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Marvel temperaments: Difference between revisions

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{{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]]
* ''[[Quintapole]]'' (+7812500/7411887) → [[Quintaleap family #Quintapole|Quintaleap 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]]
* ''[[Decic]]'' (+16807/16384) → [[Cloudy clan #Decic|Cloudy clan]]
* ''[[Amavil]]'' (+17496/16807) → [[Mabila family #Amavil|Mabila family]]
* ''[[Betic]]'' (+1071875/1062882) → [[Sycamore family #Betic|Sycamore family]]
* ''[[Hendeca]]'' (+122880/117649) → [[11th-octave temperaments #Hendeca|11th-octave temperaments]]
* [[Compton]] (+250047/250000) → [[Compton family #Compton|Compton family]]
* ''[[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]]


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.
Considered below are wizard, tritonic, septimin, merman, slender, triton, marvolo, enneaportent, gracecordial, alphorn, misneb, untriton, naiadical, quintannic, gwazy, and tertiosec, in the order of increasing [[badness]].  


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.)
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.


= Negri =
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.
{{main| Negri }}


== 5-limit ==
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}}.)
Note that this is technically not a marvel temperament until the 7-limit, but also placed here for reference.  


Comma list: 16875/16384
== Wizard ==
{{Main| Wizard }}
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Wizard]].''


[[POTE generator]]: ~15/14 = 125.7549
Wizard has a [[semi-octave]] period and is generated by an interval that can be treated as [[~]][[17/15]]. The semi-octave complement of this interval is ~[[5/4]]. Wizard can be described as {{nowrap| 22 & 72 }}. Its [[ploidacot]] is diploid alpha-hexacot, so six generator steps plus a semi-octave period gives the [[3/1|perfect twelfth]]. [[72edo]], [[94edo]], and especially [[166edo]] are good tunings for it.  


[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
[[Subgroup]]: 2.3.5.7


[[Wedgie]]: {{wedgie| 4 -3 -14 }}
[[Comma list]]: 225/224, 118098/117649


{{Val list|legend=1| 9, 10, 19, 86 }}
{{Mapping|legend=1| 2 1 5 2 | 0 6 -1 10 }}
: mapping generators: ~1225/864, ~245/216


== 7-limit ==
[[Optimal tuning]]s:
Comma list: 49/48, 225/224
* [[WE]]: ~1225/864 = 600.3438{{c}}, ~245/216 = 216.8680{{c}}
: [[error map]]: {{val| +0.688 -0.403 -1.463 +0.541 }}
* [[CWE]]: ~1225/864 = 600.0000{{c}}, ~245/216 = 216.7977{{c}}
: error map: {{val| 0.000 -1.169 -3.111 -0.849 }}


[[POTE generator]]: ~15/14 = 125.608
{{Optimal ET sequence|legend=1| 22, 50, 72, 238c, 310c, 382c, 454bccd }}


[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}]
[[Badness]] (Sintel): 1.03


[[Wedgie]]: {{wedgie| 4 -3 2 -14 -8 13 }}
=== 11-limit ===
Subgroup: 2.3.5.7.11


{{Val list|legend=1| 9, 10, 19, 86 }}
Comma list: 225/224, 385/384, 4000/3993


== 11-limit ==
Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}
Comma list: 45/44, 49/48, 56/55


[[POTE generator]]: ~15/14 = 126.474
Optimal tunings:  
* WE: ~99/70 = 600.3051{{c}}, ~25/22 = 216.8782{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.7961{{c}}


Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]
{{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}


{{Val list|legend=1| 9, 10, 19 }}
Badness (Sintel): 0.613


[[Badness]]: 0.0262
==== Lizard ====
Subgroup: 2.3.5.7.11.13


=== 13-limit ===
Comma list: 225/224, 351/350, 364/363, 385/384
Comma list: 45/44, 49/48, 56/55, 78/77


[[POTE generator]]: ~14/13 = 126.431
Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}


Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}]
Optimal tunings:  
* WE: ~55/39 = 600.4824{{c}}, ~25/22 = 216.7852{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~25/22 = 216.6247{{c}}


{{Val list|legend=1| 9, 10, 19 }}
{{Optimal ET sequence|legend=0| 22, 50, 72 }}


== Negril ==
Badness (Sintel): 0.900
Comma list: 49/48, 100/99, 225/224


POTE generator: ~15/14 = 124.767
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17


Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]
Comma list: 221/220, 273/272, 289/288, 351/350, 375/374


