Vavoom family: Difference between revisions

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The '''vavoom family''' includes tunings that temper out the vavoom comma ({{monzo| -68 18 17 }}).
{{Todo|inline=1|review|comment=Normalize the comma lists. Work out the optimal ET sequences and badnesses. }}


== Vavoom (118 & 665) ==
The '''vavoom family''' includes [[temperaments]] that [[tempering out|temper out]] the vavoom comma ({{monzo| -68 18 17 }}).
 
== Vavoom ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 16: Line 18:
Badness: 0.0984
Badness: 0.0984


 
== Doubloon ==
=== Doubloon ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 30: Line 31:
Recommended ETs: {{EDOs|118, 161}}
Recommended ETs: {{EDOs|118, 161}}


==== 11-limit ====
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 43: Line 44:
Recommended ETs: {{EDOs|43, 118}}
Recommended ETs: {{EDOs|43, 118}}


===== 13-limit =====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 56: Line 57:
Recommended ETs: {{EDOs|118, 161}}
Recommended ETs: {{EDOs|118, 161}}


 
== Kaboom ==
=== Kaboom ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 70: Line 70:
Recommended ETs: {{EDOs|118, 311}}
Recommended ETs: {{EDOs|118, 311}}


==== 11-limit ====
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 83: Line 83:
Recommended ETs: {{EDOs|75, 118}}
Recommended ETs: {{EDOs|75, 118}}


===== 13-limit =====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 96: Line 96:
Recommended ETs: {{EDOs|118, 311}}
Recommended ETs: {{EDOs|118, 311}}


 
== Vacuum ==
=== Vacuum ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 110: Line 109:
Recommended ETs: {{EDOs|118, 665}}
Recommended ETs: {{EDOs|118, 665}}


==== Vortex ====
=== Vortex ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 123: Line 122:
Recommended ETs: {{EDOs|118, 547}}
Recommended ETs: {{EDOs|118, 547}}


==== Void ====
=== Void ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 136: Line 135:
Recommended ETs: {{EDOs|118, 665}}
Recommended ETs: {{EDOs|118, 665}}


[[Category:Temperament families]][[Category:Todo:intro]]
[[Category:Temperament families]]

Revision as of 13:39, 19 February 2024

Todo: review

Normalize the comma lists. Work out the optimal ET sequences and badnesses.

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

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

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