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__FORCETOC__
{{Technical data page}}
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]].
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 }}


=Negri=
Optimal tunings:
{{main|Negri}}
* WE: ~2 = 1201.3100{{c}}, ~10/7 = 620.6509{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9328{{c}}


==5-limit==
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
Note that this is technically not a Marvel temperament until the 7-limit, but also placed here for reference.


[[Comma|Comma]]s: 16875/16384
Badness (Sintel): 1.03


[[POTE_tuning|POTE temperament]]: ~15/14 = 125.7549
==== 23-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23


[[Map|Map]]: [&lt;1 2 2|, &lt;0 -4 3|]
Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195


[[wedgie|Wedgie]]: &lt;&lt;4 -3 -14||
{{Mapping|legend=0| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}


EDOs: {{EDOs|9, 10, 19, 86}}
Optimal tunings:  
* WE: ~2 = 1201.4074{{c}}, ~10/7 = 620.7185{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9548{{c}}


==7-limit==
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
[[Comma|Comma]]s: 49/48, 225/224


[[POTE_tuning|POTE temperament]]: ~15/14 = 125.608
Badness (Sintel): 1.04


[[Map|Map]]: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]
=== Tritoni ===
Subgroup: 2.3.5.7.11


[[wedgie|Wedgie]]: &lt;&lt;4 -3 2 -14 -8 13||
Comma list: 225/224, 385/384, 27783/27500


EDOs: {{EDOs|9, 10, 19, 86}}
{{Mapping|legend=0| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}


==11-limit==
Optimal tunings:
Commas: 45/44, 49/48, 56/55
* WE: ~2 = 1201.0888{{c}}, ~10/7 = 620.1733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6146{{c}}


[[POTE_tuning|POTE generator]]: ~15/14 = 126.474
{{Optimal ET sequence|legend=0| 31, 91, 122, 153d }}


Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]
Badness (Sintel): 1.50


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


[[Badness|Badness]]: 0.0262
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.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 84035/82944
 
{{Mapping|legend=1| 1 -7 7 -5 | 0 11 -6 10 }}
: mapping generators: ~2, ~12/7
 
[[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 ===
Commas: 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


[[POTE_tuning|POTE generator]]: ~14/13 = 126.431
{{Mapping|legend=0| 1 -2 10 11 22 32 | 0 7 -15 -16 38 58 }}


Map: [&lt;1 2 2 3 4 4|, &lt;0 -4 3 -2 -5 -3|]
Optimal tunings:  
* WE: ~2 = 1200.5126{{c}}, ~10/7 = 614.7152{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4562{{c}}


EDOs: {{EDOs|9, 10, 19}}
{{Optimal ET sequence|legend=0| 41, 84ef, 125f, 166 }}


== Negril ==
Badness (Sintel): 1.47
Commas: 49/48, 100/99, 225/224


POTE generator: ~15/14 = 124.767
== 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.  


Map: [&lt;1 2 2 3 2|, &lt;0 -4 3 -2 14|]
The name was likely derived from ''slendro diesis'', one of the names for the interval 49/48.


EDOs: {{EDOs|19, 29, 48df, 77cdf}}
[[Subgroup]]: 2.3.5.7


Badness: 0.0387
[[Comma list]]: 225/224, 589824/588245
 
{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
: mapping generators: ~2, ~49/48
 
[[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 }}
 
{{Optimal ET sequence|legend=1| 31, 94, 125, 406c }}
 
[[Badness]] (Sintel): 1.44
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 1331/1323
 
{{Mapping|legend=0| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
 
Optimal tunings:
* WE: ~2 = 1199.4983{{c}}, ~49/48 = 38.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3775{{c}}
 
{{Optimal ET sequence|legend=0| 31, 63, 94, 125 }}
 
Badness (Sintel): 0.838


=== 13-limit ===
=== 13-limit ===
Commas: 49/48, 65/64, 91/90, 875/858
Subgroup: 2.3.5.7.11.13


POTE generator: ~15/14 = 124.716
Comma list: 225/224, 275/273, 385/384, 1331/1323


Map: [&lt;1 2 2 3 2 4|, &lt;0 -4 3 -2 14 -3|]
{{Mapping|legend=0| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}


EDOs: {{EDOs|9, 10, 19, 29, 48, 77}}
Optimal tunings:  
* WE: ~2 = 1200.1728{{c}}, ~49/48 = 38.3192{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3129{{c}}


Badness: 0.0244
{{Optimal ET sequence|legend=0| 31, 63, 94 }}


== Negric ==
Badness (Sintel): 1.07
Commas: 33/32, 49/48, 77/75


POTE generator: ~15/14 = 127.039
== Triton ==
: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''


Map: [&lt;1 2 2 3 3|, &lt;0 -4 3 -2 4|]
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.


