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]]
[[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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