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Ragismic microtemperaments: Difference between revisions

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== Deca ==
== Orga ==
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).
Subgroup: 2.3.5.7


[[Subgroup]]: 2.3.5.7
[[Comma list]]: 4375/4374, 54975581388800/54936068900769


[[Comma list]]: 4375/4374, 165288374272/164794921875
[[Mapping]]: [{{val|2 21 36 5}}, {{val|0 -29 -51 1}}]


[[Mapping]]: [{{val| 10 4 9 2 }}, {{val| 0 5 6 11 }}]
[[Wedgie]]: {{multival|58 102 -2 27 -166 -291}}


{{Multival|legend=1| 50 60 110 -21 34 87 }}
[[POTE generator]]: ~8/7 = 231.104


[[POTE generator]]: ~6/5 = 315.577
{{Val list|legend=1| 26, 244, 270, 836, 1106, 1376, 2482 }}


{{Val list|legend=1| 80, 190, 270, 1270, 1540, 1810, 2080 }}
[[Badness]]: 0.040236
 
[[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, 391314/390625
Comma list: 3025/3024, 4375/4374, 5767168/5764801


Mapping: [{{val| 10 4 9 2 18 }}, {{val| 0 5 6 11 7 }}]
Mapping: [{{val|2 21 36 5 2}}, {{val|0 -29 -51 1 8}}]


POTE generator: ~6/5 = 315.582
POTE generator: ~8/7 = 231.103


Optimal GPV sequence: {{Val list| 80, 190, 270, 1000, 1270, 1540e, 1810e }}
Optimal GPV sequence: {{Val list| 26, 244, 270, 566, 836, 1106 }}


Badness: 0.024329
Badness: 0.016188


=== 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: 1716/1715, 2080/2079, 3025/3024, 15379/15360
 
Mapping: [{{val|2 21 36 5 2 24}}, {{val|0 -29 -51 1 8 -27}}]


Mapping: [{{val| 10 4 9 2 18 37 }}, {{val| 0 5 6 11 7 0 }}]
POTE generator: ~8/7 = 231.103


POTE generator: ~6/5 = 315.602
Optimal GPV sequence: {{Val list| 26, 244, 270, 566, 836f, 1106f }}


Optimal GPV sequence: {{Val list| 80, 190, 270, 730, 1000 }}
Badness: 0.021762


Badness: 0.016810
== Seniority ==
{{see also|Very high accuracy temperaments #Senior}}


== Sfourth ==
Aside from the ragisma, the seniority temperament (26&145) tempers out the wadisma, 201768035/201326592. It is so named because the senior comma ({{monzo|-17 62 -35}}, quadla-sepquingu) is tempered out.
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Sfourth]].''


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 4375/4374, 64827/64000
[[Comma list]]: 4375/4374, 201768035/201326592


[[Mapping]]: [{{val|1 2 3 3}}, {{val|0 -19 -31 -9}}]
[[Mapping]]: [{{val|1 11 19 2}}, {{val|0 -35 -62 3}}]


{{Multival|legend=1|19 31 9 5 -39 -66}}
[[Wedgie]]: {{multival|35 62 -3 17 -103 -181}}


[[POTE generator]]: ~49/48 = 26.287
[[POTE generator]]: ~3087/2560 = 322.804


{{Val list|legend=1| 45, 46, 91, 137d }}
{{Val list|legend=1| 26, 145, 171, 1513d, 1684d, 1855d, 2026d, 2197d, 2368d, 2539d, 2710d }}


[[Badness]]: 0.123291
[[Badness]]: 0.044877


=== 11-limit ===
=== Senator ===
Subgroup: 2.3.5.7.11
The senator temperament (26&145) is an 11-limit extension of the seniority, which tempers out 441/440 and 65536/65219. It can be extended to the 13- and 17-limit immediately, by adding 364/363 and 595/594 to the comma list in this order.
 
