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This page discusses some of the temperaments tempering out {{monzo|-5 2 2 -1}} = [[225/224]], the [[Marvel_family|marvel]] comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are [[Meantone family #Septimal meantone|meantone]], [[Gamelismic clan #Miracle|miracle]], [[Magic family|magic]], [[Diaschismic family #Pajara|pajara]], [[orwell]], [[Kleismic family #Catakleismic|catakleismic]], [[Schismatic family #Garibaldi|garibaldi]], [[Augmented family #August|august]], [[Pythagorean family #Compton|compton]], [[Dicot family #Sharp|sharp]], [[Escapade family #Escapade|escapade]] and [[Pelogic family #Mavila|mavila]].
{{Technical data page}}
This page discusses miscellaneous [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] [[tempering out]] [[225/224]], the marvel comma or septimal kleisma.  


Since (5/4)<sup>2</sup> = 225/224 × 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.
Temperaments considered in families and clans are:
* ''[[Pelogic]]'' (+21/20 or 135/128) → [[Mavila family #Pelogic|Mavila family]]
* [[Meantone]] (+81/80 or 126/125) → [[Meantone family #Septimal meantone|Meantone family]]
* [[Garibaldi]] (+3125/3087) → [[Schismatic family #Garibaldi|Schismatic family]]
* [[Pajara]] (+50/49 or 64/63) → [[Diaschismic family #Pajara|Diaschismic family]]
* ''[[Sharpie]]'' (+25/24 or 28/27) → [[Dicot family #Sharpie|Dicot family]]
* ''[[Immune]]'' (+781250/750141) → [[Immunity family #Immune|Immunity family]]
* ''[[August]]'' (+36/35 or 128/125) → [[Augmented family #August|Augmented family]]
* ''[[Fog]]'' (+156250/151263) → [[Misty family #Fog|Misty family]]
* [[Bunya]] (+15625/15309) → [[Tetracot family #Bunya|Tetracot family]]
* [[Negri]] (+49/48) → [[Semaphoresmic clan #Negri|Semaphoresmic clan]]
* [[Magic]] (+245/243) → [[Magic family #Magic|Magic family]]
* ''[[Passive]]'' (+256/245) → [[Passion family #Passive|Passion family]]
* ''[[Houborizic]]'' (+1250000/1240029) → [[Amity family #Houborizic|Amity family]]
* ''[[Qintosec]]'' (+2560000/2470629) → [[Quintosec family #Qintosec|Quintosec family]]
* [[Miracle]] (+1029/1024) → [[Gamelismic clan #Miracle|Gamelismic clan]]
* [[Catakleismic]] (+4375/4374) → [[Kleismic family #Catakleismic|Kleismic family]]
* ''[[Marvo]]'' (+78125000/78121827) → [[Gravity family #Marvo|Gravity family]]
* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell|Semicomma family]]
* ''[[Snipes]]'' (+6125/5832)  → [[Wesley family #Snipes|Wesley family]]
* ''[[Demibuzzard]]'' (+65536/64827) → [[Buzzardsmic clan #Demibuzzard|Buzzardsmic clan]]
* ''[[Escapist]]'' (+65625/65536) → [[Escapade family #Escapist|Escapade family]]
* ''[[Amavil]]'' (+17496/16807) → [[Mabila family #Amavil|Mabila family]]
* ''[[Betic]]'' (+1071875/1062882) → [[Sycamore family #Betic|Sycamore family]]
* [[Wizard]] (+118098/117649) → [[Stearnsmic clan #Wizard|Stearnsmic clan]]
* ''[[Raccoon]]'' (+41943040/40353607) → [[Vavoom family #Raccoon|Vavoom family]]
* ''[[Maquila]]'' (+30233088/28824005) → [[Maquila family #Septimal maquila|Maquila family]]
* ''[[Gammy]]'' (+94143178827/91913281250) → [[Gammic family #Gammy|Gammic family]]
* [[Compton]] (+250047/250000) → [[Compton family #Compton|Compton family]]
 
Considered below are tritonic, septimin, merman, slender, triton, marvolo, decic, enneaportent, gracecordial, alphorn, misneb, untriton, naiadical, quintannic, hendeca, gwazy, and tertiosec, in the order of increasing [[badness]].
 
Since {{nowrap|(5/4)<sup>2</sup> {{=}} (225/224)⋅(14/9)}}, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.


The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.
The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.


Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4) = 64/45. Setting this equal to 10/7 gives (10/7)/(64/45) = 225/224.)
Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is {{nowrap|(16/9)/(5/4) {{=}} 64/45}}. Setting this equal to 10/7 gives {{nowrap|(10/7)/(64/45) {{=}} 225/224}}.)
 
== Tritonic ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tritonic]].''
 
Tritonic tempers out [[50421/50000]] and may be described as the {{nowrap| 29 & 31 }} temperament. It splits the [[6/1|6th]] [[harmonic]] into five generators of [[~]][[10/7]] [[tritone]]s, hence the name. Its [[ploidacot]] is beta-pentacot. [[60edo]] may be used as a tuning, which in the 11-limit entails the 60e val.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 50421/50000
 
{{Mapping|legend=1| 1 -1 8 9 | 0 5 -11 -12 }}
: mapping generators: ~2, ~10/7
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.3539{{c}}, ~10/7 = 620.4131{{c}}
: [[error map]]: {{val| +1.354 -1.243 -0.027 -1.598 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 619.6778{{c}}
: error map: {{val| 0.000 -3.566 -2.769 -4.959 }}
 
{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}
 
[[Badness]] (Sintel): 1.20
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 225/224, 441/440
 
{{Mapping|legend=0| 1 -1 8 9 5 | 0 5 -11 -12 -3 }}
 
Optimal tunings:
* WE: ~2 = 1201.7116{{c}}, ~10/7 = 620.6166{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6890{{c}}
 
{{Optimal ET sequence|legend=0| 29, 31, 60e, 91e, 213bcdeee }}
 
Badness (Sintel): 0.782
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 121/120, 196/195, 275/273
 
{{Mapping|legend=0| 1 -1 8 9 5 13 | 0 5 -11 -12 -3 -18 }}
 
Optimal tunings:
* WE: ~2 = 1201.5355{{c}}, ~10/7 = 620.6855{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8469{{c}}
 
{{Optimal ET sequence|legend=0| 29, 31, 60e }}
 
Badness (Sintel): 0.950
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 105/104, 121/120, 154/153, 196/195, 273/272
 
{{Mapping|legend=0| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}
 
Optimal tunings:
* WE: ~2 = 1201.5260{{c}}, ~10/7 = 620.7330{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8986{{c}}
 
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
 
Badness (Sintel): 0.973
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272
 
{{Mapping|legend=0| 1 -1 8 9 5 13 17 12 | 0 5 -11 -12 -3 -18 -25 -15 }}
 
Optimal tunings:
* WE: ~2 = 1201.3100{{c}}, ~10/7 = 620.6509{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9328{{c}}
 
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
 
Badness (Sintel): 1.03
 
==== 23-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23


= Negri =
Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195
{{main| Negri }}


== 5-limit ==
{{Mapping|legend=0| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}
Note that this is technically not a marvel temperament until the 7-limit, but also placed here for reference.


