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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 }}
 
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.
 
== 5-limit ==
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~16/15 = 125.7549
 
EDO generators: [[9edo|1\9]], [[10edo|1\10]], [[19edo|2\19]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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Subgroup: 2.3.5


[[Comma list]]: 16875/16384
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}}.)


[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
== Wizard ==
{{Main| Wizard }}
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Wizard]].''


[[Wedgie]]: {{wedgie| 4 -3 -14 }}
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.


{{Val list|legend=1| 9, 10, 19, 67c, 86c, 105c }}
[[Subgroup]]: 2.3.5.7


</div></div>
[[Comma list]]: 225/224, 118098/117649


== 7-limit ==
{{Mapping|legend=1| 2 1 5 2 | 0 6 -1 10 }}
: mapping generators: ~1225/864, ~245/216


Period: 1\1
[[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 }}


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


EDO generators: [[9edo|1\9]], [[10edo|1\10]], [[19edo|2\19]]
[[Badness]] (Sintel): 1.03
 
Scales (Scala files):
 
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Subgroup: 2.3.5.7
 
[[Comma list]]: 49/48, 225/224
 
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}]
 
[[Wedgie]]: {{wedgie| 4 -3 2 -14 -8 13 }}
 
{{Val list|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
 
</div></div>
 
=== Negra ===
 
This is the 2.3.5.7.13 extension of negri.
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~14/13 = 125.567
 
EDO generators: [[9edo|1\9]], [[10edo|1\10]], [[19edo|2\19]]
 
Scales (Scala files):
 
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Subgroup: 2.3.5.7.13
 
[[Comma list]]: 49/48, 65/64, 91/90
 
[[Mapping]]: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -3 }}]
 
Gencom map: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}]
 
Gencom: [2 14/13; 49/48 65/64 91/90]
 
{{Val list|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}
 
</div></div>
 
== 11-limit ==
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~15/14 = 126.474
 
EDO generators: [[9edo|1\9]], [[10edo|1\10]], [[19edo|2\19]]
 
Scales (Scala files):
 
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=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 45/44, 49/48, 56/55
Comma list: 225/224, 385/384, 4000/3993
 
Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]
 
{{Val list|legend=1| 9, 10, 19 }}
 
[[Badness]]: 0.0262
 
</div></div>


=== 13-limit ===
Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}


Period: 1\1
Optimal tunings:  
* WE: ~99/70 = 600.3051{{c}}, ~25/22 = 216.8782{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.7961{{c}}


Optimal ([[POTE]]) generator: ~14/13 = 126.431
{{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}


EDO generators: [[9edo|1\9]], [[10edo|1\10]], [[19edo|2\19]]
Badness (Sintel): 0.613
 
Scales (Scala files):  
 
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==== Lizard ====
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, 351/350, 364/363, 385/384


[[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 }}


</div></div>
Badness (Sintel): 0.900


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


Period: 1\1
Comma list: 221/220, 273/272, 289/288, 351/350, 375/374


Optimal ([[POTE]]) generator: ~15/14 = 124.767
Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}


EDO generators: [[19edo|2\19]], [[29edo|3\29]]
Optimal tunings:  
* WE: ~17/12 = 600.5032{{c}}, ~17/15 = 216.8002{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.6361{{c}}


Scales (Scala files):
{{Optimal ET sequence|legend=0| 22, 50, 72 }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Badness (Sintel): 0.741
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 49/48, 100/99, 225/224
Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
 
Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]
 
{{Val list|legend=1| 19, 29, 48d, 77cdd }}
 
Badness: 0.0387
 
</div></div>


=== 13-limit ===
Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}


Period: 1\1
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 ([[POTE]]) generator: ~14/13 = 124.716
{{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}


EDO generators: [[19edo|2\19]], [[29edo|3\29]]
Badness (Sintel): 0.955
 
Scales (Scala files):  
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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==== Gizzard ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 49/48, 65/64, 91/90, 875/858
Comma list: 225/224, 325/324, 385/384, 1573/1568


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


{{Val list|legend=1| 19, 29, 48df, 77cddf }}
Optimal tunings:
* WE: ~99/70 = 600.2896{{c}}, ~25/22 = 216.9343{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.8501{{c}}


Badness: 0.0244
{{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}


</div></div>
Badness (Sintel): 0.837


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


Period: 1\1
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384


Optimal ([[POTE]]) generator: ~15/14 = 127.039
Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}


EDO generators: [[9edo|1\9]], [[19edo|2\19]]
Optimal tunings:  
* WE: ~17/12 = 600.3227{{c}}, ~17/15 = 216.9414{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8469{{c}}


Scales (Scala files):
{{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Badness (Sintel): 0.694
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 33/32, 49/48, 77/75
Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594


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


{{Val list|legend=1| 9, 19e, 47…, 66…, 85… }}
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: 0.0306
{{Optimal ET sequence|legend=0| 72, 94, 166g }}


</div></div>
Badness (Sintel): 0.901
 
=== 13-limit ===
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~14/13 = 127.039
 