Comma list: 121/120, 441/440, 4375/4374
 
Mapping: [{{val|1 2 3 3 4}}, {{val|0 -19 -31 -9 -25}}]
 
POTE generator: ~49/48 = 26.286


Optimal GPV sequence: {{Val list| 45e, 46, 91e, 137de }}
Badness: 0.054098
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 169/168, 325/324, 441/440
Mapping: [{{val|1 2 3 3 4 4}}, {{val|0 -19 -31 -9 -25 -14}}]
POTE generator: ~49/48 = 26.310
Optimal GPV sequence: {{Val list| 45ef, 46, 91ef, 137def }}
Badness: 0.033067
=== Sfour ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 385/384, 2401/2376, 4375/4374
Comma list: 441/440, 4375/4374, 65536/65219


Mapping: [{{val|1 2 3 3 3}}, {{val|0 -19 -31 -9 21}}]
Mapping: [{{val|1 11 19 2 4}}, {{val|0 -35 -62 3 -2}}]


POTE generator: ~49/48 = 26.246
POTE generator: ~77/64 = 322.793


Optimal GPV sequence: {{Val list| 45, 46, 91, 137d }}
Optimal GPV sequence: {{Val list| 26, 119c, 145, 171, 316e, 487ee }}


Badness: 0.076567
Badness: 0.092238


==== 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: 364/363, 441/440, 2200/2197, 4375/4374


Mapping: [{{val|1 2 3 3 3 3}}, {{val|0 -19 -31 -9 21 32}}]
Mapping: [{{val|1 11 19 2 4 15}}, {{val|0 -35 -62 3 -2 -42}}]


POTE generator: ~49/48 = 26.239
POTE generator: ~77/64 = 322.793


Optimal GPV sequence: {{Val list| 45, 46, 91, 137d }}
Optimal GPV sequence: {{Val list| 26, 119c, 145, 171, 316ef, 487eef }}


Badness: 0.051893
Badness: 0.044662


== Quasithird ==
==== 17-limit ====
The '''quasithird''' temperament is featured by a major third interval which is 1600000/1594323 ([[amity comma]]) or 5120/5103 ([[5120/5103|hemifamity comma]]) below the just major third [[5/4]] as a generator, five of which give a fifth with octave reduction. This temperament has a period of a quarter octave, which allows to temper out the [[4375/4374|ragisma]] and {{monzo|-60 29 0 5}}.
Subgroup: 2.3.5.7.11.13.17


Subgroup: 2.3.5
Comma list: 364/363, 441/440, 595/594, 1156/1155, 2200/2197


[[Comma]]: {{monzo| 55 -64 20 }}
Mapping: [{{val|1 11 19 2 4 15 17}}, {{val|0 -35 -62 3 -2 -42 -48}}]


[[Mapping]]: [{{val| 4 0 -11 }}, {{val| 0 5 16 }}]
POTE generator: ~77/64 = 322.793


Mapping generators: ~51200000/43046721, ~1594323/1280000
Optimal GPV sequence: {{Val list| 26, 119c, 145, 171, 316ef, 487eef }}


[[POTE generator]]: ~1594323/1280000 = 380.395
Badness: 0.026562


{{Val list|legend=1| 60, 104c, 164, 224, 388, 612, 1612, 2224, 2836, 6284, 9120, 15404 }}
== Monzismic ==
{{See also| Very high accuracy temperaments #Monzismic }}


[[Badness]]: 0.099519
The ''monzismic'' temperament (53&612) tempers out the [[monzisma]], {{monzo| 54 -37 2 }}, and in the 7-limit, the [[nanisma]], {{monzo| 109 -67 0 -1 }}, as well as the ragisma, [[4375/4374]].  


