Trienstonic clan: Difference between revisions

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{{see also| Father family #Father }}
{{see also| Father family #Father }}


Commas: 16/15, 28/27
Comma list: 16/15, 28/27


7-limit minimax
[[POTE generator]]: ~3/2 = 742.002


[<1 0 0 0|, <3/2 0 -1/4 1/4|, <5/2 0 1/4 -1/4|, <5/2 0 -3/4 3/4|]
Mapping: [{{val| 1 0 4 -2 }}, {{val| 0 1 -1 3 }}]


[[Eigenmonzo subgroup]]: 2.7/5
Wedgie: {{wedgie| 1 -1 3 -4 2 10 }}


9-limit eigenmonzo subgroup: 2.9/5
Minimax tuning:
* 7-odd-limit
: [{{monzo| 1 0 0 0 }}, {{monzo| 3/2 0 -1/4 1/4 }}, {{monzo| 5/2 0 1/4 -1/4 }}, {{monzo| 5/2 0 -3/4 3/4 }}]
: [[Eigenmonzo subgroup]]: 2.7/5
* 9-odd-limit
: Eigenmonzo subgroup: 2.9/5


[[POTE generator]]: 742.002
{{Val list|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }}
 
Map: [<1 0 4 -2|, <0 1 -1 3|]
 
Wedgie: <<1 -1 3 -4 2 10||
 
EDOs: 5, 8d, 13cd, 21bcd


Badness: 0.0213
Badness: 0.0213


= Uncle =
= Uncle =
Commas: 28/27, 256/245
Comma list: 28/27, 256/245


7-limit eigenmonzo subgroup: 2.5/3
Mapping: [{{val| 1 0 12 -2 }}, {{val| 0 1 -6 3 }}]


9-limit eigenmonzo subgroup: 2.9/5
Wedgie: {{wedgie| 1 -6 3 -12 2 24 }}


Map: [<1 0 12 -2|, <0 1 -6 3|]
Minimax tuning:  
* 7-odd-limit eigenmonzo subgroup: 2.5/3
* 9-odd-limit eigenmonzo subgroup: 2.9/5


Wedgie: <<1 -6 3 -12 2 24||
{{Val list|legend=1| 13d, 18, 23bc, 41bcd }}
 
EDOs: 13d, 18, 23bc, 41bcd


Badness: 0.0727
Badness: 0.0727


= Octokaidecal =
= Octokaidecal =
Commas: 28/27, 50/49
Comma list: 28/27, 50/49


7-limit eigenmonzo subgroup: 2.5
[[POTE generator]]: ~3/2 = 728.874


9-limit eigenmonzo subgroup: 2.5
Mapping: [{{val| 2 0 -5 -4 }}, {{val| 0 1 3 3 }}]


[[POTE generator]]: 728.874
Wedgie: {{wedgie| 2 6 6 5 4 -2 }}


Map: [<2 0 -5 -4|, <0 1 3 3|]
Minimax tuning:
* 7-odd-limit eigenmonzo subgroup: 2.5
* 9-odd-limit eigenmonzo subgroup: 2.5


Wedgie: <<2 6 6 5 4 -2||
{{Val list|legend=1| 10, 18, 28b }}
 
EDOs: 10, 18, 28b


Badness: 0.0367
Badness: 0.0367


== 11-limit ==
== 11-limit ==
Commas: 28/27, 50/49, 55/54
Comma list: 28/27, 50/49, 55/54


POTE generator: ~3/2 = 732.330
POTE generator: ~3/2 = 732.330


Map: [<2 0 -5 -4 7|, <0 1 3 3 0|]
Mapping: [{{val| 2 0 -5 -4 7 }}, {{val| 0 1 3 3 0 }}]


EDOs: 10, 18e
{{Val list|legend=1| 10, 18e }}


Badness: 0.0302
Badness: 0.0302


= Opossum =
= Opossum =
Commas: 28/27, 126/125
Comma list: 28/27, 126/125


7-limit eigenmonzo subgroup: 2.7
[[POTE generator]]: ~10/9 = 159.691


9-limit eigenmonzo subgroup: 2.7
Mapping: [{{val| 1 2 3 4 }}, {{val| 0 -3 -5 -9 }}]


[[POTE generator]]: ~10/9 = 159.691
Wedgie: {{wedgie| 3 5 9 1 6 7 }}


Map: [<1 2 3 4|, <0 -3 -5 -9|]
Minimax tuning:
* 7-odd-limit eigenmonzo subgroup: 2.7
* 9-odd-limit eigenmonzo subgroup: 2.7


Wedgie: <<3 5 9 1 6 7||
{{Val list|legend=1| 7d, 8d, 15 }}
 
EDOs: 7d, 8d, 15


Badness: 0.0407
Badness: 0.0407


== 11-limit ==
== 11-limit ==
Commas: 28/27, 55/54, 77/75
Comma list: 28/27, 55/54, 77/75


