List of 12et rank two temperaments by badness
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Below are listed rank-2 temperaments supported by the 12et patent val, below the indicated cutoff in TE logflat badness.
5-limit temperaments
Listed is the TE badness times 1000 for six temperaments with badness less than 0.1.
| Rank | Name | Badness | Comma List |
|---|---|---|---|
| 1 | Atomic | 3.802 | [161 -84 -12⟩ |
| 2 | Helmholtz | 4.259 | 32805/32768 |
| 3 | Meantone | 7.381 | 81/80 |
| 4 | Diaschismic | 19.915 | 2048/2025 |
| 5 | Augmented | 22.315 | 128/125 |
| 6 | Diminished | 47.231 | 648/625 |
7-limit temperaments
Listed is the TE badness times 1000 for 18 temperaments with badness less than 0.06.
| Rank | Name | Badness | Comma List |
|---|---|---|---|
| 1 | Meantone | 13.707 | 81/80 126/125 |
| 2 | Term | 19.950 | 32805/32768 250047/250000 |
| 3 | Pajara | 20.033 | 50/49 64/63 |
| 4 | Dominant | 20.690 | 36/35 64/63 |
| 5 | Garibaldi | 21.644 | 225/224 3125/3087 |
| 6 | Diminished | 22.401 | 36/35 50/49 |
| 7 | Augene | 24.816 | 64/63 126/125 |
| 8 | August | 26.459 | 36/35 128/125 |
| 9 | Injera | 31.130 | 50/49 81/80 |
| 10 | Compton | 35.686 | 225/224 250047/250000 |
| 11 | Misty | 36.802 | 3136/3125 5120/5103 |
| 12 | Diaschismic | 37.914 | 126/125 2048/2025 |
| 13 | Catler | 50.297 | 81/80 128/125 |
| 14 | Bischismic | 54.744 | 3136/3125 32805/32768 |
| 15 | Bidia | 56.474 | 2048/2025 3136/3125 |
| 16 | Schism | 56.648 | 64/63 360/343 |
| 17 | Hexe | 57.730 | 50/49 128/125 |
| 18 | Rip | 59.735 | 36/35 2560/2401 |
11-limit temperaments
Listed is the TE badness times 1000 for 40 temperaments with badness less than 0.05.
| Rank | Name | Badness | Comma List |
|---|---|---|---|
| 1 | Meantone | 17.027 | 81/80 99/98 126/125 |
| 2 | Augene | 19.613 | 56/55 64/63 100/99 |
| 3 | August | 20.191 | 36/35 45/44 56/55 |
| 4 | Pajara | 20.343 | 50/49 64/63 99/98 |
| 5 | Meanenneadecal | 21.423 | 45/44 56/55 81/80 |
| 6 | Domineering | 21.978 | 36/35 45/44 64/63 |
| 7 | Diminished | 22.132 | 36/35 50/49 56/55 |
| 8 | Compton | 22.235 | 225/224 441/440 4375/4356 |
| 9 | Injera | 23.124 | 45/44 50/49 99/98 |
| 10 | Andromeda | 23.556 | 100/99 225/224 245/242 |
| 11 | Pajaric | 23.798 | 45/44 50/49 56/55 |
| 12 | Dominant | 24.18 | 36/35 56/55 64/63 |
| 13 | Diaschismic | 25.034 | 126/125 176/175 5488/5445 |
| 14 | Demolished | 26.574 | 36/35 45/44 50/49 |
| 15 | Bischismic | 28.160 | 441/440 3136/3125 8019/8000 |
| 16 | Duodecim | 30.536 | 36/35 50/49 64/63 |
| 17 | Catnip | 34.478 | 56/55 81/80 128/125 |
| 18 | Undim | 34.837 | 1375/1372 5120/5103 5632/5625 |
| 19 | Helenus | 35.637 | 99/98 176/175 3125/3087 |
| 20 | Misty | 35.932 | 441/440 3136/3125 4375/4356 |
| 22 | Bimeantone | 38.122 | 81/80 126/125 245/242 |
| 24 | Rip | 38.811 | 36/35 80/77 126/121 |
| 26 | Bidia | 40.191 | 176/175 896/891 1375/1372 |
| 27 | Ripple | 40.347 | 45/44 99/98 126/125 |
| 28 | Passion | 40.809 | 64/63 100/99 1375/1372 |