EDO generators: [[9edo|1\9]], [[19edo|2\19]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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Subgroup: 2.3.5.7.11.13
 
Comma list: 33/32, 49/48, 65/64, 91/90
 
Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]
 
{{Val list|legend=1| 9, 19e, 47…, 66…, 85… }}
 
Badness: 0.0202
 
</div></div>
 
== Negroni ==
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~15/14 = 124.539
 
EDO generators: [[10edo|1\10]], [[19edo|2\19]], [[29edo|3\29]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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=== Mage ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 49/48, 55/54, 225/224
Comma list: 99/98, 176/175, 1331/1296
 
Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]
 
{{Val list|legend=1| 10, 19e, 29, 77cddee }}
 
Badness: 0.0353
 
</div></div>
 
=== 13-limit ===
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~14/13 = 124.545
 
EDO generators: [[10edo|1\10]], [[19edo|2\19]], [[29edo|3\29]]
 
Scales (Scala files):


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }}
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11.13
Optimal tunings:  
* WE: ~77/54 = 600.6486{{c}}, ~55/48 = 217.1099{{c}}
* CWE: ~77/54 = 600.0000{{c}}, ~55/48 = 216.9841{{c}}


Comma list: 49/48, 55/54, 65/64, 91/90
{{Optimal ET sequence|legend=0| 22, 50e, 72ee }}


Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]
Badness (Sintel): 1.91


{{Val list|legend=1| 10, 19e, 29, 77cddeef }}
== Tritonic ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tritonic]].''


Badness: 0.0216
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.  


</div></div>
[[Subgroup]]: 2.3.5.7


== Wilsec ==
[[Comma list]]: 225/224, 50421/50000


Period: 1\1
{{Mapping|legend=1| 1 -1 8 9 | 0 5 -11 -12 }}
: mapping generators: ~2, ~10/7


Optimal ([[POTE]]) generator: ~11/8 = 537.186
[[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 }}


EDO generators: [[29edo|13\29]], [[38edo|17\38]]
{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}


Scales (Scala files):
[[Badness]] (Sintel): 1.20
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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<div class="mw-collapsible-content">


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


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


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


{{Val list|legend=1| 9, 20, 29, 38d, 67cdde }}
Optimal tunings:
* WE: ~2 = 1201.7116{{c}}, ~10/7 = 620.6166{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6890{{c}}


Badness: 0.0419
{{Optimal ET sequence|legend=0| 29, 31, 60e, 91e, 213bcdeee }}


</div></div>
Badness (Sintel): 0.782
 
=== 13-limit ===
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~11/8 = 537.208
 
EDO generators: [[29edo|13\29]], [[38edo|17\38]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


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


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


{{Val list|legend=1| 9, 20, 29, 38df, 67cddef }}
Optimal tunings:
* WE: ~2 = 1201.5355{{c}}, ~10/7 = 620.6855{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8469{{c}}


Badness: 0.0252
{{Optimal ET sequence|legend=0| 29, 31, 60e }}


</div></div>
Badness (Sintel): 0.950
 
=== 17-limit ===
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~11/8 = 537.230
 
EDO generators: [[29edo|13\29]], [[38edo|17\38]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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<div class="mw-collapsible-content">


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


Comma list: 49/48, 65/64, 91/90, 121/120, 154/153
Comma list: 105/104, 121/120, 154/153, 196/195, 273/272


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 | 0 5 -11 -12 -3 -18 -25 }}


{{Val list|legend=1| 9, 20g, 29g, 38df, 67cddefg }}
Optimal tunings:
* WE: ~2 = 1201.5260{{c}}, ~10/7 = 620.7330{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8986{{c}}


Badness: 0.0218
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}


</div></div>
Badness (Sintel): 0.973
 
=== 19-limit ===
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~11/8 = 537.214
 
EDO generators: [[29edo|13\29]], [[38edo|17\38]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153
Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272


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


{{Val list|legend=1| 9, 20g, 29g, 38df, 67cddefgh }}
Optimal tunings:
* WE: ~2 = 1201.3100{{c}}, ~10/7 = 620.6509{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9328{{c}}


Badness: 0.0168
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}


</div></div>
Badness (Sintel): 1.03


= Passive =
==== 23-limit ====
{{see also | Archytas clan #Passion }}
Subgroup: 2.3.5.7.11.13.17.19.23


Period: 1\1
Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195


Optimal ([[POTE]]) generator: ~16/15 = 98.809
Mapping: {{mapping| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}


EDO generators: [[12edo|1\12]], [[13edo|1\13]]
Optimal tunings:  
* WE: ~2 = 1201.4074{{c}}, ~10/7 = 620.7185{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9548{{c}}


Scales (Scala files):
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Badness (Sintel): 1.04
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
=== Tritoni ===
Subgroup: 2.3.5.7.11


Comma list: 225/224, 256/245
Comma list: 225/224, 385/384, 27783/27500


Mapping: [{{val| 1 2 2 3 }}, {{val| 0 -5 4 -2 }}]
Mapping: {{mapping| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}


{{Val list|legend=1| 12, 49dd }}
Optimal tunings:
* WE: ~2 = 1201.0888{{c}}, ~10/7 = 620.1733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6146{{c}}


Badness: 0.0751
{{Optimal ET sequence|legend=0| 31, 91, 122, 153d }}


</div></div>
Badness (Sintel): 1.50


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


: ''For the 5-limit version of this temperament, see [[High badness temperaments #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.  


