Dicot family: Difference between revisions

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The [[5-limit]] parent [[comma]] for the dicot family is 25/24, the [[chromatic semitone]]. Its [[monzo]] is {{monzo| -3 -1 2 }}, and flipping that yields {{wedgie| 2 1 -3}} for the [[wedgie]]. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are [[7edo]], [[24edo]] using the val {{val|24 38 55}} (24c) and [[31edo]] using the val {{val|31 49 71}} (31c). In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending, dicot is at the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]].
The [[5-limit]] parent [[comma]] for the dicot family is 25/24, the [[chromatic semitone]]. Its [[monzo]] is {{monzo| -3 -1 2 }}, and flipping that yields {{wedgie| 2 1 -3}} for the [[wedgie]]. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are [[7edo|7EDO]], [[24edo|24EDO]] using the val {{val|24 38 55}} (24c) and [[31edo|31EDO]] using the val {{val|31 49 71}} (31c). In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending, dicot is at the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]].


=== Seven limit children ===
=== Seven limit children ===
Line 5: Line 5:


== Dicot ==
== Dicot ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 15: Line 14:


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[diamond monotone]] range: [300.000, 400.000] (1\4 to 1\3)
* [[Diamond monotone]] range: ~5/4 = [300.000, 400.000] (1\4 to 1\3)
* [[Diamond tradeoff]] range: ~5/4 = [315.641, 386.314]
* Diamond monotone and tradeoff: ~5/4 = [315.641, 386.314]


{{Val list|legend=1| 3, 4, 7, 17, 24c, 31c }}
{{Val list|legend=1| 3, 4, 7, 17, 24c, 31c }}
Line 22: Line 23:


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 15/14, 25/24
[[Comma list]]: 15/14, 25/24
[[POTE generator]]: ~5/4 = 336.381


[[Mapping]]: [{{val|1 1 2 2}}, {{val|0 2 1 3}}]
[[Mapping]]: [{{val|1 1 2 2}}, {{val|0 2 1 3}}]


[[Wedgie]]: {{wedgie|2 1 3 -3 -1 4}}
[[Wedgie]]: {{wedgie|2 1 3 -3 -1 4}}
[[POTE generator]]: ~5/4 = 336.381


{{Val list|legend=1| 3d, 4, 7, 18bc, 25bccd }}
{{Val list|legend=1| 3d, 4, 7, 18bc, 25bccd }}
Line 35: Line 38:


=== 11-limit ===
=== 11-limit ===
[[Comma list]]: 15/14, 22/21, 25/24
Subgroup: 2.3.5.7.11
 
Comma list: 15/14, 22/21, 25/24


[[POTE generator]]: ~5/4 = 342.125
Mapping: [{{val|1 1 2 2 2}}, {{val|0 2 1 3 5}}]


[[Mapping]]: [{{val|1 1 2 2 2}}, {{val|0 2 1 3 5}}]
POTE generator: ~5/4 = 342.125


{{Val list|legend=1| 3de, 4e, 7 }}
Vals: {{Val list| 3de, 4e, 7 }}


Badness: 0.019854
Badness: 0.019854


== Eudicot ==
=== Eudicot ===
[[Comma list]]: 15/14, 25/24, 33/32
Subgroup: 2.3.5.7.11
 
Comma list: 15/14, 25/24, 33/32


[[POTE generator]]: ~5/4 = 336.051
Mapping: [{{val|1 1 2 2 4}}, {{val|0 2 1 3 -2}}]


[[Mapping]]: [{{val|1 1 2 2 4}}, {{val|0 2 1 3 -2}}]
POTE generator: ~5/4 = 336.051


{{Val list|legend=1| 3d, 4, 7, 18bc, 25bccd }}
Vals: {{Val list| 3d, 4, 7, 18bc, 25bccd }}


Badness: 0.027114
Badness: 0.027114


=== 13-limit ===
==== 13-limit ====
[[Comma list]]: 15/14, 25/24, 33/32, 40/39
Subgroup: 2.3.5.7.11.13
 
Comma list: 15/14, 25/24, 33/32, 40/39


[[POTE generator]]: ~5/4 = 338.846
Mapping: [{{val|1 1 2 2 4 4}}, {{val|0 2 1 3 -2 -1}}]


[[Mapping]]: [{{val|1 1 2 2 4 4}}, {{val|0 2 1 3 -2 -1}}]
POTE generator: ~5/4 = 338.846