{{Val list|legend=1| 19, 29, 48df, 77cdf }}
Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}


Badness: 0.0387
Optimal tunings:  
* WE: ~17/12 = 600.5032{{c}}, ~17/15 = 216.8002{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.6361{{c}}


=== 13-limit ===
{{Optimal ET sequence|legend=0| 22, 50, 72 }}
Comma list: 49/48, 65/64, 91/90, 875/858


POTE generator: ~15/14 = 124.716
Badness (Sintel): 0.741


Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19


{{Val list|legend=1| 9, 10, 19, 29, 48, 77 }}
Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342


Badness: 0.0244
Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}


== Negric ==
Optimal tunings:
Comma list: 33/32, 49/48, 77/75
* WE: ~17/12 = 600.4698{{c}}, ~17/15 = 216.6925{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.5434{{c}}


POTE generator: ~15/14 = 127.039
{{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}


Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}]
Badness (Sintel): 0.955


{{Val list|legend=1| 9, 19, 85 }}
==== Gizzard ====
Subgroup: 2.3.5.7.11.13


Badness: 0.0306
Comma list: 225/224, 325/324, 385/384, 1573/1568


=== 13-limit ===
Mapping: {{mapping| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }}
Comma list: 33/32, 49/48, 65/64, 91/90


POTE generator: ~15/14 = 127.039
Optimal tunings:  
* WE: ~99/70 = 600.2896{{c}}, ~25/22 = 216.9343{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.8501{{c}}


Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]
{{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}


{{Val list|legend=1| 9, 19, 85 }}
Badness (Sintel): 0.837


Badness: 0.0202
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17


== Negroni ==
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384
Comma list: 49/48, 55/54, 225/224


POTE generator: ~15/14 = 124.539
Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}


Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]
Optimal tunings:  
* WE: ~17/12 = 600.3227{{c}}, ~17/15 = 216.9414{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8469{{c}}


{{Val list|legend=1| 10, 19e, 29, 77cde }}
{{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}


Badness: 0.0353
Badness (Sintel): 0.694


=== 13-limit ===
===== 19-limit =====
Comma list: 49/48, 55/54, 65/64, 91/90
Subgroup: 2.3.5.7.11.13.17.19


POTE generator: ~15/14 = 124.545
Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594


Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]
Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}


{{Val list|legend=1| 10, 19e, 29, 77cdef }}
Optimal tunings:
* WE: ~17/12 = 600.2637{{c}}, ~17/15 = 216.9570{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8687{{c}}


Badness: 0.0216
{{Optimal ET sequence|legend=0| 72, 94, 166g }}


= Passive =
Badness (Sintel): 0.901
{{see also | Archytas clan #Passion }}


Comma list: 225/224, 256/245
=== Mage ===
Subgroup: 2.3.5.7.11


POTE generator: ~16/15 = 98.809
Comma list: 99/98, 176/175, 1331/1296


Mapping: [{{val| 1 2 2 3 }}, {{val| 0 -5 4 -2 }}]
Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }}


{{Val list|legend=1| 1, 11, 12, 49d }}
Optimal tunings:
* WE: ~77/54 = 600.6486{{c}}, ~55/48 = 217.1099{{c}}
* CWE: ~77/54 = 600.0000{{c}}, ~55/48 = 216.9841{{c}}


Badness: 0.0751
{{Optimal ET sequence|legend=0| 22, 50e, 72ee }}


=Wizard=
Badness (Sintel): 1.91
Comma: 2197265625/2147483648


POTE generator: ~5/4 = 383.212
== Tritonic ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tritonic]].''


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


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


Badness: 0.3864
[[Comma list]]: 225/224, 50421/50000


==7-limit==
{{Mapping|legend=1| 1 -1 8 9 | 0 5 -11 -12 }}
Commas: 225/224, 118098/117649
: mapping generators: ~2, ~10/7


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


Map: [&lt;2 1 5 2|, &lt;0 6 -1 10|]
{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}


Wedgie: &lt;&lt;12 -2 20 -31 -2 52||
[[Badness]] (Sintel): 1.20


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


Badness: 0.0408
Comma list: 121/120, 225/224, 441/440


==11-limit==
Mapping: {{mapping| 1 -1 8 9 5 | 0 5 -11 -12 -3 }}
Commas: 225/224, 385/384, 4000/3993


[[POTE_tuning|POTE temperament]]: 383.232
Optimal tunings:  
* WE: ~2 = 1201.7116{{c}}, ~10/7 = 620.6166{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6890{{c}}


