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Marvel temperaments: Difference between revisions

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


Since (5/4)<sup>2</sup> = 225/224 × 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.
Temperaments considered in families and clans are:
* ''[[Pelogic]]'' (+21/20 or 135/128) → [[Mavila family #Pelogic|Mavila family]]
* [[Meantone]] (+81/80 or 126/125) → [[Meantone family #Septimal meantone|Meantone family]]
* [[Garibaldi]] (+3125/3087) → [[Schismatic family #Garibaldi|Schismatic family]]
* [[Pajara]] (+50/49 or 64/63) → [[Diaschismic family #Pajara|Diaschismic family]]
* ''[[Sharpie]]'' (+25/24 or 28/27) → [[Dicot family #Sharpie|Dicot family]]
* ''[[Immune]]'' (+781250/750141) → [[Immunity family #Immune|Immunity family]]
* ''[[August]]'' (+36/35 or 128/125) → [[Augmented family #August|Augmented family]]
* ''[[Fog]]'' (+156250/151263) → [[Misty family #Fog|Misty family]]
* [[Bunya]] (+15625/15309) → [[Tetracot family #Bunya|Tetracot family]]
* [[Negri]] (+49/48) → [[Semaphoresmic clan #Negri|Semaphoresmic clan]]
* [[Magic]] (+245/243) → [[Magic family #Magic|Magic family]]
* ''[[Passive]]'' (+256/245) → [[Passion family #Passive|Passion family]]
* ''[[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
== 5-limit ==
Comma list: 2197265625/2147483648


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


Mapping: [{{val| 2 1 5 }}, {{val| 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.


{{Val list|legend=1| 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 }}
Comma list: 225/224, 118098/117649
: mapping generators: ~2, ~10/7


[[POTE generator]]: ~5/4 = 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 }}


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


Wedgie: {{wedgie| 12 -2 20 -31 -2 52 }}
[[Badness]] (Sintel): 1.20


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


[[POTE generator]]: ~5/4 = 383.232
Optimal tunings:  
* WE: ~2 = 1201.7116{{c}}, ~10/7 = 620.6166{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6890{{c}}


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


{{Val list|legend=1| 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
Comma list: 225/224, 351/350, 364/363, 385/384


[[POTE generator]]: ~5/4 = 383.389
Mapping: {{mapping| 1 -1 8 9 5 13 | 0 5 -11 -12 -3 -18 }}


Mapping: [{{val| 2 1 5 2 8 11 }}, {{val| 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}}


{{Val list|legend=1| 22, 50, 72, 122, 194df }}
{{Optimal ET sequence|legend=0| 29, 31, 60e }}


Badness: 0.0218
Badness (Sintel): 0.950


==== 17-limit ====
==== 17-limit ====
Comma list: 221/220, 273/272, 289/288, 351/350, 375/374
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 105/104, 121/120, 154/153, 196/195, 273/272


[[POTE generator]]: ~5/4 = 383.381
Mapping: {{mapping| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}


Mapping: [{{val| 2 1 5 2 8 11 6 }}, {{val| 0 6 -1 10 -3 -10 6 }}]
Optimal tunings:  
* WE: ~2 = 1201.5260{{c}}, ~10/7 = 620.7330{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8986{{c}}


{{Val list|legend=1| 22, 50, 72, 122g, 194dfg }}
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}


Badness: 0.0145
Badness (Sintel): 0.973


==== 19-limit ====
==== 19-limit ====
Comma list: 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 }}
 
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: {{mapping| 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 generator]]: ~5/4 = 383.477
Mapping: {{mapping| 1 -2 10 11 22 32 | 0 7 -15 -16 38 58 }}


Mapping: [{{val| 2 1 5 2 8 11 6 2 }}, {{val| 0 6 -1 10 -3 -10 6 18 }}]
Optimal tunings:  
* WE: ~2 = 1200.5126{{c}}, ~10/7 = 614.7152{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4562{{c}}


{{Val list|legend=1| 22h, 50, 72, 122g, 194dfg }}
{{Optimal ET sequence|legend=0| 41, 84ef, 125f, 166 }}


Badness: 0.0157
Badness (Sintel): 1.47


=== Gizzard ===
== Slender ==
Comma list: 225/224, 385/384, 325/324, 1573/1568
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.


