Vavoom family: Difference between revisions

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


== Raccoon ==
Subgroup: 2.3.5.7


Comma list: 225/224, 41943040/40353607


{{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 | 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


== 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 }}


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 }}
Line 42: Line 57:
: 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 = 111.8563


Recommended ETs: {{EDOs|43, 118}}
Optimal ET sequence: {{Optimal ET sequence| 43, 75d, 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 }}
Line 55: Line 72:
: 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 }}


Recommended ETs: {{EDOs|118, 161}}
Badness: 0.042899


== Kaboom ==
== Kaboom ==

Revision as of 22:28, 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

Todo: review

For all below temperaments: Normalize the comma lists. Work out the optimal ET sequences and badnesses.

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

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

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 = 111.8563

Optimal ET sequence: 43, 75d, 118

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: 118, 161

Badness: 0.042899

Kaboom

Subgroup: 2.3.5.7

Comma list: 65625/65536, 4802000/4782969, 359661568/358722675, 6565234375/6530347008

Mapping: [⟨1 0 4 -4], ⟨0 17 -18 73]]

mapping generators: ~2, ~16/15

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

Recommended ETs: 118, 311

11-limit

Subgroup: 2.3.5.7.11

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

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

Recommended ETs: 75, 118

13-limit

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

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

Recommended ETs: 118, 311

Vacuum

Subgroup: 2.3.5.7

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

Mapping: [⟨1 0 4 -15], ⟨0 17 -18 191]]

mapping generators: ~2, ~16/15

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

Recommended ETs: 118, 665

Vortex

Subgroup: 2.3.5.7.11

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

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

Recommended ETs: 118, 547

Void

Subgroup: 2.3.5.7.11

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

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

Recommended ETs: 118, 665

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