{{Val list|legend=1| 3d, 4, 7, 25bccd, 32bccddef, 39bcccdddef }}
Vals: {{Val list| 3d, 4, 7, 25bccd, 32bccddef, 39bcccdddef }}


Badness: 0.023828
Badness: 0.023828


== Flat ==
== Flat ==
Subgroup: 2.3.5.7
[[Comma list]]: 21/20, 25/24
[[Comma list]]: 21/20, 25/24


[[POTE tuning|POTE generator]]: ~5/4 = 331.916
[[Mapping]]: [{{val|1 1 2 3}}, {{val|0 2 1 -1}}]


[[Map]]: [{{val|1 1 2 3}}, {{val|0 2 1 -1}}]
{{Multival|legend=1|2 1 -1 -3 -7 -5}}


Wedgie: {{wedgie|2 1 -1 -3 -7 -5}}
[[POTE generator]]: ~5/4 = 331.916


{{Vals|legend=1| 3, 4, 7d, 11cd, 18bcddd }}
{{Val list|legend=1| 3, 4, 7d, 11cd, 18bcddd }}


[[Badness]]: 0.025381
[[Badness]]: 0.025381


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 21/20, 25/24, 33/32
Comma list: 21/20, 25/24, 33/32
Mapping: [{{val|1 1 2 3 4}}, {{val|0 2 1 -1 -2}}]


POTE generator: ~5/4 = 337.532
POTE generator: ~5/4 = 337.532


Map: [{{val|1 1 2 3 4}}, {{val|0 2 1 -1 -2}}]
Vals: {{Val list| 3, 4, 7d }}
 
Vals: {{Vals| 3, 4, 7d }}


Badness: 0.024988
Badness: 0.024988


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 14/13, 21/20, 25/24, 33/32
Comma list: 14/13, 21/20, 25/24, 33/32
Mapping: [{{val|1 1 2 3 4 4}}, {{val|0 2 1 -1 -2 -1}}]


POTE generator: ~5/4 = 341.023
POTE generator: ~5/4 = 341.023


Map: [{{val|1 1 2 3 4 4}}, {{val|0 2 1 -1 -2 -1}}]
Vals: {{Val list| 3, 4, 7d }}
 
Vals: {{Vals| 3, 4, 7d }}


Badness: 0.023420
Badness: 0.023420


== Sharp ==
== Sharp ==
Subgroup: 2.3.5.7
[[Comma list]]: 25/24, 28/27
[[Comma list]]: 25/24, 28/27


[[POTE tuning|POTE generator]]: ~5/4 = 357.938
[[Mapping]]: [{{val|1 1 2 1}}, {{val|0 2 1 6}}]


[[Map]]: [{{val|1 1 2 1}}, {{val|0 2 1 6}}]
[[POTE generator]]: ~5/4 = 357.938


Wedgie: {{wedgie|2 1 6 -3 4 11}}
{{Multival|legend=1|2 1 6 -3 4 11}}


{{Vals|legend=1| 3d, 7d, 10, 37cd, 47bccd, 57bccdd }}
{{Val list|legend=1| 3d, 7d, 10, 37cd, 47bccd, 57bccdd }}


[[Badness]]: 0.028942
[[Badness]]: 0.028942


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 25/24, 28/27, 35/33
Comma list: 25/24, 28/27, 35/33
Mapping: [{{val|1 1 2 1 2}}, {{val|0 2 1 6 5}}]


POTE generator: ~5/4 = 356.106
POTE generator: ~5/4 = 356.106


Map: [{{val|1 1 2 1 2}}, {{val|0 2 1 6 5}}]
Vals: {{Val list| 3de, 7d, 10, 17d, 27cde }}
 
Vals: {{Vals| 3de, 7d, 10, 17d, 27cde }}


Badness: 0.022366
Badness: 0.022366


== Decimal ==
== Decimal ==
Subgroup: 2.3.5.7
[[Comma list]]: 25/24, 49/48
[[Comma list]]: 25/24, 49/48


[[POTE tuning|POTE generator]]: ~7/6 = 251.557
[[Mapping]]: [{{val|2 0 3 4}}, {{val|0 2 1 1}}]


[[Map]]: [{{val|2 0 3 4}}, {{val|0 2 1 1}}]
{{Multival|legend=1|4 2 2 -6 -8 -1}}


Wedgie: {{wedgie|4 2 2 -6 -8 -1}}
[[POTE generator]]: ~7/6 = 251.557


{{Vals|legend=1| 4, 10, 14c, 24c, 38ccd, 62cccdd }}
{{Val list|legend=1| 4, 10, 14c, 24c, 38ccd, 62cccdd }}