Map: [&lt;2 1 5 2 8|, &lt;0 6 -1 10 -3|]
{{Optimal ET sequence|legend=0| 29, 31, 60e, 91e, 213bcdeee }}


EDOs: {{EDOs|22, 50, 72, 94, 166, 238c, 310c}}
Badness (Sintel): 0.782


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


=== Lizard ===
Comma list: 105/104, 121/120, 196/195, 275/273
Commas: 225/224, 351/350, 364/363, 385/384


[[POTE_tuning|POTE temperament]]: 383.389
Mapping: {{mapping| 1 -1 8 9 5 13 | 0 5 -11 -12 -3 -18 }}


Map: [&lt;2 1 5 2 8 11|, &lt;0 6 -1 10 -3 -10|]
Optimal tunings:  
* WE: ~2 = 1201.5355{{c}}, ~10/7 = 620.6855{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8469{{c}}


EDOs: {{EDOs|22, 50, 72, 122, 194df}}
{{Optimal ET sequence|legend=0| 29, 31, 60e }}


Badness: 0.0218
Badness (Sintel): 0.950


==== 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, 121/120, 154/153, 196/195, 273/272


Map: [&lt;2 1 5 2 8 11 6|, &lt;0 6 -1 10 -3 -10 6|]
Mapping: {{mapping| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}


EDOs: {{EDOs|22, 50, 72, 122g, 194dfg}}
Optimal tunings:  
* WE: ~2 = 1201.5260{{c}}, ~10/7 = 620.7330{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8986{{c}}


Badness: 0.0145
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
 
Badness (Sintel): 0.973


==== 19-limit ====
==== 19-limit ====
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272
 
Mapping: {{mapping| 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
 
Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195
 
Mapping: {{mapping| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}
 
Optimal tunings:
* WE: ~2 = 1201.4074{{c}}, ~10/7 = 620.7185{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9548{{c}}
 
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
 
Badness (Sintel): 1.04
 
=== Tritoni ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 27783/27500
 
Mapping: {{mapping| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}
 
Optimal tunings:
* WE: ~2 = 1201.0888{{c}}, ~10/7 = 620.1733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6146{{c}}
 
{{Optimal ET sequence|legend=0| 31, 91, 122, 153d }}
 
Badness (Sintel): 1.50
 
== Septimin ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Septimin]].''
 
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| 41, 91, 132d }}
 
[[Badness]] (Sintel): 1.38
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 245/242, 385/384
 
Mapping: {{mapping| 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| 41, 91, 223cdef }}
 
Badness (Sintel): 1.04
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 144/143, 196/195, 245/242
 
Mapping: {{mapping| 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| 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: {{mapping| 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: {{mapping| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}


[[POTE_tuning|POTE generator]]: ~5/4 = 383.477
Optimal tunings:  
* WE: ~2 = 1199.7422{{c}}, ~10/7 = 614.2110{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3442{{c}}


Map: [&lt;2 1 5 2 8 11 6 2|, &lt;0 6 -1 10 -3 -10 6 18|]
{{Optimal ET sequence|legend=0| 41, 84, 125e, 209ef, 293ef }}


EDOs: {{EDOs|22h, 50, 72, 122g, 194dfg}}
Badness (Sintel): 1.14


Badness: 0.0157
=== Mermaid ===
Subgroup: 2.3.5.7.11


=== Gizzard ===
Comma list: 225/224, 385/384, 532400/531441
Commas: 225/224, 385/384, 325/324, 1573/1568


POTE generator: ~5/4 = 383.170
Mapping: {{mapping| 1 -2 10 11 -16 | 0 7 -15 -16 38 }}


Map: [&lt;2 1 5 2 8 -2|, &lt;0 6 -1 10 -3 26|]
Optimal tunings:  
* WE: ~2 = 1199.4973{{c}}, ~10/7 = 614.7004{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4470{{c}}


EDOs: {{EDOs|22, 72, 94, 166, 238cf}}
{{Optimal ET sequence|legend=0| 41, 84e, 125, 166 }}


Badness: 0.0203
Badness (Sintel): 1.46


==== 17-limit ====
==== 13-limit ====
Commas: 225/224, 289/288, 325/324, 375/374, 385/384
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 325/324, 385/384, 10648/10647
 
Mapping: {{mapping| 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
 
[[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 }}


POTE generator: ~5/4 = 383.175
{{Optimal ET sequence|legend=1| 31, 94, 125, 406c }}