[[Comma list]]: 16875/16384
Optimal tunings:  
* WE: ~2 = 1201.4074{{c}}, ~10/7 = 620.7185{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9548{{c}}


[[POTE generator]]: ~15/14 = 125.7549
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}


[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
Badness (Sintel): 1.04


[[Wedgie]]: {{wedgie| 4 -3 -14 }}
=== Tritoni ===
Subgroup: 2.3.5.7.11


{{Val list|legend=1| 9, 10, 19, 86 }}
Comma list: 225/224, 385/384, 27783/27500


== 7-limit ==
{{Mapping|legend=0| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}
[[Comma list]]: 49/48, 225/224


[[POTE generator]]: ~15/14 = 125.608
Optimal tunings:  
* WE: ~2 = 1201.0888{{c}}, ~10/7 = 620.1733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6146{{c}}


[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}]
{{Optimal ET sequence|legend=0| 31, 91, 122, 153d }}


[[Wedgie]]: {{wedgie| 4 -3 2 -14 -8 13 }}
Badness (Sintel): 1.50


{{Val list|legend=1| 9, 10, 19, 86 }}
== Septimin ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Septimin]].''


== 11-limit ==
Septimin may be described as the {{nowrap| 41 & 50 }} temperament. It is generated by a septimal minor third ([[7/6]]), which gives rise to the name, but the generator can be taken to be the [[octave complement]], [[12/7]], such that eleven of them [[octave reduction|octave reduced]] give the [[3/2|perfect fifth]]; its [[ploidacot]] is thus eta-hendecacot. [[91edo]] may be recommended as a tuning.
Comma list: 45/44, 49/48, 56/55


[[POTE generator]]: ~15/14 = 126.474
[[Subgroup]]: 2.3.5.7


Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]
[[Comma list]]: 225/224, 84035/82944


{{Val list|legend=1| 9, 10, 19 }}
{{Mapping|legend=1| 1 -7 7 -5 | 0 11 -6 10 }}
: mapping generators: ~2, ~12/7


[[Badness]]: 0.0262
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.2452{{c}}, ~12/7 = 937.3394{{c}}
: [[error map]]: {{val| +1.245 +0.062 -1.633 -1.658 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~12/7 = 936.4036{{c}}
: error map: {{val| 0.000 -1.516 -4.735 -4.790 }}
 
{{Optimal ET sequence|legend=1| 9, 23, 32, 41, 91, 132d }}
 
[[Badness]] (Sintel): 1.38
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 245/242, 385/384
 
{{Mapping|legend=0| 1 -7 7 -5 -2 | 0 11 -6 10 7 }}
 
Optimal tunings:
* WE: ~2 = 1200.8059{{c}}, ~12/7 = 936.9952{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3906{{c}}
 
{{Optimal ET sequence|legend=0| 9, 23, 32, 41, 91, 223cdef }}
 
Badness (Sintel): 1.04


=== 13-limit ===
=== 13-limit ===
Comma list: 45/44, 49/48, 56/55, 78/77
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 144/143, 196/195, 245/242
 
{{Mapping|legend=0| 1 -7 7 -5 -2 -8 | 0 11 -6 10 7 15 }}
 
Optimal tunings:
* WE: ~2 = 1200.5990{{c}}, ~12/7 = 936.7670{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3196{{c}}
 
{{Optimal ET sequence|legend=0| 9, 32f, 41, 91 }}
 
Badness (Sintel): 0.955
 
== Merman ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Merman]].''
 
Merman may be described as the {{nowrap| 41 & 43 }} temperament. Like [[#Tritonic|tritonic]], it is generated by a [[~]][[10/7]] [[tritone]], but here, seven generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is gamma-heptacot.
 
The name was likely derived from {{w|Triton (mythology)|''Triton''}}, which was in turn derived from ''tritonic''.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 2500000/2470629
 
{{Mapping|legend=1| 1 -2 10 11 | 0 7 -15 -16 }}
: mapping generators: ~2, ~10/7
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.3898{{c}}, ~10/7 = 614.6413{{c}}
: [[error map]]: {{val| +0.390 -0.435 -1.630 +1.634 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 614.4073{{c}}
: error map: {{val| 0.000 -1.104 -2.423 +0.657 }}
 
{{Optimal ET sequence|legend=1| 41, 84, 125 }}
 
[[Badness]] (Sintel): 1.39
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 441/440, 1344/1331
 
{{Mapping|legend=0| 1 -2 10 11 5 | 0 7 -15 -16 -3 }}
 
Optimal tunings:
* WE: ~2 = 1199.9578{{c}}, ~10/7 = 614.3720{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3943{{c}}
 
{{Optimal ET sequence|legend=0| 41, 84, 125e }}
 
Badness (Sintel): 1.20
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 144/143, 225/224, 364/363, 441/440
 
{{Mapping|legend=0| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}
 
Optimal tunings:
* WE: ~2 = 1199.7422{{c}}, ~10/7 = 614.2110{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3442{{c}}
 
{{Optimal ET sequence|legend=0| 41, 84, 125e, 209ef, 293ef }}
 
Badness (Sintel): 1.14
 
=== Mermaid ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 532400/531441
 
{{Mapping|legend=0| 1 -2 10 11 -16 | 0 7 -15 -16 38 }}
 
Optimal tunings:
* WE: ~2 = 1199.4973{{c}}, ~10/7 = 614.7004{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4470{{c}}
 
{{Optimal ET sequence|legend=0| 41, 84e, 125, 166 }}
 
Badness (Sintel): 1.46
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 325/324, 385/384, 10648/10647
 
{{Mapping|legend=0| 1 -2 10 11 22 32 | 0 7 -15 -16 38 58 }}
 
Optimal tunings:
* WE: ~2 = 1200.5126{{c}}, ~10/7 = 614.7152{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4562{{c}}
 
{{Optimal ET sequence|legend=0| 41, 84ef, 125f, 166 }}
 
Badness (Sintel): 1.47
 
== Slender ==
Slender tempers out the [[hewuermera comma]] in addition to the marvel comma, and may be described as the {{nowrap| 31 & 32 }} temperament. This temperament has a generator of [[49/48]], three of which equal marvel's [[16/15]][[~]][[15/14]], and ten generators give [[5/4]]. Its [[ploidacot]] is omega-13-cot.
 
The name was likely derived from ''slendro diesis'', one of the names for the interval 49/48.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 589824/588245
 
{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
: mapping generators: ~2, ~49/48


[[POTE generator]]: ~14/13 = 126.431
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.3816{{c}}, ~49/48 = 38.4256{{c}}
: [[error map]]: {{val| +0.382 -0.725 -1.295 +1.765 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/48 = 38.4079{{c}}
: error map: {{val| 0.000 -1.257 -2.235 +0.727 }}


Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}]
{{Optimal ET sequence|legend=1| 31, 94, 125, 406c }}


{{Val list|legend=1| 9, 10, 19 }}
[[Badness]] (Sintel): 1.44


== Negril ==
=== 11-limit ===
Comma list: 49/48, 100/99, 225/224
Subgroup: 2.3.5.7.11


POTE generator: ~15/14 = 124.767
Comma list: 225/224, 385/384, 1331/1323


Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]
{{Mapping|legend=0| 1 2 2 3 4 | 0 -13 10 -6 -17 }}


{{Val list|legend=1| 19, 29, 48df, 77cdf }}
Optimal tunings:
* WE: ~2 = 1199.4983{{c}}, ~49/48 = 38.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3775{{c}}


Badness: 0.0387
{{Optimal ET sequence|legend=0| 31, 63, 94, 125 }}
 
Badness (Sintel): 0.838


=== 13-limit ===
=== 13-limit ===
Comma list: 49/48, 65/64, 91/90, 875/858
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 275/273, 385/384, 1331/1323
 
{{Mapping|legend=0| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}
 
Optimal tunings:
* WE: ~2 = 1200.1728{{c}}, ~49/48 = 38.3192{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3129{{c}}
 
{{Optimal ET sequence|legend=0| 31, 63, 94 }}
 
Badness (Sintel): 1.07
 
== Triton ==
: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''
 
