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This page discusses miscellaneous rank-2 temperaments tempering out {{monzo|-5 2 2 -1}} = [[225/224]], the marvel comma or septimal kleisma.  
{{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.  


Temperaments considered in families and clans are:  
Temperaments considered in families and clans are:  
* ''[[Sharp]]'', {25/24, 28/27} → [[Dicot family #Sharp|Dicot family]]
* ''[[Pelogic]]'' (+21/20 or 135/128) → [[Mavila family #Pelogic|Mavila family]]
* ''[[Pelogic]]'', {21/20, 135/128} → [[Pelogic family #Pelogic|Pelogic family]]
* [[Meantone]] (+81/80 or 126/125) → [[Meantone family #Septimal meantone|Meantone family]]
* ''[[August]]'', {36/35, 128/125} → [[Augmented family #August|Augmented family]]
* [[Garibaldi]] (+3125/3087) → [[Schismatic family #Garibaldi|Schismatic family]]
* [[Pajara]], {50/49, 64/63} → [[Diaschismic family #Pajara|Diaschismic family]]
* [[Pajara]] (+50/49 or 64/63) → [[Diaschismic family #Pajara|Diaschismic family]]
* [[Meantone]], {81/80, 126/125} → [[Meantone family #Septimal meantone|Meantone family]]
* ''[[Sharpie]]'' (+25/24 or 28/27) → [[Dicot family #Sharpie|Dicot family]]
* [[Magic]], {225/224, 245/243} → [[Magic family #Magic|Magic family]]
* ''[[Immune]]'' (+781250/750141) → [[Immunity family #Immune|Immunity family]]
* ''[[Passive]]'', {225/224, 256/245} → [[Passion family #Passive|Passion family]]
* ''[[August]]'' (+36/35 or 128/125) → [[Augmented family #August|Augmented family]]
* [[Miracle]], {225/224, 1029/1024} → [[Gamelismic clan #Miracle|Gamelismic clan]]
* ''[[Fog]]'' (+156250/151263) → [[Misty family #Fog|Misty family]]
* [[Orwell]], {225/224, 1728/1715} → [[Semicomma family #Orwell|Semicomma family]]
* [[Bunya]] (+15625/15309) → [[Tetracot family #Bunya|Tetracot family]]
* [[Garibaldi temperament|Garibaldi]], {225/224, 3125/3087} → [[Schismatic family #Garibaldi|Schismatic family]]
* [[Negri]] (+49/48) → [[Semaphoresmic clan #Negri|Semaphoresmic clan]]
* [[Catakleismic]], {225/224, 4375/4374} → [[Kleismic family #Catakleismic|Kleismic family]]
* [[Magic]] (+245/243) → [[Magic family #Magic|Magic family]]
* ''[[Decic]]'', {225/224, 16807/16384} → [[Cloudy clan #Decic|Cloudy clan]]
* ''[[Passive]]'' (+256/245) → [[Passion family #Passive|Passion family]]
* ''[[Amavil]]'', {225/224, 17496/16807} → [[Mabila family #Amavil|Mabila family]]
* ''[[Houborizic]]'' (+1250000/1240029) → [[Amity family #Houborizic|Amity family]]
* ''[[Escapade]]'', {225/224, 65625/65536} → [[Escapade family #Escapade|Escapade family]]
* ''[[Qintosec]]'' (+2560000/2470629) → [[Quintosec family #Qintosec|Quintosec family]]
* ''[[Fog]]'', {225/224, 156250/151263} → [[Misty family #Fog|Misty family]]
* [[Miracle]] (+1029/1024) → [[Gamelismic clan #Miracle|Gamelismic clan]]
* ''[[Compton]]'', {225/224, 250047/250000} → [[Compton family #Compton|Compton family]]
* [[Catakleismic]] (+4375/4374) → [[Kleismic family #Catakleismic|Kleismic family]]
* ''[[Immune]]'', {225/224, 781250/750141} → [[Immunity family #Immune|Immunity family]]
* ''[[Marvo]]'' (+78125000/78121827) → [[Gravity family #Marvo|Gravity family]]
* ''[[Betic]]'', {225/224, 1071875/1062882} → [[Sycamore family #Betic|Sycamore family]]
* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell|Semicomma family]]
* ''[[Houborizic]]'' {225/224, 1250000/1240029} → [[Amity family #Houborizic|Amity family]]
* ''[[Snipes]]'' (+6125/5832)  → [[Wesley family #Snipes|Wesley family]]
* ''[[Qintosec]]'', {225/224, 2560000/2470629} → [[Qintosec family #Qintosec|Qintosec family]]
* ''[[Demibuzzard]]'' (+65536/64827) → [[Buzzardsmic clan #Demibuzzard|Buzzardsmic clan]]
* ''[[Quintapole]]'', {225/224, 7812500/7411887} → [[Quintaleap family #Quintapole|Quintaleap family]]
* ''[[Escapist]]'' (+65625/65536) → [[Escapade family #Escapist|Escapade family]]
* ''[[Maquila]]'', {225/224, 30233088/28824005} → [[Maquila family #Septimal maquila|Maquila family]]
* ''[[Amavil]]'' (+17496/16807) → [[Mabila family #Amavil|Mabila family]]
* ''[[Marvo]]'', {225/224, 78125000/78121827} → [[Gravity family #Marvo|Gravity family]]
* ''[[Betic]]'' (+1071875/1062882) → [[Sycamore family #Betic|Sycamore family]]
* [[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]]


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


Since (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.
Since {{nowrap|(5/4)<sup>2</sup> {{=}} (225/224)⋅(14/9)}}, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.


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


Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4) = 64/45. Setting this equal to 10/7 gives (10/7)/(64/45) = 225/224.)
Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is {{nowrap|(16/9)/(5/4) {{=}} 64/45}}. Setting this equal to 10/7 gives {{nowrap|(10/7)/(64/45) {{=}} 225/224}}.)


== Negri ==
== Wizard ==
{{main| Negri }}
{{Main| Wizard }}
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Wizard]].''


Negri tempers out the [[negri comma]] in the 5-limit, [[49/48]] and [[225/224]] in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding [[91/90]] to the comma list; this will be discussed below under the title of negra.  
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.  


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 16875/16384
[[Comma list]]: 225/224, 118098/117649


[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
{{Mapping|legend=1| 2 1 5 2 | 0 6 -1 10 }}
: mapping generators: ~1225/864, ~245/216


{{Multival|legend=1| 4 -3 -14 }}
[[Optimal tuning]]s:
* [[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]]: ~16/15 = 125.7549
{{Optimal ET sequence|legend=1| 22, 50, 72, 238c, 310c, 382c, 454bccd }}


{{Val list|legend=1| 9, 10, 19, 67c, 86c, 105c }}
[[Badness]] (Sintel): 1.03


[[Badness]]: 0.086856
=== 11-limit ===
Subgroup: 2.3.5.7.11


=== 7-limit ===
Comma list: 225/224, 385/384, 4000/3993
Subgroup: 2.3.5.7


[[Comma list]]: 49/48, 225/224
Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}


[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}]
Optimal tunings:  
* WE: ~99/70 = 600.3051{{c}}, ~25/22 = 216.8782{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.7961{{c}}


{{Multival|legend=1| 4 -3 2 -14 -8 13 }}
{{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}


[[POTE generator]]: ~15/14 = 125.608
Badness (Sintel): 0.613


{{Val list|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
==== Lizard ====
Subgroup: 2.3.5.7.11.13


[[Badness]]: 0.026483
Comma list: 225/224, 351/350, 364/363, 385/384


==== Negra ====
Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}
This is the 2.3.5.7.13 extension of negri.


