Misty family: Difference between revisions

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__FORCETOC__
The '''misty family''' tempers out the [[misty comma]], 67108864/66430125 = {{monzo| 26 -12 -3 }}.
The '''misty family''' tempers out the [[misty comma]], 67108864/66430125 = {{monzo|26 -12 -3}}.


= Misty =
= Misty =
Comma: 67108864/66430125 = {{monzo|26 -12 -3}}
Subgroup: 2.3.5


POTE generator: ~3/2 = 703.111
[[Comma list]]: 67108864/66430125


Map: [<3 0 26|, <0 1 -4|]
[[Mapping]]: [{{val| 3 0 26 }}, {{val| 0 1 -4 }}]


EDOs: {{EDOs|12, 51, 63, 75, 87, 99, 285, 384}}
[[POTE generator]]: ~3/2 = 703.111


Badness: 0.1065
{{Multival|legend=1| 12, 51, 63, 75, 87, 99, 285, 384 }}
 
[[Badness]]: 0.1065


= 7-limit =
= 7-limit =
{{see also|Hemimean clan #Misty}}
{{see also|Hemimean clan #Misty}}


Commas: 3136/3125, 5120/5103
Subgroup: 2.3.5.7


[[POTE_tuning|POTE generator]]: ~3/2 = 703.021
[[Comma list]]: 3136/3125, 5120/5103


Map: [<3 0 26 56|, <0 1 -4 -10|]
[[Mapping]]: [{{val| 3 0 26 56 }}, {{val| 0 1 -4 -10 }}]


Wedgie: <<3 -12 -30 -26 -56 -36||
{{Multival|legend=1| 3 -12 -30 -26 -56 -36 }}


EDOs: {{EDOs|12, 87, 99}}
[[POTE generator]]: ~3/2 = 703.021
 
{{Val list|legend=1| 12, 87, 99 }}
 
[[Badness]]: 0.036802


== 11-limit ==
== 11-limit ==
Commas: 441/440, 3136/3125, 4375/4356
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 3136/3125, 4375/4356
 
Mapping: [{{val| 3 0 26 56 77 }}, {{val| 0 1 -4 -10 -14 }}]


[[POTE_tuning|POTE generator]]: ~3/2 = 703.210
POTE generator: ~3/2 = 703.210


Map: [<3 0 26 56 77|, <0 1 -4 -10 -14|]
Vals: {{Val list| 12, 87, 99e, 186e }}


EDOs: {{EDOs|12, 87, 99e, 186e}}
Badness: 0.035932


=== 13-limit ===
=== 13-limit ===
Commas: 196/195, 352/351, 364/363, 625/624
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 352/351, 364/363, 625/624


[[POTE_tuning|POTE generator]]: ~3/2 = 703.303
Mapping: [{{val| 3 0 26 56 77 92 }}, {{val| 0 1 -4 -10 -14 -17 }}]


Map: [<3 0 26 56 77 92|, <0 1 -4 -10 -14 -17|]
POTE generator: ~3/2 = 703.303


EDOs: {{EDOs|12f, 87, 99ef, 186ef, 273ef}}
Vals: {{Val list| 12f, 87, 99ef, 186ef, 273ef }}
 
Badness: 0.027820


==== 17-limit ====
==== 17-limit ====
Commas: 196/195, 352/351, 364/363, 375/374, 595/594
Subgroup: 2.3.5.7.11.13.17


[[POTE_tuning|POTE generator]]: ~3/2 = 703.233
Comma list: 196/195, 352/351, 364/363, 375/374, 595/594


Map: [<3 0 26 56 77 92 -2|, <0 1 -4 -10 -14 -17 3|]
Mapping: [{{val| 3 0 26 56 77 92 -2 }}, {{val| 0 1 -4 -10 -14 -17 3 }}]


EDOs: {{EDOs|12f, 87, 99ef, 186efg}}
POTE generator: ~3/2 = 703.233
 
Vals: {{Val list| 12f, 87, 99ef, 186efg }}
 
Badness: 0.023908


==== 19-limit ====
==== 19-limit ====
Commas: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594
Subgroup: 2.3.5.7.11.13.17.19


[[POTE_tuning|POTE generator]]: ~3/2 = 703.253
Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594


Map: [<3 0 26 56 77 92 -2 8|, <0 1 -4 -10 -14 -17 3 1|]
Mapping: [{{val| 3 0 26 56 77 92 -2 8 }}, {{val| 0 1 -4 -10 -14 -17 3 1 }}]