Triton may be described as the {{nowrap| 19 & 21 }} temperament. Like [[#Tritonic|tritonic]], it is generated by a [[~]][[10/7]] [[tritone]], but here, three generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is alpha-tricot.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 1029/1000
 
{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}
: mapping generators: ~2, ~10/7
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.3828{{c}}, ~10/7 = 632.9137{{c}}
: [[error map]]: {{val| +3.383 -3.214 +3.587 -8.457 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 630.9827{{c}}
: error map: {{val| 0.000 -9.007 -3.192 -16.687 }}
 
{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
 
[[Badness]] (Sintel): 1.50
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 45/44, 56/55, 1029/1000
 
{{Mapping|legend=0| 1 0 6 7 4 | 0 3 -7 -8 -1 }}
 
Optimal tunings:
* WE: ~2 = 1201.3875{{c}}, ~10/7 = 631.5852{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 630.8007{{c}}
 
{{Optimal ET sequence|legend=0| 2, 17d, 19 }}
 
Badness (Sintel): 1.51
 
== Marvolo ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 156250000/155649627


POTE generator: ~15/14 = 124.716
{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
: mapping generators: ~2, ~21/20


Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.7714{{c}}, ~21/20 = 83.4014{{c}}
: [[error map]]: {{val| +0.772 -0.820 -0.916 +0.381 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 83.3640{{c}}
: error map: {{val| 0.000 -2.139 -2.398 -1.362 }}


{{Val list|legend=1| 9, 10, 19, 29, 48, 77 }}
{{Optimal ET sequence|legend=1| 29, 43, 72, 619bbccd, 691bbccd }}


Badness: 0.0244
[[Badness]] (Sintel): 2.11


== Negric ==
=== 11-limit ===
Comma list: 33/32, 49/48, 77/75
Subgroup: 2.3.5.7.11


POTE generator: ~15/14 = 127.039
Comma list: 225/224, 441/440, 4000/3993


Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}]
{{Mapping|legend=0| 1 2 1 1 2 | 0 -6 19 26 21 }}


{{Val list|legend=1| 9, 19, 85 }}
Optimal tunings:
* WE: ~2 = 1200.7075{{c}}, ~21/20 = 83.3888{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3564{{c}}


Badness: 0.0306
{{Optimal ET sequence|legend=0| 29, 43, 72 }}
 
Badness (Sintel): 0.958


=== 13-limit ===
=== 13-limit ===
Comma list: 33/32, 49/48, 65/64, 91/90
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 225/224, 364/363, 441/440
 
{{Mapping|legend=0| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}
 
Optimal tunings:
* WE: ~2 = 1200.9467{{c}}, ~21/20 = 83.3956{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3516{{c}}
 
{{Optimal ET sequence|legend=0| 29, 43, 72 }}
 
Badness (Sintel): 0.887
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 169/168, 221/220, 225/224, 364/363, 441/440
 
{{Mapping|legend=0| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}
 
Optimal tunings:
* WE: ~2 = 1200.9606{{c}}, ~21/20 = 83.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3594{{c}}
 
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}
 
Badness (Sintel): 0.760
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440


POTE generator: ~15/14 = 127.039
{{Mapping|legend=0| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}


Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]
Optimal tunings:  
* WE: ~2 = 1200.7625{{c}}, ~21/20 = 83.3895{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3551{{c}}


{{Val list|legend=1| 9, 19, 85 }}
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}


Badness: 0.0202
Badness (Sintel): 0.895


== Negroni ==
== Decic ==
Comma list: 49/48, 55/54, 225/224
{{Main| Decic }}


POTE generator: ~15/14 = 124.539
Named by [[Xenllium]] in 2021, decic tempers out 16807/16384, the [[cloudy comma]], and {{monzo| 11 -10 -10 10 }}, the [[linus comma]], in addition to the marvel comma. It may be described as the {{nowrap| 50 & 60 }} temperament, with a period of 1/10 octave and a [[ploidacot]] signature of decaploid monocot. It is [[support]]ed by [[10edo|10-]], [[50edo|50-]], and [[60edo]].  


Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]
It can be extended to the 11-, 13-, and 17-limit by adding [[385/384]], [[105/104]], and [[170/169]] to the comma list in this order.


{{Val list|legend=1| 10, 19e, 29, 77cde }}
[[Subgroup]]: 2.3.5.7


Badness: 0.0353
[[Comma list]]: 225/224, 16807/16384


=== 13-limit ===
{{Mapping|legend=1| 10 0 39 28 | 0 1 -1 0 }}
Comma list: 49/48, 55/54, 65/64, 91/90
: mapping generators: ~15/14, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~15/14 = 120.1837{{c}}, ~3/2 = 699.7654{{c}} (~49/48 = 21.3366{{c}})
: [[error map]]: {{val| +1.837 -0.353 -0.753 -3.683 }}
* [[CWE]]: ~15/14 = 120.0000{{c}}, ~3/2 = 698.8236{{c}} (~49/48 = 21.1764{{c}})
: error map: {{val| 0.000 -3.131 -5.137 -8.826 }}
 
{{Optimal ET sequence|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}


POTE generator: ~15/14 = 124.545
[[Badness]] (Sintel): 2.26


Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]
=== 11-limit ===
Subgroup: 2.3.5.7.11


{{Val list|legend=1| 10, 19e, 29, 77cdef }}
Comma list: 225/224, 385/384, 3087/3025


Badness: 0.0216
{{Mapping|legend=0| 10 0 39 28 3 | 0 1 -1 0 2 }}


= Passive =
Optimal tunings:
{{see also | Archytas clan #Passion }}
* WE: ~15/14 = 120.1406{{c}}, ~3/2 = 697.6075{{c}} (~56/55 = 23.2360{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.0142{{c}} (~56/55 = 22.9858{{c}})


Comma list: 225/224, 256/245
{{Optimal ET sequence|legend=0| 10, 40, 50 }}


POTE generator: ~16/15 = 98.809
Badness (Sintel): 2.11


Mapping: [{{val| 1 2 2 3 }}, {{val| 0 -5 4 -2 }}]
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


{{Val list|legend=1| 1, 11, 12, 49d }}
Comma list: 105/104, 144/143, 196/195, 2200/2197


Badness: 0.0751
{{Mapping|legend=0| 10 0 39 28 3 37 | 0 1 -1 0 2 0 }}


= Wizard =
Optimal tunings:
== 5-limit ==
* WE: ~15/14 = 120.1166{{c}}, ~3/2 = 697.6705{{c}} (~78/77 = 23.0289{{c}})
Comma list: 2197265625/2147483648
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.1492{{c}} (~78/77 = 22.8508{{c}})


POTE generator: ~5/4 = 383.212
{{Optimal ET sequence|legend=0| 10, 40, 50 }}


Mapping: [{{val| 2 1 5 }}, {{val| 0 6 -1 }}]
Badness (Sintel): 1.52


{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


Badness: 0.3864
Comma list: 105/104, 144/143, 170/169, 196/195, 221/220


== 7-limit ==
{{Mapping|legend=0| 10 0 39 28 3 37 25 | 0 1 -1 0 2 0 1 }}
Comma list: 225/224, 118098/117649


[[POTE generator]]: ~5/4 = 383.256
Optimal tunings:  
* WE: ~15/14 = 120.1262{{c}}, ~3/2 = 697.8185{{c}} (~78/77 = 22.9388{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.2757{{c}} (~78/77 = 22.7243{{c}})


Mapping: [{{val| 2 1 5 2 }}, {{val| 0 6 -1 10 }}]
{{Optimal ET sequence|legend=0| 10, 40, 50 }}


Wedgie: {{wedgie| 12 -2 20 -31 -2 52 }}
Badness (Sintel): 1.28


{{Val list|legend=1| 22, 50, 72, 94, 166, 238c, 310c, 382c }}
=== Splendecic ===
Splendecic (50 & 60e) is an alternative extension of decic, tempering out 1617/1600, 2401/2376 and 4375/4356 in the 11-limit. As a temperament of the [[fantastic]] rank-3 temperament, its name is a portmanteau of ''splendid'' and ''decic''.