EDOs: {{EDOs|9, 19, 85}}
[[Subgroup]]: 2.3.5.7


Badness: 0.0306
[[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
 
{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
: mapping generators: ~2, ~21/20
 
[[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 }}
 
{{Optimal ET sequence|legend=1| 29, 43, 72, 619bbccd, 691bbccd }}
 
[[Badness]] (Sintel): 2.11
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 441/440, 4000/3993
 
{{Mapping|legend=0| 1 2 1 1 2 | 0 -6 19 26 21 }}
 
Optimal tunings:
* WE: ~2 = 1200.7075{{c}}, ~21/20 = 83.3888{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3564{{c}}
 
{{Optimal ET sequence|legend=0| 29, 43, 72 }}
 
Badness (Sintel): 0.958


=== 13-limit ===
=== 13-limit ===
Commas: 33/32, 49/48, 65/64, 91/90
Subgroup: 2.3.5.7.11.13


POTE generator: ~15/14 = 127.039
Comma list: 169/168, 225/224, 364/363, 441/440


Map: [&lt;1 2 2 3 3 4|, &lt;0 -4 3 -2 4 -3|]
{{Mapping|legend=0| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}


EDOs: {{EDOs|9, 19, 85}}
Optimal tunings:  
* WE: ~2 = 1200.9467{{c}}, ~21/20 = 83.3956{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3516{{c}}


Badness: 0.0202
{{Optimal ET sequence|legend=0| 29, 43, 72 }}


== Negroni ==
Badness (Sintel): 0.887
Commas: 49/48, 55/54, 225/224


POTE generator: ~15/14 = 124.539
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Map: [&lt;1 2 2 3 5|, &lt;0 -4 3 -2 -15|]
Comma list: 169/168, 221/220, 225/224, 364/363, 441/440


EDOs: {{EDOs|10, 19e, 29, 77cde}}
{{Mapping|legend=0| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}


Badness: 0.0353
Optimal tunings:  
* WE: ~2 = 1200.9606{{c}}, ~21/20 = 83.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3594{{c}}


=== 13-limit ===
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}
Commas: 49/48, 55/54, 65/64, 91/90
 
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 = 124.545
{{Mapping|legend=0| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}


Map: [&lt;1 2 2 3 5 4|, &lt;0 -4 3 -2 -15 -3|]
Optimal tunings:  
* WE: ~2 = 1200.7625{{c}}, ~21/20 = 83.3895{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3551{{c}}


EDOs: {{EDOs|10, 19e, 29, 77cdef}}
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}


Badness: 0.0216
Badness (Sintel): 0.895


=Wizard=
== Decic ==
Comma: 2197265625/2147483648
{{Main| Decic }}


POTE generator: ~5/4 = 383.212
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]].  


Map: [&lt;2 1 5|, &lt;0 6 -1|]
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.


EDOs: {{EDOs|22, 50, 72, 166, 238c, 310c, 548bc}}
[[Subgroup]]: 2.3.5.7


Badness: 0.3864
[[Comma list]]: 225/224, 16807/16384


==7-limit==
{{Mapping|legend=1| 10 0 39 28 | 0 1 -1 0 }}
Commas: 225/224, 118098/117649
: mapping generators: ~15/14, ~3


[[POTE_tuning|POTE temperament]]: 383.256
[[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 }}


Map: [&lt;2 1 5 2|, &lt;0 6 -1 10|]
{{Optimal ET sequence|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}


Wedgie: &lt;&lt;12 -2 20 -31 -2 52||
[[Badness]] (Sintel): 2.26


EDOs: {{EDOs|22, 50, 72, 94, 166, 238c, 310c, 382c}}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.0408
Comma list: 225/224, 385/384, 3087/3025


==11-limit==
{{Mapping|legend=0| 10 0 39 28 3 | 0 1 -1 0 2 }}
Commas: 225/224, 385/384, 4000/3993


[[POTE_tuning|POTE temperament]]: 383.232
Optimal tunings:  
* 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}})


Map: [&lt;2 1 5 2 8|, &lt;0 6 -1 10 -3|]
{{Optimal ET sequence|legend=0| 10, 40, 50 }}


EDOs: {{EDOs|22, 50, 72, 94, 166, 238c, 310c}}
Badness (Sintel): 2.11


Badness: 0.0185
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


=== Lizard ===
Comma list: 105/104, 144/143, 196/195, 2200/2197
Commas: 225/224, 351/350, 364/363, 385/384