Period: 1\2
[[Subgroup]]: 2.3.5.7


Optimal ([[POTE]]) generator: ~5/4 = 383.256
[[Comma list]]: 225/224, 84035/82944


EDO generators: [[22edo|7\22]], [[50edo|16\50]], [[72edo|23\72]], [[94edo|30\94]]
{{Mapping|legend=1| 1 -7 7 -5 | 0 11 -6 10 }}
: mapping generators: ~2, ~12/7


Scales (Scala files): [[wizard22]]
[[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 }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
{{Optimal ET sequence|legend=1| 41, 91, 132d }}
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
[[Badness]] (Sintel): 1.38
 
Comma list: 225/224, 118098/117649
 
Mapping: [{{val| 2 1 5 2 }}, {{val| 0 6 -1 10 }}]
 
Mapping generators: ~1225/864, ~245/216
 
Wedgie: {{wedgie| 12 -2 20 -31 -2 52 }}
 
{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }}
 
Badness: 0.0408
 
</div></div>
 
== 11-limit ==
 
Period: 1\2
 
Optimal ([[POTE]]) generator: ~5/4 = 383.232
 
EDO generators: [[22edo|7\22]], [[50edo|16\50]], [[72edo|23\72]], [[94edo|30\94]]
 
Scales (Scala files): [[wizard22]]
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 225/224, 385/384, 4000/3993
Comma list: 225/224, 245/242, 385/384


Mapping: [{{val| 2 1 5 2 8 }}, {{val| 0 6 -1 10 -3 }}]
Mapping: {{mapping| 1 -7 7 -5 -2 | 0 11 -6 10 7 }}


Mapping generators: ~99/70, ~25/22
Optimal tunings:
* WE: ~2 = 1200.8059{{c}}, ~12/7 = 936.9952{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3906{{c}}


{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c }}
{{Optimal ET sequence|legend=0| 41, 91, 223cdef }}


Badness: 0.0185
Badness (Sintel): 1.04
 
</div></div>
 
=== Lizard ===
 
Period: 1\2
 
Optimal ([[POTE]]) generator: ~5/4 = 383.389
 
EDO generators: [[50edo|16\50]], [[72edo|23\72]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 225/224, 351/350, 364/363, 385/384
Comma list: 105/104, 144/143, 196/195, 245/242


Mapping: [{{val| 2 1 5 2 8 11 }}, {{val| 0 6 -1 10 -3 -10 }}]
Mapping: {{mapping| 1 -7 7 -5 -2 -8 | 0 11 -6 10 7 15 }}


Mapping generators: ~99/70, ~25/22
Optimal tunings:
* WE: ~2 = 1200.5990{{c}}, ~12/7 = 936.7670{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3196{{c}}


{{Val list|legend=1| 22, 50, 72, 122, 194df }}
{{Optimal ET sequence|legend=0| 41, 91 }}


Badness: 0.0218
Badness (Sintel): 0.955


</div></div>
== Merman ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Merman]].''


==== 17-limit ====
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.


Period: 1\2
The name was likely derived from {{w|Triton (mythology)|''Triton''}}, which was in turn derived from ''tritonic''.


Optimal ([[POTE]]) generator: ~5/4 = 383.381
[[Subgroup]]: 2.3.5.7


EDO generators: [[50edo|16\50]], [[72edo|23\72]]
[[Comma list]]: 225/224, 2500000/2470629


Scales (Scala files):  
{{Mapping|legend=1| 1 -2 10 11 | 0 7 -15 -16 }}
: mapping generators: ~2, ~10/7


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[Optimal tuning]]s:
<div style="line-height:1.6;">Technical data</div>
* [[WE]]: ~2 = 1200.3898{{c}}, ~10/7 = 614.6413{{c}}
<div class="mw-collapsible-content">
: [[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 }}


Subgroup: 2.3.5.7.11.13.17
{{Optimal ET sequence|legend=1| 41, 84, 125 }}


Comma list: 221/220, 273/272, 289/288, 351/350, 375/374
[[Badness]] (Sintel): 1.39


Mapping: [{{val| 2 1 5 2 8 11 6 }}, {{val| 0 6 -1 10 -3 -10 6 }}]
=== 11-limit ===
Subgroup: 2.3.5.7.11


Mapping generators: ~17/12, ~17/15
Comma list: 225/224, 441/440, 1344/1331


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


Badness: 0.0145
Optimal tunings:  
* WE: ~2 = 1199.9578{{c}}, ~10/7 = 614.3720{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3943{{c}}