EDOs: {{EDOs|12f, 87, 99ef, 186efgh}}
POTE generator: ~3/2 = 703.253
 
Vals: {{Val list| 12f, 87, 99ef, 186efgh }}
 
Badness: 0.019878


=== Mystic ===
=== Mystic ===
Commas: 325/324, 441/440, 896/891, 1001/1000
Subgroup: 2.3.5.7.11.13


[[POTE_tuning|POTE generator]]: ~3/2 = 703.311
Comma list: 325/324, 441/440, 896/891, 1001/1000


Map: [<3 0 26 56 77 -46|, <0 1 -4 -10 -14 12|]
Mapping: [{{val| 3 0 26 56 77 -46 }}, {{val| 0 1 -4 -10 -14 12 }}]


EDOs: {{EDOs|12, 87, 186e, 273e}}
POTE generator: ~3/2 = 703.311
 
Vals: {{Val list| 12, 87, 186e, 273e }}
 
Badness: 0.036872


== Hemimist ==
== Hemimist ==
Commas: 3136/3125, 5120/5103, 3025/3024
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 3136/3125, 5120/5103
 
Mapping: [{{val| 3 0 26 56 8 }}, {{val| 0 2 -8 -20 1 }}]


POTE generator: ~11/8 = 551.527
POTE generator: ~11/8 = 551.527


Map: [<3 0 26 56 8|, <0 2 -8 -20 1|]
Vals: {{Val list| 24d, 87, 111, 198 }}


EDOs: {{EDOs|24d, 87, 111, 198}}
Badness: 0.047439


Badness: 0.0474
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 676/675, 847/845, 3025/3024


=== 13-limit ===
Mapping: [{{val| 3 0 26 56 8 23 }}, {{val| 0 2 -8 -20 1 -5 }}]
Commas: 352/351, 676/675, 847/845, 3025/3024


POTE generator: ~11/8 = 551.525
POTE generator: ~11/8 = 551.525


Map: [<3 0 26 56 8 23|, <0 2 -8 -20 1 -5|]
Vals: {{Val list| 24d, 87, 111, 198 }}
 
EDOs: {{EDOs|24d, 87, 111, 198}}


Badness: 0.0229
Badness: 0.022923


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Misty]]
[[Category:Misty]]
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 16:18, 28 April 2021

The misty family tempers out the misty comma, 67108864/66430125 = [26 -12 -3⟩.

Misty

Subgroup: 2.3.5

Comma list: 67108864/66430125

Mapping: [⟨3 0 26], ⟨0 1 -4]]

POTE generator: ~3/2 = 703.111

Wedgie: ⟨⟨ 12, 51, 63, 75, 87, 99, 285, 384 ]]

Badness: 0.1065

7-limit

See also: Hemimean clan § Misty

Subgroup: 2.3.5.7

Comma list: 3136/3125, 5120/5103

Mapping: [⟨3 0 26 56], ⟨0 1 -4 -10]]

Wedgie: ⟨⟨ 3 -12 -30 -26 -56 -36 ]]

POTE generator: ~3/2 = 703.021

Template:Val list

Badness: 0.036802

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 3136/3125, 4375/4356

Mapping: [⟨3 0 26 56 77], ⟨0 1 -4 -10 -14]]

POTE generator: ~3/2 = 703.210

Vals: Template:Val list

Badness: 0.035932

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 364/363, 625/624

Mapping: [⟨3 0 26 56 77 92], ⟨0 1 -4 -10 -14 -17]]

POTE generator: ~3/2 = 703.303

Vals: Template:Val list

Badness: 0.027820

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 196/195, 352/351, 364/363, 375/374, 595/594

Mapping: [⟨3 0 26 56 77 92 -2], ⟨0 1 -4 -10 -14 -17 3]]

POTE generator: ~3/2 = 703.233

Vals: Template:Val list

Badness: 0.023908

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594

Mapping: [⟨3 0 26 56 77 92 -2 8], ⟨0 1 -4 -10 -14 -17 3 1]]

POTE generator: ~3/2 = 703.253

Vals: Template:Val list

Badness: 0.019878

Mystic

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 441/440, 896/891, 1001/1000

Mapping: [⟨3 0 26 56 77 -46], ⟨0 1 -4 -10 -14 12]]

POTE generator: ~3/2 = 703.311

Vals: Template:Val list

Badness: 0.036872

Hemimist

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 3136/3125, 5120/5103

Mapping: [⟨3 0 26 56 8], ⟨0 2 -8 -20 1]]

POTE generator: ~11/8 = 551.527

Vals: Template:Val list

Badness: 0.047439

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 676/675, 847/845, 3025/3024

Mapping: [⟨3 0 26 56 8 23], ⟨0 2 -8 -20 1 -5]]

POTE generator: ~11/8 = 551.525

Vals: Template:Val list

Badness: 0.022923

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