{2,3,5,13} temperaments

The rationale for this subgroup is that while the 11-th partial is a
little awkwardly placed, between 10 and 12, the 13-th partial can
substitute for the 12; so that we have 8:10:13 as a variant on 8:10:12.

Clearly the standout system for this sort of thing is kleismic, but
orwell and (various forms of) meantone are possibilities, and
especially so if 7 is added to the mix.

[[1, 0, 1, 0], [0, 6, 5, 14]] [6, 5, 14, -6, 0, 14]
[1200., 317.1782480]

bad 1544.881453 comp 28.167578 rms .935507

[[1, 3, -9, -18], [0, -3, 24, 46]] [3, -24, -46, -45, -84, -18]
[1200., 566.0950734]

bad 2739.918388 comp 91.512154 rms .157192

[[1, 0, 3, 8], [0, 7, -3, -19]] [7, -3, -19, -21, -56, -33]
[1200., 271.5856780]

bad 2754.217033 comp 44.981181 rms .654015

[[1, 2, 2, 3], [0, -1, 1, 2]] [1, -1, -2, -4, -7, -1]
[1200., 440.2031692]

bad 3009.058093 comp 6.220665 rms 37.360090

[[1, 1, 2, 4], [0, 2, 1, -1]] [2, 1, -1, -3, -9, -6]
[1200., 357.0595734]

bad 3392.073388 comp 8.035192 rms 25.241994

[[1, 0, -6, -7], [0, 4, 21, 27]] [4, 21, 27, 24, 28, -15]
[1200., 475.5692196]

bad 3690.343087 comp 59.467771 rms .501365

[[1, 2, 4, 2], [0, -1, -4, 4]] [1, 4, -4, 4, -10, -24]
[1200., 506.7816758]

bad 3722.944279 comp 14.138269 rms 8.948391

[[1, 2, 4, 10], [0, -1, -4, -15]] [1, 4, 15, 4, 20, 20]
[1200., 504.1468810]

bad 4152.345940 comp 23.774699 rms 3.529510

[[1, 2, 1, 5], [0, -1, 3, -3]] [1, -3, 3, -7, 1, 18]
[1200., 523.6054531]

bad 4497.303591 comp 12.018087 rms 14.960028

[[1, 2, -1, 1], [0, -2, 16, 13]] [2, -16, -13, -30, -28, 29]
[1200., 249.1776838]

bad 4773.426380 comp 47.050279 rms 1.035993

[[1, 1, 1, 4], [0, 4, 9, -2]] [4, 9, -2, 5, -18, -38]
[1200., 176.6699375]

bad 5379.129474 comp 26.393924 rms 3.709838

[[1, 3, 6, 2], [0, -5, -13, 6]] [5, 13, -6, 9, -28, -62]
[1200., 339.6788753]

bad 5779.802130 comp 39.791279 rms 1.753832

[[1, 2, 4, 6], [0, -2, -8, -11]] [2, 8, 11, 8, 10, -4]
[1200., 251.2502482]

bad 6102.317289 comp 23.089213 rms 5.499554

[[1, 2, 4, 5], [0, -1, -4, -3]] [1, 4, 3, 4, 1, -8]
[1200., 508.8799915]

bad 7120.742538 comp 10.122731 rms 33.387264

[[1, 6, 3, 2], [0, -13, -2, 5]] [13, 2, -5, -27, -56, -19]
[1200., 407.6681316]

bad 7410.380474 comp 51.533064 rms 1.340663

[[1, 2, 2, 4], [0, -18, 14, -13]] [18, -14, 13, -64, -46, 82]
[1200., 27.63474175]

bad 7479.765169 comp 92.776267 rms .417508

[[2, 4, 3, 7], [0, -2, 4, 1]] [4, -8, -2, -22, -18, 25]
[600.0000000, 247.2146790]

bad 7497.983252 comp 30.330961 rms 3.915823

[[5, 8, 12, 19], [0, 0, -1, -1]] [0, 5, 5, 8, 8, -7]
[240.0000000, 97.55681404]

bad 7507.779571 comp 14.089424 rms 18.170879

[[1, -2, 8, 4], [0, 12, -19, -1]] [12, -19, -1, -58, -46, 68]
[1200., 358.5725813]

bad 8255.528931 comp 79.858910 rms .621941

[[1, -1, 2, 5], [0, 8, 1, -4]] [8, 1, -4, -17, -36, -13]
[1200., 388.3457874]

bad 8421.189302 comp 32.305788 rms 3.876713

[[1, 0, 2, 4], [0, 5, 1, -1]] [5, 1, -1, -10, -20, -6]
[1200., 378.0513539]

bad 8474.812895 comp 19.307163 rms 10.923055

[[1, 2, 5, 7], [0, -2, -13, -16]] [2, 13, 16, 16, 18, -11]
[1200., 247.2780982]

bad 8599.283217 comp 36.528785 rms 3.096298

[[1, 2, 3, 5], [0, -2, -3, -6]] [2, 3, 6, 0, 2, 3]
[1200., 261.2358895]

bad 8643.523519 comp 11.353199 rms 32.218493

[[1, 1, 0, 4], [0, 2, 8, -1]] [2, 8, -1, 8, -9, -32]
[1200., 349.0071836]

bad 8752.986475 comp 21.665053 rms 8.959581

[[1, 6, 1, 9], [0, -10, 3, -12]] [10, -3, 12, -28, -18, 39]
[1200., 529.7378924]

bad 8815.473407 comp 45.742838 rms 2.024186

[[2, 3, 4, 7], [0, 1, 3, 2]] [2, 6, 4, 5, -1, -13]
[600.0000000, 129.7513798]

bad 9013.794934 comp 15.225397 rms 18.681914

[[1, 2, 2, 4], [0, -4, 3, -3]] [4, -3, 3, -14, -10, 18]
[1200., 125.2778176]

bad 9082.656432 comp 20.450477 rms 10.434146

[[1, 4, -1, 4], [0, -8, 11, -1]] [8, -11, 1, -36, -28, 43]
[1200., 362.3182973]

bad 9114.550166 comp 49.778173 rms 1.767292

[[1, 2, 4, 3], [0, -3, -12, 5]] [3, 12, -5, 12, -19, -56]
[1200., 167.8627430]

bad 9124.252538 comp 35.157654 rms 3.546569

[[1, -1, -4, 6], [0, 9, 22, -8]] [9, 22, -8, 14, -46, -100]
[1200., 344.8448843]

bad 9271.450153 comp 66.030899 rms 1.021655

[[1, 2, 3, 3], [0, -2, -3, 3]] [2, 3, -3, 0, -12, -18]
[1200., 272.5300013]

bad 9320.064406 comp 12.132575 rms 30.420327

[[3, 5, 7, 11], [0, -1, 0, 0]] [3, 0, 0, -7, -11, 0]
[400.0000000, 106.9921230]

bad 9369.193334 comp 11.759093 rms 32.554085

[[1, 10, 5, 19], [0, -22, -7, -40]] [22, 7, 40, -40, -18, 67]
[1200., 458.9800321]

bad 9445.710500 comp 95.904963 rms .493405

[[1, 2, 3, 4], [0, -3, -5, -2]] [3, 5, 2, 1, -8, -14]
[1200., 161.8078498]

bad 9831.730783 comp 14.481501 rms 22.524428