[[POTE_tuning|POTE temperament]]: 383.389
{{Mapping|legend=0| 10 0 39 28 3 37 | 0 1 -1 0 2 0 }}


Map: [&lt;2 1 5 2 8 11|, &lt;0 6 -1 10 -3 -10|]
Optimal tunings:  
* WE: ~15/14 = 120.1166{{c}}, ~3/2 = 697.6705{{c}} (~78/77 = 23.0289{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.1492{{c}} (~78/77 = 22.8508{{c}})


EDOs: {{EDOs|22, 50, 72, 122, 194df}}
{{Optimal ET sequence|legend=0| 10, 40, 50 }}


Badness: 0.0218
Badness (Sintel): 1.52


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


[[POTE_tuning|POTE temperament]]: 383.381
Comma list: 105/104, 144/143, 170/169, 196/195, 221/220


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


EDOs: {{EDOs|22, 50, 72, 122g, 194dfg}}
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}})


Badness: 0.0145
{{Optimal ET sequence|legend=0| 10, 40, 50 }}


==== 19-limit ====
Badness (Sintel): 1.28
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342


[[POTE_tuning|POTE generator]]: ~5/4 = 383.477
=== 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''.


Map: [&lt;2 1 5 2 8 11 6 2|, &lt;0 6 -1 10 -3 -10 6 18|]
Subgroup: 2.3.5.7.11


EDOs: {{EDOs|22h, 50, 72, 122g, 194dfg}}
Comma list: 225/224, 1617/1600, 2401/2376


Badness: 0.0157
{{Mapping|legend=0| 10 0 39 28 82 | 0 1 -1 0 -3 }}


=== Gizzard ===
Optimal tunings:
Commas: 225/224, 385/384, 325/324, 1573/1568
* 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}})


POTE generator: ~5/4 = 383.170
{{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de, 170cddee }}


Map: [&lt;2 1 5 2 8 -2|, &lt;0 6 -1 10 -3 26|]
Badness (Sintel): 1.98


EDOs: {{EDOs|22, 72, 94, 166, 238cf}}
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Badness: 0.0203
Comma list: 105/104, 196/195, 1001/1000, 1188/1183


==== 17-limit ====
{{Mapping|legend=0| 10 0 39 28 82 37 | 0 1 -1 0 -3 0 }}
Commas: 225/224, 289/288, 325/324, 375/374, 385/384


POTE generator: ~5/4 = 383.175
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}})


Map: [&lt;2 1 5 2 8 -2 6|, &lt;0 6 -1 10 -3 26 6|]
{{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de }}


EDOs: {{EDOs|22f, 72, 94, 166g, 238cfg}}
Badness (Sintel): 1.57


Badness: 0.0136
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


==== 19-limit ====
Comma list: 105/104, 170/169, 196/195, 289/288, 375/374
Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399


POTE generator: ~5/4 = 383.138
{{Mapping|legend=0| 10 0 39 28 82 37 25 | 0 1 -1 0 -3 0 1 }}


Map: [&lt;2 1 5 2 8 -2 6 15|, &lt;0 6 -1 10 -3 26 6 -18|]
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}})


EDOs: {{EDOs|22f, 72, 94, 166g}}
{{Optimal ET sequence|legend=0| 10e, 50, 60e, 110deg }}


Badness: 0.0148
Badness (Sintel): 1.33


== Mage ==
=== Prodecic ===
Commas: 99/98, 176/175, 1331/1296
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''.


POTE generator: ~55/48 = 216.876
Subgroup: 2.3.5.7.11


Map: [&lt;2 1 5 2 4|, &lt;0 6 -1 10 8|]
Comma list: 225/224, 441/440, 5929/5832


EDOs: {{EDOs|22, 72e, 94e}}
{{Mapping|legend=0| 10 0 39 28 -13 | 0 1 -1 0 3 }}


Badness: 0.0578
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}})


=Triton=
{{Optimal ET sequence|legend=0| 10, 50e, 60e }}
Commas: 225/224, 1029/1000


[[POTE_tuning|POTE temperament]]: ~7/5 = 568.865
Badness (Sintel): 2.20


Map: [&lt;1 0 6 7|, &lt;0 3 -7 -8|]
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Wedgie: &lt;&lt;3 -7 -8 -18 -21 1||
Comma list: 105/104, 196/195, 275/273, 5929/5832


EDOs: {{EDOs|17d, 19, 78bd, 97bd}}
{{Mapping|legend=0| 10 0 39 28 -13 37 | 0 1 -1 0 3 0 }}


Badness: 0.0592
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}})


==11-limit==
{{Optimal ET sequence|legend=0| 10, 50e, 60e }}
Commas: 45/44, 56/55, 1029/1000


