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


== Vavoom ==
== Vavoom ==
Line 15: Line 15:


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 32: Line 30:


Badness: 0.272586
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 ==
Line 44: Line 57:
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 55: Line 68:
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


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 70: Line 83:
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


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 94:
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
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: {{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
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: {{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]]

Revision as of 23:49, 30 May 2024

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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