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 6: Line 7:
Comma list: {{monzo| -68 18 17 }}
Comma list: {{monzo| -68 18 17 }}


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


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


Badness: 0.098376
Badness: 0.098376
{{Todo|inline=1|review|comment=For all below temperaments: Normalize the comma lists. Work out the optimal ET sequences and badnesses. }}


== Raccoon ==
== Raccoon ==
Line 23: Line 22:
Comma list: 225/224, 41943040/40353607
Comma list: 225/224, 41943040/40353607


Mapping: {{mapping| 1 0 4 3 | 0 17 -18 -2 }}
{{Mapping|legend=0| 1 0 4 3 | 0 17 -18 -2 }}


: Mapping generators: ~2, ~16/15
: Mapping generators: ~2, ~16/15
Line 32: Line 31:


Badness: 0.272586
Badness: 0.272586
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 225/224, 1344/1331, 2420/2401
{{Mapping|legend=0| 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 ==
Line 38: Line 52:
Comma list: 3136/3125, 33756345/33554432
Comma list: 3136/3125, 33756345/33554432


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


: Mapping generators: ~2, ~16/15
: Mapping generators: ~2, ~16/15
Line 44: Line 58:
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 }}
Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 118, 279, 397d }}


Badness: 0.173974
Badness: 0.173974
Line 53: Line 67:
Comma list: 441/440, 3136/3125, 35937/35840
Comma list: 441/440, 3136/3125, 35937/35840


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


Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 118 }}
Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 118, 279, 397d }}


Badness: 0.049755
Badness: 0.049755
Line 68: Line 82:
Comma list: 441/440, 1001/1000, 1188/1183, 3136/3125
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|legend=0| 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


Optimal ET sequence: {{Optimal ET sequence| 118, 161 }}
Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 118, 161, 279f }}


Badness: 0.042899
Badness: 0.042899
Line 81: Line 95:
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|legend=0| 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|legend=0| 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
Optimal ET sequence: {{Optimal ET sequence| 75e, 118, 193, 311 }}


Recommended ETs: {{EDOs|75, 118}}
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|legend=0| 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|legend=0| 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|legend=0| 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
Optimal ET sequence: {{Optimal ET sequence| 118, 429d, 547, 665e }}


Recommended ETs: {{EDOs|118, 547}}
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|legend=0| 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]]

Latest revision as of 12:32, 24 September 2026

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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