POTE generator: ~5/4 = 383.170
The name was likely derived from ''slendro diesis'', one of the names for the interval 49/48.  


Mapping: [{{val| 2 1 5 2 8 -2 }}, {{val| 0 6 -1 10 -3 26 }}]
[[Subgroup]]: 2.3.5.7


{{Val list|legend=1| 22, 72, 94, 166, 238cf }}
[[Comma list]]: 225/224, 589824/588245


Badness: 0.0203
{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
: mapping generators: ~2, ~49/48


==== 17-limit ====
[[Optimal tuning]]s:
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384
* [[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 }}


Mapping: [{{val| 2 1 5 2 8 -2 6 }}, {{val| 0 6 -1 10 -3 26 6 }}]
[[Badness]] (Sintel): 1.44


{{Val list|legend=1| 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 }}
Comma list: 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}}


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


{{Val list|legend=1| 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
Comma list: 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: [{{val| 2 1 5 2 4 }}, {{val| 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}}


{{Val list|legend=1| 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


POTE generator: ~7/5 = 580.108
Comma list: 169/168, 225/224, 364/363, 441/440


Map: [&lt;1 4 -3 -3 2 -5|, &lt;0 -5 11 12 3 18|]
Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}


EDOs: {{EDOs|29, 31, 60e, 151cde}}
Optimal tunings:  
* WE: ~2 = 1200.9467{{c}}, ~21/20 = 83.3956{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3516{{c}}


Badness: 0.0230
{{Optimal ET sequence|legend=0| 29, 43, 72 }}


== Tritoni ==
Badness (Sintel): 0.887
Commas: 225/224, 385/384, 27783/27500


POTE generator: ~7/5 = 580.389
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]
Comma list: 169/168, 221/220, 225/224, 364/363, 441/440


EDOs: {{EDOs|31, 91, 122}}
Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}


Badness: 0.0455
Optimal tunings:  
* WE: ~2 = 1200.9606{{c}}, ~21/20 = 83.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3594{{c}}


=Merman=
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}
Comma: 1121008359375/1099511627776


POTE generator: ~45/32 = 585.634
Badness (Sintel): 0.760


Map: [&lt;1 5 -5|, &lt;0 -7 15|]
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19


EDOs: {{EDOs|41, 84, 125, 209, 334c, 543bc}}
Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440


Badness: 0.4538
Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}


==7-limit==
Optimal tunings:
Commas: 225/224, 2500000/2470629
* WE: ~2 = 1200.7625{{c}}, ~21/20 = 83.3895{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3551{{c}}


POTE generator: ~7/5 = 585.585
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}


Map: [&lt;1 5 -5 -5|, &lt;0 -7 15 16|]
Badness (Sintel): 0.895


Wedgie: &lt;&lt;7 -15 -16 -40 -45 5||
== Enneaportent ==
[[Subgroup]]: 2.3.5.7


EDOs: {{EDOs|41, 84, 125}}
[[Comma list]]: 225/224, 40353607/40310784


Badness: 0.0551
{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
: mapping generators: ~2592/2401, ~12005/6912


==11-limit==
[[Optimal tuning]]s:
Commas: 225/224, 441/440, 1344/1331
* [[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 }}


POTE generator: ~7/5 = 585.606
{{Optimal ET sequence|legend=1| 9, 54, 63, 72, 495bccd, 567bcccd }}


Map: [&lt;1 5 -5 -5 2|, &lt;0 -7 15 16 3]]
[[Badness]] (Sintel): 2.37


EDOs: {{EDOs|41, 84, 125e}}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.0364
Comma list: 225/224, 385/384, 12005/11979


==13-limit==
Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}
Commas: 144/143, 225/224, 364/363, 441/440


POTE generator: ~7/5 = 585.657
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}})


