Vavoom family: Difference between revisions
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Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
Comma list: [[3136/3125]], 33756345/33554432, 330812181/327680000, 2152828125/2147483648 | Comma list: [[3136/3125]], [[33756345/33554432]], [[330812181/327680000]], [[2152828125/2147483648]] | ||
Mapping: {{mapping| 1 0 4 7 | 0 17 -18 -45 }} | Mapping: {{mapping| 1 0 4 7 | 0 17 -18 -45 }} | ||
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Recommended ETs: {{EDOs|118, 161}} | Recommended ETs: {{EDOs|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: {{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: {{EDOs|43, 118}} | |||
=== Kaboom === | === Kaboom === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
Comma list: [[65625/65536]], [[4802000/4782969]], 359661568/358722675, 6565234375/6530347008 | Comma list: [[65625/65536]], [[4802000/4782969]], [[359661568/358722675]], [[6565234375/6530347008]] | ||
Mapping: {{mapping| 1 0 4 -4 | 0 17 -18 73 }} | Mapping: {{mapping| 1 0 4 -4 | 0 17 -18 73 }} | ||
Revision as of 08:34, 18 February 2024
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
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
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
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