POTE generator: ~7/5 = 569.144
Badness (Sintel): 1.73


Map: [&lt;1 0 6 7 4|, &lt;0 3 -7 -8 -1|]
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


EDOs: {{EDOs|19, 59bde, 78bde, 97bde}}
Comma list: 105/104, 154/153, 170/169, 196/195, 289/288


Badness: 0.0457
{{Mapping|legend=0| 10 0 39 28 -13 37 25 | 0 1 -1 0 3 0 1 }}


= Tritonic =
Optimal tunings:
== 5-limit ==
* WE: ~15/14 = 120.1577{{c}}, ~3/2 = 701.3950{{c}} (~91/90 = 19.5514{{c}})
Comnma: 553584375/536870912
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.6932{{c}} (~91/90 = 19.3068{{c}})


POTE generator: ~45/32 = 580.219
{{Optimal ET sequence|legend=0| 10, 50e, 60e }}


Map: [&lt;1 4 -3|, &lt;0 -5 11|]
Badness (Sintel): 1.41


EDOs: {{EDOs|29, 31, 60, 91}}
== Enneaportent ==
[[Subgroup]]: 2.3.5.7


Badness: 0.3785
[[Comma list]]: 225/224, 40353607/40310784


== 7-limit ==
{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
Commas: 225/224, 50421/50000
: mapping generators: ~2592/2401, ~12005/6912


[[POTE_tuning|POTE temperament]]: 580.286
[[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 }}


Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]
{{Optimal ET sequence|legend=1| 9, 54, 63, 72, 495bccd, 567bcccd }}


Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||
[[Badness]] (Sintel): 2.37


EDOs: {{EDOs|29, 31, 60, 91, 122, 213bcd}}
=== 11-limit ===
Subgroup: 2.3.5.7.11


== 11-limit ==
Comma list: 225/224, 385/384, 12005/11979
Commas: 121/120, 225/224, 441/440


[[POTE_tuning|POTE generator]]: ~7/5 = 580.267
{{Mapping|legend=0| 9 0 28 11 24 | 0 2 -1 2 1 }}


Map: [&lt;1 4 -3 -3 2|, &lt;0 -5 11 12 3|]
Optimal tunings:  
* 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}})


EDOs: {{EDOs|29, 31, 60e}}
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


Badness: 0.0237
Badness (Sintel): 1.01


=== 13-limit ===
=== 13-limit ===
Commas: 105/104, 121/120, 196/195, 275/273
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 225/224, 364/363, 1716/1715
 
{{Mapping|legend=0| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}


POTE generator: ~7/5 = 580.108
Optimal tunings:  
* 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}})


Map: [&lt;1 4 -3 -3 2 -5|, &lt;0 -5 11 12 3 18|]
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


EDOs: {{EDOs|29, 31, 60e, 151cde}}
Badness (Sintel): 0.922


Badness: 0.0230
== Gracecordial ==
: ''For the 5-limit version, see [[Schismic–Pythagorean equivalence continuum #Gracecordial (5-limit)]].''


== Tritoni ==
[[Subgroup]]: 2.3.5.7
Commas: 225/224, 385/384, 27783/27500


POTE generator: ~7/5 = 580.389
[[Comma list]]: 225/224, 781250000/771895089


Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]
{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
: mapping generators: ~2, ~3


EDOs: {{EDOs|31, 91, 122}}
[[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 }}


Badness: 0.0455
{{Optimal ET sequence|legend=1| 12, …, 113, 125, 238c, 363c }}


=Merman=
[[Badness]] (Sintel): 2.44
Comma: 1121008359375/1099511627776


POTE generator: ~45/32 = 585.634
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 5 -5|, &lt;0 -7 15|]
Comma list: 225/224, 385/384, 236328125/234365481


EDOs: {{EDOs|41, 84, 125, 209, 334c, 543bc}}
{{Mapping|legend=0| 1 0 34 63 -90 | 0 1 -20 -38 59 }}


Badness: 0.4538
Optimal tunings:  
* WE: ~2 = 1200.5571{{c}}, ~3/2 = 701.1589{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8328{{c}}


==7-limit==
{{Optimal ET sequence|legend=0| 12e, 113, 125, 238c }}
Commas: 225/224, 2500000/2470629


POTE generator: ~7/5 = 585.585
Badness (Sintel): 2.96


Map: [&lt;1 5 -5 -5|, &lt;0 -7 15 16|]
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Wedgie: &lt;&lt;7 -15 -16 -40 -45 5||
Comma list: 225/224, 325/324, 385/384, 831875/830466