Map: [&lt;2 1 5 2 8 -2 6|, &lt;0 6 -1 10 -3 26 6|]
[[Badness]] (Sintel): 1.44


EDOs: {{EDOs|22f, 72, 94, 166g, 238cfg}}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.0136
Comma list: 225/224, 385/384, 1331/1323


==== 19-limit ====
Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399


POTE generator: ~5/4 = 383.138
Optimal tunings:  
* WE: ~2 = 1199.4983{{c}}, ~49/48 = 38.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3775{{c}}


Map: [&lt;2 1 5 2 8 -2 6 15|, &lt;0 6 -1 10 -3 26 6 -18|]
{{Optimal ET sequence|legend=0| 31, 63, 94, 125 }}


EDOs: {{EDOs|22f, 72, 94, 166g}}
Badness (Sintel): 0.838


Badness: 0.0148
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


== Mage ==
Comma list: 225/224, 275/273, 385/384, 1331/1323
Commas: 99/98, 176/175, 1331/1296


POTE generator: ~55/48 = 216.876
Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}


Map: [&lt;2 1 5 2 4|, &lt;0 6 -1 10 8|]
Optimal tunings:  
* WE: ~2 = 1200.1728{{c}}, ~49/48 = 38.3192{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3129{{c}}


EDOs: {{EDOs|22, 72e, 94e}}
{{Optimal ET sequence|legend=0| 31, 63, 94 }}


Badness: 0.0578
Badness (Sintel): 1.07


=Triton=
== Triton ==
Commas: 225/224, 1029/1000
: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''


[[POTE_tuning|POTE temperament]]: ~7/5 = 568.865
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.  


Map: [&lt;1 0 6 7|, &lt;0 3 -7 -8|]
[[Subgroup]]: 2.3.5.7


Wedgie: &lt;&lt;3 -7 -8 -18 -21 1||
[[Comma list]]: 225/224, 1029/1000


EDOs: {{EDOs|17d, 19, 78bd, 97bd}}
{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}
: mapping generators: ~2, ~10/7


Badness: 0.0592
[[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 }}


==11-limit==
{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
Commas: 45/44, 56/55, 1029/1000


POTE generator: ~7/5 = 569.144
[[Badness]] (Sintel): 1.50


Map: [&lt;1 0 6 7 4|, &lt;0 3 -7 -8 -1|]
=== 11-limit ===
Subgroup: 2.3.5.7.11


EDOs: {{EDOs|19, 59bde, 78bde, 97bde}}
Comma list: 45/44, 56/55, 1029/1000


Badness: 0.0457
Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}


= Tritonic =
Optimal tunings:
== 5-limit ==
* WE: ~2 = 1201.3875{{c}}, ~10/7 = 631.5852{{c}}
Comnma: 553584375/536870912
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 630.8007{{c}}


POTE generator: ~45/32 = 580.219
{{Optimal ET sequence|legend=0| 2, 17d, 19 }}


Map: [&lt;1 4 -3|, &lt;0 -5 11|]
Badness (Sintel): 1.51


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


Badness: 0.3785
[[Comma list]]: 225/224, 156250000/155649627


== 7-limit ==
{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
Commas: 225/224, 50421/50000
: mapping generators: ~2, ~21/20


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


Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]
{{Optimal ET sequence|legend=1| 29, 43, 72, 619bbccd, 691bbccd }}


Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||
[[Badness]] (Sintel): 2.11


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


== 11-limit ==
Comma list: 225/224, 441/440, 4000/3993
Commas: 121/120, 225/224, 441/440


[[POTE_tuning|POTE generator]]: ~7/5 = 580.267
Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}


Map: [&lt;1 4 -3 -3 2|, &lt;0 -5 11 12 3|]
Optimal tunings:  
* WE: ~2 = 1200.7075{{c}}, ~21/20 = 83.3888{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3564{{c}}


EDOs: {{EDOs|29, 31, 60e}}
{{Optimal ET sequence|legend=0| 29, 43, 72 }}


Badness: 0.0237
Badness (Sintel): 0.958


=== 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, 441/440
 
Mapping: {{mapping| 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: {{mapping| 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
 
Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}
 
Optimal tunings:
* WE: ~2 = 1200.7625{{c}}, ~21/20 = 83.3895{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3551{{c}}
 
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}
 
Badness (Sintel): 0.895
 
== Enneaportent ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 40353607/40310784