Badness: 0.0408
Subgroup: 2.3.5.7.11


== 11-limit ==
Comma list: 225/224, 1617/1600, 2401/2376
Comma list: 225/224, 385/384, 4000/3993


[[POTE generator]]: ~5/4 = 383.232
{{Mapping|legend=0| 10 0 39 28 82 | 0 1 -1 0 -3 }}


Mapping: [{{val| 2 1 5 2 8 }}, {{val| 0 6 -1 10 -3 }}]
Optimal tunings:  
* WE: ~15/14 = 120.1874{{c}}, ~3/2 = 699.6085{{c}} (~99/98 = 21.5156{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.3531{{c}} (~99/98 = 21.6469{{c}})


{{Val list|legend=1| 22, 50, 72, 94, 166, 238c, 310c }}
{{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de, 170cddee }}


Badness: 0.0185
Badness (Sintel): 1.98


=== Lizard ===
==== 13-limit ====
Comma list: 225/224, 351/350, 364/363, 385/384
Subgroup: 2.3.5.7.11.13


[[POTE generator]]: ~5/4 = 383.389
Comma list: 105/104, 196/195, 1001/1000, 1188/1183


Mapping: [{{val| 2 1 5 2 8 11 }}, {{val| 0 6 -1 10 -3 -10 }}]
{{Mapping|legend=0| 10 0 39 28 82 37 | 0 1 -1 0 -3 0 }}


{{Val list|legend=1| 22, 50, 72, 122, 194df }}
Optimal tunings:
* WE: ~15/14 = 120.1565{{c}}, ~3/2 = 699.2756{{c}} (~91/90 = 21.6631{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.2480{{c}} (~91/90 = 21.7520{{c}})


Badness: 0.0218
{{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de }}
 
Badness (Sintel): 1.57


==== 17-limit ====
==== 17-limit ====
Comma list: 221/220, 273/272, 289/288, 351/350, 375/374
Subgroup: 2.3.5.7.11.13.17


[[POTE generator]]: ~5/4 = 383.381
Comma list: 105/104, 170/169, 196/195, 289/288, 375/374


Mapping: [{{val| 2 1 5 2 8 11 6 }}, {{val| 0 6 -1 10 -3 -10 6 }}]
{{Mapping|legend=0| 10 0 39 28 82 37 25 | 0 1 -1 0 -3 0 1 }}


{{Val list|legend=1| 22, 50, 72, 122g, 194dfg }}
Optimal tunings:
* WE: ~15/14 = 120.1571{{c}}, ~3/2 = 699.2892{{c}} (~91/90 = 21.6536{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.3144{{c}} (~91/90 = 21.6856{{c}})


Badness: 0.0145
{{Optimal ET sequence|legend=0| 10e, 50, 60e, 110deg }}


==== 19-limit ====
Badness (Sintel): 1.33
Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
 
=== Prodecic ===
Prodecic (50e & 60e) is an alternative extension of decic, tempering out 441/440, 1375/1372 and 4375/4356 in the 11-limit. As a temperament of the [[prodigy]] rank-3 temperament, its name is a portmanteau of ''prodigy'' and ''decic''.
 
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 441/440, 5929/5832
 
{{Mapping|legend=0| 10 0 39 28 -13 | 0 1 -1 0 3 }}


[[POTE generator]]: ~5/4 = 383.477
Optimal tunings:  
* WE: ~15/14 = 120.2024{{c}}, ~3/2 = 701.3908{{c}} (~55/54 = 19.8237{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.5235{{c}} (~55/54 = 19.4765{{c}})


Mapping: [{{val| 2 1 5 2 8 11 6 2 }}, {{val| 0 6 -1 10 -3 -10 6 18 }}]
{{Optimal ET sequence|legend=0| 10, 50e, 60e }}


{{Val list|legend=1| 22h, 50, 72, 122g, 194dfg }}
Badness (Sintel): 2.20


Badness: 0.0157
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


=== Gizzard ===
Comma list: 105/104, 196/195, 275/273, 5929/5832
Comma list: 225/224, 385/384, 325/324, 1573/1568


POTE generator: ~5/4 = 383.170
{{Mapping|legend=0| 10 0 39 28 -13 37 | 0 1 -1 0 3 0 }}


Mapping: [{{val| 2 1 5 2 8 -2 }}, {{val| 0 6 -1 10 -3 26 }}]
Optimal tunings:  
* WE: ~15/14 = 120.1654{{c}}, ~3/2 = 701.4683{{c}} (~91/90 = 19.5242{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.7175{{c}} (~91/90 = 19.2825{{c}})


{{Val list|legend=1| 22, 72, 94, 166, 238cf }}
{{Optimal ET sequence|legend=0| 10, 50e, 60e }}


Badness: 0.0203
Badness (Sintel): 1.73


==== 17-limit ====
==== 17-limit ====
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384
Subgroup: 2.3.5.7.11.13.17


POTE generator: ~5/4 = 383.175
Comma list: 105/104, 154/153, 170/169, 196/195, 289/288


Mapping: [{{val| 2 1 5 2 8 -2 6 }}, {{val| 0 6 -1 10 -3 26 6 }}]
{{Mapping|legend=0| 10 0 39 28 -13 37 25 | 0 1 -1 0 3 0 1 }}


{{Val list|legend=1| 22f, 72, 94, 166g, 238cfg }}
Optimal tunings:
* WE: ~15/14 = 120.1577{{c}}, ~3/2 = 701.3950{{c}} (~91/90 = 19.5514{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.6932{{c}} (~91/90 = 19.3068{{c}})


Badness: 0.0136
{{Optimal ET sequence|legend=0| 10, 50e, 60e }}


==== 19-limit ====
Badness (Sintel): 1.41
Comma list: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399


POTE generator: ~5/4 = 383.138
== Enneaportent ==
[[Subgroup]]: 2.3.5.7


Mapping: [{{val| 2 1 5 2 8 -2 6 15 }}, {{val| 0 6 -1 10 -3 26 6 -18 }}]
[[Comma list]]: 225/224, 40353607/40310784


{{Val list|legend=1| 22f, 72, 94, 166g }}
{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
: mapping generators: ~2592/2401, ~12005/6912


Badness: 0.0148
[[Optimal tuning]]s:  
* [[WE]]: ~2592/2401 = 133.4174{{c}}, ~12005/6912 = 950.7667{{c}} (~1728/1715 = 16.8452{{c}})
: [[error map]]: {{val| +0.756 -0.422 -1.395 +0.298 }}
* [[CWE]]: ~2592/2401 = 133.3333{{c}}, ~12005/6912 = 950.2969{{c}} (~1728/1715 = 16.9636{{c}})
: error map: {{val| 0.000 -1.361 -3.277 -1.565 }}


== Mage ==
{{Optimal ET sequence|legend=1| 9, 54, 63, 72, 495bccd, 567bcccd }}
Comma list: 99/98, 176/175, 1331/1296


POTE generator: ~55/48 = 216.876
[[Badness]] (Sintel): 2.37


Map: [{{val| 2 1 5 2 4 }}, {{val| 0 6 -1 10 8 }}]
=== 11-limit ===
Subgroup: 2.3.5.7.11