Subgroup: 2.3.5.7.13
Optimal tunings:  
* WE: ~55/39 = 600.4824{{c}}, ~25/22 = 216.7852{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~25/22 = 216.6247{{c}}


[[Comma list]]: 49/48, 65/64, 91/90
{{Optimal ET sequence|legend=0| 22, 50, 72 }}
 
Badness (Sintel): 0.900
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17


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


[[Gencom]] [[mapping]]: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}]
Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}


[[Gencom]]: [2 14/13; 49/48 65/64 91/90]
Optimal tunings:  
* WE: ~17/12 = 600.5032{{c}}, ~17/15 = 216.8002{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.6361{{c}}


[[POTE generator]]: ~14/13 = 125.567
{{Optimal ET sequence|legend=0| 22, 50, 72 }}


{{Val list|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}
Badness (Sintel): 0.741


=== 11-limit ===
===== 19-limit =====
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 45/44, 49/48, 56/55
Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342


Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]
Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}


POTE generator: ~15/14 = 126.474
Optimal tunings:  
* WE: ~17/12 = 600.4698{{c}}, ~17/15 = 216.6925{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.5434{{c}}


Optimal GPV sequence: {{Val list| 9, 10, 19 }}
{{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}


Badness: 0.026190
Badness (Sintel): 0.955


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


Comma list: 45/44, 49/48, 56/55, 78/77
Comma list: 225/224, 325/324, 385/384, 1573/1568


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


POTE generator: ~14/13 = 126.431
Optimal tunings:  
* WE: ~99/70 = 600.2896{{c}}, ~25/22 = 216.9343{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.8501{{c}}


Optimal GPV sequence: {{Val list| 9, 10, 19 }}
{{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}


Badness: 0.017833
Badness (Sintel): 0.837


=== Negril ===
===== 17-limit =====
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13.17


Comma list: 49/48, 100/99, 225/224
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384


Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]
Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}


POTE generator: ~15/14 = 124.767
Optimal tunings:  
* WE: ~17/12 = 600.3227{{c}}, ~17/15 = 216.9414{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8469{{c}}


Optimal GPV sequence: {{Val list| 19, 29, 48d, 77cdd }}
{{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}


Badness: 0.038679
Badness (Sintel): 0.694


==== 13-limit ====
===== 19-limit =====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 49/48, 65/64, 91/90, 875/858
Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594


Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]
Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}


POTE generator: ~14/13 = 124.716
Optimal tunings:  
* WE: ~17/12 = 600.2637{{c}}, ~17/15 = 216.9570{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8687{{c}}


Optimal GPV sequence: {{Val list| 19, 29, 48df, 77cddf }}
{{Optimal ET sequence|legend=0| 72, 94, 166g }}


Badness: 0.024383
Badness (Sintel): 0.901


=== Negric ===
=== Mage ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 33/32, 49/48, 77/75
Comma list: 99/98, 176/175, 1331/1296


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


POTE generator: ~15/14 = 127.039
Optimal tunings:  
* WE: ~77/54 = 600.6486{{c}}, ~55/48 = 217.1099{{c}}
* CWE: ~77/54 = 600.0000{{c}}, ~55/48 = 216.9841{{c}}


Optimal GPV sequence: {{Val list| 9, 19e }}
{{Optimal ET sequence|legend=0| 22, 50e, 72ee }}


Badness: 0.030617
Badness (Sintel): 1.91


==== 13-limit ====
== Tritonic ==
Subgroup: 2.3.5.7.11.13
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tritonic]].''
 
Tritonic tempers out [[50421/50000]] and may be described as the {{nowrap| 29 & 31 }} temperament. It splits the [[6/1|6th]] [[harmonic]] into five generators of [[~]][[10/7]] [[tritone]]s, hence the name. Its [[ploidacot]] is beta-pentacot. [[60edo]] may be used as a tuning, which in the 11-limit entails the 60e val.
 
[[Subgroup]]: 2.3.5.7


Comma list: 33/32, 49/48, 65/64, 91/90
[[Comma list]]: 225/224, 50421/50000


Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]
{{Mapping|legend=1| 1 -1 8 9 | 0 5 -11 -12 }}
: mapping generators: ~2, ~10/7


POTE generator: ~14/13 = 127.039
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1201.3539{{c}}, ~10/7 = 620.4131{{c}}
: [[error map]]: {{val| +1.354 -1.243 -0.027 -1.598 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 619.6778{{c}}
: error map: {{val| 0.000 -3.566 -2.769 -4.959 }}


Optimal GPV sequence: {{Val list| 9, 19e }}
{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}


Badness: 0.020205
[[Badness]] (Sintel): 1.20


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


Comma list: 49/48, 55/54, 225/224
Comma list: 121/120, 225/224, 441/440


Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]
Mapping: {{mapping| 1 -1 8 9 5 | 0 5 -11 -12 -3 }}


POTE generator: ~15/14 = 124.539
Optimal tunings:  
* WE: ~2 = 1201.7116{{c}}, ~10/7 = 620.6166{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6890{{c}}


Optimal GPV sequence: {{Val list| 10, 19e, 29, 77cddee }}
{{Optimal ET sequence|legend=0| 29, 31, 60e, 91e, 213bcdeee }}


Badness: 0.035296
Badness (Sintel): 0.782


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


Comma list: 49/48, 55/54, 65/64, 91/90
Comma list: 105/104, 121/120, 196/195, 275/273


Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]
Mapping: {{mapping| 1 -1 8 9 5 13 | 0 5 -11 -12 -3 -18 }}


POTE generator: ~14/13 = 124.545
Optimal tunings:  
* WE: ~2 = 1201.5355{{c}}, ~10/7 = 620.6855{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8469{{c}}


Optimal GPV sequence: {{Val list| 10, 19e, 29, 77cddeef }}
{{Optimal ET sequence|legend=0| 29, 31, 60e }}


Badness: 0.021559
Badness (Sintel): 0.950


=== Wilsec ===
==== 17-limit ====
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13.17


Comma list: 49/48, 121/120, 225/224
Comma list: 105/104, 121/120, 154/153, 196/195, 273/272


Mapping: [{{val| 1 6 -1 5 4 }}, {{val| 0 -8 6 -4 -1 }}]
Mapping: {{mapping| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}


POTE generator: ~11/8 = 537.186
Optimal tunings:  
* WE: ~2 = 1201.5260{{c}}, ~10/7 = 620.7330{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8986{{c}}


Optimal GPV sequence: {{Val list| 9, 20, 29, 38d, 67cdde }}
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}


Badness: 0.041886
Badness (Sintel): 0.973


==== 13-limit ====
==== 19-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 49/48, 65/64, 91/90, 121/120
Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272


Mapping: [{{val| 1 6 -1 5 4 7 }}, {{val| 0 -8 6 -4 -1 -6 }}]
Mapping: {{mapping| 1 -1 8 9 5 13 17 12 | 0 5 -11 -12 -3 -18 -25 -15 }}


POTE generator: ~11/8 = 537.208
Optimal tunings:  
* WE: ~2 = 1201.3100{{c}}, ~10/7 = 620.6509{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9328{{c}}


Optimal GPV sequence: {{Val list| 9, 20, 29, 38df, 67cddef }}
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}


Badness: 0.025192
Badness (Sintel): 1.03


==== 17-limit ====
==== 23-limit ====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17.19.23


Comma list: 49/48, 65/64, 91/90, 121/120, 154/153
Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195


Mapping: [{{val| 1 6 -1 5 4 7 -2 }}, {{val| 0 -8 6 -4 -1 -6 11 }}]
Mapping: {{mapping| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}


POTE generator: ~11/8 = 537.230
Optimal tunings:  
* WE: ~2 = 1201.4074{{c}}, ~10/7 = 620.7185{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9548{{c}}


Optimal GPV sequence: {{Val list| 9, 20g, 29g, 38df, 67cddefg }}
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}


Badness: 0.021778
Badness (Sintel): 1.04


==== 19-limit ====
=== Tritoni ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 27783/27500


Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153
Mapping: {{mapping| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}


Mapping: [{{val| 1 6 -1 5 4 7 -2 7 }}, {{val| 0 -8 6 -4 -1 -6 11 -5 }}]
Optimal tunings:  
* WE: ~2 = 1201.0888{{c}}, ~10/7 = 620.1733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6146{{c}}


POTE generator: ~11/8 = 537.214
{{Optimal ET sequence|legend=0| 31, 91, 122, 153d }}


Optimal GPV sequence: {{Val list| 9, 20g, 29g, 38df, 67cddefgh }}
Badness (Sintel): 1.50


Badness: 0.016828
== Septimin ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Septimin]].''