=== 7-limit ===
[[Subgroup]]: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 4375/4374, 1153470752371588581/1152921504606846976
[[Comma list]]: 4375/4374, {{monzo| -55 30 2 1 }}


[[Mapping]]: [{{val| 4 0 -11 48 }}, {{val| 0 5 16 -29 }}]
[[Mapping]]: [{{val| 1 2 10 -25 }}, {{val| 0 -2 -37 134 }}]


{{Multival|legend=1| 20 64 -116 55 -240 -449 }}
{{Multival|legend=1| 2 37 -134 54 -218 -415 }}


[[POTE generator]]: ~5103/4096 = 380.388
[[Optimal tuning]] ([[POTE]]): ~{{monzo| -27 11 3 1 }} = 249.0207


{{Val list|legend=1| 60d, 164, 224, 388, 612, 1448, 2060 }}
{{Val list|legend=1| 53, …, 559, 612, 1277, 1889 }}


[[Badness]]: 0.061813
[[Badness]]: 0.046569


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


Comma list: 3025/3024, 4375/4374, 4296700485/4294967296
Comma list: 4375/4374, 41503/41472, 184549376/184528125


Mapping: [{{val| 4 0 -11 48 43 }}, {{val| 0 5 16 -29 -23 }}]
Mapping: [{{val| 1 2 10 -25 46 }}, {{val| 0 -2 -37 134 -205 }}]


POTE generator: ~5103/4096 = 380.387 (or ~22/21 = 80.387)
Optimal tuning (POTE): ~231/200 = 249.0193


Optimal GPV sequence: {{Val list| 60d, 164, 224, 388, 612, 836, 1448 }}
Optimal GPV sequence: {{Val list| 53, 559, 612 }}


Badness: 0.021125
Badness: 0.057083


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


Comma list: 2200/2197, 3025/3024, 4096/4095, 4375/4374
Comma list: 2200/2197, 4096/4095, 4375/4374, 40656/40625


Mapping: [{{val| 4 0 -11 48 43 11 }}, {{val| 0 5 16 -29 -23 3 }}]
Mapping: [{{val| 1 2 10 -25 46 23 }}, {{val| 0 -2 -37 134 -205 -93 }}]


POTE generator: ~81/65 = 380.385 (or ~22/21 = 80.385)
Optimal tuning (POTE): ~231/200 = 249.0199


Optimal GPV sequence: {{Val list| 60d, 164, 224, 388, 612, 836, 1448f, 2284f }}
Optimal GPV sequence: {{Val list| 53, 559, 612 }}


Badness: 0.029501
Badness: 0.053780


== Semidimfourth ==
== Semidimfourth ==
Line 1,048: Line 1,024:
Badness: 0.026028
Badness: 0.026028


== Seniority ==
== Quasithird ==
{{see also|Very high accuracy temperaments #Senior}}
The '''quasithird''' temperament is featured by a major third interval which is 1600000/1594323 ([[amity comma]]) or 5120/5103 ([[5120/5103|hemifamity comma]]) below the just major third [[5/4]] as a generator, five of which give a fifth with octave reduction. This temperament has a period of a quarter octave, which allows to temper out the [[4375/4374|ragisma]] and {{monzo|-60 29 0 5}}.
 
Subgroup: 2.3.5
 
[[Comma]]: {{monzo| 55 -64 20 }}
 
[[Mapping]]: [{{val| 4 0 -11 }}, {{val| 0 5 16 }}]
 
Mapping generators: ~51200000/43046721, ~1594323/1280000
 
[[POTE generator]]: ~1594323/1280000 = 380.395
 
{{Val list|legend=1| 60, 104c, 164, 224, 388, 612, 1612, 2224, 2836, 6284, 9120, 15404 }}


Aside from the ragisma, the seniority temperament (26&145) tempers out the wadisma, 201768035/201326592. It is so named because the senior comma ({{monzo|-17 62 -35}}, quadla-sepquingu) is tempered out.
[[Badness]]: 0.099519


=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 4375/4374, 201768035/201326592
[[Comma list]]: 4375/4374, 1153470752371588581/1152921504606846976


[[Mapping]]: [{{val|1 11 19 2}}, {{val|0 -35 -62 3}}]
[[Mapping]]: [{{val| 4 0 -11 48 }}, {{val| 0 5 16 -29 }}]