</div></div>
{{Optimal ET sequence|legend=0| 41, 84, 125e }}


==== 19-limit ====
Badness (Sintel): 1.20


Period: 1\2
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Optimal ([[POTE]]) generator: ~5/4 = 383.477
Comma list: 144/143, 225/224, 364/363, 441/440


EDO generators: [[50edo|16\50]], [[72edo|23\72]]
Mapping: {{mapping| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}


Scales (Scala files):  
Optimal tunings:  
* WE: ~2 = 1199.7422{{c}}, ~10/7 = 614.2110{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3442{{c}}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
{{Optimal ET sequence|legend=0| 41, 84, 125e, 209ef, 293ef }}
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11.13.17.19
Badness (Sintel): 1.14


Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
=== Mermaid ===
 
Subgroup: 2.3.5.7.11
Mapping: [{{val| 2 1 5 2 8 11 6 2 }}, {{val| 0 6 -1 10 -3 -10 6 18 }}]
 
Mapping generators: ~17/12, ~17/15


{{Val list|legend=1| 22h, 50, 72, 122g, 194dfg }}
Comma list: 225/224, 385/384, 532400/531441


Badness: 0.0157
Mapping: {{mapping| 1 -2 10 11 -16 | 0 7 -15 -16 38 }}


</div></div>
Optimal tunings:
* WE: ~2 = 1199.4973{{c}}, ~10/7 = 614.7004{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4470{{c}}


=== Gizzard ===
{{Optimal ET sequence|legend=0| 41, 84e, 125, 166 }}


Period: 1\2
Badness (Sintel): 1.46
 
Optimal ([[POTE]]) generator: ~5/4 = 383.170
 
EDO generators: [[72edo|23\72]], [[94edo|30\94]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 225/224, 325/324, 385/384, 1573/1568
Comma list: 225/224, 325/324, 385/384, 10648/10647
 
Mapping: [{{val| 2 1 5 2 8 -2 }}, {{val| 0 6 -1 10 -3 26 }}]
 
Mapping generators: ~99/70, ~25/22
 
{{Val list|legend=1| 72, 166, 238cf }}
 
Badness: 0.0203
 
</div></div>
 
==== 17-limit ====
 
Period: 1\2
 
Optimal ([[POTE]]) generator: ~5/4 = 383.175
 
EDO generators: [[72edo|23\72]], [[94edo|30\94]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384
 
Mapping: [{{val| 2 1 5 2 8 -2 6 }}, {{val| 0 6 -1 10 -3 26 6 }}]
 
Mapping generators: ~17/12, ~17/15
 
{{Val list|legend=1| 72, 166g, 238cfg }}
 
Badness: 0.0136
 
</div></div>


==== 19-limit ====
Mapping: {{mapping| 1 -2 10 11 22 32 | 0 7 -15 -16 38 58 }}
 
Period: 1\2
 
Optimal ([[POTE]]) generator: ~5/4 = 383.138
 
EDO generators: [[72edo|23\72]], [[94edo|30\94]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594


Mapping: [{{val| 2 1 5 2 8 -2 6 15 }}, {{val| 0 6 -1 10 -3 26 6 -18 }}]
Optimal tunings:  
* WE: ~2 = 1200.5126{{c}}, ~10/7 = 614.7152{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4562{{c}}


Mapping generators: ~17/12, ~17/15
{{Optimal ET sequence|legend=0| 41, 84ef, 125f, 166 }}


{{Val list|legend=1| 72, 94, 166g }}
Badness (Sintel): 1.47


Badness: 0.0148
== 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.  


</div></div>
The name was likely derived from ''slendro diesis'', one of the names for the interval 49/48.


== Mage ==
[[Subgroup]]: 2.3.5.7


Period: 1\2
[[Comma list]]: 225/224, 589824/588245


Optimal ([[POTE]]) generator: ~5/4 = 383.124
{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
: mapping generators: ~2, ~49/48


EDO generators: [[22edo|7\22]], [[50edo|16\50]], [[72edo|23\72]], [[94edo|30\94]]
[[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 }}


Scales (Scala files):
{{Optimal ET sequence|legend=1| 31, 94, 125, 406c }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[Badness]] (Sintel): 1.44
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


=== 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: [{{val| 2 1 5 2 4 }}, {{val| 0 6 -1 10 8 }}]
Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}


Mapping generators: ~77/54, ~55/48
Optimal tunings:  
* WE: ~2 = 1199.4983{{c}}, ~49/48 = 38.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3775{{c}}


{{Val list|legend=1| 22, 50e, 72ee, 94ee }}
{{Optimal ET sequence|legend=0| 31, 63, 94, 125 }}


Badness: 0.0578
Badness (Sintel): 0.838


</div></div>
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


= Triton =
Comma list: 225/224, 275/273, 385/384, 1331/1323


: ''For the 5-limit version of this temperament, see [[High badness temperaments #Stump]].''
Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}


