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Ragismic microtemperaments: Difference between revisions

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Badness: 0.029812
Badness: 0.029812
== Gamera ==
Subgroup: 2.3.5.7
[[Comma list]]: 4375/4374, 589824/588245
[[Mapping]]: [{{val| 1 6 10 3 }}, {{val| 0 -23 -40 -1 }}]
Mapping generators: ~2, ~8/7
{{Multival|legend=1| 23 40 1 10 -63 -110 }}
[[POTE generator]] ~8/7 = 230.336
{{Val list|legend=1| 26, 73, 99, 224, 323, 422, 745d }}
[[Badness]]: 0.037648
=== Hemigamera ===
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374, 589824/588245
Mapping: [{{val| 2 12 20 6 5 }}, {{val| 0 -23 -40 -1 5 }}]
Mapping generators: ~99/70, ~8/7
POTE generator: ~8/7 = 230.3370
Optimal GPV sequence: {{Val list| 26, 198, 224, 422, 646, 1068d }}
Badness: 0.040955
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 2200/2197, 3025/3024
Mapping: [{{val| 2 12 20 6 5 17 }}, {{val| 0 -23 -40 -1 5 -25 }}]
POTE generator: ~8/7 = 230.3373
Optimal GPV sequence: {{Val list| 26, 198, 224, 422, 646f, 1068df }}
Badness: 0.020416
=== Semigamera ===
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 14641/14580, 15488/15435
Mapping: [{{val| 1 6 10 3 12 }}, {{val| 0 -46 -80 -2 -89 }}]
Mapping generators: ~2, ~77/72
POTE generator: ~77/72 = 115.1642
Optimal GPV sequence: {{Val list| 73, 125, 198, 323, 521 }}
Badness: 0.078
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 4375/4374, 14641/14580
Mapping: [{{val| 1 6 10 3 12 18 }}, {{val| 0 -46 -80 -2 -89 -149 }}]
POTE generator: ~77/72 = 115.1628
Optimal GPV sequence: {{Val list| 73f, 125f, 198, 323, 521 }}
Badness: 0.044


== Supermajor ==
== Supermajor ==
Line 663: Line 590:
Badness: 0.014694
Badness: 0.014694


== Deca ==
== Semidimi ==
Deca temperament has a period of 1/10 octave and tempers out the [[15/14 equal-step tuning|linus comma]], {{monzo| 11 -10 -10 10 }} and {{monzo| 12 -3 -14 9 }} = 165288374272/164794921875 (satritrizo-asepbigu).
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Semidimi]].''
 
The generator of semidimi temperament is a semi-diminished fourth interval tuned between 162/125 and 35/27. It tempers out 5-limit {{monzo|-12 -73 55}} and 7-limit 3955078125/3954653486, as well as 4375/4374.
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 4375/4374, 3955078125/3954653486
 
[[Mapping]]: [{{val|1 36 48 61}}, {{val|0 -55 -73 -93}}]
 
{{Multival|legend=1|55 73 93 -12 -7 11}}
 
[[POTE generator]]: ~35/27 = 449.1270
 
{{Val list|legend=1| 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}
 
[[Badness]]: 0.015075
 
== Brahmagupta ==
The brahmagupta temperament has a period of 1/7 octave, tempering out the [[akjaysma]], {{monzo|47 -7 -7 -7}} = 140737488355328 / 140710042265625.


[[Subgroup]]: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 4375/4374, 165288374272/164794921875
[[Comma list]]: 4375/4374, 70368744177664/70338939985125


[[Mapping]]: [{{val| 10 4 9 2 }}, {{val| 0 5 6 11 }}]
[[Mapping]]: [{{val|7 2 -8 53}}, {{val|0 3 8 -11}}]


{{Multival|legend=1| 50 60 110 -21 34 87 }}
{{Multival|legend=1|21 56 -77 40 -181 -336}}


[[POTE generator]]: ~6/5 = 315.577
[[POTE generator]]: ~27/20 = 519.716


{{Val list|legend=1| 80, 190, 270, 1270, 1540, 1810, 2080 }}
{{Val list|legend=1| 7, 217, 224, 441, 1106, 1547 }}


[[Badness]]: 0.080637
[[Badness]]: 0.029122


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 3025/3024, 4375/4374, 391314/390625
Comma list: 4000/3993, 4375/4374, 131072/130977