[[Wedgie]]: {{multival|35 62 -3 17 -103 -181}}
{{Multival|legend=1| 20 64 -116 55 -240 -449 }}


[[POTE generator]]: ~3087/2560 = 322.804
[[POTE generator]]: ~5103/4096 = 380.388


{{Val list|legend=1| 26, 145, 171, 1513d, 1684d, 1855d, 2026d, 2197d, 2368d, 2539d, 2710d }}
{{Val list|legend=1| 60d, 164, 224, 388, 612, 1448, 2060 }}


[[Badness]]: 0.044877
[[Badness]]: 0.061813
 
=== Senator ===
The senator temperament (26&145) is an 11-limit extension of the seniority, which tempers out 441/440 and 65536/65219. It can be extended to the 13- and 17-limit immediately, by adding 364/363 and 595/594 to the comma list in this order.


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


Comma list: 441/440, 4375/4374, 65536/65219
Comma list: 3025/3024, 4375/4374, 4296700485/4294967296


Mapping: [{{val|1 11 19 2 4}}, {{val|0 -35 -62 3 -2}}]
Mapping: [{{val| 4 0 -11 48 43 }}, {{val| 0 5 16 -29 -23 }}]


POTE generator: ~77/64 = 322.793
POTE generator: ~5103/4096 = 380.387 (or ~22/21 = 80.387)


Optimal GPV sequence: {{Val list| 26, 119c, 145, 171, 316e, 487ee }}
Optimal GPV sequence: {{Val list| 60d, 164, 224, 388, 612, 836, 1448 }}


Badness: 0.092238
Badness: 0.021125


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


Comma list: 364/363, 441/440, 2200/2197, 4375/4374
Comma list: 2200/2197, 3025/3024, 4096/4095, 4375/4374
 
Mapping: [{{val| 4 0 -11 48 43 11 }}, {{val| 0 5 16 -29 -23 3 }}]
 
POTE generator: ~81/65 = 380.385 (or ~22/21 = 80.385)
 
Optimal GPV sequence: {{Val list| 60d, 164, 224, 388, 612, 836, 1448f, 2284f }}


Mapping: [{{val|1 11 19 2 4 15}}, {{val|0 -35 -62 3 -2 -42}}]
Badness: 0.029501


POTE generator: ~77/64 = 322.793
== Chlorine ==
The name of chlorine temperament comes from Chlorine, the 17th element.


Optimal GPV sequence: {{Val list| 26, 119c, 145, 171, 316ef, 487eef }}
Chlorine temperament has a period of 1/17 octave. It tempers out the septendecima, {{monzo|-52 -17 34}}, by which 17 chromatic semitones (25/24) exceed an octave. This temperament can be described as 289&323 temperament, which tempers out {{monzo|-49 4 22 -3}} as well as the ragisma. Not only the semitwelfth, but also the ~5/4 can be used as a generator.


Badness: 0.044662
Subgroup: 2.3.5


==== 17-limit ====
[[Comma]]: {{monzo| -52 -17 34 }}
Subgroup: 2.3.5.7.11.13.17


Comma list: 364/363, 441/440, 595/594, 1156/1155, 2200/2197
[[Mapping]]: [{{val| 17 0 26 }}, {{val| 0 2 1 }}]


Mapping: [{{val|1 11 19 2 4 15 17}}, {{val|0 -35 -62 3 -2 -42 -48}}]
Mapping generators: ~25/24, ~{{monzo| 26 9 -17 }}


POTE generator: ~77/64 = 322.793
[[POTE generator]]: ~{{monzo| 26 9 -17 }} = 950.9746


Optimal GPV sequence: {{Val list| 26, 119c, 145, 171, 316ef, 487eef }}
{{Val list|legend=1| 34, 153, 187, 221, 255, 289, 323, 612, 3349, 3961, 4573, 5185, 5797 }}


Badness: 0.026562
[[Badness]]: 0.077072


== Orga ==
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 4375/4374, 54975581388800/54936068900769
[[Comma list]]: 4375/4374, 193119049072265625/193091834023510016
 
