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Vavoom family: Difference between revisions

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The '''vavoom family''' includes [[temperaments]] that [[tempering out|temper out]] the [[vavoom comma]], ({{monzo| -68 18 17 }}).
{{Technical data page}}
The '''vavoom family''' includes [[temperaments]] that [[tempering out|temper out]] the [[vavoom comma]], {{monzo| -68 18 17 }}.


== Vavoom ==
== Vavoom ==
Line 8: 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


{{Todo|inline=1|review|comment=For all below temperaments: Normalize the comma lists. Work out the optimal ET sequences and badnesses. }}
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 ==
== Doubloon ==
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


Mapping: {{mapping| 1 0 4 7 | 0 17 -18 -45 }}
Mapping: {{mapping| 1 0 4 7 | 0 17 -18 -45 }}


: mapping generators: ~2, ~16/15
: Mapping generators: ~2, ~16/15
 
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8391


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8391
Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 118, 279, 397d }}


Recommended ETs: {{EDOs|118, 161}}
Badness: 0.173974


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


Comma list: [[441/440]], [[3136/3125]], [[5632/5625]], [[35937/35840]], [[43923/43750]], [[43923/43904]]
Comma list: 441/440, 3136/3125, 35937/35840


Mapping: {{mapping| 1 0 4 7 7 | 0 17 -18 -45 -38 }}
Mapping: {{mapping| 1 0 4 7 7 | 0 17 -18 -45 -38 }}


: mapping generators: ~2, ~16/15
: Mapping generators: ~2, ~16/15
 
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8368


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8563
Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 118, 279, 397d }}


Recommended ETs: {{EDOs|43, 118}}
Badness: 0.049755


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
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]]
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: {{mapping| 1 0 4 7 7 1 | 0 17 -18 -45 -38 29 }}


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


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


Recommended ETs: {{EDOs|118, 161}}
Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 118, 161, 279f }}
 
Badness: 0.042899


== 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


Mapping: {{mapping| 1 0 4 -4 | 0 17 -18 73 }}
Mapping: {{mapping| 1 0 4 -4 | 0 17 -18 73 }}


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


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8782
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8950


Recommended ETs: {{EDOs|118, 311}}
Optimal ET sequence: {{Optimal ET sequence| 75, 118, 193, 311 }}
 
Badness: 0.124539


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


Comma list: [[3025/3024]], [[12005/11979]], [[19712/19683]], [[42875/42768]], [[65625/65536]], [[200704/200475]]
Comma list: 3025/3024, 12005/11979, 19712/19683


Mapping: {{mapping| 1 0 4 -4 -4 | 0 17 -18 73 80 }}
Mapping: {{mapping| 1 0 4 -4 -4 | 0 17 -18 73 80 }}


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


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8930
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8930


Recommended ETs: {{EDOs|75, 118}}
Optimal ET sequence: {{Optimal ET sequence| 75e, 118, 193, 311 }}
 
Badness: 0.038829


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
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]]
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: {{mapping| 1 0 4 -4 -4 12 | 0 17 -18 73 80 -89 }}


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


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


Recommended ETs: {{EDOs|118, 311}}
Optimal ET sequence: {{Optimal ET sequence| 118, 193, 311 }}
 
Badness: 0.036509


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


Comma list: [[4375/4374]], [-68, 18, 17, 0⟩, [-69, 11, 21, 1⟩, [-67, 25, 13, -1⟩
Comma list: 4375/4374, [-68 18 17⟩


Mapping: {{mapping| 1 0 4 -15 | 0 17 -18 191 }}
Mapping: {{mapping| 1 0 4 -15 | 0 17 -18 191 }}


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


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8950
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8782


Recommended ETs: {{EDOs|118, 665}}
Optimal ET sequence: {{Optimal ET sequence| 118, 429d, 547, 665, 783, 1448, 2231, 3679 }}
 
Badness: 0.092961


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


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


Mapping: {{mapping| 1 0 4 -15 -4 | 0 17 -18 191 80 }}
Mapping: {{mapping| 1 0 4 -15 -4 | 0 17 -18 191 80 }}


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


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


Recommended ETs: {{EDOs|118, 547}}
Optimal ET sequence: {{Optimal ET sequence| 118, 429d, 547, 665e }}
 
Badness: 0.108400


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


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


Mapping: {{mapping| 1 0 4 -15 -15 | 0 17 -18 191 198 }}
Mapping: {{mapping| 1 0 4 -15 -15 | 0 17 -18 191 198 }}


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


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8770
Optimal ET sequence: {{Optimal ET sequence| 118, …, 665, 783 }}


Recommended ETs: {{EDOs|118, 665}}
Badness: 0.082642


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
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