Map: [&lt;1 5 -5 -5 2 12|, &lt;0 -7 15 16 3 -17|]
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


EDOs: {{EDOs|41, 84, 125e, 209ef, 293ef}}
Badness (Sintel): 1.01


Badness: 0.0275
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=Septimin=
Comma list: 169/168, 225/224, 364/363, 1716/1715
Comma: 35595703125/34359738368


POTE generator: ~75/64 = 263.658
Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}


Map: [&lt;1 4 1|, &lt;0 -11 6|]
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}})


EDOs: {{EDOs|9, 32, 41, 91, 132, 223c, 355bc}}
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


Badness: 0.6709
Badness (Sintel): 0.922


==7-limit==
== Gracecordial ==
Commas: 225/224, 84035/82944
: ''For the 5-limit version, see [[Schismic–Pythagorean equivalence continuum #Gracecordial (5-limit)]].''


[[POTE_tuning|POTE temperament]]: 263.632
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]
[[Comma list]]: 225/224, 781250000/771895089


Wedgie: &lt;&lt;11 -6 10 -35 -15 40||
{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
: mapping generators: ~2, ~3


EDOs: {{EDOs|9, 32, 41, 91, 132}}
[[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 }}


==11-limit==
{{Optimal ET sequence|legend=1| 12, …, 113, 125, 238c, 363c }}
Commas: 225/224, 385/384, 2401/2376


[[POTE_tuning|POTE temperament]]: 263.634
[[Badness]] (Sintel): 2.44


Map: [&lt;1 4 1 5 5|, &lt;0 -11 6 -10 -7|]
=== 11-limit ===
Subgroup: 2.3.5.7.11


EDOs: {{EDOs|9, 32, 41, 91, 223cdef}}
Comma list: 225/224, 385/384, 236328125/234365481


==13-limit==
Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}
Commas: 105/104, 144/143, 196/195, 245/242


[[POTE_tuning|POTE temperament]]: 263.700
Optimal tunings:  
* WE: ~2 = 1200.5571{{c}}, ~3/2 = 701.1589{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8328{{c}}


Map: [&lt;1 4 1 5 5 7|, &lt;0 -11 6 -10 -7 -15|]
{{Optimal ET sequence|legend=0| 12e, 113, 125, 238c }}


EDOs: {{EDOs|9, 41, 91}}
Badness (Sintel): 2.96


=Slender=
==== 13-limit ====
Commas: 225/224, 589824/588245
Subgroup: 2.3.5.7.11.13


[[POTE_tuning|POTE temperament]]: ~49/48 = 38.413
Comma list: 225/224, 325/324, 385/384, 831875/830466


Map: [&lt;1 2 2 3|, &lt;0 -13 10 -6|]
Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}


Wedgie: &lt;&lt;13 -10 6 -46 -27 42||
Optimal tunings:  
* WE: ~2 = 1200.6282{{c}}, ~3/2 = 701.2080{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8421{{c}}


EDOs: {{EDOs|31, 94, 125}}
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


Badness: 0.0569
Badness (Sintel): 2.16


==11-limit==
==== 17-limit ====
Commas: 225/224, 385/384, 1331/1323
Subgroup: 2.3.5.7.11.13.17


[[POTE_tuning|POTE temperament]]: ~49/48 = 38.387
Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913


Map: [&lt;1 2 2 3 4|, &lt;0 -13 10 -6 -17|]
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}


EDOs: {{EDOs|31, 63, 94, 125}}
Optimal tunings:  
* WE: ~2 = 1200.5058{{c}}, ~3/2 = 701.1360{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8414{{c}}


Badness: 25.342
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


==13-limit==
Badness (Sintel): 1.96
Commas: 225/224, 275/273, 385/384, 1331/1323


POTE generator: ~49/48 = 38.314
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


Map: [&lt;1 2 2 3 4 3|, &lt;0 -13 10 -6 -17 22|]
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444


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


Badness: 25.913
Optimal tunings:  
* WE: ~2 = 1200.4418{{c}}, ~3/2 = 701.0999{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8425{{c}}