== Wizard ==
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.  
{{Main|Wizard}}
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Wizard]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 118098/117649
[[Comma list]]: 225/224, 84035/82944


[[Mapping]]: [{{val| 2 1 5 2 }}, {{val| 0 6 -1 10 }}]
{{Mapping|legend=1| 1 -7 7 -5 | 0 11 -6 10 }}
: mapping generators: ~2, ~12/7


Mapping generators: ~1225/864, ~245/216
[[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 }}


[[POTE generator]]: ~5/4 = 383.256
{{Optimal ET sequence|legend=1| 9, 23, 32, 41, 91, 132d }}


{{Multival|legend=1| 12 -2 20 -31 -2 52 }}
[[Badness]] (Sintel): 1.38


{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }}
=== 11-limit ===
Subgroup: 2.3.5.7.11


[[Badness]]: 0.040846
Comma list: 225/224, 245/242, 385/384


Scales: [[wizard22]]
Mapping: {{mapping| 1 -7 7 -5 -2 | 0 11 -6 10 7 }}


=== 11-limit ===
Optimal tunings:
Subgroup: 2.3.5.7.11
* WE: ~2 = 1200.8059{{c}}, ~12/7 = 936.9952{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3906{{c}}


Comma list: 225/224, 385/384, 4000/3993
{{Optimal ET sequence|legend=0| 9, 23, 32, 41, 91, 223cdef }}


Mapping: [{{val| 2 1 5 2 8 }}, {{val| 0 6 -1 10 -3 }}]
Badness (Sintel): 1.04


Mapping generators: ~99/70, ~25/22
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


POTE generator: ~5/4 = 383.232
Comma list: 105/104, 144/143, 196/195, 245/242


Optimal GPV sequence: {{Val list| 22, 50, 72, 166, 238c, 310c }}
Mapping: {{mapping| 1 -7 7 -5 -2 -8 | 0 11 -6 10 7 15 }}


Badness: 0.018539
Optimal tunings:  
* WE: ~2 = 1200.5990{{c}}, ~12/7 = 936.7670{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3196{{c}}


Scales: [[wizard22]]
{{Optimal ET sequence|legend=0| 9, 32f, 41, 91 }}


==== Lizard ====
Badness (Sintel): 0.955
Subgroup: 2.3.5.7.11.13


Comma list: 225/224, 351/350, 364/363, 385/384
== Merman ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Merman]].''


Mapping: [{{val| 2 1 5 2 8 11 }}, {{val| 0 6 -1 10 -3 -10 }}]
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.


Mapping generators: ~99/70, ~25/22
The name was likely derived from {{w|Triton (mythology)|''Triton''}}, which was in turn derived from ''tritonic''.


POTE generator: ~5/4 = 383.389
[[Subgroup]]: 2.3.5.7


Optimal GPV sequence: {{Val list| 22, 50, 72, 122, 194df }}
[[Comma list]]: 225/224, 2500000/2470629


Badness: 0.021781
{{Mapping|legend=1| 1 -2 10 11 | 0 7 -15 -16 }}
: mapping generators: ~2, ~10/7


===== 17-limit =====
[[Optimal tuning]]s:
Subgroup: 2.3.5.7.11.13.17
* [[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 }}


Comma list: 221/220, 273/272, 289/288, 351/350, 375/374
{{Optimal ET sequence|legend=1| 41, 84, 125 }}


Mapping: [{{val| 2 1 5 2 8 11 6 }}, {{val| 0 6 -1 10 -3 -10 6 }}]
[[Badness]] (Sintel): 1.39


Mapping generators: ~17/12, ~17/15
=== 11-limit ===
Subgroup: 2.3.5.7.11


POTE generator: ~5/4 = 383.381
Comma list: 225/224, 441/440, 1344/1331


Optimal GPV sequence: {{Val list| 22, 50, 72, 122g, 194dfg }}
Mapping: {{mapping| 1 -2 10 11 5 | 0 7 -15 -16 -3 }}


Badness: 0.014536
Optimal tunings:  
* WE: ~2 = 1199.9578{{c}}, ~10/7 = 614.3720{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3943{{c}}


===== 19-limit =====
{{Optimal ET sequence|legend=0| 41, 84, 125e }}
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
Badness (Sintel): 1.20


Mapping: [{{val| 2 1 5 2 8 11 6 2 }}, {{val| 0 6 -1 10 -3 -10 6 18 }}]
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Mapping generators: ~17/12, ~17/15
Comma list: 144/143, 225/224, 364/363, 441/440


POTE generator: ~5/4 = 383.477
Mapping: {{mapping| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}


Optimal GPV sequence: {{Val list| 22h, 50, 72, 122g, 194dfg }}
Optimal tunings:  
* WE: ~2 = 1199.7422{{c}}, ~10/7 = 614.2110{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3442{{c}}


Badness: 0.015702
{{Optimal ET sequence|legend=0| 41, 84, 125e, 209ef, 293ef }}


==== Gizzard ====
Badness (Sintel): 1.14
Subgroup: 2.3.5.7.11.13


Comma list: 225/224, 325/324, 385/384, 1573/1568
=== Mermaid ===
Subgroup: 2.3.5.7.11


Mapping: [{{val| 2 1 5 2 8 -2 }}, {{val| 0 6 -1 10 -3 26 }}]
Comma list: 225/224, 385/384, 532400/531441


Mapping generators: ~99/70, ~25/22
Mapping: {{mapping| 1 -2 10 11 -16 | 0 7 -15 -16 38 }}


POTE generator: ~5/4 = 383.170
Optimal tunings:  
* WE: ~2 = 1199.4973{{c}}, ~10/7 = 614.7004{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4470{{c}}


Optimal GPV sequence: {{Val list| 72, 166, 238cf }}
{{Optimal ET sequence|legend=0| 41, 84e, 125, 166 }}


Badness: 0.020252
Badness (Sintel): 1.46


===== 17-limit =====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13


Comma list: 225/224, 289/288, 325/324, 375/374, 385/384
Comma list: 225/224, 325/324, 385/384, 10648/10647


Mapping: [{{val| 2 1 5 2 8 -2 6 }}, {{val| 0 6 -1 10 -3 26 6 }}]
Mapping: {{mapping| 1 -2 10 11 22 32 | 0 7 -15 -16 38 58 }}


Mapping generators: ~17/12, ~17/15
Optimal tunings:
* WE: ~2 = 1200.5126{{c}}, ~10/7 = 614.7152{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4562{{c}}


POTE generator: ~5/4 = 383.175
{{Optimal ET sequence|legend=0| 41, 84ef, 125f, 166 }}


Optimal GPV sequence: {{Val list| 72, 166g, 238cfg }}
Badness (Sintel): 1.47


Badness: 0.013624
== 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.  


===== 19-limit =====
The name was likely derived from ''slendro diesis'', one of the names for the interval 49/48.  
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594
[[Subgroup]]: 2.3.5.7


Mapping: [{{val| 2 1 5 2 8 -2 6 15 }}, {{val| 0 6 -1 10 -3 26 6 -18 }}]
[[Comma list]]: 225/224, 589824/588245


Mapping generators: ~17/12, ~17/15
{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
: mapping generators: ~2, ~49/48


POTE generator: ~5/4 = 383.138
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.3816{{c}}, ~49/48 = 38.4256{{c}}
: [[error map]]: {{val| +0.382 -0.725 -1.295 +1.765 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/48 = 38.4079{{c}}
: error map: {{val| 0.000 -1.257 -2.235 +0.727 }}


Optimal GPV sequence: {{Val list| 72, 94, 166g }}
{{Optimal ET sequence|legend=1| 31, 94, 125, 406c }}


Badness: 0.014810
[[Badness]] (Sintel): 1.44


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


Comma list: 99/98, 176/175, 1331/1296
Comma list: 225/224, 385/384, 1331/1323
 
Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
 
Optimal tunings:
* WE: ~2 = 1199.4983{{c}}, ~49/48 = 38.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3775{{c}}
 
{{Optimal ET sequence|legend=0| 31, 63, 94, 125 }}
 
Badness (Sintel): 0.838
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Mapping: [{{val| 2 1 5 2 4 }}, {{val| 0 6 -1 10 8 }}]
Comma list: 225/224, 275/273, 385/384, 1331/1323


Mapping generators: ~77/54, ~55/48
Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}


POTE generator: ~5/4 = 383.124
Optimal tunings:  
* WE: ~2 = 1200.1728{{c}}, ~49/48 = 38.3192{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3129{{c}}


Optimal GPV sequence: {{Val list| 22, 50e, 72ee, 94ee }}
{{Optimal ET sequence|legend=0| 31, 63, 94 }}


Badness: 0.057799
Badness (Sintel): 1.07


== Triton ==
== Triton ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Stump]].''
: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''


Subgroup: 2.3.5.7
Triton may be described as the {{nowrap| 19 & 21 }} temperament. Like [[#Tritonic|tritonic]], it is generated by a [[~]][[10/7]] [[tritone]], but here, three generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is alpha-tricot.
 
