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Vavoom family: Difference between revisions

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Created page with " == Vavoom (118 & 665) == Subgroup: 2.3.5 Comma list: {{monzo| -68 18 17 }} Mapping: {{mapping| 1 0 4 | 0 17 -18 }} : mapping generators: ~2, ~16/15 Optimal tuning (POTE):..."
 
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{{Technical data page}}
The '''vavoom family''' includes [[temperaments]] that [[tempering out|temper out]] the [[vavoom comma]], {{monzo| -68 18 17 }}.


== Vavoom (118 & 665) ==
== Vavoom ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 7: Line 9:
Mapping: {{mapping| 1 0 4 | 0 17 -18 }}
Mapping: {{mapping| 1 0 4 | 0 17 -18 }}


: mapping generators: ~2, ~16/15
: Mapping generators: ~2, ~16/15


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


{{Optimal ET sequence|legend=1| 32, 43, 75, 118, 429, 547, 665, 783, 901, 1684 }}
{{Optimal ET sequence|legend=1| 32, 43, 75, 118, 429, 547, 665, 783, 901, 1684 }}


Badness: 0.0984
Badness: 0.098376
 
== Raccoon ==
Subgroup: 2.3.5.7
 
Comma list: 225/224, 41943040/40353607
 
Mapping: {{mapping| 1 0 4 3 | 0 17 -18 -2 }}
 
: Mapping generators: ~2, ~16/15
 
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8960
 
Optimal ET sequence: {{Optimal ET sequence| 32, 43, 75, 118d }}
 
Badness: 0.272586
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 1344/1331, 2420/2401
 
Mapping: {{mapping| 1 0 4 3 3 | 0 17 -18 -2 5 }}
 
: Mapping generators: ~2, ~16/15
 
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8892
 
Optimal ET sequence: {{Optimal ET sequence| 32, 43, 75e }}
 
Badness: 0.095405
 
== Doubloon ==
Subgroup: 2.3.5.7
 
Comma list: 3136/3125, 33756345/33554432
 
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
 
Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 118, 279, 397d }}
 
Badness: 0.173974
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 3136/3125, 35937/35840
 
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 = 111.8368
 
Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 118, 279, 397d }}
 
Badness: 0.049755
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 441/440, 1001/1000, 1188/1183, 3136/3125
 
Mapping: {{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
 
Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 118, 161, 279f }}
 
Badness: 0.042899
 
== Kaboom ==
Subgroup: 2.3.5.7
 
Comma list: 65625/65536, 4802000/4782969
 
Mapping: {{mapping| 1 0 4 -4 | 0 17 -18 73 }}
 
: Mapping generators: ~2, ~16/15
 
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8950
 
Optimal ET sequence: {{Optimal ET sequence| 75, 118, 193, 311 }}
 
Badness: 0.124539
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 12005/11979, 19712/19683
 
Mapping: {{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
 
Optimal ET sequence: {{Optimal ET sequence| 75e, 118, 193, 311 }}
 
Badness: 0.038829
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 625/624, 1575/1573, 4096/4095, 4459/4455
 
Mapping: {{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
 
Optimal ET sequence: {{Optimal ET sequence| 118, 193, 311 }}
 
Badness: 0.036509
 
== Vacuum ==
Subgroup: 2.3.5.7
 
Comma list: 4375/4374, [-68 18 17⟩
 
Mapping: {{mapping| 1 0 4 -15 | 0 17 -18 191 }}
 
: Mapping generators: ~2, ~16/15
 
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8782
 
Optimal ET sequence: {{Optimal ET sequence| 118, 429d, 547, 665, 783, 1448, 2231, 3679 }}
 
Badness: 0.092961
 
=== Vortex ===
Subgroup: 2.3.5.7.11
 
Comma list: 4375/4374, 42592/42525, 805255/802816
 
Mapping: {{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
 
Optimal ET sequence: {{Optimal ET sequence| 118, 429d, 547, 665e }}
 
Badness: 0.108400
 
=== Void ===
Subgroup: 2.3.5.7.11
 
Comma list: 4375/4374, 496125/495616, 806736/805255
 
Mapping: {{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
 
Optimal ET sequence: {{Optimal ET sequence| 118, …, 665, 783 }}
 
Badness: 0.082642
 
[[Category:Temperament families]]
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