POTE generator: ~7/5 = 580.108
{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
: mapping generators: ~2592/2401, ~12005/6912


Map: [&lt;1 4 -3 -3 2 -5|, &lt;0 -5 11 12 3 18|]
[[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 }}


EDOs: {{EDOs|29, 31, 60e, 151cde}}
{{Optimal ET sequence|legend=1| 9, 54, 63, 72, 495bccd, 567bcccd }}


Badness: 0.0230
[[Badness]] (Sintel): 2.37


== Tritoni ==
=== 11-limit ===
Commas: 225/224, 385/384, 27783/27500
Subgroup: 2.3.5.7.11


POTE generator: ~7/5 = 580.389
Comma list: 225/224, 385/384, 12005/11979


Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]
Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}


EDOs: {{EDOs|31, 91, 122}}
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}})
 
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}
 
Badness (Sintel): 1.01
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Badness: 0.0455
Comma list: 169/168, 225/224, 364/363, 1716/1715


=Merman=
Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}
Comma: 1121008359375/1099511627776


POTE generator: ~45/32 = 585.634
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 5 -5|, &lt;0 -7 15|]
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


EDOs: {{EDOs|41, 84, 125, 209, 334c, 543bc}}
Badness (Sintel): 0.922


Badness: 0.4538
== Gracecordial ==
: ''For the 5-limit version, see [[Schismic–Pythagorean equivalence continuum #Gracecordial (5-limit)]].''


==7-limit==
[[Subgroup]]: 2.3.5.7
Commas: 225/224, 2500000/2470629


POTE generator: ~7/5 = 585.585
[[Comma list]]: 225/224, 781250000/771895089


Map: [&lt;1 5 -5 -5|, &lt;0 -7 15 16|]
{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
: mapping generators: ~2, ~3


Wedgie: &lt;&lt;7 -15 -16 -40 -45 5||
[[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 = 1200.3333{{c}}, ~3/2 = 700.8112{{c}}
: error map: {{val| 0.000 -1.144 -2.537 +0.349 }}


EDOs: {{EDOs|41, 84, 125}}
{{Optimal ET sequence|legend=1| 12, …, 113, 125, 238c, 363c }}


Badness: 0.0551
[[Badness]] (Sintel): 2.44


==11-limit==
=== 11-limit ===
Commas: 225/224, 441/440, 1344/1331
Subgroup: 2.3.5.7.11


POTE generator: ~7/5 = 585.606
Comma list: 225/224, 385/384, 236328125/234365481


Map: [&lt;1 5 -5 -5 2|, &lt;0 -7 15 16 3]]
Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}


EDOs: {{EDOs|41, 84, 125e}}
Optimal tunings:  
* WE: ~2 = 1200.5571{{c}}, ~3/2 = 701.1589{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8328{{c}}


Badness: 0.0364
{{Optimal ET sequence|legend=0| 12e, 113, 125, 238c }}


==13-limit==
Badness (Sintel): 2.96
Commas: 144/143, 225/224, 364/363, 441/440


POTE generator: ~7/5 = 585.657
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 5 -5 -5 2 12|, &lt;0 -7 15 16 3 -17|]
Comma list: 225/224, 325/324, 385/384, 831875/830466


EDOs: {{EDOs|41, 84, 125e, 209ef, 293ef}}
Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}


Badness: 0.0275
Optimal tunings:  
* WE: ~2 = 1200.6282{{c}}, ~3/2 = 701.2080{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8421{{c}}


=Septimin=
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
Comma: 35595703125/34359738368


POTE generator: ~75/64 = 263.658
Badness (Sintel): 2.16


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


EDOs: {{EDOs|9, 32, 41, 91, 132, 223c, 355bc}}
Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913


Badness: 0.6709
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}


==7-limit==
Optimal tunings:
Commas: 225/224, 84035/82944
* WE: ~2 = 1200.5058{{c}}, ~3/2 = 701.1360{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8414{{c}}


[[POTE_tuning|POTE temperament]]: 263.632
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]
Badness (Sintel): 1.96


Wedgie: &lt;&lt;11 -6 10 -35 -15 40||
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


EDOs: {{EDOs|9, 32, 41, 91, 132}}
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444


==11-limit==
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}
Commas: 225/224, 385/384, 2401/2376


[[POTE_tuning|POTE temperament]]: 263.634
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 5 5|, &lt;0 -11 6 -10 -7|]
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