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 1029/1000
[[Comma list]]: 225/224, 1029/1000


[[Mapping]]: [{{val| 1 0 6 7 }}, {{val| 0 3 -7 -8 }}]
{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}
: mapping generators: ~2, ~10/7


{{Multival|legend=1| 3 -7 -8 -18 -21 1 }}
[[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 }}


[[POTE generator]]: ~7/5 = 568.865
{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}


{{Val list|legend=1| 2, 17d, 19, 78bd, 97bd }}
[[Badness]] (Sintel): 1.50
 
[[Badness]]: 0.059245


=== 11-limit ===
=== 11-limit ===
Line 407: Line 509:
Comma list: 45/44, 56/55, 1029/1000
Comma list: 45/44, 56/55, 1029/1000


Mapping: [{{val| 1 0 6 7 4 }}, {{val| 0 3 -7 -8 -1 }}]
Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}


POTE generator: ~7/5 = 569.144
Optimal tunings:  
* WE: ~2 = 1201.3875{{c}}, ~10/7 = 631.5852{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 630.8007{{c}}


Optimal GPV sequence: {{Val list| 2, 17d, 19, 59bde, 78bde, 97bde }}
{{Optimal ET sequence|legend=0| 2, 17d, 19 }}


Badness: 0.045675
Badness (Sintel): 1.51


== Tritonic ==
== Marvolo ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tritonic]].''
[[Subgroup]]: 2.3.5.7


Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 156250000/155649627


[[Comma list]]: 225/224, 50421/50000
{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
: mapping generators: ~2, ~21/20


[[Mapping]]: [{{val| 1 4 -3 -3 }}, {{val| 0 -5 11 12 }}]
[[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 }}


{{Multival|legend=1| 5 -11 -12 -29 -33 3 }}
{{Optimal ET sequence|legend=1| 29, 43, 72, 619bbccd, 691bbccd }}


[[POTE generator]]: ~7/5 = 580.286
[[Badness]] (Sintel): 2.11
 
{{Val list|legend=1| 29, 31, 60, 91, 122, 213bcd }}
 
[[Badness]]: 0.047578


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


Comma list: 121/120, 225/224, 441/440
Comma list: 225/224, 441/440, 4000/3993


Mapping: [{{val| 1 4 -3 -3 2 }}, {{val| 0 -5 11 12 3 }}]
Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}


POTE generator: ~7/5 = 580.267
Optimal tunings:  
* WE: ~2 = 1200.7075{{c}}, ~21/20 = 83.3888{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3564{{c}}


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


Badness: 0.023659
Badness (Sintel): 0.958


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


Comma list: 105/104, 121/120, 196/195, 275/273
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 }}


Mapping: [{{val| 1 4 -3 -3 2 -5 }}, {{val| 0 -5 11 12 3 18 }}]
Optimal tunings:  
* WE: ~2 = 1200.9606{{c}}, ~21/20 = 83.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3594{{c}}


POTE generator: ~7/5 = 580.108
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}


Optimal GPV sequence: {{Val list| 29, 31, 60e, 151cde }}
Badness (Sintel): 0.760


Badness: 0.022993
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19


=== Tritoni ===
Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440
Subgroup: 2.3.5.7.11


Comma list: 225/224, 385/384, 27783/27500
Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}


Mapping: [{{val| 1 4 -3 -3 17 }}, {{val| 0 -5 11 12 -28 }}]
Optimal tunings:  
* WE: ~2 = 1200.7625{{c}}, ~21/20 = 83.3895{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3551{{c}}


POTE generator: ~7/5 = 580.389
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}


Optimal GPV sequence: {{Val list| 31, 91, 122, 153d }}
Badness (Sintel): 0.895


Badness: 0.045456
== Decic ==
{{Main| Decic }}


== Merman ==
Named by [[Xenllium]] in 2021, decic tempers out 16807/16384, the [[cloudy comma]], and {{monzo| 11 -10 -10 10 }}, the [[linus comma]], in addition to the marvel comma. It may be described as the {{nowrap| 50 & 60 }} temperament, with a period of 1/10 octave and a [[ploidacot]] signature of decaploid monocot. It is [[support]]ed by [[10edo|10-]], [[50edo|50-]], and [[60edo]].  
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Merman]].''


Subgroup: 2.3.5.7
It can be extended to the 11-, 13-, and 17-limit by adding [[385/384]], [[105/104]], and [[170/169]] to the comma list in this order.


[[Comma list]]: 225/224, 2500000/2470629
[[Subgroup]]: 2.3.5.7


[[Mapping]]: [{{val| 1 5 -5 -5 }}, {{val| 0 -7 15 16 }}]
[[Comma list]]: 225/224, 16807/16384


{{Multival|legend=1| 7 -15 -16 -40 -45 5 }}
{{Mapping|legend=1| 10 0 39 28 | 0 1 -1 0 }}
: mapping generators: ~15/14, ~3


[[POTE generator]]: ~7/5 = 585.585
[[Optimal tuning]]s:
* [[WE]]: ~15/14 = 120.1837{{c}}, ~3/2 = 699.7654{{c}} (~49/48 = 21.3366{{c}})
: [[error map]]: {{val| +1.837 -0.353 -0.753 -3.683 }}
* [[CWE]]: ~15/14 = 120.0000{{c}}, ~3/2 = 698.8236{{c}} (~49/48 = 21.1764{{c}})
: error map: {{val| 0.000 -3.131 -5.137 -8.826 }}


{{Val list|legend=1| 41, 84, 125 }}
{{Optimal ET sequence|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}


[[Badness]]: 0.055078
[[Badness]] (Sintel): 2.26


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


Comma list: 225/224, 441/440, 1344/1331
Comma list: 225/224, 385/384, 3087/3025


Mapping: [{{val| 1 5 -5 -5 2 }}, {{val| 0 -7 15 16 3 }}]
Mapping: {{mapping| 10 0 39 28 3 | 0 1 -1 0 2 }}


POTE generator: ~7/5 = 585.606
Optimal tunings:  
* WE: ~15/14 = 120.1406{{c}}, ~3/2 = 697.6075{{c}} (~56/55 = 23.2360{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.0142{{c}} (~56/55 = 22.9858{{c}})


Optimal GPV sequence: {{Val list| 41, 84, 125e }}
{{Optimal ET sequence|legend=0| 10, 40, 50 }}


Badness: 0.036383
Badness (Sintel): 2.11


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


Comma list: 144/143, 225/224, 364/363, 441/440
Comma list: 105/104, 144/143, 196/195, 2200/2197


Mapping: [{{val| 1 5 -5 -5 2 12 }}, {{val| 0 -7 15 16 3 -17 }}]
Mapping: {{mapping| 10 0 39 28 3 37 | 0 1 -1 0 2 0 }}


POTE generator: ~7/5 = 585.657
Optimal tunings:  
* WE: ~15/14 = 120.1166{{c}}, ~3/2 = 697.6705{{c}} (~78/77 = 23.0289{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.1492{{c}} (~78/77 = 22.8508{{c}})


Optimal GPV sequence: {{Val list| 41, 84, 125e, 209ef, 293ef }}
{{Optimal ET sequence|legend=0| 10, 40, 50 }}


Badness: 0.027544
Badness (Sintel): 1.52


== Untriton ==
==== 17-limit ====
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Untriton]].''
Subgroup: 2.3.5.7.11.13.17
 
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 125000000/121060821
Comma list: 105/104, 144/143, 170/169, 196/195, 221/220


[[Mapping]]: [{{Val|1 6 -7 -7}}, {{Val|0 -9 19 20}}]
Mapping: {{mapping| 10 0 39 28 3 37 25 | 0 1 -1 0 2 0 1 }}


{{Multival|legend=1|9 -19 -20 -51 -57 7}}
Optimal tunings:
* WE: ~15/14 = 120.1262{{c}}, ~3/2 = 697.8185{{c}} (~78/77 = 22.9388{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.2757{{c}} (~78/77 = 22.7243{{c}})


[[POTE generator]]: ~7/5 = 588.641
{{Optimal ET sequence|legend=0| 10, 40, 50 }}


{{Val list|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
Badness (Sintel): 1.28


[[Badness]]: 0.143976
=== Splendecic ===
Splendecic (50 & 60e) is an alternative extension of decic, tempering out 1617/1600, 2401/2376 and 4375/4356 in the 11-limit. As a temperament of the [[fantastic]] rank-3 temperament, its name is a portmanteau of ''splendid'' and ''decic''.