{{Val list|legend=1| 22, 72e, 94e }}
Comma list: 225/224, 385/384, 12005/11979


Badness: 0.0578
{{Mapping|legend=0| 9 0 28 11 24 | 0 2 -1 2 1 }}


=Triton=
Optimal tunings:
Commas: 225/224, 1029/1000
* WE: ~121/112 = 133.4071{{c}}, ~210/121 = 950.7131{{c}} (~99/98 = 16.8633{{c}})
* CWE: ~121/112 = 133.3333{{c}}, ~210/121 = 950.2994{{c}} (~99/98 = 16.9661{{c}})


[[POTE_tuning|POTE temperament]]: ~7/5 = 568.865
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


Map: [&lt;1 0 6 7|, &lt;0 3 -7 -8|]
Badness (Sintel): 1.01


Wedgie: &lt;&lt;3 -7 -8 -18 -21 1||
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


EDOs: {{EDOs|17d, 19, 78bd, 97bd}}
Comma list: 169/168, 225/224, 364/363, 1716/1715


Badness: 0.0592
{{Mapping|legend=0| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}


==11-limit==
Optimal tunings:
Commas: 45/44, 56/55, 1029/1000
* WE: ~14/13 = 133.4245{{c}}, ~26/15 = 950.9362{{c}} (~105/104 = 16.9650{{c}})
* CWE: ~14/13 = 133.3333{{c}}, ~26/15 = 950.4364{{c}} (~99/98 = 17.1031{{c}})


POTE generator: ~7/5 = 569.144
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


Map: [&lt;1 0 6 7 4|, &lt;0 3 -7 -8 -1|]
Badness (Sintel): 0.922


EDOs: {{EDOs|19, 59bde, 78bde, 97bde}}
== Gracecordial ==
: ''For the 5-limit version, see [[Schismic–Pythagorean equivalence continuum #Gracecordial (5-limit)]].''


Badness: 0.0457
[[Subgroup]]: 2.3.5.7


= Tritonic =
[[Comma list]]: 225/224, 781250000/771895089
== 5-limit ==
Comnma: 553584375/536870912


POTE generator: ~45/32 = 580.219
{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
: mapping generators: ~2, ~3


Map: [&lt;1 4 -3|, &lt;0 -5 11|]
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.4904{{c}}, ~3/2 = 701.1103{{c}}
: [[error map]]: {{val| +0.490 -0.354 -1.655 +1.241 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.8112{{c}}
: error map: {{val| 0.000 -1.144 -2.537 +0.349 }}


EDOs: {{EDOs|29, 31, 60, 91}}
{{Optimal ET sequence|legend=1| 12, …, 113, 125, 238c, 363c }}


Badness: 0.3785
[[Badness]] (Sintel): 2.44


== 7-limit ==
=== 11-limit ===
Commas: 225/224, 50421/50000
Subgroup: 2.3.5.7.11


[[POTE_tuning|POTE temperament]]: 580.286
Comma list: 225/224, 385/384, 236328125/234365481


Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]
{{Mapping|legend=0| 1 0 34 63 -90 | 0 1 -20 -38 59 }}


Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||
Optimal tunings:  
* WE: ~2 = 1200.5571{{c}}, ~3/2 = 701.1589{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8328{{c}}


EDOs: {{EDOs|29, 31, 60, 91, 122, 213bcd}}
{{Optimal ET sequence|legend=0| 12e, 113, 125, 238c }}


== 11-limit ==
Badness (Sintel): 2.96
Commas: 121/120, 225/224, 441/440


[[POTE_tuning|POTE generator]]: ~7/5 = 580.267
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 4 -3 -3 2|, &lt;0 -5 11 12 3|]
Comma list: 225/224, 325/324, 385/384, 831875/830466


EDOs: {{EDOs|29, 31, 60e}}
{{Mapping|legend=0| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}


Badness: 0.0237
Optimal tunings:  
* WE: ~2 = 1200.6282{{c}}, ~3/2 = 701.2080{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8421{{c}}


=== 13-limit ===
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
Commas: 105/104, 121/120, 196/195, 275/273
 
Badness (Sintel): 2.16


POTE generator: ~7/5 = 580.108
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


Map: [&lt;1 4 -3 -3 2 -5|, &lt;0 -5 11 12 3 18|]
Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913


EDOs: {{EDOs|29, 31, 60e, 151cde}}
{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}


Badness: 0.0230
Optimal tunings:  
* WE: ~2 = 1200.5058{{c}}, ~3/2 = 701.1360{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8414{{c}}


== Tritoni ==
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
Commas: 225/224, 385/384, 27783/27500


POTE generator: ~7/5 = 580.389
Badness (Sintel): 1.96


Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


EDOs: {{EDOs|31, 91, 122}}
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444


Badness: 0.0455
{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}


=Merman=
Optimal tunings:
Comma: 1121008359375/1099511627776
* WE: ~2 = 1200.4418{{c}}, ~3/2 = 701.0999{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8425{{c}}


POTE generator: ~45/32 = 585.634
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


Map: [&lt;1 5 -5|, &lt;0 -7 15|]
Badness (Sintel): 1.71


EDOs: {{EDOs|41, 84, 125, 209, 334c, 543bc}}
==== 23-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23


Badness: 0.4538
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528


==7-limit==
{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}
Commas: 225/224, 2500000/2470629


POTE generator: ~7/5 = 585.585
Optimal tunings:  
* WE: ~2 = 1200.4641{{c}}, ~3/2 = 701.1145{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8444{{c}}


Map: [&lt;1 5 -5 -5|, &lt;0 -7 15 16|]
{{Optimal ET sequence|legend=0| 12e, 113, 238cfi }}


Wedgie: &lt;&lt;7 -15 -16 -40 -45 5||
Badness (Sintel): 1.57


EDOs: {{EDOs|41, 84, 125}}
==== 29-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29


Badness: 0.0551
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493


==11-limit==
{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}
Commas: 225/224, 441/440, 1344/1331


POTE generator: ~7/5 = 585.606
Optimal tunings:  
* WE: ~2 = 1200.4400{{c}}, ~3/2 = 701.0986{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8428{{c}}


Map: [&lt;1 5 -5 -5 2|, &lt;0 -7 15 16 3]]
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}


EDOs: {{EDOs|41, 84, 125e}}
Badness (Sintel): 1.50


Badness: 0.0364
==== 31-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31


==13-limit==
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493
Commas: 144/143, 225/224, 364/363, 441/440


POTE generator: ~7/5 = 585.657
{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}


Map: [&lt;1 5 -5 -5 2 12|, &lt;0 -7 15 16 3 -17|]
Optimal tunings:  
* WE: ~2 = 1200.4178{{c}}, ~3/2 = 701.0822{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8396{{c}}


EDOs: {{EDOs|41, 84, 125e, 209ef, 293ef}}
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}


Badness: 0.0275
Badness (Sintel): 1.53


=Septimin=
=== Gracecord ===
Comma: 35595703125/34359738368
Subgroup: 2.3.5.7.11


POTE generator: ~75/64 = 263.658
Comma list: 225/224, 441/440, 109375/107811


Map: [&lt;1 4 1|, &lt;0 -11 6|]
{{Mapping|legend=0| 1 0 34 63 89 | 0 1 -20 -38 -54 }}


EDOs: {{EDOs|9, 32, 41, 91, 132, 223c, 355bc}}
Optimal tunings:  
* WE: ~2 = 1200.6064{{c}}, ~3/2 = 701.2398{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8718{{c}}