Mapping: [{{val| 10 4 9 2 18 }}, {{val| 0 5 6 11 7 }}]
Mapping: [{{val|7 2 -8 53 3}}, {{val|0 3 8 -11 7}}]


POTE generator: ~6/5 = 315.582
POTE generator: ~27/20 = 519.704


Optimal GPV sequence: {{Val list| 80, 190, 270, 1000, 1270, 1540e, 1810e }}
Optimal GPV sequence: {{Val list| 7, 217, 224, 441, 665, 1771ee }}


Badness: 0.024329
Badness: 0.052190


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 1001/1000, 3025/3024, 4225/4224, 4375/4374
Comma list: 1575/1573, 2080/2079, 4096/4095, 4375/4374
 
Mapping: [{{val|7 2 -8 53 3 35}}, {{val|0 3 8 -11 7 -3}}]
 
POTE generator: ~27/20 = 519.706
 
Optimal GPV sequence: {{Val list| 7, 217, 224, 441, 665, 1771eef }}
 
Badness: 0.023132
 
== Abigail ==
Subgroup: 2.3.5.7
 
[[Comma list]]: 4375/4374, 2147483648/2144153025
 
[[Mapping]]: [{{val|2 7 13 -1}}, {{val|0 -11 -24 19}}]
 
{{Multival|legend=1|22 48 -38 25 -122 -223}}
 
[[POTE generator]]: ~6912/6125 = 208.899
 
{{Val list|legend=1| 46, 132, 178, 224, 270, 494, 764, 1034, 1798 }}
 
[[Badness]]: 0.037000
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 4375/4374, 131072/130977
 
Mapping: [{{val|2 7 13 -1 1}}, {{val|0 -11 -24 19 17}}]
 
POTE generator: ~1155/1024 = 208.901
 
Optimal GPV sequence: {{Val list| 46, 132, 178, 224, 270, 494, 764 }}
 
Badness: 0.012860
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Mapping: [{{val| 10 4 9 2 18 37 }}, {{val| 0 5 6 11 7 0 }}]
Comma list: 1716/1715, 2080/2079, 3025/3024, 4096/4095


POTE generator: ~6/5 = 315.602
Mapping: [{{val|2 7 13 -1 1 -2}}, {{val|0 -11 -24 19 17 27}}]


Optimal GPV sequence: {{Val list| 80, 190, 270, 730, 1000 }}
POTE generator: ~44/39 = 208.903


Badness: 0.016810
Optimal GPV sequence: {{Val list| 46, 178, 224, 270, 494, 764, 1258 }}


== Sfourth ==
Badness: 0.008856
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Sfourth]].''


== Gamera ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 4375/4374, 64827/64000
[[Comma list]]: 4375/4374, 589824/588245
 
[[Mapping]]: [{{val| 1 6 10 3 }}, {{val| 0 -23 -40 -1 }}]


[[Mapping]]: [{{val|1 2 3 3}}, {{val|0 -19 -31 -9}}]
Mapping generators: ~2, ~8/7


{{Multival|legend=1|19 31 9 5 -39 -66}}
{{Multival|legend=1| 23 40 1 10 -63 -110 }}


[[POTE generator]]: ~49/48 = 26.287
[[POTE generator]] ~8/7 = 230.336


{{Val list|legend=1| 45, 46, 91, 137d }}
{{Val list|legend=1| 26, 73, 99, 224, 323, 422, 745d }}


[[Badness]]: 0.123291
[[Badness]]: 0.037648


=== 11-limit ===
=== Hemigamera ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 121/120, 441/440, 4375/4374
Comma list: 3025/3024, 4375/4374, 589824/588245
 
Mapping: [{{val| 2 12 20 6 5 }}, {{val| 0 -23 -40 -1 5 }}]


Mapping: [{{val|1 2 3 3 4}}, {{val|0 -19 -31 -9 -25}}]
Mapping generators: ~99/70, ~8/7


POTE generator: ~49/48 = 26.286
POTE generator: ~8/7 = 230.3370


Optimal GPV sequence: {{Val list| 45e, 46, 91e, 137de }}
Optimal GPV sequence: {{Val list| 26, 198, 224, 422, 646, 1068d }}


Badness: 0.054098
Badness: 0.040955


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 121/120, 169/168, 325/324, 441/440
Comma list: 1716/1715, 2080/2079, 2200/2197, 3025/3024


