Vavoom family

The vavoom family includes tunings that temper out the vavoom comma ([-68 18 17⟩).

Vavoom (118 & 665)

Subgroup: 2.3.5

Comma list: [-68 18 17⟩

Mapping: [⟨1 0 4], ⟨0 17 -18]]

mapping generators: ~2, ~16/15

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8765

Optimal ET sequence: 32, 43, 75, 118, 429, 547, 665, 783, 901, 1684

Badness: 0.0984

Doubloon

Subgroup: 2.3.5.7

Comma list: 3136/3125, 33756345/33554432, 330812181/327680000, 2152828125/2147483648

Mapping: [⟨1 0 4 7], ⟨0 17 -18 -45]]

mapping generators: ~2, ~16/15

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8391

Recommended ETs: 118, 161

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 3136/3125, 5632/5625, 35937/35840, 43923/43750, 43923/43904

Mapping: [⟨1 0 4 7 7], ⟨0 17 -18 -45 -38]]

mapping generators: ~2, ~16/15

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8563

Recommended ETs: 43, 118

Kaboom

Subgroup: 2.3.5.7

Comma list: 65625/65536, 4802000/4782969, 359661568/358722675, 6565234375/6530347008

Mapping: [⟨1 0 4 -4], ⟨0 17 -18 73]]

mapping generators: ~2, ~16/15

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8782

Recommended ETs: 118, 311

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 12005/11979, 19712/19683, 42875/42768, 65625/65536, 200704/200475

Mapping: [⟨1 0 4 -4 -4], ⟨0 17 -18 73 80]]

mapping generators: ~2, ~16/15

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8930

Recommended ETs: 75, 118

Vacuum

Subgroup: 2.3.5.7

Comma list: 4375/4374, [-68, 18, 17, 0⟩, [-69, 11, 21, 1⟩, [-67, 25, 13, -1⟩

Mapping: [⟨1 0 4 -15], ⟨0 17 -18 191]]

mapping generators: ~2, ~16/15

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8950

Recommended ETs: 118, 665