Badness: 0.6709
{{Optimal ET sequence|legend=0| 12, …, 101cd, 113 }}


==7-limit==
Badness (Sintel): 2.21
Commas: 225/224, 84035/82944


[[POTE_tuning|POTE temperament]]: 263.632
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]
Comma list: 225/224, 364/363, 441/440, 6125/6084


Wedgie: &lt;&lt;11 -6 10 -35 -15 40||
{{Mapping|legend=0| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}


EDOs: {{EDOs|9, 32, 41, 91, 132}}
Optimal tunings:  
* WE: ~2 = 1200.6225{{c}}, ~3/2 = 701.2539{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8781{{c}}


==11-limit==
{{Optimal ET sequence|legend=0| 12f, …, 101cdf, 113 }}
Commas: 225/224, 385/384, 2401/2376


[[POTE_tuning|POTE temperament]]: 263.634
Badness (Sintel): 1.83


Map: [&lt;1 4 1 5 5|, &lt;0 -11 6 -10 -7|]
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


EDOs: {{EDOs|9, 32, 41, 91, 223cdef}}
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989


==13-limit==
{{Mapping|legend=0| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}
Commas: 105/104, 144/143, 196/195, 245/242


[[POTE_tuning|POTE temperament]]: 263.700
Optimal tunings:  
* WE: ~2 = 1200.3308{{c}}, ~3/2 = 701.0632{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8654{{c}}


Map: [&lt;1 4 1 5 5 7|, &lt;0 -11 6 -10 -7 -15|]
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


EDOs: {{EDOs|9, 41, 91}}
Badness (Sintel): 1.87


=Slender=
==== 19-limit ====
Commas: 225/224, 589824/588245
Subgroup: 2.3.5.7.11.13.17.19


[[POTE_tuning|POTE temperament]]: ~49/48 = 38.413
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663


Map: [&lt;1 2 2 3|, &lt;0 -13 10 -6|]
{{Mapping|legend=0| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}


Wedgie: &lt;&lt;13 -10 6 -46 -27 42||
Optimal tunings:  
* WE: ~2 = 1200.2658{{c}}, ~3/2 = 701.0213{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8629{{c}}


EDOs: {{EDOs|31, 94, 125}}
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


Badness: 0.0569
Badness (Sintel): 1.68


==11-limit==
== Alphorn ==
Commas: 225/224, 385/384, 1331/1323
[[Subgroup]]: 2.3.5.7


[[POTE_tuning|POTE temperament]]: ~49/48 = 38.387
[[Comma list]]: 225/224, 5764801/5668704


Map: [&lt;1 2 2 3 4|, &lt;0 -13 10 -6 -17|]
{{Mapping|legend=1| 1 -7 5 -9 | 0 16 -5 22 }}
: mapping generators: ~2, ~35/24


EDOs: {{EDOs|31, 63, 94, 125}}
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1201.3004{{c}}, ~35/24 = 644.4767{{c}}
: [[error map]]: {{val| +1.300 +0.569 -2.195 -2.043 }}
* [[CWE]]: ~2 = 1200.3333{{c}}, ~35/24 = 643.8137{{c}}
: error map: {{val| 0.000 -0.936 -5.382 -4.924 }}


Badness: 25.342
{{Optimal ET sequence|legend=1| 13d, 28d, 41, 151cd, 192cdd, 233ccdd }}


==13-limit==
[[Badness]] (Sintel): 3.27
Commas: 225/224, 275/273, 385/384, 1331/1323


POTE generator: ~49/48 = 38.314
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 2 2 3 4 3|, &lt;0 -13 10 -6 -17 22|]
Comma list: 225/224, 385/384, 12250/11979


EDOs: {{EDOs|31, 63, 94}}
{{Mapping|legend=0| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}


Badness: 25.913
Optimal tunings:  
* WE: ~2 = 1200.5123{{c}}, ~16/11 = 644.1307{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 643.8662{{c}}


=Marvo=
{{Optimal ET sequence|legend=0| 13d, 28d, 41 }}
Commas: 225/224, 78125000/78121827


[[POTE_tuning|POTE generator]]: ~27/20 = 516.694
Badness (Sintel): 2.43


Map: [&lt;1 5 12 29|, &lt;0 -6 -17 -46|]
== Misneb ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Misneb]].''


Wedgie: &lt;&lt;6 17 46 13 56 59||
[[Subgroup]]: 2.3.5.7


EDOs: {{EDOs|7d, 65d, 72, 137, 209, 281, 569bcc}}
[[Comma list]]: 225/224, 4194304/4117715


Badness: 0.0976
{{Mapping|legend=1| 1 -12 15 1 | 0 15 -14 2 }}
: mapping generators: ~2, ~15/8


==11-limit==
[[Optimal tuning]]s:
Commas: 225/224, 243/242, 4000/3993
* [[WE]]: ~2 = 1199.7642{{c}}, ~15/8 = 1086.5513{{c}}
: [[error map]]: {{val| -0.236 -0.856 -1.569 +4.041 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/8 = 1086.7633{{c}}
: error map: {{val| 0.000 -0.506 -0.999 +4.701 }}


POTE generator: ~27/20 = 516.699
{{Optimal ET sequence|legend=1| 21, 32, 53 }}


Map: [&lt;1 5 12 29 12|, &lt;0 -6 -17 -46 -15|]
[[Badness]] (Sintel): 3.57


EDOs: {{EDOs|7d, 65d, 72, 281, 353c, 425bc, 497bc}}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.0317
Comma list: 99/98, 176/175, 1310720/1294139


==13-limit==
{{Mapping|legend=0| 1 -12 15 1 27 | 0 15 -14 2 -26 }}
Commas: 225/224, 243/242, 351/350, 1625/1617


POTE generator: ~27/20 = 516.730
Optimal tunings:  
* WE: ~2 = 1200.1654{{c}}, ~15/8 = 1086.8269{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6766{{c}}


Map: [&lt;1 5 12 29 12 39|, &lt;0 -6 -17 -46 -15 -62|]
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


EDOs: {{EDOs|72, 137, 209, 281f, 490bcf}}
Badness (Sintel): 2.82


Badness: 0.0269
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


=Marvolo=
Comma list: 99/98, 176/175, 640/637, 847/845
Commas: 225/224, 156250000/155649627


POTE generator: ~21/20 = 83.348
{{Mapping|legend=0| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}


Map: [&lt;1 2 1 1|, &lt;0 -6 19 26|]
Optimal tunings:  
* WE: ~2 = 1200.1687{{c}}, ~15/8 = 1086.8295{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6757{{c}}


Wedgie: &lt;&lt;6 -19 -26 -44 -58 -7||
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


EDOs: {{EDOs|29, 43, 72, 619bcd, 691bcd}}
Badness (Sintel): 1.88


Badness: 0.0833
=== Musneb ===
Subgroup: 2.3.5.7.11


==11-limit==
Comma list: 225/224, 385/384, 66550/64827
Commas: 225/224, 441/440, 4000/3993


POTE generator: ~21/20 = 83.340
{{Mapping|legend=0| 1 3 1 3 6 | 0 -15 14 -2 -27 }}


Map: [&lt;1 2 1 1 2|, &lt;0 -6 19 26 21|]
Optimal tunings:  
* WE: ~2 = 1200.0839{{c}}, ~15/8 = 1086.9343{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.8593{{c}}


EDOs: {{EDOs|29, 43, 72}}
{{Optimal ET sequence|legend=0| 21e, 32, 53 }}


Badness: 0.0290
Badness (Sintel): 2.89


==13-limit==
== Untriton ==
Commas: 169/168, 225/224, 364/363, 441/440
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''


POTE generator: ~21/20 = 83.330
Named by [[Petr Pařízek]] in 2011<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, untriton may be described as the {{nowrap| 51 & 53 }} temperament. Like [[#Tritonic|tritonic]], it is generated by a [[~]][[10/7]] [[tritone]], but here, nine generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is delta-enneacot.  