[[Mapping]]: [{{val| 17 0 26 -87 }}, {{val| 0 2 1 10 }}]
 
{{Multival|legend=1| 34 17 170 -52 174 347 }}
 
[[POTE generator]]: ~822083584/474609375 = 950.9995
 
{{Val list|legend=1| 289, 323, 612, 935, 1547 }}
 
[[Badness]]: 0.041658
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 4375/4374, 41503/41472, 1879453125/1879048192
 
Mapping: [{{val| 17 0 26 -87 207 }}, {{val| 0 2 1 10 -11 }}]
 
POTE generators: ~822083584/474609375 = 950.9749
 
Optimal GPV sequence: {{Val list| 289, 323, 612 }}
 
Badness: 0.063706
 
== 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).
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 4375/4374, 165288374272/164794921875


[[Mapping]]: [{{val|2 21 36 5}}, {{val|0 -29 -51 1}}]
[[Mapping]]: [{{val| 10 4 9 2 }}, {{val| 0 5 6 11 }}]


[[Wedgie]]: {{multival|58 102 -2 27 -166 -291}}
{{Multival|legend=1| 50 60 110 -21 34 87 }}


[[POTE generator]]: ~8/7 = 231.104
[[POTE generator]]: ~6/5 = 315.577


{{Val list|legend=1| 26, 244, 270, 836, 1106, 1376, 2482 }}
{{Val list|legend=1| 80, 190, 270, 1270, 1540, 1810, 2080 }}


[[Badness]]: 0.040236
[[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, 5767168/5764801
Comma list: 3025/3024, 4375/4374, 391314/390625


Mapping: [{{val|2 21 36 5 2}}, {{val|0 -29 -51 1 8}}]
Mapping: [{{val| 10 4 9 2 18 }}, {{val| 0 5 6 11 7 }}]


POTE generator: ~8/7 = 231.103
POTE generator: ~6/5 = 315.582


Optimal GPV sequence: {{Val list| 26, 244, 270, 566, 836, 1106 }}
Optimal GPV sequence: {{Val list| 80, 190, 270, 1000, 1270, 1540e, 1810e }}


Badness: 0.016188
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, 15379/15360
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 }}
 
Badness: 0.016810
 
== Sfourth ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Sfourth]].''
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 4375/4374, 64827/64000
 
[[Mapping]]: [{{val|1 2 3 3}}, {{val|0 -19 -31 -9}}]
 
{{Multival|legend=1|19 31 9 5 -39 -66}}
 
[[POTE generator]]: ~49/48 = 26.287
 
{{Val list|legend=1| 45, 46, 91, 137d }}
 
[[Badness]]: 0.123291
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 441/440, 4375/4374
 
Mapping: [{{val|1 2 3 3 4}}, {{val|0 -19 -31 -9 -25}}]
 
POTE generator: ~49/48 = 26.286
 
Optimal GPV sequence: {{Val list| 45e, 46, 91e, 137de }}
 
Badness: 0.054098
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 121/120, 169/168, 325/324, 441/440
 
Mapping: [{{val|1 2 3 3 4 4}}, {{val|0 -19 -31 -9 -25 -14}}]
 
POTE generator: ~49/48 = 26.310
 
Optimal GPV sequence: {{Val list| 45ef, 46, 91ef, 137def }}
 
Badness: 0.033067
 
=== Sfour ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 2401/2376, 4375/4374
 
Mapping: [{{val|1 2 3 3 3}}, {{val|0 -19 -31 -9 21}}]
 
POTE generator: ~49/48 = 26.246
 
Optimal GPV sequence: {{Val list| 45, 46, 91, 137d }}
 
Badness: 0.076567
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 364/363, 385/384, 4375/4374


Mapping: [{{val|2 21 36 5 2 24}}, {{val|0 -29 -51 1 8 -27}}]
Mapping: [{{val|1 2 3 3 3 3}}, {{val|0 -19 -31 -9 21 32}}]