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


Comma list: 121/120, 225/224, 22000/21609
Comma list: 225/224, 1617/1600, 2401/2376


Mapping: [{{Val|1 6 -7 -7 1}}, {{Val|0 -9 19 20 5}}]
Mapping: {{mapping| 10 0 39 28 82 | 0 1 -1 0 -3 }}


POTE generator: ~7/5 = 588.626
Optimal tunings:  
* WE: ~15/14 = 120.1874{{c}}, ~3/2 = 699.6085{{c}} (~99/98 = 21.5156{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.3531{{c}} (~99/98 = 21.6469{{c}})


Optimal GPV sequence: {{Val list| 51, 53 }}
{{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de, 170cddee }}


Badness: 0.074295
Badness (Sintel): 1.98


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


Comma list: 121/120, 225/224, 275/273, 1040/1029
Comma list: 105/104, 196/195, 1001/1000, 1188/1183


Mapping: [{{Val|1 6 -7 -7 1 -12}}, {{Val|0 -9 19 20 5 32}}]
Mapping: {{mapping| 10 0 39 28 82 37 | 0 1 -1 0 -3 0 }}


POTE generator: ~7/5 = 588.654
Optimal tunings:  
* WE: ~15/14 = 120.1565{{c}}, ~3/2 = 699.2756{{c}} (~91/90 = 21.6631{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.2480{{c}} (~91/90 = 21.7520{{c}})


Optimal GPV sequence: {{Val list| 51f, 53 }}
{{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de }}


Badness: 0.047441
Badness (Sintel): 1.57


== Septimin ==
==== 17-limit ====
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Septimin]].''
Subgroup: 2.3.5.7.11.13.17


Subgroup: 2.3.5.7
Comma list: 105/104, 170/169, 196/195, 289/288, 375/374


[[Comma list]]: 225/224, 84035/82944
Mapping: {{mapping| 10 0 39 28 82 37 25 | 0 1 -1 0 -3 0 1 }}


[[Mapping]]: [{{val| 1 4 1 5 }}, {{val| 0 -11 6 -10 }}]
Optimal tunings:  
* WE: ~15/14 = 120.1571{{c}}, ~3/2 = 699.2892{{c}} (~91/90 = 21.6536{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.3144{{c}} (~91/90 = 21.6856{{c}})


{{Multival|legend=1| 11 -6 10 -35 -15 40 }}
{{Optimal ET sequence|legend=0| 10e, 50, 60e, 110deg }}


[[POTE generator]]: ~7/6 = 263.632
Badness (Sintel): 1.33


{{Val list|legend=1| 41, 91, 132d }}
=== Prodecic ===
Prodecic (50e & 60e) is an alternative extension of decic, tempering out 441/440, 1375/1372 and 4375/4356 in the 11-limit. As a temperament of the [[prodigy]] rank-3 temperament, its name is a portmanteau of ''prodigy'' and ''decic''.


[[Badness]]: 0.054502
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 225/224, 385/384, 2401/2376
Comma list: 225/224, 441/440, 5929/5832


Mapping: [{{val| 1 4 1 5 5 }}, {{val| 0 -11 6 -10 -7 }}]
Mapping: {{mapping| 10 0 39 28 -13 | 0 1 -1 0 3 }}


POTE generator: ~7/6 = 263.634
Optimal tunings:  
* WE: ~15/14 = 120.2024{{c}}, ~3/2 = 701.3908{{c}} (~55/54 = 19.8237{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.5235{{c}} (~55/54 = 19.4765{{c}})


Optimal GPV sequence: {{Val list| 41, 91, 223cdef }}
{{Optimal ET sequence|legend=0| 10, 50e, 60e }}


Badness: 0.031309
Badness (Sintel): 2.20


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


Comma list: 105/104, 144/143, 196/195, 245/242
Comma list: 105/104, 196/195, 275/273, 5929/5832
 
Mapping: {{mapping| 10 0 39 28 -13 37 | 0 1 -1 0 3 0 }}
 
Optimal tunings:
* WE: ~15/14 = 120.1654{{c}}, ~3/2 = 701.4683{{c}} (~91/90 = 19.5242{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.7175{{c}} (~91/90 = 19.2825{{c}})
 
{{Optimal ET sequence|legend=0| 10, 50e, 60e }}
 
Badness (Sintel): 1.73


Mapping: [{{val| 1 4 1 5 5 7 }}, {{val| 0 -11 6 -10 -7 -15 }}]
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


POTE generator: ~7/6 = 263.700
Comma list: 105/104, 154/153, 170/169, 196/195, 289/288


Optimal GPV sequence: {{Val list| 41, 91 }}
Mapping: {{mapping| 10 0 39 28 -13 37 25 | 0 1 -1 0 3 0 1 }}


Badness: 0.023117
Optimal tunings:  
* WE: ~15/14 = 120.1577{{c}}, ~3/2 = 701.3950{{c}} (~91/90 = 19.5514{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.6932{{c}} (~91/90 = 19.3068{{c}})


== Misneb ==
{{Optimal ET sequence|legend=0| 10, 50e, 60e }}
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Misneb]].''


Subgroup: 2.3.5.7
Badness (Sintel): 1.41


[[Comma list]]: 225/224, 4194304/4117715
== Enneaportent ==
[[Subgroup]]: 2.3.5.7


[[Mapping]]: [{{Val|1 3 1 3}}, {{Val|0 -15 14 -2}}]
[[Comma list]]: 225/224, 40353607/40310784


{{Multival|legend=1|15 -14 2 -57 -39 44}}
{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
: mapping generators: ~2592/2401, ~12005/6912


[[POTE generator]]: ~16/15 = 113.235
[[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 }}


{{Val list|legend=1| 21, 32, 53 }}
{{Optimal ET sequence|legend=1| 9, 54, 63, 72, 495bccd, 567bcccd }}


[[Badness]]: 0.140970
[[Badness]] (Sintel): 2.37


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


Comma list: 99/98, 176/175, 1310720/1294139
Comma list: 225/224, 385/384, 12005/11979


Mapping: [{{Val|1 3 1 3 1}}, {{Val|0 -15 14 -2 26}}]
Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}


POTE generator: ~16/15 = 113.323
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 GPV sequence: {{Val list| 21, 32e, 53, 127, 180de }}
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


Badness: 0.085390
Badness (Sintel): 1.01


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


Comma list: 99/98, 176/175, 640/637, 847/845
Comma list: 169/168, 225/224, 364/363, 1716/1715


Mapping: [{{Val|1 3 1 3 1 2}}, {{Val|0 -15 14 -2 26 18}}]
Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}


POTE generator: ~16/15 = 113.323
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}})


Optimal GPV sequence: {{Val list| 21, 32e, 53, 127, 180de }}
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


Badness: 0.045569
Badness (Sintel): 0.922


=== Musneb ===
== Gracecordial ==
Subgroup: 2.3.5.7.11
: ''For the 5-limit version, see [[Schismic–Pythagorean equivalence continuum #Gracecordial (5-limit)]].''


Comma list: 225/224, 385/384, 66550/64827
[[Subgroup]]: 2.3.5.7


Mapping: [{{Val|1 3 1 3 6}}, {{Val|0 -15 14 -2 -27}}]
[[Comma list]]: 225/224, 781250000/771895089


POTE generator: ~16/15 = 113.142
{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
: mapping generators: ~2, ~3


Optimal GPV sequence: {{Val list| 32, 53, 191de, 244cddee, 297cddee }}
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.4904{{c}}, ~3/2 = 701.1103{{c}}
: [[error map]]: {{val| +0.490 -0.354 -1.655 +1.241 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.8112{{c}}
: error map: {{val| 0.000 -1.144 -2.537 +0.349 }}


Badness: 0.087333
{{Optimal ET sequence|legend=1| 12, …, 113, 125, 238c, 363c }}


== Slender ==
[[Badness]] (Sintel): 2.44
Slender (31&amp;32) tempers out the [[Hewuermera temperaments|hewuermera comma]] in addition to the marvel comma, this has a generator [[49/48]], 3 of which equal marvel's 16/15 - 15/14, and 10 generators is 5/4.