Period: 1\1
Optimal tunings:  
* WE: ~2 = 1200.1728{{c}}, ~49/48 = 38.3192{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3129{{c}}


Optimal ([[POTE]]) generator: ~7/5 = 568.865
{{Optimal ET sequence|legend=0| 31, 63, 94 }}


EDO generators: [[19edo|9\19]], [[21edo|10\21]]
Badness (Sintel): 1.07


Scales (Scala files):  
== Triton ==
: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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.
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
[[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


Wedgie: {{wedgie| 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 }}


{{Val list|legend=1| 19, 78bd, 97bd }}
{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}


Badness: 0.0592
[[Badness]] (Sintel): 1.50
 
</div></div>
 
== 11-limit ==
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~7/5 = 569.144
 
EDO generators: [[19edo|9\19]], [[21edo|10\21]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


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 }}
 
{{Val list|legend=1| 19, 59bde, 78bde, 97bde }}
 
Badness: 0.0457
 
</div></div>
 
= Tritonic =
 
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tritonic]].''
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~7/5 = 580.286
 
EDO generators: [[29edo|14\29]], [[31edo|15\31]], [[60edo|29\60]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7


Comma list: 225/224, 50421/50000
Optimal tunings:  
* WE: ~2 = 1201.3875{{c}}, ~10/7 = 631.5852{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 630.8007{{c}}


Mapping: [{{val| 1 4 -3 -3 }}, {{val| 0 -5 11 12 }}]
{{Optimal ET sequence|legend=0| 2, 17d, 19 }}


Wedgie: {{wedgie| 5 -11 -12 -29 -33 3 }}
Badness (Sintel): 1.51


{{Val list|legend=1| 29, 31, 60, 91, 122, 213bcd }}
== Marvolo ==
[[Subgroup]]: 2.3.5.7


</div></div>
[[Comma list]]: 225/224, 156250000/155649627


== 11-limit ==
{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
: mapping generators: ~2, ~21/20


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


Optimal ([[POTE]]) generator: ~7/5 = 580.267
{{Optimal ET sequence|legend=1| 29, 43, 72, 619bbccd, 691bbccd }}


EDO generators: [[29edo|14\29]], [[31edo|15\31]], [[60edo|29\60]]
[[Badness]] (Sintel): 2.11
 
Scales (Scala files):  
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


=== 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 }}


{{Val list|legend=1| 29, 31, 60e }}
Optimal tunings:
* WE: ~2 = 1200.7075{{c}}, ~21/20 = 83.3888{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3564{{c}}


Badness: 0.0237
{{Optimal ET sequence|legend=0| 29, 43, 72 }}


</div></div>
Badness (Sintel): 0.958


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 580.108
EDO generators: [[29edo|14\29]], [[31edo|15\31]], [[60edo|29\60]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
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: [{{val| 1 4 -3 -3 2 -5 }}, {{val| 0 -5 11 12 3 18 }}]
Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}


{{Val list|legend=1| 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 }}


</div></div>
Badness (Sintel): 0.887


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


Period: 1\1
Comma list: 169/168, 221/220, 225/224, 364/363, 441/440


Optimal ([[POTE]]) generator: ~7/5 = 580.389
Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}


EDO generators: [[31edo|15\31]], [[91edo|44\91]], [[122edo|59\122]]
Optimal tunings:  
* WE: ~2 = 1200.9606{{c}}, ~21/20 = 83.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3594{{c}}


Scales (Scala files):
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Badness (Sintel): 0.760
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 225/224, 385/384, 27783/27500
Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440
 
Mapping: [{{val| 1 4 -3 -3 17 }}, {{val| 0 -5 11 12 -28 }}]
 
{{Val list|legend=1| 31, 91, 122, 153d }}
 
Badness: 0.0455
 
</div></div>
 
= Merman =
 
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Merman]].''
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~7/5 = 585.585
 
EDO generators: [[41edo|20\41]], [[43edo|21\43]], [[84edo|41\84]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7
 
Comma list: 225/224, 2500000/2470629
 
Mapping: [{{val| 1 5 -5 -5 }}, {{val| 0 -7 15 16 }}]


Wedgie: {{wedgie| 7 -15 -16 -40 -45 5 }}
Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}


{{Val list|legend=1| 41, 84, 125 }}
Optimal tunings:
* WE: ~2 = 1200.7625{{c}}, ~21/20 = 83.3895{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3551{{c}}


Badness: 0.0551
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}


</div></div>
Badness (Sintel): 0.895


== 11-limit ==
== Enneaportent ==
[[Subgroup]]: 2.3.5.7


Period: 1\1
[[Comma list]]: 225/224, 40353607/40310784


Optimal ([[POTE]]) generator: ~7/5 = 585.606
{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
: mapping generators: ~2592/2401, ~12005/6912


EDO generators: [[41edo|20\41]], [[43edo|21\43]], [[84edo|41\84]]
[[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 }}


