Vavoom family: Difference between revisions
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Documented the 3 lowest complexity 7 limit extensions of vavoom which x31eq gave me |
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The '''vavoom family''' includes tunings that temper out the vavoom comma ({{monzo| -68 18 17 }}). | |||
== Vavoom (118 & 665) == | == Vavoom (118 & 665) == | ||
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Badness: 0.0984 | Badness: 0.0984 | ||
== Doubloon == | |||
Subgroup: 2.3.5.7 | |||
Comma list: [[3136/3125]], 33756345/33554432, 330812181/327680000, 2152828125/2147483648 | |||
Mapping: {{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: {{EDOs|118, 161}} | |||
== Kaboom == | |||
Subgroup: 2.3.5.7 | |||
Comma list: [[65625/65536]], [[4802000/4782969]], 359661568/358722675, 6565234375/6530347008 | |||
Mapping: {{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: {{EDOs|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: {{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: {{EDOs|118, 665}} | |||
{{stub}} | {{stub}} | ||
[[Category:Temperament families]][[Category:Todo:intro]] | [[Category:Temperament families]][[Category:Todo:intro]] | ||
Revision as of 07:56, 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
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
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