[[Badness]]: 0.028334
[[Badness]]: 0.028334


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 25/24, 45/44, 49/48
Comma list: 25/24, 45/44, 49/48
Mapping: [{{val|2 0 3 4 -1}}, {{val|0 2 1 1 5}}]


POTE generator: ~7/6 = 253.493
POTE generator: ~7/6 = 253.493


Map: [{{val|2 0 3 4 -1}}, {{val|0 2 1 1 5}}]
Vals: {{Val list| 10, 14c, 24c, 38ccd, 52cccde }}
 
Vals: {{Vals| 10, 14c, 24c, 38ccd, 52cccde }}


Badness: 0.026712
Badness: 0.026712


=== Decimated ===
=== Decimated ===
Subgroup: 2.3.5.7.11
Comma list: 25/24, 33/32, 49/48
Comma list: 25/24, 33/32, 49/48
Mapping: [{{val|2 0 3 4 10}}, {{val|0 2 1 1 -2}}]


POTE generator: ~7/6 = 255.066
POTE generator: ~7/6 = 255.066


Map: [{{val|2 0 3 4 10}}, {{val|0 2 1 1 -2}}]
Vals: {{Val list| 4, 10e, 14c }}
 
Vals: {{Vals| 4, 10e, 14c }}


Badness: 0.031456
Badness: 0.031456


=== Decibel ===
=== Decibel ===
Subgroup: 2.3.5.7.11
Comma list: 25/24, 35/33, 49/48
Comma list: 25/24, 35/33, 49/48
Mapping: [{{val|2 0 3 4 7}}, {{val|0 2 1 1 0}}]


POTE generator: ~8/7 = 243.493
POTE generator: ~8/7 = 243.493


Map: [{{val|2 0 3 4 7}}, {{val|0 2 1 1 0}}]
Vals: {{Val list| 4, 6, 10 }}
 
Vals: {{Vals| 4, 6, 10 }}


Badness: 0.032385
Badness: 0.032385


== Dichotic ==
== Dichotic ==
Subgroup: 2.3.5.7
[[Comma list]]: 25/24, 64/63
[[Comma list]]: 25/24, 64/63


[[POTE tuning|POTE generator]]: ~5/4 = 356.264
[[Mapping]]: [{{val|1 1 2 4}}, {{val|0 2 1 -4}}]


[[Map]]: [{{val|1 1 2 4}}, {{val|0 2 1 -4}}]
{{Multival|legend=1|2 1 -4 -3 -12 -12}}


Wedgie: {{wedgie|2 1 -4 -3 -12 -12}}
[[POTE generator]]: ~5/4 = 356.264


{{Vals|legend=1| 3, 7, 10, 17, 27c, 37c, 64bccc }}
{{Val list|legend=1| 3, 7, 10, 17, 27c, 37c, 64bccc }}


[[Badness]]: 0.037565
[[Badness]]: 0.037565


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 25/24, 45/44, 64/63
Comma list: 25/24, 45/44, 64/63
Mapping: [{{val|1 1 2 4 2}}, {{val|0 2 1 -4 5}}]


POTE generator: ~5/4 = 354.262
POTE generator: ~5/4 = 354.262


Map: [{{val|1 1 2 4 2}}, {{val|0 2 1 -4 5}}]
Vals: {{Val list| 7, 10, 17, 27ce, 44cce }}
 
Vals: {{Vals| 7, 10, 17, 27ce, 44cce }}


Badness: 0.030680
Badness: 0.030680


=== Dichosis ===
=== Dichosis ===
Subgroup: 2.3.5.7.11
Comma list: 25/24, 35/33, 64/63
Comma list: 25/24, 35/33, 64/63
Mapping: [{{val|1 1 2 4 5}}, {{val|0 2 1 -4 -5}}]


POTE generator: ~5/4 = 360.659
POTE generator: ~5/4 = 360.659


Map: [{{val|1 1 2 4 5}}, {{val|0 2 1 -4 -5}}]
Vals: {{Val list| 3, 7e, 10 }}
 
Vals: {{Vals| 3, 7e, 10 }}


Badness: 0.041361
Badness: 0.041361


== Jamesbond ==
== Jamesbond ==
Subgroup: 2.3.5.7
[[Comma list]]: 25/24, 81/80
[[Comma list]]: 25/24, 81/80