Scales (Scala files):
{{Optimal ET sequence|legend=1| 9, 54, 63, 72, 495bccd, 567bcccd }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[Badness]] (Sintel): 2.37
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


=== 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, 12005/11979


Mapping: [{{val| 1 5 -5 -5 2 }}, {{val| 0 -7 15 16 3 }}]
Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}


{{Val list|legend=1| 41, 84, 125e }}
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}})


Badness: 0.0364
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


</div></div>
Badness (Sintel): 1.01
 
== 13-limit ==
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~7/5 = 585.657
 
EDO generators: [[41edo|20\41]], [[43edo|21\43]], [[84edo|41\84]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


=== 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: 169/168, 225/224, 364/363, 1716/1715


Mapping: [{{val| 1 5 -5 -5 2 12 }}, {{val| 0 -7 15 16 3 -17 }}]
Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}


{{Val list|legend=1| 41, 84, 125e, 209ef, 293ef }}
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}})


Badness: 0.0275
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}


</div></div>
Badness (Sintel): 0.922


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


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


Period: 1\1
[[Comma list]]: 225/224, 781250000/771895089


Optimal ([[POTE]]) generator: ~7/6 = 263.632
{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
: mapping generators: ~2, ~3


EDO generators: [[41edo|9\41]], [[50edo|11\50]], [[91edo|20\91]]
[[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 }}


Scales (Scala files):
{{Optimal ET sequence|legend=1| 12, …, 113, 125, 238c, 363c }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[Badness]] (Sintel): 2.44
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 225/224, 84035/82944
Comma list: 225/224, 385/384, 236328125/234365481


Mapping: [{{val| 1 4 1 5 }}, {{val| 0 -11 6 -10 }}]
Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}


Wedgie: {{wedgie| 11 -6 10 -35 -15 40 }}
Optimal tunings:  
* WE: ~2 = 1200.5571{{c}}, ~3/2 = 701.1589{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8328{{c}}


{{Val list|legend=1| 41, 91, 132 }}
{{Optimal ET sequence|legend=0| 12e, 113, 125, 238c }}


</div></div>
Badness (Sintel): 2.96


== 11-limit ==
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Period: 1\1
Comma list: 225/224, 325/324, 385/384, 831875/830466


Optimal ([[POTE]]) generator: ~7/6 = 263.634
Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}


EDO generators: [[41edo|9\41]], [[50edo|11\50]], [[91edo|20\91]]
Optimal tunings:  
* WE: ~2 = 1200.6282{{c}}, ~3/2 = 701.2080{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8421{{c}}


Scales (Scala files):
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Badness (Sintel): 2.16
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 225/224, 385/384, 2401/2376
Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913


Mapping: [{{val| 1 4 1 5 5 }}, {{val| 0 -11 6 -10 -7 }}]
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}


{{Val list|legend=1| 41, 91, 223cdef }}
Optimal tunings:
* WE: ~2 = 1200.5058{{c}}, ~3/2 = 701.1360{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8414{{c}}


</div></div>
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


== 13-limit ==
Badness (Sintel): 1.96


Period: 1\1
==== 19-limit ====
 
Subgroup: 2.3.5.7.11.13.17.19
Optimal ([[POTE]]) generator: ~7/6 = 263.700
 
EDO generators: [[41edo|9\41]], [[50edo|11\50]], [[91edo|20\91]]


Scales (Scala files):  
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11.13
Optimal tunings:  
* WE: ~2 = 1200.4418{{c}}, ~3/2 = 701.0999{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8425{{c}}


Comma list: 105/104, 144/143, 196/195, 245/242
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}


Mapping: [{{val| 1 4 1 5 5 7 }}, {{val| 0 -11 6 -10 -7 -15 }}]
Badness (Sintel): 1.71


{{Val list|legend=1| 41, 91 }}
==== 23-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23


</div></div>
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528


= Slender =
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}


Period: 1\1
Optimal tunings:  
* WE: ~2 = 1200.4641{{c}}, ~3/2 = 701.1145{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8444{{c}}


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


EDO generators: [[31edo|1\31]], [[32edo|1\32]], [[63edo|2\63]], [[94edo|3\94]]
Badness (Sintel): 1.57


Scales (Scala files):  
==== 29-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}


Comma list: 225/224, 589824/588245
Optimal tunings:  
* WE: ~2 = 1200.4400{{c}}, ~3/2 = 701.0986{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8428{{c}}


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


Wedgie: {{wedgie| 13 -10 6 -46 -27 42 }}
Badness (Sintel): 1.50


{{Val list|legend=1| 31, 94, 125 }}
==== 31-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31


Badness: 0.0569
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493


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


== 11-limit ==
Optimal tunings:
* WE: ~2 = 1200.4178{{c}}, ~3/2 = 701.0822{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8396{{c}}


Period: 1\1
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}


Optimal ([[POTE]]) generator: ~49/48 = 38.387
Badness (Sintel): 1.53
 
EDO generators: [[31edo|1\31]], [[32edo|1\32]], [[63edo|2\63]], [[94edo|3\94]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


