Temperament lattice bases

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Below are tabulated bases (temperamental Minkowski bases) of minimal temperamental complexity for the pitch classes of various regular temperaments.

Rank three

Seven limit

Comma Name Gen 1 Length Gen 2 Length Angle
686/675 senga 15/14 0.6977 3/2 1.4208 103.732
64/63 Archytas' 3/2 1.0508 5/4 2.3219 90.000
875/864 keema 6/5 0.8879 3/2 1.3391 77.834
81/80 Didymus' 3/2 0.5451 8/7 2.8074 90.000
3125/3087 gariboh 25/21 0.5928 21/20 1.2018 80.810
2430/2401 nuwell 7/6 0.6247 9/7 1.1894 94.044
50421/50000 trimyna 7/5 0.3158 5/4 1.7938 94.101
245/243 sensamagic 3/2 0.9644 9/7 1.0807 96.914
126/125 starling 6/5 1.068 5/4 1.206 100.364
4000/3969 octagar 63/50 0.8966 21/20 1.0605 97.743
1728/1715 orwellisma 7/6 0.7526 3/2 1.3931 97.508
1029/1024 gamelisma 8/7 0.5192 5/4 2.3219 90.000
225/224 marvel 16/15 1.256 3/2 1.369 106.958
3136/3125 hemimean 28/25 0.5055 3/2 1.5849 90.000
5120/5103 hemifamity 3/2 0.5670 10/9 1.8063 82.112
6144/6125 porwell 35/32 0.9584 35/24 1.1877 92.681
65625/65536 horwell 5/4 0.6213 16/15 1.3863 64.638
703125/702464 meter 75/56 0.7305 375/224 0.7675 97.289
420175/419904 wizma 245/216 0.5541 324/245 0.9731 79.663
2401/2400 breedsma 49/40 0.7858 8/7 1.1241 107.367
4375/4374 ragisma 10/9 0.7890 6/5 0.9208 105.299

Eleven limit

Commas Name Gen 1 Length Gen 2 Length Angle
225/224, 385/384 marvel 16/15 1.0364 5/4 1.0759 104.028
225/224, 441/440 prodigy 16/15 0.9111 3/2 0.9477 65.933
99/98, 176/175 minerva 16/15 0.8997 5/4 1.0457 98.604
126/125, 176/175 thrush 5/4 0.8576 6/5 0.9314 74.624
56/55, 100/99 thrasher 6/5 0.9089 5/4 1.2007 98.845