[[POTE tuning|POTE generator]]: ~8/7 = 258.139
[[Mapping]]: [{{val|7 11 16 0}}, {{val|0 0 0 1}}]


[[Map]]: [{{val|7 11 16 0}}, {{val|0 0 0 1}}]
{{Multival|legend=1|0 0 7 0 11 16}}


Wedgie: {{wedgie|0 0 7 0 11 16}}
[[POTE generator]]: ~8/7 = 258.139


{{Vals|legend=1| 7, 14c }}
{{Val list|legend=1| 7, 14c }}


[[Badness]]: 0.041714
[[Badness]]: 0.041714


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 25/24, 33/32, 45/44
Comma list: 25/24, 33/32, 45/44
Mapping: [{{val|7 11 16 0 24}}, {{val|0 0 0 1 0}}]


POTE generator: ~8/7 = 258.910
POTE generator: ~8/7 = 258.910


Map: [{{val|7 11 16 0 24}}, {{val|0 0 0 1 0}}]
Vals: {{Val list| 7, 14c }}
 
Vals: {{Vals| 7, 14c }}


Badness: 0.023524
Badness: 0.023524


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 25/24, 27/26, 33/32, 40/39
Comma list: 25/24, 27/26, 33/32, 40/39
Mapping: [{{val|7 11 16 0 24 26}}, {{val|0 0 0 1 0 0}}]


POTE generator: ~8/7 = 250.764
POTE generator: ~8/7 = 250.764


Map: [{{val|7 11 16 0 24 26}}, {{val|0 0 0 1 0 0}}]
Vals: {{Val list| 7, 14c }}
 
Vals: {{Vals| 7, 14c }}


Badness: 0.023003
Badness: 0.023003


=== Septimal ===
=== Septimal ===
Subgroup: 2.3.5.7.11.13
Comma list: 25/24, 33/32, 45/44, 65/63
Comma list: 25/24, 33/32, 45/44, 65/63
Mapping: [{{val|7 11 16 0 24 6}}, {{val|0 0 0 1 0 1}}]


POTE generator: ~8/7 = 247.445
POTE generator: ~8/7 = 247.445


Map: [{{val|7 11 16 0 24 6}}, {{val|0 0 0 1 0 1}}]
Vals: {{Val list| 7, 14cf }}
 
Vals: {{Vals| 7, 14cf }}


Badness: 0.022569
Badness: 0.022569


== Sidi ==
== Sidi ==
Subgroup: 2.3.5.7
[[Comma list]]: 25/24, 245/243
[[Comma list]]: 25/24, 245/243


[[POTE tuning|POTE generator]]: ~9/7 = 427.208
[[Mapping]]: [{{val|1 3 3 6}}, {{val|0 -4 -2 -9}}]


[[Map]]: [{{val|1 3 3 6}}, {{val|0 -4 -2 -9}}]
{{Multival|legend=1|4 2 9 -12 3 15}}


Wedgie: {{wedgie|4 2 9 -12 3 15}}
[[POTE generator]]: ~9/7 = 427.208


{{Vals|legend=1| 3d, 14c, 45cc, 59bcccd }}
{{Val list|legend=1| 3d, 14c, 45cc, 59bcccd }}


[[Badness]]: 0.056586
[[Badness]]: 0.056586


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 25/24, 45/44, 99/98
Comma list: 25/24, 45/44, 99/98
Mapping: [{{val|1 3 3 6 7}}, {{val|0 -4 -2 -9 -10}}]


POTE generator: ~9/7 = 427.273
POTE generator: ~9/7 = 427.273


Map: [{{val|1 3 3 6 7}}, {{val|0 -4 -2 -9 -10}}]
Vals: {{Val list| 3de, 14c, 45cce, 59bcccdee }}
 
Vals: {{Vals| 3de, 14c, 17, 45cce, 59bcccdee }}


Badness: 0.032957
Badness: 0.032957


== Quad ==
== Quad ==
Subgroup: 2.3.5.7
[[Comma list]]: 9/8, 25/24
[[Comma list]]: 9/8, 25/24


[[POTE tuning|POTE generator]]: ~8/7 = 324.482
[[Mapping]]: [{{val|4 6 9 0}}, {{val|0 0 0 1}}]