11-limit eigenmonzo subgroup: 2.7
[[POTE generator]]: ~10/9 = 159.807


[[POTE generator]]: ~10/9 = 159.807
Mapping: [{{val| 1 2 3 4 4 }}, {{val| 0 -3 -5 -9 -4 }}]


Map: [<1 2 3 4 4|, <0 -3 -5 -9 -4|]
Minimax tuning: 11-odd-limit eigenmonzo subgroup: 2.7


EDOs: 7d, 8d, 15
{{Val list|legend=1| 7d, 8d, 15 }}


Badness: 0.0223
Badness: 0.0223


== 13-limit ==
== 13-limit ==
Commas: 28/27, 40/39, 55/54, 66/65
Comma list: 28/27, 40/39, 55/54, 66/65


13-limit eigenmonzo subgroup: 2.7
[[POTE generator]]: ~10/9 = 158.805


15-limit eigenmonzo subgroup: 2.7
Mapping: [{{val| 1 2 3 4 4 4 }}, {{val| 0 -3 -5 -9 -4 -2 }}]
 
[[POTE generator]]: ~10/9 = 158.805


Map: [<1 2 3 4 4 4|, <0 -3 -5 -9 -4 -2|]
Minimax tuning:  
* 13-odd-limit eigenmonzo subgroup: 2.7
* 15-odd-limit eigenmonzo subgroup: 2.7


EDOs: 7d, 8d, 15, 38bcef
{{Val list|legend=1| 7d, 8d, 15, 38bcef }}


Badness: 0.0194
Badness: 0.0194


= Wallaby =
= Wallaby =
Commas: 28/27, 35/32
Comma list: 28/27, 35/32


POTE generator: ~3/2 = 691.351
POTE generator: ~3/2 = 691.351


Map: [<1 0 7 -2|, <0 1 -3 3|]
Mapping: [{{val| 1 0 7 -2 }}, {{val| 0 1 -3 3 }}]


Wedgie: <<1 -3 3 -7 2 15||
Wedgie: {{wedgie| 1 -3 3 -7 2 15 }}


EDOs: 2d, 5c, 19ccdd
{{Val list|legend=1| 2d, 5c, 19ccdd }}


Badness: 0.0585
Badness: 0.0585
Line 129: Line 128:
= Kangaroo =
= Kangaroo =
== 5-limit ==
== 5-limit ==
Comma: 64000/59049
Comma list: 64000/59049


POTE generator: ~27/20 = 561.195
POTE generator: ~27/20 = 561.195


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


EDOs: 15, 47b, 62b
{{Val list|legend=1| 15, 47b, 62b }}


Badness: 0.2958
Badness: 0.2958


== 7-limit ==
== 7-limit ==
Commas: 28/27, 1029/1000
Comma list: 28/27, 1029/1000


POTE generator: ~7/5 = 560.328
POTE generator: ~7/5 = 560.328


Map: [<1 0 -3 -2|, <0 3 10 9|]
Mapping: [{{val| 1 0 -3 -2 }}, {{val| 0 3 10 9 }}]


Wedgie: <<3 10 9 9 6 -7||
Wedgie: {{wedgie| 3 10 9 9 6 -7 }}


EDOs: 15
{{Val list|legend=1| 15 }}


Badness: 0.0779
Badness: 0.0779


== 11-limit ==
== 11-limit ==
Commas: 28/27, 77/75, 245/242
Comma list: 28/27, 77/75, 245/242


POTE generator: ~7/5 = 560.155
POTE generator: ~7/5 = 560.155


Map: [<1 0 -3 -2 -4|, <0 3 10 9 14|]
Mapping: [{{val| 1 0 -3 -2 -4 }}, {{val| 0 3 10 9 14 }}]


EDOs: 15
{{Val list|legend=1| 15 }}


Badness: 0.0432
Badness: 0.0432


== 13-limit ==
== 13-limit ==
Commas: 28/27, 40/39, 77/75, 147/143
Comma list: 28/27, 40/39, 77/75, 147/143


POTE generator: ~7/5 = 559.770
POTE generator: ~7/5 = 559.770


Map: [<1 0 -3 -2 -4 0|, <0 3 10 9 14 7|]
Mapping: [{{val| 1 0 -3 -2 -4 0 }}, {{val| 0 3 10 9 14 7 }}]


EDOs: 15
{{Val list|legend=1| 15 }}


Badness: 0.0327
Badness: 0.0327


= Quindecic =
= Quindecic =
Commas: 28/27, 49/48, 55/54, 77/75
Comma list: 28/27, 49/48, 55/54, 77/75


POTE generator: ~13/8 = 852.924
POTE generator: ~13/8 = 852.924


Map: [<15 24 35 42 52 0|, <0 0 0 0 0 1|]
Mapping: [{{val| 15 24 35 42 52 0 }}, {{val| 0 0 0 0 0 1 }}]


EDOs: 15, 30, 45bc
{{Val list|legend=1| 15, 30, 45bc }}


Badness: 0.0289
Badness: 0.0289

Revision as of 17:17, 10 February 2021

The trienstonic clan of temperaments tempers out 28/27, the septimal third-tone or trienstonic comma.