=== Gracecord ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 225/224, 385/384, 1331/1323
Comma list: 225/224, 441/440, 109375/107811
 
Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -13 10 -6 -17 }}]
 
{{Val list|legend=1| 31, 63, 94, 125 }}


Badness: 0.02534
Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}


</div></div>
Optimal tunings:
* WE: ~2 = 1200.6064{{c}}, ~3/2 = 701.2398{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8718{{c}}


== 13-limit ==
{{Optimal ET sequence|legend=0| 12, …, 101cd, 113 }}


Period: 1\1
Badness (Sintel): 2.21
 
Optimal ([[POTE]]) generator: ~49/48 = 38.314
 
EDO generators: [[31edo|1\31]], [[32edo|1\32]], [[63edo|2\63]], [[94edo|3\94]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 225/224, 275/273, 385/384, 1331/1323
Comma list: 225/224, 364/363, 441/440, 6125/6084


Mapping: [{{val| 1 2 2 3 4 3 }}, {{val| 0 -13 10 -6 -17 22 }}]
Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}


{{Val list|legend=1| 31, 63, 94 }}
Optimal tunings:
* WE: ~2 = 1200.6225{{c}}, ~3/2 = 701.2539{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8781{{c}}


Badness: 0.02591
{{Optimal ET sequence|legend=0| 12f, …, 101cdf, 113 }}


</div></div>
Badness (Sintel): 1.83


= Marvo =
==== 17-limit ====
{{see also| Gravity family }}
Subgroup: 2.3.5.7.11.13.17


Period: 1\1
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989


Optimal ([[POTE]]) generator: ~27/20 = 516.694
Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}


EDO generators: [[65edo|28\65]], [[72edo|31\72]], [[137edo|59\137]]
Optimal tunings:  
* WE: ~2 = 1200.3308{{c}}, ~3/2 = 701.0632{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8654{{c}}


Scales (Scala files):
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Badness (Sintel): 1.87
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 225/224, 78125000/78121827
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663


Mapping: [{{val| 1 5 12 29 }}, {{val| 0 -6 -17 -46 }}]
Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}


Wedgie: {{wedgie| 6 17 46 13 56 59 }}
Optimal tunings:  
* WE: ~2 = 1200.2658{{c}}, ~3/2 = 701.0213{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8629{{c}}


{{Val list|legend=1| 65d, 72, 137, 209, 281, 569bcc }}
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}


Badness: 0.0976
Badness (Sintel): 1.68


</div></div>
== Alphorn ==
[[Subgroup]]: 2.3.5.7


== 11-limit ==
[[Comma list]]: 225/224, 5764801/5668704


Period: 1\1
{{Mapping|legend=1| 1 -7 5 -9 | 0 16 -5 22 }}
: mapping generators: ~2, ~35/24


Optimal ([[POTE]]) generator: ~27/20 = 516.699
[[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 }}


EDO generators: [[65edo|28\65]], [[72edo|31\72]], [[137edo|59\137]]
{{Optimal ET sequence|legend=1| 13d, 28d, 41, 151cd, 192cdd, 233ccdd }}


Scales (Scala files):  
[[Badness]] (Sintel): 3.27
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 225/224, 243/242, 4000/3993
Comma list: 225/224, 385/384, 12250/11979
 
Mapping: [{{val| 1 5 12 29 12 }}, {{val| 0 -6 -17 -46 -15 }}]
 
{{Val list|legend=1| 65d, 72, 281, 353c, 425bc, 497bc }}
 
Badness: 0.0317
 
</div></div>
 
== 13-limit ==
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~27/20 = 516.730
 
EDO generators: [[65edo|28\65]], [[72edo|31\72]], [[137edo|59\137]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 243/242, 351/350, 1625/1617
 
Mapping: [{{val| 1 5 12 29 12 39 }}, {{val| 0 -6 -17 -46 -15 -62 }}]
 
{{Val list|legend=1| 65d, 72, 137, 209, 281f, 490bcf }}


Badness: 0.0269
Mapping: {{mapping| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}


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


= Marvolo =
{{Optimal ET sequence|legend=0| 13d, 28d, 41 }}


Period: 1\1
Badness (Sintel): 2.43


Optimal ([[POTE]]) generator: ~21/20 = 83.348
== Misneb ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Misneb]].''