Mapping: [{{val|1 2 3 3 4 4}}, {{val|0 -19 -31 -9 -25 -14}}]
Mapping: [{{val| 2 12 20 6 5 17 }}, {{val| 0 -23 -40 -1 5 -25 }}]


POTE generator: ~49/48 = 26.310
POTE generator: ~8/7 = 230.3373


Optimal GPV sequence: {{Val list| 45ef, 46, 91ef, 137def }}
Optimal GPV sequence: {{Val list| 26, 198, 224, 422, 646f, 1068df }}


Badness: 0.033067
Badness: 0.020416


=== Sfour ===
=== Semigamera ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 385/384, 2401/2376, 4375/4374
Comma list: 4375/4374, 14641/14580, 15488/15435
 
Mapping: [{{val| 1 6 10 3 12 }}, {{val| 0 -46 -80 -2 -89 }}]


Mapping: [{{val|1 2 3 3 3}}, {{val|0 -19 -31 -9 21}}]
Mapping generators: ~2, ~77/72


POTE generator: ~49/48 = 26.246
POTE generator: ~77/72 = 115.1642


Optimal GPV sequence: {{Val list| 45, 46, 91, 137d }}
Optimal GPV sequence: {{Val list| 73, 125, 198, 323, 521 }}


Badness: 0.076567
Badness: 0.078


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 196/195, 364/363, 385/384, 4375/4374
Comma list: 676/675, 1001/1000, 4375/4374, 14641/14580
 
Mapping: [{{val| 1 6 10 3 12 18 }}, {{val| 0 -46 -80 -2 -89 -149 }}]


Mapping: [{{val|1 2 3 3 3 3}}, {{val|0 -19 -31 -9 21 32}}]
POTE generator: ~77/72 = 115.1628


POTE generator: ~49/48 = 26.239
Optimal GPV sequence: {{Val list| 73f, 125f, 198, 323, 521 }}


Optimal GPV sequence: {{Val list| 45, 46, 91, 137d }}
Badness: 0.044


Badness: 0.051893
== Deca ==
Deca temperament has a period of 1/10 octave and tempers out the [[15/14 equal-step tuning|linus comma]], {{monzo| 11 -10 -10 10 }} and {{monzo| 12 -3 -14 9 }} = 165288374272/164794921875 (satritrizo-asepbigu).


== Abigail ==
[[Subgroup]]: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 4375/4374, 2147483648/2144153025
[[Comma list]]: 4375/4374, 165288374272/164794921875


[[Mapping]]: [{{val|2 7 13 -1}}, {{val|0 -11 -24 19}}]
[[Mapping]]: [{{val| 10 4 9 2 }}, {{val| 0 5 6 11 }}]


{{Multival|legend=1|22 48 -38 25 -122 -223}}
{{Multival|legend=1| 50 60 110 -21 34 87 }}


[[POTE generator]]: ~6912/6125 = 208.899
[[POTE generator]]: ~6/5 = 315.577


{{Val list|legend=1| 46, 132, 178, 224, 270, 494, 764, 1034, 1798 }}
{{Val list|legend=1| 80, 190, 270, 1270, 1540, 1810, 2080 }}


[[Badness]]: 0.037000
[[Badness]]: 0.080637


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 3025/3024, 4375/4374, 131072/130977
Comma list: 3025/3024, 4375/4374, 391314/390625


Mapping: [{{val|2 7 13 -1 1}}, {{val|0 -11 -24 19 17}}]
Mapping: [{{val| 10 4 9 2 18 }}, {{val| 0 5 6 11 7 }}]


POTE generator: ~1155/1024 = 208.901
POTE generator: ~6/5 = 315.582


Optimal GPV sequence: {{Val list| 46, 132, 178, 224, 270, 494, 764 }}
Optimal GPV sequence: {{Val list| 80, 190, 270, 1000, 1270, 1540e, 1810e }}


Badness: 0.012860
Badness: 0.024329


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 1716/1715, 2080/2079, 3025/3024, 4096/4095
Comma list: 1001/1000, 3025/3024, 4225/4224, 4375/4374
 
Mapping: [{{val| 10 4 9 2 18 37 }}, {{val| 0 5 6 11 7 0 }}]
 
POTE generator: ~6/5 = 315.602
 
Optimal GPV sequence: {{Val list| 80, 190, 270, 730, 1000 }}


Mapping: [{{val|2 7 13 -1 1 -2}}, {{val|0 -11 -24 19 17 27}}]
Badness: 0.016810


POTE generator: ~44/39 = 208.903
== Sfourth ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Sfourth]].''