Subgroup: 2.3.5.7
=== 11-limit ===
Subgroup: 2.3.5.7.11


[[Comma list]]: 225/224, 589824/588245
Comma list: 225/224, 385/384, 236328125/234365481


[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -13 10 -6 }}]
Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}


{{Multival|legend=1| 13 -10 6 -46 -27 42 }}
Optimal tunings:
* WE: ~2 = 1200.5571{{c}}, ~3/2 = 701.1589{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8328{{c}}


[[POTE generator]]: ~49/48 = 38.413
{{Optimal ET sequence|legend=0| 12e, 113, 125, 238c }}


{{Val list|legend=1| 31, 94, 125 }}
Badness (Sintel): 2.96


[[Badness]]: 0.056934
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


=== 11-limit ===
Comma list: 225/224, 325/324, 385/384, 831875/830466
Subgroup: 2.3.5.7.11


Comma list: 225/224, 385/384, 1331/1323
Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}


Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -13 10 -6 -17 }}]
Optimal tunings:  
* WE: ~2 = 1200.6282{{c}}, ~3/2 = 701.2080{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8421{{c}}


POTE generator: ~49/48 = 38.387
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


Optimal GPV sequence: {{Val list| 31, 63, 94, 125 }}
Badness (Sintel): 2.16


Badness: 0.025342
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


=== 13-limit ===
Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913
Subgroup: 2.3.5.7.11.13
 
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}
 
Optimal tunings:
* WE: ~2 = 1200.5058{{c}}, ~3/2 = 701.1360{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8414{{c}}


Comma list: 225/224, 275/273, 385/384, 1331/1323
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


Mapping: [{{val| 1 2 2 3 4 3 }}, {{val| 0 -13 10 -6 -17 22 }}]
Badness (Sintel): 1.96


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


Optimal GPV sequence: {{Val list| 31, 63, 94 }}
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444


Badness: 0.025913
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}


== Marvolo ==
Optimal tunings:
Subgroup: 2.3.5.7
* WE: ~2 = 1200.4418{{c}}, ~3/2 = 701.0999{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8425{{c}}


[[Comma list]]: 225/224, 156250000/155649627
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


[[Mapping]]: [{{val| 1 2 1 1 }}, {{val| 0 -6 19 26 }}]
Badness (Sintel): 1.71


{{Multival|legend=1| 6 -19 -26 -44 -58 -7 }}
==== 23-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23


[[POTE generator]]: ~21/20 = 83.348
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528


{{Val list|legend=1| 29, 43, 72, 619bcd, 691bcd }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}


[[Badness]]: 0.083338
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 }}
Subgroup: 2.3.5.7.11


Comma list: 225/224, 441/440, 4000/3993
Badness (Sintel): 1.57


Mapping: [{{val| 1 2 1 1 2 }}, {{val| 0 -6 19 26 21 }}]
==== 29-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29


POTE generator: ~21/20 = 83.340
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493


Optimal GPV sequence: {{Val list| 29, 43, 72 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}


Badness: 0.028965
Optimal tunings:  
* WE: ~2 = 1200.4400{{c}}, ~3/2 = 701.0986{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8428{{c}}


=== 13-limit ===
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
Subgroup: 2.3.5.7.11.13


Comma list: 169/168, 225/224, 364/363, 441/440
Badness (Sintel): 1.50


Mapping: [{{val| 1 2 1 1 2 3 }}, {{val| 0 -6 19 26 21 10 }}]
==== 31-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31


POTE generator: ~21/20 = 83.330
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493


Optimal GPV sequence: {{Val list| 29, 43, 72, 115f }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}


Badness: 0.021470
Optimal tunings:  
* WE: ~2 = 1200.4178{{c}}, ~3/2 = 701.0822{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8396{{c}}


== Enneaportent ==
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 40353607/40310784
Badness (Sintel): 1.53


[[Mapping]]: [{{val| 9 0 28 11 }}, {{val| 0 2 -1 2 }}]
=== Gracecord ===
Subgroup: 2.3.5.7.11


{{Multival|legend=1| 18 -9 18 -56 -22 67 }}
Comma list: 225/224, 441/440, 109375/107811


[[POTE generator]]: ~5/4 = 383.165
Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}


{{Val list|legend=1| 9, 63, 72, 495bcd }}
Optimal tunings:
* WE: ~2 = 1200.6064{{c}}, ~3/2 = 701.2398{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8718{{c}}


[[Badness]]: 0.093679
{{Optimal ET sequence|legend=0| 12, …, 101cd, 113 }}


=== 11-limit ===
Badness (Sintel): 2.21
Subgroup: 2.3.5.7.11


Comma list: 225/224, 385/384, 12005/11979
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Mapping: [{{val| 9 0 28 11 24 }}, {{val| 0 2 -1 2 1 }}]
Comma list: 225/224, 364/363, 441/440, 6125/6084


POTE generator: ~5/4 = 383.146
Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}


Optimal GPV sequence: {{Val list| 9, 63, 72, 423cd, 495bcd }}
Optimal tunings:  
* WE: ~2 = 1200.6225{{c}}, ~3/2 = 701.2539{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8781{{c}}


Badness: 0.030426
{{Optimal ET sequence|legend=0| 12f, …, 101cdf, 113 }}


=== 13-limit ===
Badness (Sintel): 1.83
Subgroup: 2.3.5.7.11.13


Comma list: 169/168, 225/224, 364/363, 1716/1715
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


Mapping: [{{val| 9 0 28 11 24 19 }}, {{val| 0 2 -1 2 1 2 }}]
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989


POTE generator: ~5/4 = 383.047
Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}


Optimal GPV sequence: {{Val list| 9, 63, 72, 279cf }}
Optimal tunings:  
* WE: ~2 = 1200.3308{{c}}, ~3/2 = 701.0632{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8654{{c}}


Badness: 0.022322
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


== Submajor ==
Badness (Sintel): 1.87
Subgroup: 2.3.5


[[Comma list]]: 69198046875/68719476736
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


[[Mapping]]: [{{val| 1 4 -1 }}, {{val| 0 -8 11 }}]
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663


[[POTE generator]]: ~10125/8192 = 362.321
Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}


{{Val list|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc }}
Optimal tunings:
* WE: ~2 = 1200.2658{{c}}, ~3/2 = 701.0213{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8629{{c}}


[[Badness]]: 0.130236
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


=== 7-limit ===
Badness (Sintel): 1.68
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 51200/50421
== Alphorn ==
[[Subgroup]]: 2.3.5.7


[[Mapping]]: [{{val| 1 4 -1 1 }}, {{val| 0 -8 11 6 }}]
[[Comma list]]: 225/224, 5764801/5668704


{{Multival|legend=1| 8 -11 -6 -36 -32 17 }}
{{Mapping|legend=1| 1 -7 5 -9 | 0 16 -5 22 }}
: mapping generators: ~2, ~35/24


[[POTE generator]]: ~49/40 = 362.255
[[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 }}


{{Val list|legend=1| 10, 33, 43, 53 }}
{{Optimal ET sequence|legend=1| 13d, 28d, 41, 151cd, 192cdd, 233ccdd }}


[[Badness]]: 0.060533
[[Badness]] (Sintel): 3.27


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


Comma list: 225/224, 385/384, 6655/6561
Comma list: 225/224, 385/384, 12250/11979


Mapping: [{{val| 1 4 -1 1 11 }}, {{val| 0 -8 11 6 -25 }}]
Mapping: {{mapping| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}


POTE generator: ~27/22 = 362.101
Optimal tunings:  
* WE: ~2 = 1200.5123{{c}}, ~16/11 = 644.1307{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 643.8662{{c}}


Optimal GPV sequence: {{Val list| 10, 43e, 53, 116, 169de, 285cde }}
{{Optimal ET sequence|legend=0| 13d, 28d, 41 }}


Badness: 0.050582
Badness (Sintel): 2.43


==== 13-limit ====
== Misneb ==
Subgroup: 2.3.5.7.11.13
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Misneb]].''
 