EDOs: {{EDOs|41, 84, 125}}
{{Mapping|legend=0| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}


Badness: 0.0551
Optimal tunings:  
* WE: ~2 = 1200.6282{{c}}, ~3/2 = 701.2080{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8421{{c}}


==11-limit==
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
Commas: 225/224, 441/440, 1344/1331


POTE generator: ~7/5 = 585.606
Badness (Sintel): 2.16


Map: [&lt;1 5 -5 -5 2|, &lt;0 -7 15 16 3]]
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


EDOs: {{EDOs|41, 84, 125e}}
Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913


Badness: 0.0364
{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}


==13-limit==
Optimal tunings:
Commas: 144/143, 225/224, 364/363, 441/440
* WE: ~2 = 1200.5058{{c}}, ~3/2 = 701.1360{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8414{{c}}


POTE generator: ~7/5 = 585.657
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


Map: [&lt;1 5 -5 -5 2 12|, &lt;0 -7 15 16 3 -17|]
Badness (Sintel): 1.96


EDOs: {{EDOs|41, 84, 125e, 209ef, 293ef}}
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


Badness: 0.0275
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444


=Septimin=
{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}
Comma: 35595703125/34359738368


POTE generator: ~75/64 = 263.658
Optimal tunings:  
* WE: ~2 = 1200.4418{{c}}, ~3/2 = 701.0999{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8425{{c}}


Map: [&lt;1 4 1|, &lt;0 -11 6|]
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


EDOs: {{EDOs|9, 32, 41, 91, 132, 223c, 355bc}}
Badness (Sintel): 1.71


Badness: 0.6709
==== 23-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23


==7-limit==
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528
Commas: 225/224, 84035/82944


[[POTE_tuning|POTE temperament]]: 263.632
{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}


Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]
Optimal tunings:  
* WE: ~2 = 1200.4641{{c}}, ~3/2 = 701.1145{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8444{{c}}


Wedgie: &lt;&lt;11 -6 10 -35 -15 40||
{{Optimal ET sequence|legend=0| 12e, 113, 238cfi }}


EDOs: {{EDOs|9, 32, 41, 91, 132}}
Badness (Sintel): 1.57


==11-limit==
==== 29-limit ====
Commas: 225/224, 385/384, 2401/2376
Subgroup: 2.3.5.7.11.13.17.19.23.29


[[POTE_tuning|POTE temperament]]: 263.634
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493


Map: [&lt;1 4 1 5 5|, &lt;0 -11 6 -10 -7|]
{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}


EDOs: {{EDOs|9, 32, 41, 91, 223cdef}}
Optimal tunings:  
* WE: ~2 = 1200.4400{{c}}, ~3/2 = 701.0986{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8428{{c}}


==13-limit==
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
Commas: 105/104, 144/143, 196/195, 245/242


[[POTE_tuning|POTE temperament]]: 263.700
Badness (Sintel): 1.50


Map: [&lt;1 4 1 5 5 7|, &lt;0 -11 6 -10 -7 -15|]
==== 31-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31


EDOs: {{EDOs|9, 41, 91}}
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493


=Slender=
{{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 }}
Commas: 225/224, 589824/588245


[[POTE_tuning|POTE temperament]]: ~49/48 = 38.413
Optimal tunings:  
* WE: ~2 = 1200.4178{{c}}, ~3/2 = 701.0822{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8396{{c}}


Map: [&lt;1 2 2 3|, &lt;0 -13 10 -6|]
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}


Wedgie: &lt;&lt;13 -10 6 -46 -27 42||
Badness (Sintel): 1.53


EDOs: {{EDOs|31, 94, 125}}
=== Gracecord ===
Subgroup: 2.3.5.7.11


Badness: 0.0569
Comma list: 225/224, 441/440, 109375/107811


==11-limit==
{{Mapping|legend=0| 1 0 34 63 89 | 0 1 -20 -38 -54 }}
Commas: 225/224, 385/384, 1331/1323


[[POTE_tuning|POTE temperament]]: ~49/48 = 38.387
Optimal tunings:  
* WE: ~2 = 1200.6064{{c}}, ~3/2 = 701.2398{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8718{{c}}


Map: [&lt;1 2 2 3 4|, &lt;0 -13 10 -6 -17|]
{{Optimal ET sequence|legend=0| 12, …, 101cd, 113 }}


EDOs: {{EDOs|31, 63, 94, 125}}
Badness (Sintel): 2.21


Badness: 25.342
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


==13-limit==
Comma list: 225/224, 364/363, 441/440, 6125/6084
Commas: 225/224, 275/273, 385/384, 1331/1323