=Marvo=
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
Commas: 225/224, 78125000/78121827


[[POTE_tuning|POTE generator]]: ~27/20 = 516.694
Badness (Sintel): 1.71


Map: [&lt;1 5 12 29|, &lt;0 -6 -17 -46|]
==== 23-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23


Wedgie: &lt;&lt;6 17 46 13 56 59||
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528


EDOs: {{EDOs|7d, 65d, 72, 137, 209, 281, 569bcc}}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}


Badness: 0.0976
Optimal tunings:  
* WE: ~2 = 1200.4641{{c}}, ~3/2 = 701.1145{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8444{{c}}


==11-limit==
{{Optimal ET sequence|legend=0| 12e, 113, 238cfi }}
Commas: 225/224, 243/242, 4000/3993


POTE generator: ~27/20 = 516.699
Badness (Sintel): 1.57


Map: [&lt;1 5 12 29 12|, &lt;0 -6 -17 -46 -15|]
==== 29-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29


EDOs: {{EDOs|7d, 65d, 72, 281, 353c, 425bc, 497bc}}
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493
 
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}
 
Optimal tunings:
* WE: ~2 = 1200.4400{{c}}, ~3/2 = 701.0986{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8428{{c}}
 
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
 
Badness (Sintel): 1.50
 
==== 31-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
 
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493
 
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}
 
Optimal tunings:
* WE: ~2 = 1200.4178{{c}}, ~3/2 = 701.0822{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8396{{c}}
 
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
 
Badness (Sintel): 1.53
 
=== Gracecord ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 441/440, 109375/107811
 
Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}
 
Optimal tunings:
* WE: ~2 = 1200.6064{{c}}, ~3/2 = 701.2398{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8718{{c}}
 
{{Optimal ET sequence|legend=0| 12, …, 101cd, 113 }}
 
Badness (Sintel): 2.21
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 364/363, 441/440, 6125/6084
 
Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}
 
Optimal tunings:
* WE: ~2 = 1200.6225{{c}}, ~3/2 = 701.2539{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8781{{c}}
 
{{Optimal ET sequence|legend=0| 12f, …, 101cdf, 113 }}
 
Badness (Sintel): 1.83
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989
 
Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}
 
Optimal tunings:
* WE: ~2 = 1200.3308{{c}}, ~3/2 = 701.0632{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8654{{c}}
 
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}
 
Badness (Sintel): 1.87
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


Badness: 0.0317
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663


==13-limit==
Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}
Commas: 225/224, 243/242, 351/350, 1625/1617


POTE generator: ~27/20 = 516.730
Optimal tunings:  
* WE: ~2 = 1200.2658{{c}}, ~3/2 = 701.0213{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8629{{c}}


Map: [&lt;1 5 12 29 12 39|, &lt;0 -6 -17 -46 -15 -62|]
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


EDOs: {{EDOs|72, 137, 209, 281f, 490bcf}}
Badness (Sintel): 1.68


Badness: 0.0269
== Alphorn ==
[[Subgroup]]: 2.3.5.7


=Marvolo=
[[Comma list]]: 225/224, 5764801/5668704
Commas: 225/224, 156250000/155649627


POTE generator: ~21/20 = 83.348
{{Mapping|legend=1| 1 -7 5 -9 | 0 16 -5 22 }}
: mapping generators: ~2, ~35/24


Map: [&lt;1 2 1 1|, &lt;0 -6 19 26|]
[[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 }}


Wedgie: &lt;&lt;6 -19 -26 -44 -58 -7||
{{Optimal ET sequence|legend=1| 13d, 28d, 41, 151cd, 192cdd, 233ccdd }}


EDOs: {{EDOs|29, 43, 72, 619bcd, 691bcd}}
[[Badness]] (Sintel): 3.27


Badness: 0.0833
=== 11-limit ===
Subgroup: 2.3.5.7.11


==11-limit==
Comma list: 225/224, 385/384, 12250/11979
Commas: 225/224, 441/440, 4000/3993


POTE generator: ~21/20 = 83.340
Mapping: {{mapping| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}