[[Subgroup]]: 2.3.5.7


Comma list: 169/168, 225/224, 275/273, 385/384
[[Comma list]]: 225/224, 4194304/4117715


Mapping: [{{val| 1 4 -1 1 11 4 }}, {{val| 0 -8 11 6 -25 -1 }}]
{{Mapping|legend=1| 1 -12 15 1 | 0 15 -14 2 }}
: mapping generators: ~2, ~15/8


POTE generator: ~16/13 = 362.105
[[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 }}


Optimal GPV sequence: {{Val list| 10, 43e, 53, 116, 169de, 285cdef }}
{{Optimal ET sequence|legend=1| 21, 32, 53 }}


Badness: 0.027689
[[Badness]] (Sintel): 3.57


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


Comma list: 99/98, 176/175, 51200/50421
Comma list: 99/98, 176/175, 1310720/1294139
 
POTE generator: ~49/40 = 362.418


Mapping: [{{val| 1 4 -1 1 -5 }}, {{val| 0 -8 11 6 28 }}]
Mapping: {{mapping| 1 -12 15 1 27 | 0 15 -14 2 -26 }}


POTE generator: ~49/40 = 362.418
Optimal tunings:  
* WE: ~2 = 1200.1654{{c}}, ~15/8 = 1086.8269{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6766{{c}}


Optimal GPV sequence: {{Val list| 43, 53, 96, 149d }}
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


Badness: 0.051806
Badness (Sintel): 2.82


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


Comma list: 99/98, 169/168, 176/175, 640/637
Comma list: 99/98, 176/175, 640/637, 847/845
 
Mapping: {{mapping| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}
 
Optimal tunings:
* WE: ~2 = 1200.1687{{c}}, ~15/8 = 1086.8295{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6757{{c}}


POTE generator: ~16/13 = 362.402
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


Mapping: [{{val| 1 4 -1 1 -5 4 }}, {{val| 0 -8 11 6 28 -1 }}]
Badness (Sintel): 1.88


POTE generator: ~16/13 = 362.402
=== Musneb ===
Subgroup: 2.3.5.7.11


Optimal GPV sequence: {{Val list| 43, 53, 96, 149d }}
Comma list: 225/224, 385/384, 66550/64827


Badness: 0.029680
Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}
 
Optimal tunings:
* WE: ~2 = 1200.0839{{c}}, ~15/8 = 1086.9343{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.8593{{c}}
 
{{Optimal ET sequence|legend=0| 21e, 32, 53 }}
 
Badness (Sintel): 2.89
 
== Untriton ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''


== Alphorn ==
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.  
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 5764801/5668704
[[Subgroup]]: 2.3.5.7


[[Mapping]]: [{{val| 1 9 0 13 }}, {{val| 0 -16 5 -22 }}]
[[Comma list]]: 225/224, 125000000/121060821


{{Multival|legend=1| 16 -5 22 -45 -10 65 }}
{{Mapping|legend=1| 1 -3 12 13 | 0 9 -19 -20 }}
: mapping generators: ~2, ~10/7


[[POTE generator]]: ~48/35 = 556.221
[[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 }}


{{Val list|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
{{Optimal ET sequence|legend=1| 51, 53 }}


[[Badness]]: 0.129258
[[Badness]] (Sintel): 3.64


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


Comma list: 225/224, 385/384, 12250/11979
Comma list: 121/120, 225/224, 22000/21609
 
Mapping: {{mapping| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}
 
Optimal tunings:
* WE: ~2 = 1200.3591{{c}}, ~10/7 = 611.5569{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3690{{c}}


Mapping: [{{val| 1 9 0 13 3 }}, {{val| 0 -16 5 -22 1 }}]
{{Optimal ET sequence|legend=0| 51, 53 }}


POTE generator: ~11/8 = 556.144
Badness (Sintel): 2.46


Optimal GPV sequence: {{Val list| 28d, 41, 315cde }}
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Badness: 0.073459
Comma list: 121/120, 225/224, 275/273, 1040/1029


== Tertiosec ==
Mapping: {{mapping| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tertiosec]].''


Subgroup: 2.3.5.7
Optimal tunings:  
* WE: ~2 = 1200.4078{{c}}, ~10/7 = 611.5536{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3392{{c}}


[[Comma list]]: 225/224, 14495514624/13841287201
{{Optimal ET sequence|legend=0| 51f, 53 }}


[[Mapping]]: [{{val| 3 7 5 9 }}, {{val| 0 -8 7 -2 }}]
Badness (Sintel): 1.96


{{Multival|legend=1| 24 -21 6 -89 -58 73 }}
== Naiadical ==
Named by [[Xenllium]] in 2026, naiadical may be described as the {{nowrap| 21 & 29 }} temperament.


[[POTE generator]]: ~15/14 = 112.283
[[Subgroup]]: 2.3.5.7


{{Val list|legend=1| 21, 54, 75, 96, 171d }}
[[Comma list]]: 225/224, 823543/800000


[[Badness]]: 0.431636
{{Mapping|legend=1| 1 -4 11 9 | 0 9 -14 -10 }}
: mapping generators: ~2, ~32/21


=== 11-limit ===
[[Optimal tuning]]s:
Subgroup: 2.3.5.7.11
* [[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 }}


Comma list: 225/224, 3840/3773, 12005/11979
{{Optimal ET sequence|legend=1| 21, 29, 50, 79d, 129cdd, 179bcddd }}


Mapping: [{{val| 3 7 5 9 9 }}, {{val| 0 -8 7 -2 5 }}]
[[Badness]] (Sintel): 3.67


POTE generator: ~15/14 = 112.171
=== 11-limit ===
Subgroup: 2.3.5.7.11


Optimal GPV sequence: {{Val list| 21, 54, 75e }}
Comma list: 225/224, 245/242, 1617/1600


Badness: 0.173485
Mapping: {{Mapping| 1 -4 11 9 14 | 0 9 -14 -10 -17 }}


== Gwazy ==
Optimal tunings:
{{see also|Very high accuracy temperaments #Kwazy}}
* WE: ~2 = 1201.9008{{c}}, ~21/16 = 745.3867{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~32/21 = 744.1777{{c}}


Subgroup: 2.3.5.7
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}


[[Comma list]]: 225/224, 5971968/5764801
Badness (Sintel): 2.00


[[Mapping]]: [{{val| 2 1 6 4 }}, {{val| 0 8 -5 6 }}]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


{{Multival|legend=1| 16 -10 12 -53 -26 56 }}
Comma list: 105/104, 196/195, 245/242, 1001/1000


[[POTE generator]]: ~35/32 = 162.658
Mapping: {{Mapping| 1 -4 11 9 14 13 | 0 9 -14 -10 -17 -15 }}


{{Val list|legend=1| 22, 74, 96, 118d }}
Optimal tunings:
* WE: ~2 = 1201.7863{{c}}, ~20/13 = 745.3344{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1931{{c}}


[[Badness]]: 0.178826
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}


=== 11-limit ===
Badness (Sintel): 1.43
Subgroup: 2.3.5.7.11


Comma list: 99/98, 176/175, 65536/65219
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Mapping: [{{val| 2 1 6 4 8 }}, {{val| 0 8 -5 6 -4 }}]
Comma list: 105/104, 170/169, 196/195, 221/220, 245/242


POTE generator: ~11/10 = 162.592
Mapping: {{Mapping| 1 -4 11 9 14 13 14 | 0 9 -14 -10 -17 -15 -16 }}


Optimal GPV sequence: {{Val list| 22, 74, 96, 118d }}
Optimal tunings:  
* WE: ~2 = 1201.9208{{c}}, ~20/13 = 745.3976{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1669{{c}}


Badness: 0.068410
{{Optimal ET sequence|legend=0| 21, 29g, 50, 79dg }}


== Gracecordial ==
Badness (Sintel): 1.26
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Gracecordial]].''


Subgroup: 2.3.5.7
== Quintannic ==
Named by [[Scott Dakota]], quintannic may be described as the {{nowrap| 43 & 60 }} temperament.  