Optimal GPV sequence: {{Val list| 46, 178, 224, 270, 494, 764, 1258 }}
Subgroup: 2.3.5.7


Badness: 0.008856
[[Comma list]]: 4375/4374, 64827/64000


== Semidimi ==
[[Mapping]]: [{{val|1 2 3 3}}, {{val|0 -19 -31 -9}}]
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Semidimi]].''


The generator of semidimi temperament is a semi-diminished fourth interval tuned between 162/125 and 35/27. It tempers out 5-limit {{monzo|-12 -73 55}} and 7-limit 3955078125/3954653486, as well as 4375/4374.
{{Multival|legend=1|19 31 9 5 -39 -66}}


Subgroup: 2.3.5.7
[[POTE generator]]: ~49/48 = 26.287


[[Comma list]]: 4375/4374, 3955078125/3954653486
{{Val list|legend=1| 45, 46, 91, 137d }}


[[Mapping]]: [{{val|1 36 48 61}}, {{val|0 -55 -73 -93}}]
[[Badness]]: 0.123291


{{Multival|legend=1|55 73 93 -12 -7 11}}
=== 11-limit ===
Subgroup: 2.3.5.7.11


[[POTE generator]]: ~35/27 = 449.1270
Comma list: 121/120, 441/440, 4375/4374


{{Val list|legend=1| 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}
Mapping: [{{val|1 2 3 3 4}}, {{val|0 -19 -31 -9 -25}}]


[[Badness]]: 0.015075
POTE generator: ~49/48 = 26.286


== Brahmagupta ==
Optimal GPV sequence: {{Val list| 45e, 46, 91e, 137de }}
The brahmagupta temperament has a period of 1/7 octave, tempering out the [[akjaysma]], {{monzo|47 -7 -7 -7}} = 140737488355328 / 140710042265625.


Subgroup: 2.3.5.7
Badness: 0.054098


[[Comma list]]: 4375/4374, 70368744177664/70338939985125
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


[[Mapping]]: [{{val|7 2 -8 53}}, {{val|0 3 8 -11}}]
Comma list: 121/120, 169/168, 325/324, 441/440


{{Multival|legend=1|21 56 -77 40 -181 -336}}
Mapping: [{{val|1 2 3 3 4 4}}, {{val|0 -19 -31 -9 -25 -14}}]


[[POTE generator]]: ~27/20 = 519.716
POTE generator: ~49/48 = 26.310


{{Val list|legend=1| 7, 217, 224, 441, 1106, 1547 }}
Optimal GPV sequence: {{Val list| 45ef, 46, 91ef, 137def }}


[[Badness]]: 0.029122
Badness: 0.033067


=== 11-limit ===
=== Sfour ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 4000/3993, 4375/4374, 131072/130977
Comma list: 385/384, 2401/2376, 4375/4374


Mapping: [{{val|7 2 -8 53 3}}, {{val|0 3 8 -11 7}}]
Mapping: [{{val|1 2 3 3 3}}, {{val|0 -19 -31 -9 21}}]


POTE generator: ~27/20 = 519.704
POTE generator: ~49/48 = 26.246


Optimal GPV sequence: {{Val list| 7, 217, 224, 441, 665, 1771ee }}
Optimal GPV sequence: {{Val list| 45, 46, 91, 137d }}


Badness: 0.052190
Badness: 0.076567


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 1575/1573, 2080/2079, 4096/4095, 4375/4374
Comma list: 196/195, 364/363, 385/384, 4375/4374


Mapping: [{{val|7 2 -8 53 3 35}}, {{val|0 3 8 -11 7 -3}}]
Mapping: [{{val|1 2 3 3 3 3}}, {{val|0 -19 -31 -9 21 32}}]


POTE generator: ~27/20 = 519.706
POTE generator: ~49/48 = 26.239


Optimal GPV sequence: {{Val list| 7, 217, 224, 441, 665, 1771eef }}
Optimal GPV sequence: {{Val list| 45, 46, 91, 137d }}


Badness: 0.023132
Badness: 0.051893


== Quasithird ==
== Quasithird ==
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