Map: [&lt;1 2 1 1 2|, &lt;0 -6 19 26 21|]
Optimal tunings:  
* WE: ~2 = 1200.5123{{c}}, ~16/11 = 644.1307{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 643.8662{{c}}


EDOs: {{EDOs|29, 43, 72}}
{{Optimal ET sequence|legend=0| 13d, 28d, 41 }}


Badness: 0.0290
Badness (Sintel): 2.43


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


POTE generator: ~21/20 = 83.330
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 2 1 1 2 3|, &lt;0 -6 19 26 21 10|]
[[Comma list]]: 225/224, 4194304/4117715


EDOs: {{EDOs|29, 43, 72, 115f}}
{{Mapping|legend=1| 1 -12 15 1 | 0 15 -14 2 }}
: mapping generators: ~2, ~15/8


Badness: 0.0215
[[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 }}


= Amavil =
{{Optimal ET sequence|legend=1| 21, 32, 53 }}
== 5-limit (mabila) ==
Comma: 268435456/263671875


POTE generator: ~512/375 = 529.6849
[[Badness]] (Sintel): 3.57


Map: [<1 6 1|, <0 -10 3|]
=== 11-limit ===
Subgroup: 2.3.5.7.11


EDOs: {{EDOs| 9, 25, 34, 77, 111, 145, 256c }}
Comma list: 99/98, 176/175, 1310720/1294139


Badness: 0.2325
Mapping: {{mapping| 1 -12 15 1 27 | 0 15 -14 2 -26 }}


== 7-limit ==
Optimal tunings:
Commas: 225/224, 17496/16807
* WE: ~2 = 1200.1654{{c}}, ~15/8 = 1086.8269{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6766{{c}}


POTE generator: ~48/35 = 529.979
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


Map: [&lt;1 6 1 9|, &lt;0 -10 3 -14|]
Badness (Sintel): 2.82


Wedgie: &lt;&lt;10 -3 14 -28 -6 41||
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


EDOs: {{EDOs|9, 34d, 43, 77d}}
Comma list: 99/98, 176/175, 640/637, 847/845


Badness: 0.1096
Mapping: {{mapping| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}


== 11-limit ==
Optimal tunings:
Commas: 99/98, 176/175, 864/847
* WE: ~2 = 1200.1687{{c}}, ~15/8 = 1086.8295{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6757{{c}}


POTE generator: ~15/11 = 529.974
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


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


EDOs: {{EDOs| 9, 34d, 43, 77de }}
=== Musneb ===
Subgroup: 2.3.5.7.11


Badness: 0.0426
Comma list: 225/224, 385/384, 66550/64827


== 13-limit ==
Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}
Commas: 78/77, 99/98, 144/143, 176/175


POTE generator: ~15/11 = 529.951
Optimal tunings:  
* WE: ~2 = 1200.0839{{c}}, ~15/8 = 1086.9343{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.8593{{c}}


Map: [&lt;1 6 1 9 7 9|, &lt;0 -10 3 -14 -8 -12|]
{{Optimal ET sequence|legend=0| 21e, 32, 53 }}


EDOs: {{EDOs| 9, 34d, 43, 77de }}
Badness (Sintel): 2.89


Badness: 0.0258
== Untriton ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''


=Enneaportent=
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.
Commas: 225/224, 40353607/40310784


POTE generator: ~5/4 = 383.165
[[Subgroup]]: 2.3.5.7


Map: [&lt;9 0 28 11|, &lt;0 2 -1 2|]
[[Comma list]]: 225/224, 125000000/121060821


Wedgie: &lt;&lt;18 -9 18 -56 -22 67||
{{Mapping|legend=1| 1 -3 12 13 | 0 9 -19 -20 }}
: mapping generators: ~2, ~10/7


EDOs: {{EDOs|9, 54, 63, 72, 495bcd}}
[[Optimal tuning]]s:  
* [[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 }}


