Vavoom family

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

Vavoom

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

Todo: review
For all below temperaments: Normalize the comma lists. Work out the optimal ET sequences and badnesses.

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

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 441/440, 1001/1000, 1188/1183, 1575/1573, 1701/1690, 3136/3125, 3267/3250, 3584/3575

Mapping: [⟨1 0 4 7 7 1], ⟨0 17 -18 -45 -38 29]]

mapping generators: ~2, ~16/15

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8193

Recommended ETs: 118, 161

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

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 1575/1573, 3025/3024, 4096/4095, 4459/4455, 12005/11979, 19712/19683, 20480/20449

Mapping: [⟨1 0 4 -4 -4 12], ⟨0 17 -18 73 80 -89]]

mapping generators: ~2, ~16/15

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8979

Recommended ETs: 118, 311

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

Vortex

Subgroup: 2.3.5.7.11

Comma list: 4375/4374, 42592/42525, 532400/531441, 766656/765625, 805255/802816, 3675375/3670016

Mapping: [⟨1 0 4 -15 -4], ⟨0 17 -18 191 80]]

mapping generators: ~2, ~16/15

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8786

Recommended ETs: 118, 547

Void

Subgroup: 2.3.5.7.11

Comma list: 4375/4374, 496125/495616, 806736/805255, 1240029/1239040, 22478848/22460625, 26796875/26763264

Mapping: [⟨1 0 4 -15 -15], ⟨0 17 -18 191 198]]

mapping generators: ~2, ~16/15

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8770

Recommended ETs: 118, 665