Vavoom family: Difference between revisions

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{{Todo|inline=1|review|comment=Normalize the comma lists. Work out the optimal ET sequences and badnesses. }}
{{Technical data page}}
 
The '''vavoom family''' includes [[temperaments]] that [[tempering out|temper out]] the [[vavoom comma]], {{monzo| -68 18 17 }}.
The '''vavoom family''' includes [[temperaments]] that [[tempering out|temper out]] the vavoom comma ({{monzo| -68 18 17 }}).


== Vavoom ==
== Vavoom ==
Line 10: 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 ==
== 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


Recommended ETs: {{EDOs|118, 161}}
Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 118, 279, 397d }}
 
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 = 111.8563
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8368


Recommended ETs: {{EDOs|43, 118}}
Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 118, 279, 397d }}
 
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
Optimal ET sequence: {{Optimal ET sequence| 118, 193, 311 }}


Recommended ETs: {{EDOs|118, 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 = 111.8782


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.8950
Optimal ET sequence: {{Optimal ET sequence| 118, 429d, 547, 665, 783, 1448, 2231, 3679 }}


Recommended ETs: {{EDOs|118, 665}}
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]]

Latest revision as of 00:37, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

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: 0.098376

Raccoon

Subgroup: 2.3.5.7

Comma list: 225/224, 41943040/40353607

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: 32, 43, 75, 118d

Badness: 0.272586

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 1344/1331, 2420/2401

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: 32, 43, 75e

Badness: 0.095405

Doubloon

Subgroup: 2.3.5.7

Comma list: 3136/3125, 33756345/33554432

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: 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: [⟨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: 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: [⟨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: 43, 75d, 118, 161, 279f

Badness: 0.042899

Kaboom

Subgroup: 2.3.5.7

Comma list: 65625/65536, 4802000/4782969

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: 75, 118, 193, 311

Badness: 0.124539

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 12005/11979, 19712/19683

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: 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: [⟨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: 118, 193, 311

Badness: 0.036509

Vacuum

Subgroup: 2.3.5.7

Comma list: 4375/4374, [-68 18 17⟩

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: 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: [⟨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: 118, 429d, 547, 665e

Badness: 0.108400

Void

Subgroup: 2.3.5.7.11

Comma list: 4375/4374, 496125/495616, 806736/805255

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: 118, …, 665, 783

Badness: 0.082642

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