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 |