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 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 Commas
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 Commas
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/Waage 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.