Adding 16/15 to 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharptone, sharp, and blacksmith.

Father

See also: Father family § Father

Comma list: 16/15, 28/27

POTE generator: ~3/2 = 742.002

Mapping: [⟨1 0 4 -2], ⟨0 1 -1 3]]

Wedgie: ⟨⟨1 -1 3 -4 2 10]]

Minimax tuning:

  • 7-odd-limit
[[1 0 0 0⟩, [3/2 0 -1/4 1/4⟩, [5/2 0 1/4 -1/4⟩, [5/2 0 -3/4 3/4⟩]
Eigenmonzo subgroup: 2.7/5
  • 9-odd-limit
Eigenmonzo subgroup: 2.9/5

Template:Val list

Badness: 0.0213

Uncle

Comma list: 28/27, 256/245

Mapping: [⟨1 0 12 -2], ⟨0 1 -6 3]]

Wedgie: ⟨⟨1 -6 3 -12 2 24]]

Minimax tuning:

  • 7-odd-limit eigenmonzo subgroup: 2.5/3
  • 9-odd-limit eigenmonzo subgroup: 2.9/5

Template:Val list

Badness: 0.0727

Octokaidecal

Comma list: 28/27, 50/49

POTE generator: ~3/2 = 728.874

Mapping: [⟨2 0 -5 -4], ⟨0 1 3 3]]

Wedgie: ⟨⟨2 6 6 5 4 -2]]

Minimax tuning:

  • 7-odd-limit eigenmonzo subgroup: 2.5
  • 9-odd-limit eigenmonzo subgroup: 2.5

Template:Val list

Badness: 0.0367

11-limit

Comma list: 28/27, 50/49, 55/54

POTE generator: ~3/2 = 732.330

Mapping: [⟨2 0 -5 -4 7], ⟨0 1 3 3 0]]

Template:Val list

Badness: 0.0302

Opossum

Comma list: 28/27, 126/125

POTE generator: ~10/9 = 159.691

Mapping: [⟨1 2 3 4], ⟨0 -3 -5 -9]]

Wedgie: ⟨⟨3 5 9 1 6 7]]

Minimax tuning:

  • 7-odd-limit eigenmonzo subgroup: 2.7
  • 9-odd-limit eigenmonzo subgroup: 2.7

Template:Val list

Badness: 0.0407

11-limit

Comma list: 28/27, 55/54, 77/75

POTE generator: ~10/9 = 159.807

Mapping: [⟨1 2 3 4 4], ⟨0 -3 -5 -9 -4]]

Minimax tuning: 11-odd-limit eigenmonzo subgroup: 2.7

Template:Val list

Badness: 0.0223

13-limit

Comma list: 28/27, 40/39, 55/54, 66/65

POTE generator: ~10/9 = 158.805

Mapping: [⟨1 2 3 4 4 4], ⟨0 -3 -5 -9 -4 -2]]

Minimax tuning:

  • 13-odd-limit eigenmonzo subgroup: 2.7
  • 15-odd-limit eigenmonzo subgroup: 2.7

Template:Val list

Badness: 0.0194

Wallaby

Comma list: 28/27, 35/32

POTE generator: ~3/2 = 691.351

Mapping: [⟨1 0 7 -2], ⟨0 1 -3 3]]

Wedgie: ⟨⟨1 -3 3 -7 2 15]]

Template:Val list

Badness: 0.0585

Kangaroo

5-limit

Comma list: 64000/59049

POTE generator: ~27/20 = 561.195

Mapping: [⟨1 0 -3], ⟨0 3 10]]

Template:Val list

Badness: 0.2958

7-limit

Comma list: 28/27, 1029/1000

POTE generator: ~7/5 = 560.328

Mapping: [⟨1 0 -3 -2], ⟨0 3 10 9]]

Wedgie: ⟨⟨3 10 9 9 6 -7]]

Template:Val list

Badness: 0.0779

11-limit

Comma list: 28/27, 77/75, 245/242

POTE generator: ~7/5 = 560.155

Mapping: [⟨1 0 -3 -2 -4], ⟨0 3 10 9 14]]

Template:Val list

Badness: 0.0432

13-limit

Comma list: 28/27, 40/39, 77/75, 147/143

POTE generator: ~7/5 = 559.770

Mapping: [⟨1 0 -3 -2 -4 0], ⟨0 3 10 9 14 7]]

Template:Val list

Badness: 0.0327

Quindecic

Comma list: 28/27, 49/48, 55/54, 77/75

POTE generator: ~13/8 = 852.924

Mapping: [⟨15 24 35 42 52 0], ⟨0 0 0 0 0 1]]

Template:Val list

Badness: 0.0289

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