Map: [&lt;1 2 1 1 2 3|, &lt;0 -6 19 26 21 10|]
[[Subgroup]]: 2.3.5.7


EDOs: {{EDOs|29, 43, 72, 115f}}
[[Comma list]]: 225/224, 125000000/121060821


Badness: 0.0215
{{Mapping|legend=1| 1 -3 12 13 | 0 9 -19 -20 }}
: mapping generators: ~2, ~10/7


= Amavil =
[[Optimal tuning]]s:
== 5-limit (mabila) ==
* [[WE]]: ~2 = 1199.8275{{c}}, ~10/7 = 611.2710{{c}}
Comma: 268435456/263671875
: [[error map]]: {{val| -0.172 +0.002 -2.533 +3.511 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 611.3614{{c}}
: error map: {{val| 0.000 +0.298 -2.181 +3.946 }}


POTE generator: ~512/375 = 529.6849
{{Optimal ET sequence|legend=1| 51, 53 }}


Map: [<1 6 1|, <0 -10 3|]
[[Badness]] (Sintel): 3.64


EDOs: {{EDOs| 9, 25, 34, 77, 111, 145, 256c }}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.2325
Comma list: 121/120, 225/224, 22000/21609


== 7-limit ==
{{Mapping|legend=0| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}
Commas: 225/224, 17496/16807


POTE generator: ~48/35 = 529.979
Optimal tunings:  
* WE: ~2 = 1200.3591{{c}}, ~10/7 = 611.5569{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3690{{c}}


Map: [&lt;1 6 1 9|, &lt;0 -10 3 -14|]
{{Optimal ET sequence|legend=0| 51, 53 }}


Wedgie: &lt;&lt;10 -3 14 -28 -6 41||
Badness (Sintel): 2.46


EDOs: {{EDOs|9, 34d, 43, 77d}}
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Badness: 0.1096
Comma list: 121/120, 225/224, 275/273, 1040/1029


== 11-limit ==
{{Mapping|legend=0| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}
Commas: 99/98, 176/175, 864/847


POTE generator: ~15/11 = 529.974
Optimal tunings:  
* WE: ~2 = 1200.4078{{c}}, ~10/7 = 611.5536{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3392{{c}}


Map: [&lt;1 6 1 9 7|, &lt;0 -10 3 -14 -8|]
{{Optimal ET sequence|legend=0| 51f, 53 }}


EDOs: {{EDOs| 9, 34d, 43, 77de }}
Badness (Sintel): 1.96


Badness: 0.0426
== Naiadical ==
Named by [[Xenllium]] in 2026, naiadical may be described as the {{nowrap| 21 & 29 }} temperament.  


== 13-limit ==
[[Subgroup]]: 2.3.5.7
Commas: 78/77, 99/98, 144/143, 176/175


POTE generator: ~15/11 = 529.951
[[Comma list]]: 225/224, 823543/800000


Map: [&lt;1 6 1 9 7 9|, &lt;0 -10 3 -14 -8 -12|]
{{Mapping|legend=1| 1 -4 11 9 | 0 9 -14 -10 }}
: mapping generators: ~2, ~32/21


EDOs: {{EDOs| 9, 34d, 43, 77de }}
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1202.1198{{c}}, ~32/21 = 745.4675{{c}}
: [[error map]]: {{val| +2.120 -1.227 +0.459 -4.423 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~32/21 = 744.1318{{c}}
: error map: {{val| 0.000 -4.769 -4.159 -10.144 }}


Badness: 0.0258
{{Optimal ET sequence|legend=1| 21, 29, 50, 79d, 129cdd, 179bcddd }}


=Enneaportent=
[[Badness]] (Sintel): 3.67
Commas: 225/224, 40353607/40310784


POTE generator: ~5/4 = 383.165
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;9 0 28 11|, &lt;0 2 -1 2|]
Comma list: 225/224, 245/242, 1617/1600


Wedgie: &lt;&lt;18 -9 18 -56 -22 67||
Mapping: {{Mapping| 1 -4 11 9 14 | 0 9 -14 -10 -17 }}


EDOs: {{EDOs|9, 54, 63, 72, 495bcd}}
Optimal tunings:  
* WE: ~2 = 1201.9008{{c}}, ~21/16 = 745.3867{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~32/21 = 744.1777{{c}}


Badness: 0.0937
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}


==11-limit==
Badness (Sintel): 2.00
Commas: 225/224, 385/384, 12005/11979


POTE generator: ~5/4 = 383.146
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Map: [&lt;9 0 28 11 24|, &lt;0 2 -1 2 1|]
Comma list: 105/104, 196/195, 245/242, 1001/1000


EDOs: {{EDOs|9, 54, 63, 72, 423cd, 495bcd}}
Mapping: {{Mapping| 1 -4 11 9 14 13 | 0 9 -14 -10 -17 -15 }}


Badness: 0.0304
Optimal tunings:  
* WE: ~2 = 1201.7863{{c}}, ~20/13 = 745.3344{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1931{{c}}


==13-limit==
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
Commas: 169/168, 225/224, 364/363, 1716/1715


POTE generator: ~5/4 = 383.047
Badness (Sintel): 1.43


Map: [&lt;9 0 28 11 24 19|, &lt;0 2 -1 2 1 2|]
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


EDOs: {{EDOs|9, 54, 63, 72, 279cf}}
Comma list: 105/104, 170/169, 196/195, 221/220, 245/242


Badness: 0.0223
Mapping: {{Mapping| 1 -4 11 9 14 13 14 | 0 9 -14 -10 -17 -15 -16 }}


= Submajor =
Optimal tunings:
== 5-limit ==
* WE: ~2 = 1201.9208{{c}}, ~20/13 = 745.3976{{c}}
Comma: 69198046875/68719476736
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1669{{c}}


POTE generator: ~10125/8192 = 362.321
{{Optimal ET sequence|legend=0| 21, 29g, 50, 79dg }}


Map: [&lt;1 4 -1|, &lt;0 -8 11|]
Badness (Sintel): 1.26


EDOs: {{EDOs|10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}}
== Quintannic ==
Named by [[Scott Dakota]], quintannic may be described as the {{nowrap| 43 & 60 }} temperament.


Badness: 0.1302
[[Subgroup]]: 2.3.5.7


== 7-limit ==
[[Comma list]]: 225/224, 9805926501/9765625000
Commas: 225/224, 51200/50421


POTE generator: ~49/40 = 362.255
{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
: mapping generators: ~2, ~10000/9261


Map: [&lt;1 4 -1 1|, &lt;0 -8 11 6|]
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.9803{{c}}, ~10000/9261 = 139.9522{{c}}
: [[error map]]: {{val| +0.980 -1.214 -0.313 -0.243 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10000/9261 = 139.8184{{c}}
: error map: {{val| 0.000 -2.863 -2.136 -2.287 }}


Wedgie: &lt;&lt;8 -11 -6 -36 -32 17||
{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}


EDOs: {{EDOs|10, 33, 43, 53}}
[[Badness]] (Sintel): 3.81


Badness: 0.0605
=== 11-limit ===
Subgroup: 2.3.5.7.11


== 11-limit ==
Comma list: 225/224, 441/440, 43923/43750
Commas: 225/224, 385/384, 6655/6561


POTE generator: ~27/22 = 362.101
{{Mapping|legend=0| 1 1 5 7 8 | 0 5 -23 -36 -39 }}