POTE generator: ~49/48 = 38.314
{{Mapping|legend=0| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}


Map: [&lt;1 2 2 3 4 3|, &lt;0 -13 10 -6 -17 22|]
Optimal tunings:  
* WE: ~2 = 1200.6225{{c}}, ~3/2 = 701.2539{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8781{{c}}


EDOs: {{EDOs|31, 63, 94}}
{{Optimal ET sequence|legend=0| 12f, …, 101cdf, 113 }}


Badness: 25.913
Badness (Sintel): 1.83


=Marvo=
==== 17-limit ====
Commas: 225/224, 78125000/78121827
Subgroup: 2.3.5.7.11.13.17


[[POTE_tuning|POTE generator]]: ~27/20 = 516.694
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989


Map: [&lt;1 5 12 29|, &lt;0 -6 -17 -46|]
{{Mapping|legend=0| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}


Wedgie: &lt;&lt;6 17 46 13 56 59||
Optimal tunings:  
* WE: ~2 = 1200.3308{{c}}, ~3/2 = 701.0632{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8654{{c}}


EDOs: {{EDOs|7d, 65d, 72, 137, 209, 281, 569bcc}}
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


Badness: 0.0976
Badness (Sintel): 1.87


==11-limit==
==== 19-limit ====
Commas: 225/224, 243/242, 4000/3993
Subgroup: 2.3.5.7.11.13.17.19


POTE generator: ~27/20 = 516.699
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663


Map: [&lt;1 5 12 29 12|, &lt;0 -6 -17 -46 -15|]
{{Mapping|legend=0| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}


EDOs: {{EDOs|7d, 65d, 72, 281, 353c, 425bc, 497bc}}
Optimal tunings:  
* WE: ~2 = 1200.2658{{c}}, ~3/2 = 701.0213{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8629{{c}}


Badness: 0.0317
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


==13-limit==
Badness (Sintel): 1.68
Commas: 225/224, 243/242, 351/350, 1625/1617


POTE generator: ~27/20 = 516.730
== Alphorn ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 5 12 29 12 39|, &lt;0 -6 -17 -46 -15 -62|]
[[Comma list]]: 225/224, 5764801/5668704


EDOs: {{EDOs|72, 137, 209, 281f, 490bcf}}
{{Mapping|legend=1| 1 -7 5 -9 | 0 16 -5 22 }}
: mapping generators: ~2, ~35/24


Badness: 0.0269
[[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 }}


=Marvolo=
{{Optimal ET sequence|legend=1| 13d, 28d, 41, 151cd, 192cdd, 233ccdd }}
Commas: 225/224, 156250000/155649627


POTE generator: ~21/20 = 83.348
[[Badness]] (Sintel): 3.27


Map: [&lt;1 2 1 1|, &lt;0 -6 19 26|]
=== 11-limit ===
Subgroup: 2.3.5.7.11


Wedgie: &lt;&lt;6 -19 -26 -44 -58 -7||
Comma list: 225/224, 385/384, 12250/11979


EDOs: {{EDOs|29, 43, 72, 619bcd, 691bcd}}
{{Mapping|legend=0| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}


Badness: 0.0833
Optimal tunings:  
* WE: ~2 = 1200.5123{{c}}, ~16/11 = 644.1307{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 643.8662{{c}}


==11-limit==
{{Optimal ET sequence|legend=0| 13d, 28d, 41 }}
Commas: 225/224, 441/440, 4000/3993


POTE generator: ~21/20 = 83.340
Badness (Sintel): 2.43


Map: [&lt;1 2 1 1 2|, &lt;0 -6 19 26 21|]
== Misneb ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Misneb]].''


EDOs: {{EDOs|29, 43, 72}}
[[Subgroup]]: 2.3.5.7


Badness: 0.0290
[[Comma list]]: 225/224, 4194304/4117715


==13-limit==
{{Mapping|legend=1| 1 -12 15 1 | 0 15 -14 2 }}
Commas: 169/168, 225/224, 364/363, 441/440
: mapping generators: ~2, ~15/8


POTE generator: ~21/20 = 83.330
[[Optimal tuning]]s:  
* [[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 }}


Map: [&lt;1 2 1 1 2 3|, &lt;0 -6 19 26 21 10|]
{{Optimal ET sequence|legend=1| 21, 32, 53 }}


EDOs: {{EDOs|29, 43, 72, 115f}}
[[Badness]] (Sintel): 3.57


Badness: 0.0215
=== 11-limit ===
Subgroup: 2.3.5.7.11


=Amavil=
Comma list: 99/98, 176/175, 1310720/1294139
Commas: 225/224, 17496/16807