POTE generator: ~8/7 = 231.103
POTE generator: ~49/48 = 26.239


Optimal GPV sequence: {{Val list| 26, 244, 270, 566, 836f, 1106f }}
Optimal GPV sequence: {{Val list| 45, 46, 91, 137d }}


Badness: 0.021762
Badness: 0.051893


== Quatracot ==
== Quatracot ==
Line 1,920: Line 2,012:


Badness: 0.052366
Badness: 0.052366
== Chlorine ==
The name of chlorine temperament comes from Chlorine, the 17th element.
Chlorine temperament has a period of 1/17 octave. It tempers out the septendecima, {{monzo|-52 -17 34}}, by which 17 chromatic semitones (25/24) exceed an octave. This temperament can be described as 289&323 temperament, which tempers out {{monzo|-49 4 22 -3}} as well as the ragisma. Not only the semitwelfth, but also the ~5/4 can be used as a generator.
Subgroup: 2.3.5
[[Comma]]: {{monzo| -52 -17 34 }}
[[Mapping]]: [{{val| 17 0 26 }}, {{val| 0 2 1 }}]
Mapping generators: ~25/24, ~{{monzo| 26 9 -17 }}
[[POTE generator]]: ~{{monzo| 26 9 -17 }} = 950.9746
{{Val list|legend=1| 34, 153, 187, 221, 255, 289, 323, 612, 3349, 3961, 4573, 5185, 5797 }}
[[Badness]]: 0.077072
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 4375/4374, 193119049072265625/193091834023510016
[[Mapping]]: [{{val| 17 0 26 -87 }}, {{val| 0 2 1 10 }}]
{{Multival|legend=1| 34 17 170 -52 174 347 }}
[[POTE generator]]: ~822083584/474609375 = 950.9995
{{Val list|legend=1| 289, 323, 612, 935, 1547 }}
[[Badness]]: 0.041658
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 41503/41472, 1879453125/1879048192
Mapping: [{{val| 17 0 26 -87 207 }}, {{val| 0 2 1 10 -11 }}]
POTE generators: ~822083584/474609375 = 950.9749
Optimal GPV sequence: {{Val list| 289, 323, 612 }}
Badness: 0.063706


== Palladium ==
== Palladium ==
Line 2,023: Line 2,068:


Badness: 0.022441
Badness: 0.022441
== Monzismic ==
{{See also| Very high accuracy temperaments #Monzismic }}
The ''monzismic'' temperament (53&612) tempers out the [[monzisma]], {{monzo| 54 -37 2 }}, and in the 7-limit, the [[nanisma]], {{monzo| 109 -67 0 -1 }}, as well as the ragisma, [[4375/4374]].
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 4375/4374, {{monzo| -55 30 2 1 }}
[[Mapping]]: [{{val| 1 2 10 -25 }}, {{val| 0 -2 -37 134 }}]
{{Multival|legend=1| 2 37 -134 54 -218 -415 }}
[[Optimal tuning]] ([[POTE]]): ~{{monzo| -27 11 3 1 }} = 249.0207
{{Val list|legend=1| 53, …, 559, 612, 1277, 1889 }}
[[Badness]]: 0.046569
=== Monzism ===
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 41503/41472, 184549376/184528125
Mapping: [{{val| 1 2 10 -25 46 }}, {{val| 0 -2 -37 134 -205 }}]
Optimal tuning (POTE): ~231/200 = 249.0193
Optimal GPV sequence: {{Val list| 53, 559, 612 }}
Badness: 0.057083
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 2200/2197, 4096/4095, 4375/4374, 40656/40625
Mapping: [{{val| 1 2 10 -25 46 23 }}, {{val| 0 -2 -37 134 -205 -93 }}]
Optimal tuning (POTE): ~231/200 = 249.0199
Optimal GPV sequence: {{Val list| 53, 559, 612 }}
Badness: 0.053780


== Keenanose ==
== Keenanose ==
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