Map: [&lt;1 4 -1 1 11|, &lt;0 -8 11 6 -25|]
Optimal tunings:  
* WE: ~2 = 1201.0031{{c}}, ~320/297 = 139.9435{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~320/297 = 139.8053{{c}}


EDOs: {{EDOs|10, 53, 116, 169de, 285cde}}
{{Optimal ET sequence|legend=0| 43, 60e, 103, 369bcdeee, 472bbcddeee }}


Badness: 0.0506
Badness (Sintel): 1.74


=== 13-limit ===
=== 13-limit ===
Commas: 169/168, 225/224, 275/273, 385/384
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 441/440, 1001/1000, 1188/1183
 
{{Mapping|legend=0| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}


POTE generator: ~16/13 = 362.105
Optimal tunings:  
* WE: ~2 = 1200.8354{{c}}, ~13/12 = 139.9095{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.7997{{c}}


Map: [&lt;1 4 -1 1 11 4|, &lt;0 -8 11 6 -25 -1|]
{{Optimal ET sequence|legend=0| 43, 60e, 103 }}


EDOs: {{EDOs|10, 53, 116, 169de, 285cdef}}
Badness (Sintel): 1.35


Badness: 0.0277
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


== Interpental ==
Comma list: 225/224, 273/272, 375/374, 441/440, 891/884
Commas: 99/98, 176/175, 51200/50421


POTE generator: ~49/40 = 362.418
{{Mapping|legend=0| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}


Map: [&lt;1 4 -1 1 -5|, &lt;0 -8 11 6 28|]
Optimal tunings:  
* WE: ~2 = 1200.7402{{c}}, ~13/12 = 139.9015{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.8038{{c}}


EDOs: {{EDOs|43, 53, 96, 149d}}
{{Optimal ET sequence|legend=0| 43, 60e, 103 }}


Badness: 0.0518
Badness (Sintel): 1.17


=== 13-limit ===
== Hendeca ==
Commas: 99/98, 169/168, 176/175, 640/637
{{Distinguish| Hendec }}
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Hendecatonic]].''
 
Hendeca tempers out the same 5-limit comma as [[porwell temperaments #Hendecatonic|hendecatonic]], and has a period of 1/11 octave. However, in this temperament, nine periods represent [[7/4]], the same as [[keemic temperaments #Undeka|undeka]]. It can be tuned to [[22edo]] or [[33edo]] using the [[patent val]], or [[55edo]] using the 55d val. It was named by [[Xenllium]] in 2025 as a low-accuracy variant of hendecatonic.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 122880/117649
 
{{Mapping|legend=1| 11 0 43 31 | 0 1 -1 0 }}
: mapping generators: ~16/15, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~16/15 = 108.9526{{c}}, ~3/2 = 702.4215{{c}}
: [[error map]]: {{val| -1.521 -1.055 -2.252 +8.705 }}
* [[CWE]]: ~16/15 = 109.0909{{c}}, ~3/2 = 703.2071{{c}}
: error map: {{val| 0.000 +1.252 +1.388 +12.992 }}
 
{{Optimal ET sequence|legend=1| 22, 55d, 77d, 99dd }}
 
[[Badness]] (Sintel): 4.37
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 225/224, 352/343
 
{{Mapping|legend=0| 11 0 43 31 38 | 0 1 -1 0 0 }}
 
Optimal tunings:
* WE: ~16/15 = 109.0109{{c}}, ~3/2 = 702.5746{{c}}
* CWE: ~16/15 = 109.0909{{c}}, ~3/2 = 703.0395{{c}}
 
{{Optimal ET sequence|legend=0| 22, 55d }}
 
Badness (Sintel): 2.46
 
== Gwazy ==
: ''For the 5-limit version, see [[Very high accuracy temperaments #Kwazy]].''
 
Named by [[Petr Pařízek]] in 2011<ref name="petr's long post"/>, gwazy may be described as the {{nowrap| 22 & 74 }} temperament.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 5971968/5764801
 
{{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}
: mapping generators: ~2401/1728, ~35/32
 
[[Optimal tuning]]s:
* [[WE]]: ~2401/1728 = 599.7132{{c}}, ~35/32 = 162.5806{{c}}
: [[error map]]: {{val| -0.574 -1.597 -0.937 +5.510 }}
* [[CWE]]: ~2401/1728 = 600.0000{{c}}, ~35/32 = 162.6388{{c}}
: error map: {{val| 0.000 -0.844 +0.492 +7.007 }}
 
{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
 
[[Badness]] (Sintel): 4.53
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 99/98, 176/175, 65536/65219
 
{{Mapping|legend=0| 2 1 6 4 8 | 0 8 -5 6 -4 }}
 
Optimal tunings:
* WE: ~363/256 = 599.8517{{c}}, ~11/10 = 162.5518{{c}}
* CWE: ~363/256 = 600.0000{{c}}, ~11/10 = 162.5863{{c}}
 
{{Optimal ET sequence|legend=0| 22, 74, 96 }}
 
Badness (Sintel): 2.26


POTE generator: ~16/13 = 362.402
== Tertiosec ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tertiosec]].''


Map: [&lt;1 4 -1 1 -5 4|, &lt;0 -8 11 6 28 -1|]
Tertiosec may be described as the {{nowrap| 21 & 75 }} temperament. It was initially named ''tertiomar'' by [[Petr Pařízek]] in 2011<ref name="petr's long post"/>, but was changed to ''tertiosec'' in 2012<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104268.html Yahoo! Tuning Group | ''2D temperament names, part I -- reclassified temperaments from message #101780'']</ref>.


EDOs: {{EDOs|43, 53, 96, 149d}}
[[Subgroup]]: 2.3.5.7


Badness: 0.0297
[[Comma list]]: 225/224, 14495514624/13841287201


=Alphorn=
{{Mapping|legend=1| 3 -1 12 7 | 0 8 -7 2 }}
Commas: 225/224, 5764801/5668704
: mapping generators: ~3072/2401, ~2048/1715


POTE generator: ~48/35 = 556.221
[[Optimal tuning]]s:
* [[WE]]: ~3072/2401 = 399.8257{{c}}, ~2048/1715 = 287.5920{{c}}
: [[error map]]: {{val| -0.523 -1.044 -1.549 +5.138 }}
* [[CWE]]: ~3072/2401 = 400.0000{{c}}, ~2048/1715 = 287.7088{{c}}
: error map: {{val| 0.000 -0.284 -0.276 +6.592 }}


Map: [&lt;1 9 0 13|, &lt;0 -16 5 -22|]
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}


Wedgie: &lt;&lt;16 -5 22 -45 -10 65||
[[Badness]] (Sintel): 10.9


EDOs: 28d, 41, 151cd, 192cd, 233cd
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.1293
Comma list: 225/224, 3840/3773, 12005/11979


==11-limit==
{{Mapping|legend=0| 3 -1 12 7 14 | 0 8 -7 2 -5 }}
Commas: 225/224, 385/384, 12250/11979


POTE generator: ~11/8 = 556.144
Optimal tunings:  
* WE: ~44/35 = 399.6550{{c}}, ~33/28 = 287.5803{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~33/28 = 287.8224{{c}}


Map: [&lt;1 9 0 13 3|, &lt;0 -16 5 -22 1|]
{{Optimal ET sequence|legend=0| 21, 54, 75e }}


EDOs: 41, 315cde
Badness (Sintel): 5.74


Badness: 0.0735
== References ==


[[Category:Theory]]
[[Category:Marvel temperaments| ]] <!-- main article -->
[[Category:Temperament]]
[[Category:Temperament collections]]
[[Category:Marvel]]
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Marvel_temperaments"