[[Map]]: [{{val|4 6 9 0}}, {{val|0 0 0 1}}]
{{Multival|legend=1|0 0 4 0 6 9}}


Wedgie: {{wedgie|0 0 4 0 6 9}}
[[POTE generator]]: ~8/7 = 324.482


{{Vals|legend=1| 4 }}
{{Val list|legend=1| 4 }}


[[Badness]]: 0.045911
[[Badness]]: 0.045911

Revision as of 09:56, 6 June 2021

The 5-limit parent comma for the dicot family is 25/24, the chromatic semitone. Its monzo is [-3 -1 2⟩, and flipping that yields ⟨⟨2 1 -3]] for the wedgie. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are 7EDO, 24EDO using the val ⟨24 38 55] (24c) and 31EDO using the val ⟨31 49 71] (31c). In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending, dicot is at the edge of what can sensibly be called a temperament at all. In other words, it is an exotemperament.

Seven limit children

The second comma of the normal comma list defines which 7-limit family member we are looking at. Septimal dicot, with wedgie ⟨⟨2 1 3 -3 -1 4]] adds 36/35, sharp with wedgie ⟨⟨2 1 6 -3 4 11]] adds 28/27, and dichotic with wedgie ⟨⟨2 1 -4 -3 -12 -12]] ads 64/63, all retaining the same period and generator. Decimal with wedgie ⟨⟨4 2 2 -6 -8 -1]] adds 49/48, sidi with wedgie ⟨⟨4 2 9 -3 6 15]] adds 245/243, and jamesbond with wedgie ⟨⟨0 0 7 0 11 16]] adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.

Dicot

Subgroup: 2.3.5

Comma list: 25/24

Mapping: [⟨1 1 2], ⟨0 2 1]]

POTE generator: ~5/4 = 348.594

Tuning ranges:

  • Diamond monotone range: ~5/4 = [300.000, 400.000] (1\4 to 1\3)
  • Diamond tradeoff range: ~5/4 = [315.641, 386.314]
  • Diamond monotone and tradeoff: ~5/4 = [315.641, 386.314]

Template:Val list

Badness: 0.013028

7-limit

Subgroup: 2.3.5.7

Comma list: 15/14, 25/24

Mapping: [⟨1 1 2 2], ⟨0 2 1 3]]

Wedgie: ⟨⟨2 1 3 -3 -1 4]]

POTE generator: ~5/4 = 336.381

Template:Val list

Badness: 0.019935

11-limit

Subgroup: 2.3.5.7.11

Comma list: 15/14, 22/21, 25/24

Mapping: [⟨1 1 2 2 2], ⟨0 2 1 3 5]]

POTE generator: ~5/4 = 342.125

Vals: Template:Val list

Badness: 0.019854

Eudicot

Subgroup: 2.3.5.7.11

Comma list: 15/14, 25/24, 33/32

Mapping: [⟨1 1 2 2 4], ⟨0 2 1 3 -2]]

POTE generator: ~5/4 = 336.051

Vals: Template:Val list

Badness: 0.027114

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 15/14, 25/24, 33/32, 40/39

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

POTE generator: ~5/4 = 338.846

Vals: Template:Val list

Badness: 0.023828

Flat

Subgroup: 2.3.5.7

Comma list: 21/20, 25/24

Mapping: [⟨1 1 2 3], ⟨0 2 1 -1]]

Wedgie: ⟨⟨ 2 1 -1 -3 -7 -5 ]]

POTE generator: ~5/4 = 331.916

Template:Val list

Badness: 0.025381

11-limit

Subgroup: 2.3.5.7.11

Comma list: 21/20, 25/24, 33/32

Mapping: [⟨1 1 2 3 4], ⟨0 2 1 -1 -2]]

POTE generator: ~5/4 = 337.532

Vals: Template:Val list

Badness: 0.024988

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 14/13, 21/20, 25/24, 33/32

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

POTE generator: ~5/4 = 341.023

Vals: Template:Val list

Badness: 0.023420

Sharp

Subgroup: 2.3.5.7

Comma list: 25/24, 28/27

Mapping: [⟨1 1 2 1], ⟨0 2 1 6]]

POTE generator: ~5/4 = 357.938

Wedgie: ⟨⟨ 2 1 6 -3 4 11 ]]

Template:Val list

Badness: 0.028942

11-limit

Subgroup: 2.3.5.7.11

Comma list: 25/24, 28/27, 35/33

Mapping: [⟨1 1 2 1 2], ⟨0 2 1 6 5]]