EDOs: {{EDOs|9, 32, 41, 91, 223cdef}}
Badness (Sintel): 1.71


==13-limit==
==== 23-limit ====
Commas: 105/104, 144/143, 196/195, 245/242
Subgroup: 2.3.5.7.11.13.17.19.23


[[POTE_tuning|POTE temperament]]: 263.700
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528


Map: [&lt;1 4 1 5 5 7|, &lt;0 -11 6 -10 -7 -15|]
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}


EDOs: {{EDOs|9, 41, 91}}
Optimal tunings:  
* WE: ~2 = 1200.4641{{c}}, ~3/2 = 701.1145{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8444{{c}}


=Slender=
{{Optimal ET sequence|legend=0| 12e, 113, 238cfi }}
Commas: 225/224, 589824/588245


[[POTE_tuning|POTE temperament]]: ~49/48 = 38.413
Badness (Sintel): 1.57


Map: [&lt;1 2 2 3|, &lt;0 -13 10 -6|]
==== 29-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29


Wedgie: &lt;&lt;13 -10 6 -46 -27 42||
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493


EDOs: {{EDOs|31, 94, 125}}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}


Badness: 0.0569
Optimal tunings:  
* WE: ~2 = 1200.4400{{c}}, ~3/2 = 701.0986{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8428{{c}}


==11-limit==
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
Commas: 225/224, 385/384, 1331/1323


[[POTE_tuning|POTE temperament]]: ~49/48 = 38.387
Badness (Sintel): 1.50


Map: [&lt;1 2 2 3 4|, &lt;0 -13 10 -6 -17|]
==== 31-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31


EDOs: {{EDOs|31, 63, 94, 125}}
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493


Badness: 25.342
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}


==13-limit==
Optimal tunings:
Commas: 225/224, 275/273, 385/384, 1331/1323
* WE: ~2 = 1200.4178{{c}}, ~3/2 = 701.0822{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8396{{c}}


POTE generator: ~49/48 = 38.314
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}


Map: [&lt;1 2 2 3 4 3|, &lt;0 -13 10 -6 -17 22|]
Badness (Sintel): 1.53


EDOs: {{EDOs|31, 63, 94}}
=== Gracecord ===
Subgroup: 2.3.5.7.11


Badness: 25.913
Comma list: 225/224, 441/440, 109375/107811


=Marvo=
Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}
Commas: 225/224, 78125000/78121827


[[POTE_tuning|POTE generator]]: ~27/20 = 516.694
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 5 12 29|, &lt;0 -6 -17 -46|]
{{Optimal ET sequence|legend=0| 12, …, 101cd, 113 }}


Wedgie: &lt;&lt;6 17 46 13 56 59||
Badness (Sintel): 2.21


EDOs: {{EDOs|7d, 65d, 72, 137, 209, 281, 569bcc}}
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Badness: 0.0976
Comma list: 225/224, 364/363, 441/440, 6125/6084


==11-limit==
Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}
Commas: 225/224, 243/242, 4000/3993


POTE generator: ~27/20 = 516.699
Optimal tunings:  
* WE: ~2 = 1200.6225{{c}}, ~3/2 = 701.2539{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8781{{c}}


Map: [&lt;1 5 12 29 12|, &lt;0 -6 -17 -46 -15|]
{{Optimal ET sequence|legend=0| 12f, …, 101cdf, 113 }}


EDOs: {{EDOs|7d, 65d, 72, 281, 353c, 425bc, 497bc}}
Badness (Sintel): 1.83


Badness: 0.0317
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


==13-limit==
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989
Commas: 225/224, 243/242, 351/350, 1625/1617


POTE generator: ~27/20 = 516.730
Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}


Map: [&lt;1 5 12 29 12 39|, &lt;0 -6 -17 -46 -15 -62|]
Optimal tunings:  
* WE: ~2 = 1200.3308{{c}}, ~3/2 = 701.0632{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8654{{c}}


EDOs: {{EDOs|72, 137, 209, 281f, 490bcf}}
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


Badness: 0.0269
Badness (Sintel): 1.87


=Marvolo=
==== 19-limit ====
Commas: 225/224, 156250000/155649627
Subgroup: 2.3.5.7.11.13.17.19


POTE generator: ~21/20 = 83.348
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663


Map: [&lt;1 2 1 1|, &lt;0 -6 19 26|]
Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}


Wedgie: &lt;&lt;6 -19 -26 -44 -58 -7||
Optimal tunings:  
* WE: ~2 = 1200.2658{{c}}, ~3/2 = 701.0213{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8629{{c}}