[[Comma list]]: 225/224, 781250000/771895089
[[Subgroup]]: 2.3.5.7


[[Mapping]]: [{{val| 1 0 34 63 }}, {{val| 0 1 -20 -38 }}]
[[Comma list]]: 225/224, 9805926501/9765625000


{{Multival|legend=1| 1 -20 -38 -34 -63 -32 }}
{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
: mapping generators: ~2, ~10000/9261


[[POTE generator]]: ~3/2 = 700.824
[[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 }}


{{Val list|legend=1| 12, 113, 125, 238c, 363c }}
{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}


[[Badness]]: 0.096279
[[Badness]] (Sintel): 3.81


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


Comma list: 225/224, 385/384, 236328125/234365481
Comma list: 225/224, 441/440, 43923/43750


Mapping: [{{val| 1 0 34 63 -90 }}, {{val| 0 1 -20 -38 59 }}]
Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}


POTE generator: ~3/2 = 700.834
Optimal tunings:
* WE: ~2 = 1201.0031{{c}}, ~320/297 = 139.9435{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~320/297 = 139.8053{{c}}


Optimal GPV sequence: {{Val list| 12e, 101cde, 113, 125, 238c }}
{{Optimal ET sequence|legend=0| 43, 60e, 103, 369bcdeee, 472bbcddeee }}


Badness: 0.089588
Badness (Sintel): 1.74


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


Comma list: 225/224, 325/324, 385/384, 831875/830466
Comma list: 225/224, 441/440, 1001/1000, 1188/1183


Mapping: [{{val| 1 0 34 63 -90 -66 }}, {{val| 0 1 -20 -38 59 44 }}]
Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}


POTE generator: ~3/2 = 700.841
Optimal tunings:
* WE: ~2 = 1200.8354{{c}}, ~13/12 = 139.9095{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.7997{{c}}


Optimal GPV sequence: {{Val list| 12e, 101cde, 113, 125f, 238cf }}
{{Optimal ET sequence|legend=0| 43, 60e, 103 }}


Badness: 0.052235
Badness (Sintel): 1.35


==== 17-limit ====
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913
Comma list: 225/224, 273/272, 375/374, 441/440, 891/884


Mapping: [{{val| 1 0 34 63 -90 -66 -7 }}, {{val| 0 1 -20 -38 59 44 7 }}]
Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}


POTE generator: ~3/2 = 700.841
Optimal tunings:
* WE: ~2 = 1200.7402{{c}}, ~13/12 = 139.9015{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.8038{{c}}


Optimal GPV sequence: {{Val list| 12e, 101cde, 113, 125f, 238cf }}
{{Optimal ET sequence|legend=0| 43, 60e, 103 }}


Badness: 0.038565
Badness (Sintel): 1.17


==== 19-limit ====
== Hendeca ==
Subgroup: 2.3.5.7.11.13.17.19
{{Distinguish| Hendec }}
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Hendecatonic]].''


Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444
Hendeca tempers out the same 5-limit comma as [[porwell temperaments #Hendecatonic|hendecatonic]], and has a period of 1/11 octave. However, in this temperament, nine periods represent [[7/4]], the same as [[keemic temperaments #Undeka|undeka]]. It can be tuned to [[22edo]] or [[33edo]] using the [[patent val]], or [[55edo]] using the 55d val. It was named by [[Xenllium]] in 2025 as a low-accuracy variant of hendecatonic.


Mapping: [{{val| 1 0 34 63 -90 -66 -7 9 }}, {{val| 0 1 -20 -38 59 44 7 -3 }}]
[[Subgroup]]: 2.3.5.7


POTE generator: ~3/2 = 700.842
[[Comma list]]: 225/224, 122880/117649


Optimal GPV sequence: {{Val list| 12e, 101cde, 113, 125f, 238cf }}
{{Mapping|legend=1| 11 0 43 31 | 0 1 -1 0 }}
: mapping generators: ~16/15, ~3


Badness: 0.028165
[[Optimal tuning]]s:  
* [[WE]]: ~16/15 = 108.9526{{c}}, ~3/2 = 702.4215{{c}}
: [[error map]]: {{val| -1.521 -1.055 -2.252 +8.705 }}
* [[CWE]]: ~16/15 = 109.0909{{c}}, ~3/2 = 703.2071{{c}}
: error map: {{val| 0.000 +1.252 +1.388 +12.992 }}


==== 23-limit ====
{{Optimal ET sequence|legend=1| 22, 55d, 77d, 99dd }}
Subgroup: 2.3.5.7.11.13.17.19.23


Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528
[[Badness]] (Sintel): 4.37


Mapping: [{{val| 1 0 34 63 -90 -66 -7 9 -43 }}, {{val| 0 1 -20 -38 59 44 7 -3 30 }}]
=== 11-limit ===
Subgroup: 2.3.5.7.11


POTE generator: ~3/2 = 700.843
Comma list: 121/120, 225/224, 352/343


Optimal GPV sequence: {{Val list| 12e, 101cde, 113, 238cfi }}
Mapping: {{mapping| 11 0 43 31 38 | 0 1 -1 0 0 }}


Badness: 0.021879
Optimal tunings:  
* WE: ~16/15 = 109.0109{{c}}, ~3/2 = 702.5746{{c}}
* CWE: ~16/15 = 109.0909{{c}}, ~3/2 = 703.0395{{c}}


==== 29-limit ====
{{Optimal ET sequence|legend=0| 22, 55d }}
Subgroup: 2.3.5.7.11.13.17.19.23.29


Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493
Badness (Sintel): 2.46


Mapping: [{{val| 1 0 34 63 -90 -66 -7 9 -43 -49 }}, {{val| 0 1 -20 -38 59 44 7 -3 30 34 }}]
== Gwazy ==
: ''For the 5-limit version, see [[Very high accuracy temperaments #Kwazy]].''


POTE generator: ~3/2 = 700.842
Named by [[Petr Pařízek]] in 2011<ref name="petr's long post"/>, gwazy may be described as the {{nowrap| 22 & 74 }} temperament.  


Optimal GPV sequence: {{Val list| 12e, 101cde, 113, 125f, 238cfi }}
[[Subgroup]]: 2.3.5.7


Badness: 0.018011
[[Comma list]]: 225/224, 5971968/5764801
 
==== 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|legend=1| 2 1 6 4 | 0 8 -5 6 }}
: mapping generators: ~2401/1728, ~35/32


Mapping: [{{val| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 }}, {{val| 0 1 -20 -38 59 44 7 -3 30 34 53 }}]
[[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 }}


POTE generator: ~3/2 = 700.838
{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}


Optimal GPV sequence: {{Val list| 12e, 101cdek, 113, 125f, 238cfi }}
[[Badness]] (Sintel): 4.53


Badness: 0.016007
=== 11-limit ===
 
=== Gracecord ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 225/224, 441/440, 109375/107811
Comma list: 99/98, 176/175, 65536/65219


Mapping: [{{val| 1 0 34 63 89 }}, {{val| 0 1 -20 -38 -54 }}]
Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}


POTE generator: ~3/2 = 700.885
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 GPV sequence: {{Val list| 12, 101cd, 113 }}
{{Optimal ET sequence|legend=0| 22, 74, 96 }}


Badness: 0.066964
Badness (Sintel): 2.26


==== 13-limit ====
== Tertiosec ==
Subgroup: 2.3.5.7.11.13
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tertiosec]].''


Comma list: 225/224, 364/363, 441/440, 6125/6084
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>.


Mapping: [{{val| 1 0 34 63 89 113 }}, {{val| 0 1 -20 -38 -54 -69 }}]
[[Subgroup]]: 2.3.5.7


POTE generator: ~3/2 = 700.890
[[Comma list]]: 225/224, 14495514624/13841287201


Optimal GPV sequence: {{Val list| 12f, 101cdf, 113 }}
{{Mapping|legend=1| 3 -1 12 7 | 0 8 -7 2 }}
: mapping generators: ~3072/2401, ~2048/1715


Badness: 0.044196
[[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 }}


==== 17-limit ====
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}
Subgroup: 2.3.5.7.11.13.17


Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989
[[Badness]] (Sintel): 10.9


Mapping: [{{val| 1 0 34 63 89 113 -7 }}, {{val| 0 1 -20 -38 -54 -69 7 }}]
=== 11-limit ===
Subgroup: 2.3.5.7.11


POTE generator: ~3/2 = 700.870
Comma list: 225/224, 3840/3773, 12005/11979
 
Optimal GPV sequence: {{Val list| 12f, 101cdf, 113 }}
 
Badness: 0.036637
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663
Mapping: {{mapping| 3 -1 12 7 14 | 0 8 -7 2 -5 }}


Mapping: [{{val| 1 0 34 63 89 113 -7 9 }}, {{val| 0 1 -20 -38 -54 -69 7 -3 }}]
Optimal tunings:  
* WE: ~44/35 = 399.6550{{c}}, ~33/28 = 287.5803{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~33/28 = 287.8224{{c}}


POTE generator: ~3/2 = 700.866
{{Optimal ET sequence|legend=0| 21, 54, 75e }}


Optimal GPV sequence: {{Val list| 12f, 101cdf, 113 }}
Badness (Sintel): 5.74


Badness: 0.027559
== References ==


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