List of 12et rank two temperaments by complexity
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Below are listed rank-two temperaments supported by the 12edo patent val, below the indicated cutoff in TE logflat badness.
5-limit temperaments with badness below 0.1
Listed is the wedgie and the TE complexity for six temperaments with badness less than 0.1.
Rank | Wedgie | Name | Complexity | Comma List |
---|---|---|---|---|
1 | ⟨⟨1 4 4]] | Meantone | 1.523 | 81/80 |
2 | ⟨⟨3 0 -7]] | Augmented | 1.549 | 128/125 |
3 | ⟨⟨4 4 -3]] | Diminished | 1.826 | 648/625 |
4 | ⟨⟨2 -4 -11]] | Srutal | 2.121 | 2048/2025 |
5 | ⟨⟨1 -8 -15]] | Helmholtz | 3.103 | 32805/32768 |
6 | ⟨⟨12 -84 -161]] | Atomic | 33.065 | [161 -84 -12⟩ |
7-limit temperaments with badness below 0.06
Listed is the wedgie and the TE complexity for 18 temperaments with badness less than 0.06.
Rank | Wedgie | Name | Complexity | Comma List |
---|---|---|---|---|
1 | ⟨⟨1 4 -2 4 -6 -16]] | Dominant | 1.466 | 36/35 64/63 |
2 | ⟨⟨4 4 4 -3 -5 -2]] | Diminished | 1.494 | 36/35 50/49 |
3 | ⟨⟨3 0 6 -7 1 14]] | August | 1.655 | 36/35 128/125 |
4 | ⟨⟨2 -4 -4 -11 -12 2]] | Pajara | 1.953 | 50/49 64/63 |
5 | ⟨⟨1 4 10 4 13 12]] | Meantone | 2.204 | 81/80 126/125 |
6 | ⟨⟨2 8 8 8 7 -4]] | Injera | 2.205 | 50/49 81/80 |
7 | ⟨⟨3 0 -6 -7 -18 -14]] | Augene | 2.336 | 64/63 126/125 |
8 | ⟨⟨5 8 2 1 -11 -18]] | Ripple | 2.454 | 36/35 2560/2401 |
9 | ⟨⟨1 -8 -2 -15 -6 18]] | Schism | 2.544 | 64/63 360/343 |
10 | ⟨⟨6 0 0 -14 -17 0]] | Hexe | 2.689 | 50/49 128/125 |
11 | ⟨⟨0 0 12 0 19 28]] | Catler | 3.026 | 81/80 128/125 |
12 | ⟨⟨3 -12 -30 -26 -56 -36]] | Misty | 3.656 | 3136/3125 5120/5103 |
13 | ⟨⟨1 -8 -14 -15 -25 -10]] | Garibaldi | 3.823 | 225/224 3125/3087 |
14 | ⟨⟨2 -4 -16 -11 -31 -26]] | Diaschismic | 4.290 | 126/125 2048/2025 |
15 | ⟨⟨0 12 24 19 38 22]] | Compton | 5.927 | 225/224 250047/250000 |
16 | ⟨⟨4 -8 -20 -22 -43 -24]] | Bidia | 5.940 | 2048/2025 3136/3125 |
17 | ⟨⟨2 -16 -40 -30 -69 -48]] | Bischismic | 10.110 | 3136/3125 32805/32768 |
18 | ⟨⟨3 -24 -54 -45 -94 -58]] | Term | 13.877 | 32805/32768 250047/250000 |
11-limit temperaments with badness below 0.05
Listed is the wedgie and the TE complexity for 40 temperaments with badness less than 0.05.