198.0000000, 73.19736361]
217 [217.0000000, 80.22135305]
224 [224.0000000, 82.80913863]
270 [270.0000000, 99.81458674]

Orwell
[7, -3, 8, -21, -7, 27]
152 [152.0000000, 34.36800604]
176 [176.0000000, 39.79453331]
198 [198.0000000, 44.76884997]
217 [217.0000000, 49.06485073]
224 [224.0000000, 50.64758785]
270 [270.0000000, 61.04843178]

Miracle
[6, -7, -2, -25, -20, 15]
152 [152.0000000, 14.76590665]
176 [176.0000000, 17.09736559]
198 [198.0000000, 19.23453629]
217 [217.0000000, 21.08027462]
224 [224.0000000, 21.76028348]
270 [270.0000000, 26.22891312]

Valentine
[9, 5, -3, -13, -30, -21]
152 [152.0000000, 9.842897727]
176 [176.0000000, 11.39703947]
198 [198.0000000, 12.82166941]
217 [217.0000000, 14.05203162]
224 [224.0000000, 14.50532297]
270 [270.0000000, 17.48409465]

Mothra
[3, 12, -1, 12, -10, -36]
152 [152.0000000, 29.40231600]
176 [176.0000000, 34.04478695]
198 [198.0000000, 38.30038532]
217 [217.0000000, 41.97567482]
224 [224.0000000, 43.32972885]
270 [270.0000000, 52.22779816]

Cassandra
[1, -8, -14, -15, -25, -10]
152 [152.0000000, 63.06224620]
176 [176.0000000, 73.01944297]
198 [198.0000000, 82.14687334]
217 [217.0000000, 90.02965412]
224 [224.0000000, 92.93383651]
270 [270.0000000, 112.0184636]

Superkleismic
[9, 10, -3, -5, -30, -35]
152 [152.0000000, 40.76869616]
176 [176.0000000, 47.20585871]
198 [198.0000000, 53.10659105]
217 [217.0000000, 58.20267807]
224 [224.0000000, 60.08018381]
270 [270.0000000, 72.41807870]

Squares
[4, 16, 9, 16, 3, -24]
152 [152.0000000, 53.95482106]
176 [176.0000000, 62.47400333]
198 [198.0000000, 70.28325374]
217 [217.0000000, 77.02760638]
224 [224.0000000, 79.51236787]
270 [270.0000000, 95.84080056]

Semififths
[2, 8, -11, 8, -23, -48]
152 [152.0000000, 44.12469967]
176 [176.0000000, 51.09175752]
198 [198.0000000, 57.47822721]
217 [217.0000000, 62.99381467]
224 [224.0000000, 65.02587320]
270 [270.0000000, 78.37940074]

Diaschismic
[2, -4, -16, -11, -31, -26]
152 [76.00000000, 13.14003158]
176 [88.00000000, 15.21477341]
198 [99.00000000, 17.11662008]
217 [108.5000000, 18.75912403]
224 [112.0000000, 19.36425706]
270 [135.0000000, 23.34084557]

Octacot
[8, 18, 11, 10, -5, -25]
152 [152.0000000, 11.16508485]
176 [176.0000000, 12.92799298]
198 [198.0000000, 14.54399211]
217 [217.0000000, 15.93962771]
224 [224.0000000, 16.45380925]
270 [270.0000000, 19.83271651]

Tritonic
[5, -11, -12, -29, -33, 3]
152 [152.0000000, 73.52040056]
176 [176.0000000, 85.12888486]
198 [198.0000000, 95.76999547]
217 [217.0000000, 104.9600455]
224 [224.0000000, 108.3458535]
270 [270.0000000, 130.5954484]

Rodan
[3, 17, -1, 20, -10, -50]
152 [152.0000000, 29.69198506]
176 [176.0000000, 34.38019323]
198 [198.0000000, 38.67771739]
217 [217.0000000, 42.38921552]
224 [224.0000000, 43.75660957]
270 [270.0000000, 52.74234189]

Shrutar
[4, -8, 14, -22, 11, 55]
152 [76.00000000, 6.699845536]
176 [88.00000000, 7.757715884]
198 [99.00000000, 8.727430370]
217 [108.5000000, 9.564911062]
224 [112.0000000, 9.873456580]
270 [135.0000000, 11.90104141]

Hanson
[6, 5, 22, -6, 18, 37]
152 [152.0000000, 40.11835793]
176 [176.0000000, 46.45283549]
198 [198.0000000, 52.25943993]
217 [217.0000000, 57.27423467]
224 [224.0000000, 59.12179063]
270 [270.0000000, 71.26287263]

Hemiwuerschmidt
[16, 2, 5, -34, -37, 6]
152 [152.0000000, 24.56192537]
176 [176.0000000, 28.44012412]
198 [198.0000000, 31.99513963]
217 [217.0000000, 35.06538030]
224 [224.0000000, 36.19652160]
270 [270.0000000, 43.62973586]

Hemikleismic
[12, 10, -9, -12, -48, -49]
152 [152.0000000, 20.10611312]
176 [176.0000000, 23.28076256]
198 [198.0000000, 26.19085788]
217 [217.0000000, 28.70412202]
224 [224.0000000, 29.63006144]
270 [270.0000000, 35.71480620]

Hemithird
[15, -2, -5, -38, -50, -6]
152 [152.0000000, 24.48265552]
176 [176.0000000, 28.34833797]
198 [198.0000000, 31.89188022]
217 [217.0000000, 34.95221216]
224 [224.0000000, 36.07970287]
270 [270.0000000, 43.48892757]

Wizard
[12, -2, 20, -31, -2, 52]
152 [76.00000000, 27.45030671]
176 [88.00000000, 31.78456567]
198 [99.00000000, 35.75763637]
217 [108.5000000, 39.18892471]
224 [112.0000000, 40.45308357]
270 [135.0000000, 48.76041324]

Waage
[0, 12, 24, 19, 38, 22]
152 [12.66666667, 2.020008156]
176 [14.66666667, 2.338956812]
198 [16.50000000, 2.631326413]
217 [18.08333333, 2.883827433]
224 [18.66666667, 2.976854124]
270 [22.50000000, 3.588172382]

Slender
[13, -10, 6, -46, -27, 42]
152 [152.0000000, 4.872376045]
176 [176.0000000, 5.641698579]
198 [198.0000000, 6.346910901]
217 [217.0000000, 6.955957907]
224 [224.0000000, 7.180343645]
270 [270.0000000, 8.654878501]

Amity
[5, 13, -17, 9, -41, -76]
152 [152.0000000, 42.99253243]
176 [176.0000000, 49.78082703]
198 [198.0000000, 56.00343040]
217 [217.0000000, 61.37749696]
224 [224.0000000, 63.35741621]
270 [270.0000000, 76.36831419]

Hemififths
[2, 25, 13, 35, 15, -40]
152 [152.0000000, 44.51968719]
176 [176.0000000, 51.54911149]
198 [198.0000000, 57.99275042]
217 [217.0000000, 63.55771132]
224 [224.0000000, 65.60796007]
270 [270.0000000, 79.08102330]

Ennealimmal
[18, 27, 18, 1, -22, -34]
152 [16.88888889, 6.206559114]
176 [19.55555555, 7.186542132]
198 [22.00000000, 8.084859898]
217 [24.11111111, 8.860679788]
224 [24.88888889, 9.146508168]
270 [30.00000000, 11.02480895]