POTE generator: ~5/4 = 356.106

Vals: Template:Val list

Badness: 0.022366

Decimal

Subgroup: 2.3.5.7

Comma list: 25/24, 49/48

Mapping: [⟨2 0 3 4], ⟨0 2 1 1]]

Wedgie: ⟨⟨ 4 2 2 -6 -8 -1 ]]

POTE generator: ~7/6 = 251.557

Template:Val list

Badness: 0.028334

11-limit

Subgroup: 2.3.5.7.11

Comma list: 25/24, 45/44, 49/48

Mapping: [⟨2 0 3 4 -1], ⟨0 2 1 1 5]]

POTE generator: ~7/6 = 253.493

Vals: Template:Val list

Badness: 0.026712

Decimated

Subgroup: 2.3.5.7.11

Comma list: 25/24, 33/32, 49/48

Mapping: [⟨2 0 3 4 10], ⟨0 2 1 1 -2]]

POTE generator: ~7/6 = 255.066

Vals: Template:Val list

Badness: 0.031456

Decibel

Subgroup: 2.3.5.7.11

Comma list: 25/24, 35/33, 49/48

Mapping: [⟨2 0 3 4 7], ⟨0 2 1 1 0]]

POTE generator: ~8/7 = 243.493

Vals: Template:Val list

Badness: 0.032385

Dichotic

Subgroup: 2.3.5.7

Comma list: 25/24, 64/63

Mapping: [⟨1 1 2 4], ⟨0 2 1 -4]]

Wedgie: ⟨⟨ 2 1 -4 -3 -12 -12 ]]

POTE generator: ~5/4 = 356.264

Template:Val list

Badness: 0.037565

11-limit

Subgroup: 2.3.5.7.11

Comma list: 25/24, 45/44, 64/63

Mapping: [⟨1 1 2 4 2], ⟨0 2 1 -4 5]]

POTE generator: ~5/4 = 354.262

Vals: Template:Val list

Badness: 0.030680

Dichosis

Subgroup: 2.3.5.7.11

Comma list: 25/24, 35/33, 64/63

Mapping: [⟨1 1 2 4 5], ⟨0 2 1 -4 -5]]

POTE generator: ~5/4 = 360.659

Vals: Template:Val list

Badness: 0.041361

Jamesbond

Subgroup: 2.3.5.7

Comma list: 25/24, 81/80

Mapping: [⟨7 11 16 0], ⟨0 0 0 1]]

Wedgie: ⟨⟨ 0 0 7 0 11 16 ]]

POTE generator: ~8/7 = 258.139

Template:Val list

Badness: 0.041714

11-limit

Subgroup: 2.3.5.7.11

Comma list: 25/24, 33/32, 45/44

Mapping: [⟨7 11 16 0 24], ⟨0 0 0 1 0]]

POTE generator: ~8/7 = 258.910

Vals: Template:Val list

Badness: 0.023524

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 25/24, 27/26, 33/32, 40/39

Mapping: [⟨7 11 16 0 24 26], ⟨0 0 0 1 0 0]]

POTE generator: ~8/7 = 250.764

Vals: Template:Val list

Badness: 0.023003

Septimal

Subgroup: 2.3.5.7.11.13

Comma list: 25/24, 33/32, 45/44, 65/63

Mapping: [⟨7 11 16 0 24 6], ⟨0 0 0 1 0 1]]

POTE generator: ~8/7 = 247.445

Vals: Template:Val list

Badness: 0.022569

Sidi

Subgroup: 2.3.5.7

Comma list: 25/24, 245/243

Mapping: [⟨1 3 3 6], ⟨0 -4 -2 -9]]

Wedgie: ⟨⟨ 4 2 9 -12 3 15 ]]

POTE generator: ~9/7 = 427.208

Template:Val list

Badness: 0.056586

11-limit

Subgroup: 2.3.5.7.11

Comma list: 25/24, 45/44, 99/98

Mapping: [⟨1 3 3 6 7], ⟨0 -4 -2 -9 -10]]

POTE generator: ~9/7 = 427.273

Vals: Template:Val list

Badness: 0.032957

Quad

Subgroup: 2.3.5.7

Comma list: 9/8, 25/24

Mapping: [⟨4 6 9 0], ⟨0 0 0 1]]

Wedgie: ⟨⟨ 0 0 4 0 6 9 ]]

POTE generator: ~8/7 = 324.482

Template:Val list

Badness: 0.045911

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