EDOs: {{EDOs|29, 43, 72, 619bcd, 691bcd}}
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


Badness: 0.0833
Badness (Sintel): 1.68


==11-limit==
== Alphorn ==
Commas: 225/224, 441/440, 4000/3993
[[Subgroup]]: 2.3.5.7


POTE generator: ~21/20 = 83.340
[[Comma list]]: 225/224, 5764801/5668704


Map: [&lt;1 2 1 1 2|, &lt;0 -6 19 26 21|]
{{Mapping|legend=1| 1 -7 5 -9 | 0 16 -5 22 }}
: mapping generators: ~2, ~35/24


EDOs: {{EDOs|29, 43, 72}}
[[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: 0.0290
{{Optimal ET sequence|legend=1| 13d, 28d, 41, 151cd, 192cdd, 233ccdd }}


==13-limit==
[[Badness]] (Sintel): 3.27
Commas: 169/168, 225/224, 364/363, 441/440


POTE generator: ~21/20 = 83.330
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 2 1 1 2 3|, &lt;0 -6 19 26 21 10|]
Comma list: 225/224, 385/384, 12250/11979


EDOs: {{EDOs|29, 43, 72, 115f}}
Mapping: {{mapping| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}


Badness: 0.0215
Optimal tunings:  
* WE: ~2 = 1200.5123{{c}}, ~16/11 = 644.1307{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 643.8662{{c}}


= Amavil =
{{Optimal ET sequence|legend=0| 13d, 28d, 41 }}
== 5-limit (mabila) ==
Comma: 268435456/263671875


POTE generator: ~512/375 = 529.6849
Badness (Sintel): 2.43


Map: [<1 6 1|, <0 -10 3|]
== Misneb ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Misneb]].''


EDOs: {{EDOs| 9, 25, 34, 77, 111, 145, 256c }}
[[Subgroup]]: 2.3.5.7


Badness: 0.2325
[[Comma list]]: 225/224, 4194304/4117715


== 7-limit ==
{{Mapping|legend=1| 1 -12 15 1 | 0 15 -14 2 }}
Commas: 225/224, 17496/16807
: mapping generators: ~2, ~15/8


POTE generator: ~48/35 = 529.979
[[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 6 1 9|, &lt;0 -10 3 -14|]
{{Optimal ET sequence|legend=1| 21, 32, 53 }}


Wedgie: &lt;&lt;10 -3 14 -28 -6 41||
[[Badness]] (Sintel): 3.57


EDOs: {{EDOs|9, 34d, 43, 77d}}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.1096
Comma list: 99/98, 176/175, 1310720/1294139


== 11-limit ==
Mapping: {{mapping| 1 -12 15 1 27 | 0 15 -14 2 -26 }}
Commas: 99/98, 176/175, 864/847


POTE generator: ~15/11 = 529.974
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 6 1 9 7|, &lt;0 -10 3 -14 -8|]
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


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


Badness: 0.0426
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


== 13-limit ==
Comma list: 99/98, 176/175, 640/637, 847/845
Commas: 78/77, 99/98, 144/143, 176/175


POTE generator: ~15/11 = 529.951
Mapping: {{mapping| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}


Map: [&lt;1 6 1 9 7 9|, &lt;0 -10 3 -14 -8 -12|]
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: 0.0258
Badness (Sintel): 1.88


=Enneaportent=
=== Musneb ===
Commas: 225/224, 40353607/40310784
Subgroup: 2.3.5.7.11


POTE generator: ~5/4 = 383.165
Comma list: 225/224, 385/384, 66550/64827


Map: [&lt;9 0 28 11|, &lt;0 2 -1 2|]
Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}


Wedgie: &lt;&lt;18 -9 18 -56 -22 67||
Optimal tunings:  
* WE: ~2 = 1200.0839{{c}}, ~15/8 = 1086.9343{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.8593{{c}}


EDOs: {{EDOs|9, 54, 63, 72, 495bcd}}
{{Optimal ET sequence|legend=0| 21e, 32, 53 }}


Badness: 0.0937
Badness (Sintel): 2.89


==11-limit==
== Untriton ==
Commas: 225/224, 385/384, 12005/11979
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''


POTE generator: ~5/4 = 383.146
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;9 0 28 11 24|, &lt;0 2 -1 2 1|]
[[Subgroup]]: 2.3.5.7