Badness: 0.0937
{{Optimal ET sequence|legend=1| 51, 53 }}


==11-limit==
[[Badness]] (Sintel): 3.64
Commas: 225/224, 385/384, 12005/11979


POTE generator: ~5/4 = 383.146
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;9 0 28 11 24|, &lt;0 2 -1 2 1|]
Comma list: 121/120, 225/224, 22000/21609


EDOs: {{EDOs|9, 54, 63, 72, 423cd, 495bcd}}
Mapping: {{mapping| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}


Badness: 0.0304
Optimal tunings:  
* WE: ~2 = 1200.3591{{c}}, ~10/7 = 611.5569{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3690{{c}}


==13-limit==
{{Optimal ET sequence|legend=0| 51, 53 }}
Commas: 169/168, 225/224, 364/363, 1716/1715


POTE generator: ~5/4 = 383.047
Badness (Sintel): 2.46


Map: [&lt;9 0 28 11 24 19|, &lt;0 2 -1 2 1 2|]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


EDOs: {{EDOs|9, 54, 63, 72, 279cf}}
Comma list: 121/120, 225/224, 275/273, 1040/1029


Badness: 0.0223
Mapping: {{mapping| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}


= Submajor =
Optimal tunings:
== 5-limit ==
* WE: ~2 = 1200.4078{{c}}, ~10/7 = 611.5536{{c}}
Comma: 69198046875/68719476736
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3392{{c}}


POTE generator: ~10125/8192 = 362.321
{{Optimal ET sequence|legend=0| 51f, 53 }}


Map: [&lt;1 4 -1|, &lt;0 -8 11|]
Badness (Sintel): 1.96


EDOs: {{EDOs|10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}}
== Naiadical ==
Named by [[Xenllium]] in 2026, naiadical may be described as the {{nowrap| 21 & 29 }} temperament.


Badness: 0.1302
[[Subgroup]]: 2.3.5.7


== 7-limit ==
[[Comma list]]: 225/224, 823543/800000
Commas: 225/224, 51200/50421


POTE generator: ~49/40 = 362.255
{{Mapping|legend=1| 1 -4 11 9 | 0 9 -14 -10 }}
: mapping generators: ~2, ~32/21


Map: [&lt;1 4 -1 1|, &lt;0 -8 11 6|]
[[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 }}


Wedgie: &lt;&lt;8 -11 -6 -36 -32 17||
{{Optimal ET sequence|legend=1| 21, 29, 50, 79d, 129cdd, 179bcddd }}


EDOs: {{EDOs|10, 33, 43, 53}}
[[Badness]] (Sintel): 3.67


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


== 11-limit ==
Comma list: 225/224, 245/242, 1617/1600
Commas: 225/224, 385/384, 6655/6561


POTE generator: ~27/22 = 362.101
Mapping: {{Mapping| 1 -4 11 9 14 | 0 9 -14 -10 -17 }}


Map: [&lt;1 4 -1 1 11|, &lt;0 -8 11 6 -25|]
Optimal tunings:  
* WE: ~2 = 1201.9008{{c}}, ~21/16 = 745.3867{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~32/21 = 744.1777{{c}}


EDOs: {{EDOs|10, 53, 116, 169de, 285cde}}
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}


Badness: 0.0506
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}}


POTE generator: ~16/13 = 362.105
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}


Map: [&lt;1 4 -1 1 11 4|, &lt;0 -8 11 6 -25 -1|]
Badness (Sintel): 1.43


EDOs: {{EDOs|10, 53, 116, 169de, 285cdef}}
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Badness: 0.0277
Comma list: 105/104, 170/169, 196/195, 221/220, 245/242


== Interpental ==
Mapping: {{Mapping| 1 -4 11 9 14 13 14 | 0 9 -14 -10 -17 -15 -16 }}
Commas: 99/98, 176/175, 51200/50421


POTE generator: ~49/40 = 362.418
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 -5|, &lt;0 -8 11 6 28|]
{{Optimal ET sequence|legend=0| 21, 29g, 50, 79dg }}


EDOs: {{EDOs|43, 53, 96, 149d}}
Badness (Sintel): 1.26


Badness: 0.0518
== 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: {{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"