POTE generator: ~48/35 = 529.979
{{Mapping|legend=0| 1 -12 15 1 27 | 0 15 -14 2 -26 }}


Map: [&lt;1 6 1 9|, &lt;0 -10 3 -14|]
Optimal tunings:  
* WE: ~2 = 1200.1654{{c}}, ~15/8 = 1086.8269{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6766{{c}}


Wedgie: &lt;&lt;10 -3 14 -28 -6 41||
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


EDOs: {{EDOs|9, 34d, 43, 77d}}
Badness (Sintel): 2.82


Badness: 0.1096
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


==11-limit==
Comma list: 99/98, 176/175, 640/637, 847/845
Commas: 99/98, 176/175, 864/847


POTE generator: ~15/11 = 529.974
{{Mapping|legend=0| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}


Map: [&lt;1 6 1 9 7|, &lt;0 -10 3 -14 -8|]
Optimal tunings:  
* WE: ~2 = 1200.1687{{c}}, ~15/8 = 1086.8295{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6757{{c}}


EDOs: {{EDOs|9, 34d, 43, 77de}}
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


Badness: 0.0426
Badness (Sintel): 1.88


==13-limit==
=== Musneb ===
Commas: 78/77, 99/98, 144/143, 176/175
Subgroup: 2.3.5.7.11


POTE generator: ~15/11 = 529.951
Comma list: 225/224, 385/384, 66550/64827


Map: [&lt;1 6 1 9 7 9|, &lt;0 -10 3 -14 -8 -12|]
{{Mapping|legend=0| 1 3 1 3 6 | 0 -15 14 -2 -27 }}


EDOs: {{EDOs|9, 34d, 43, 77de}}
Optimal tunings:  
* WE: ~2 = 1200.0839{{c}}, ~15/8 = 1086.9343{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.8593{{c}}


Badness: 0.0258
{{Optimal ET sequence|legend=0| 21e, 32, 53 }}


=Enneaportent=
Badness (Sintel): 2.89
Commas: 225/224, 40353607/40310784


POTE generator: ~5/4 = 383.165
== Untriton ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''


Map: [&lt;9 0 28 11|, &lt;0 2 -1 2|]
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.


Wedgie: &lt;&lt;18 -9 18 -56 -22 67||
[[Subgroup]]: 2.3.5.7


EDOs: {{EDOs|9, 54, 63, 72, 495bcd}}
[[Comma list]]: 225/224, 125000000/121060821


Badness: 0.0937
{{Mapping|legend=1| 1 -3 12 13 | 0 9 -19 -20 }}
: mapping generators: ~2, ~10/7


==11-limit==
[[Optimal tuning]]s:
Commas: 225/224, 385/384, 12005/11979
* [[WE]]: ~2 = 1199.8275{{c}}, ~10/7 = 611.2710{{c}}
: [[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: ~5/4 = 383.146
{{Optimal ET sequence|legend=1| 51, 53 }}


Map: [&lt;9 0 28 11 24|, &lt;0 2 -1 2 1|]
[[Badness]] (Sintel): 3.64


EDOs: {{EDOs|9, 54, 63, 72, 423cd, 495bcd}}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.0304
Comma list: 121/120, 225/224, 22000/21609


==13-limit==
{{Mapping|legend=0| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}
Commas: 169/168, 225/224, 364/363, 1716/1715


POTE generator: ~5/4 = 383.047
Optimal tunings:  
* WE: ~2 = 1200.3591{{c}}, ~10/7 = 611.5569{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3690{{c}}


Map: [&lt;9 0 28 11 24 19|, &lt;0 2 -1 2 1 2|]
{{Optimal ET sequence|legend=0| 51, 53 }}


EDOs: {{EDOs|9, 54, 63, 72, 279cf}}
Badness (Sintel): 2.46


Badness: 0.0223
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


= Submajor =
Comma list: 121/120, 225/224, 275/273, 1040/1029
== 5-limit ==
Comma: 69198046875/68719476736


POTE generator: ~10125/8192 = 362.321
{{Mapping|legend=0| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}


Map: [&lt;1 4 -1|, &lt;0 -8 11|]
Optimal tunings:  
* WE: ~2 = 1200.4078{{c}}, ~10/7 = 611.5536{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3392{{c}}


EDOs: {{EDOs|10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}}
{{Optimal ET sequence|legend=0| 51f, 53 }}


Badness: 0.1302
Badness (Sintel): 1.96


== 7-limit ==
== Naiadical ==
Commas: 225/224, 51200/50421
Named by [[Xenllium]] in 2026, naiadical may be described as the {{nowrap| 21 & 29 }} temperament.