EDOs: {{EDOs|9, 54, 63, 72, 423cd, 495bcd}}
[[Comma list]]: 225/224, 125000000/121060821


Badness: 0.0304
{{Mapping|legend=1| 1 -3 12 13 | 0 9 -19 -20 }}
: mapping generators: ~2, ~10/7


==13-limit==
[[Optimal tuning]]s:
Commas: 169/168, 225/224, 364/363, 1716/1715
* [[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 = 383.047
{{Optimal ET sequence|legend=1| 51, 53 }}


Map: [&lt;9 0 28 11 24 19|, &lt;0 2 -1 2 1 2|]
[[Badness]] (Sintel): 3.64


EDOs: {{EDOs|9, 54, 63, 72, 279cf}}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.0223
Comma list: 121/120, 225/224, 22000/21609


= Submajor =
Mapping: {{mapping| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}
== 5-limit ==
Comma: 69198046875/68719476736


POTE generator: ~10125/8192 = 362.321
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 4 -1|, &lt;0 -8 11|]
{{Optimal ET sequence|legend=0| 51, 53 }}


EDOs: {{EDOs|10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}}
Badness (Sintel): 2.46


Badness: 0.1302
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


== 7-limit ==
Comma list: 121/120, 225/224, 275/273, 1040/1029
Commas: 225/224, 51200/50421


POTE generator: ~49/40 = 362.255
Mapping: {{mapping| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}


Map: [&lt;1 4 -1 1|, &lt;0 -8 11 6|]
Optimal tunings:  
* WE: ~2 = 1200.4078{{c}}, ~10/7 = 611.5536{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3392{{c}}


Wedgie: &lt;&lt;8 -11 -6 -36 -32 17||
{{Optimal ET sequence|legend=0| 51f, 53 }}


EDOs: {{EDOs|10, 33, 43, 53}}
Badness (Sintel): 1.96


Badness: 0.0605
== Naiadical ==
Named by [[Xenllium]] in 2026, naiadical may be described as the {{nowrap| 21 & 29 }} temperament.  


== 11-limit ==
[[Subgroup]]: 2.3.5.7
Commas: 225/224, 385/384, 6655/6561


POTE generator: ~27/22 = 362.101
[[Comma list]]: 225/224, 823543/800000


Map: [&lt;1 4 -1 1 11|, &lt;0 -8 11 6 -25|]
{{Mapping|legend=1| 1 -4 11 9 | 0 9 -14 -10 }}
: mapping generators: ~2, ~32/21


EDOs: {{EDOs|10, 53, 116, 169de, 285cde}}
[[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: 0.0506
{{Optimal ET sequence|legend=1| 21, 29, 50, 79d, 129cdd, 179bcddd }}
 
[[Badness]] (Sintel): 3.67
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 245/242, 1617/1600
 
Mapping: {{Mapping| 1 -4 11 9 14 | 0 9 -14 -10 -17 }}
 
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 }}
 
Optimal tunings:
* WE: ~2 = 1201.7863{{c}}, ~20/13 = 745.3344{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1931{{c}}
 
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
 
Badness (Sintel): 1.43
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 105/104, 170/169, 196/195, 221/220, 245/242
 
Mapping: {{Mapping| 1 -4 11 9 14 13 14 | 0 9 -14 -10 -17 -15 -16 }}


POTE generator: ~16/13 = 362.105
Optimal tunings:  
* WE: ~2 = 1201.9208{{c}}, ~20/13 = 745.3976{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1669{{c}}


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


EDOs: {{EDOs|10, 53, 116, 169de, 285cdef}}
Badness (Sintel): 1.26


Badness: 0.0277
== Quintannic ==
Named by [[Scott Dakota]], quintannic may be described as the {{nowrap| 43 & 60 }} temperament.  


== Interpental ==
[[Subgroup]]: 2.3.5.7
Commas: 99/98, 176/175, 51200/50421


POTE generator: ~49/40 = 362.418
[[Comma list]]: 225/224, 9805926501/9765625000


Map: [&lt;1 4 -1 1 -5|, &lt;0 -8 11 6 28|]
{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
: mapping generators: ~2, ~10000/9261


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


Badness: 0.0518
{{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: {{mapping| 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: {{mapping| 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: {{mapping| 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
 
== 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: {{mapping| 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: {{mapping| 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:Temperament collections]]
[[Category:Temperament]]
[[Category:Marvel temperaments| ]] <!-- main article -->
[[Category:Marvel]]
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Marvel_temperaments"