POTE generator: ~49/40 = 362.255
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 4 -1 1|, &lt;0 -8 11 6|]
[[Comma list]]: 225/224, 823543/800000


Wedgie: &lt;&lt;8 -11 -6 -36 -32 17||
{{Mapping|legend=1| 1 -4 11 9 | 0 9 -14 -10 }}
: mapping generators: ~2, ~32/21


EDOs: {{EDOs|10, 33, 43, 53}}
[[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: 0.0605
{{Optimal ET sequence|legend=1| 21, 29, 50, 79d, 129cdd, 179bcddd }}


== 11-limit ==
[[Badness]] (Sintel): 3.67
Commas: 225/224, 385/384, 6655/6561


POTE generator: ~27/22 = 362.101
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 4 -1 1 11|, &lt;0 -8 11 6 -25|]
Comma list: 225/224, 245/242, 1617/1600


EDOs: {{EDOs|10, 53, 116, 169de, 285cde}}
Mapping: {{Mapping| 1 -4 11 9 14 | 0 9 -14 -10 -17 }}


Badness: 0.0506
Optimal tunings:
* WE: ~2 = 1201.9008{{c}}, ~21/16 = 745.3867{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~32/21 = 744.1777{{c}}
 
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
 
Badness (Sintel): 2.00


=== 13-limit ===
=== 13-limit ===
Commas: 169/168, 225/224, 275/273, 385/384
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 196/195, 245/242, 1001/1000
 
Mapping: {{Mapping| 1 -4 11 9 14 13 | 0 9 -14 -10 -17 -15 }}


POTE generator: ~16/13 = 362.105
Optimal tunings:  
* WE: ~2 = 1201.7863{{c}}, ~20/13 = 745.3344{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1931{{c}}


Map: [&lt;1 4 -1 1 11 4|, &lt;0 -8 11 6 -25 -1|]
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}


EDOs: {{EDOs|10, 53, 116, 169de, 285cdef}}
Badness (Sintel): 1.43


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


== Interpental ==
Comma list: 105/104, 170/169, 196/195, 221/220, 245/242
Commas: 99/98, 176/175, 51200/50421


POTE generator: ~49/40 = 362.418
Mapping: {{Mapping| 1 -4 11 9 14 13 14 | 0 9 -14 -10 -17 -15 -16 }}


Map: [&lt;1 4 -1 1 -5|, &lt;0 -8 11 6 28|]
Optimal tunings:  
* WE: ~2 = 1201.9208{{c}}, ~20/13 = 745.3976{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1669{{c}}


EDOs: {{EDOs|43, 53, 96, 149d}}
{{Optimal ET sequence|legend=0| 21, 29g, 50, 79dg }}


Badness: 0.0518
Badness (Sintel): 1.26
 
== Quintannic ==
Named by [[Scott Dakota]], quintannic may be described as the {{nowrap| 43 & 60 }} temperament.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 9805926501/9765625000
 
{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
: mapping generators: ~2, ~10000/9261
 
[[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 }}
 
{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}
 
[[Badness]] (Sintel): 3.81
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 441/440, 43923/43750
 
{{Mapping|legend=0| 1 1 5 7 8 | 0 5 -23 -36 -39 }}
 
Optimal tunings:
* WE: ~2 = 1201.0031{{c}}, ~320/297 = 139.9435{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~320/297 = 139.8053{{c}}
 
{{Optimal ET sequence|legend=0| 43, 60e, 103, 369bcdeee, 472bbcddeee }}
 
Badness (Sintel): 1.74


=== 13-limit ===
=== 13-limit ===
Commas: 99/98, 169/168, 176/175, 640/637
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 }}
 
Optimal tunings:
* WE: ~2 = 1200.8354{{c}}, ~13/12 = 139.9095{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.7997{{c}}
 
{{Optimal ET sequence|legend=0| 43, 60e, 103 }}
 
Badness (Sintel): 1.35
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 225/224, 273/272, 375/374, 441/440, 891/884
 
{{Mapping|legend=0| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}
 
Optimal tunings:
* WE: ~2 = 1200.7402{{c}}, ~13/12 = 139.9015{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.8038{{c}}
 
{{Optimal ET sequence|legend=0| 43, 60e, 103 }}
 
Badness (Sintel): 1.17
 
== Hendeca ==
{{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:marvel]]
[[Category:Marvel temperaments| ]] <!-- main article -->
[[Category:overview]]
[[Category:Temperament collections]]
[[Category:rank_2]]
[[Category:Catalogs of rank-2 temperaments]]
[[Category:temperament]]
Retrieved from "https://en.xen.wiki/w/Marvel_temperaments"