EDO generators: [[29edo|2\29]], [[43edo|3\43]], [[72edo|5\72]]
[[Subgroup]]: 2.3.5.7


Scales (Scala files):  
[[Comma list]]: 225/224, 4194304/4117715


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
{{Mapping|legend=1| 1 -12 15 1 | 0 15 -14 2 }}
<div style="line-height:1.6;">Technical data</div>
: mapping generators: ~2, ~15/8
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
[[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 }}


Comma list: 225/224, 156250000/155649627
{{Optimal ET sequence|legend=1| 21, 32, 53 }}


Mapping: [{{val| 1 2 1 1 }}, {{val| 0 -6 19 26 }}]
[[Badness]] (Sintel): 3.57
 
Wedgie: {{wedgie| 6 -19 -26 -44 -58 -7 }}
 
{{Val list|legend=1| 29, 43, 72, 619bcd, 691bcd }}
 
Badness: 0.0833
 
</div></div>
 
== 11-limit ==
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~21/20 = 83.340
 
EDO generators: [[29edo|2\29]], [[43edo|3\43]], [[72edo|5\72]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 225/224, 441/440, 4000/3993
Comma list: 99/98, 176/175, 1310720/1294139
 
Mapping: [{{val| 1 2 1 1 2 }}, {{val| 0 -6 19 26 21 }}]
 
{{Val list|legend=1| 29, 43, 72 }}
 
Badness: 0.0290
 
</div></div>
 
== 13-limit ==
 
Period: 1\1


Optimal ([[POTE]]) generator: ~21/20 = 83.330
Mapping: {{mapping| 1 -12 15 1 27 | 0 15 -14 2 -26 }}


EDO generators: [[29edo|2\29]], [[43edo|3\43]], [[72edo|5\72]]
Optimal tunings:  
* WE: ~2 = 1200.1654{{c}}, ~15/8 = 1086.8269{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6766{{c}}


Scales (Scala files):
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Badness (Sintel): 2.82
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 169/168, 225/224, 364/363, 441/440
Comma list: 99/98, 176/175, 640/637, 847/845


Mapping: [{{val| 1 2 1 1 2 3 }}, {{val| 0 -6 19 26 21 10 }}]
Mapping: {{mapping| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}


{{Val list|legend=1| 29, 43, 72, 115f }}
Optimal tunings:
* WE: ~2 = 1200.1687{{c}}, ~15/8 = 1086.8295{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6757{{c}}


Badness: 0.0215
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}


</div></div>
Badness (Sintel): 1.88


= Amavil =
=== Musneb ===
== 5-limit (mabila) ==
Subgroup: 2.3.5.7.11
 
Period: 1\1


Optimal ([[POTE]]) generator: ~512/375 = 529.6849
Comma list: 225/224, 385/384, 66550/64827


EDO generators: [[34edo|15\34]], [[43edo|19\43]], [[77edo|34\77]], [[111edo|49\111]]
Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}


Scales (Scala files):  
Optimal tunings:  
* WE: ~2 = 1200.0839{{c}}, ~15/8 = 1086.9343{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.8593{{c}}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
{{Optimal ET sequence|legend=0| 21e, 32, 53 }}
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5
Badness (Sintel): 2.89


Comma list: 268435456/263671875
== Untriton ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''


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


{{Val list|legend=1| 9, 25, 34, 77, 111, 145, 256c }}
[[Subgroup]]: 2.3.5.7


Badness: 0.2325
[[Comma list]]: 225/224, 125000000/121060821


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


== 7-limit ==
[[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 }}


Period: 1\1
{{Optimal ET sequence|legend=1| 51, 53 }}


Optimal ([[POTE]]) generator: ~48/35 = 529.979
[[Badness]] (Sintel): 3.64
 
EDO generators: [[34edo|15\34]], [[43edo|19\43]]
 
Scales (Scala files):  
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7
 
Comma list: 225/224, 17496/16807
 
Mapping: [{{val| 1 6 1 9 }}, {{val| 0 -10 3 -14 }}]
 
Wedgie: {{wedgie| 10 -3 14 -28 -6 41 }}
 
{{Val list|legend=1| 9, 25d, 34d, 43, 77d }}
 
Badness: 0.1096
 
</div></div>
 
== 11-limit ==
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~15/11 = 529.974
 
EDO generators: [[34edo|15\34]], [[43edo|19\43]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 99/98, 176/175, 864/847
Comma list: 121/120, 225/224, 22000/21609


Mapping: [{{val| 1 6 1 9 7 }}, {{val| 0 -10 3 -14 -8 }}]
Mapping: {{mapping| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}


{{Val list|legend=1| 9, 34d, 43, 77de }}
Optimal tunings:
* WE: ~2 = 1200.3591{{c}}, ~10/7 = 611.5569{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3690{{c}}


Badness: 0.0426
{{Optimal ET sequence|legend=0| 51, 53 }}


</div></div>
Badness (Sintel): 2.46
 
== 13-limit ==
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~15/11 = 529.951
 
EDO generators: [[34edo|15\34]], [[43edo|19\43]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 78/77, 99/98, 144/143, 176/175
Comma list: 121/120, 225/224, 275/273, 1040/1029
 
Mapping: [{{val| 1 6 1 9 7 9 }}, {{val| 0 -10 3 -14 -8 -12 }}]
 
{{Val list|legend=1| 9, 34d, 43, 77de }}
 
Badness: 0.0258
 
</div></div>
 
= Enneaportent =
 
Period: 1\9
 
Optimal ([[POTE]]) generator: ~5/4 = 383.165
 
EDO generators: [[63edo|20\63]], [[72edo|23\72]], [[81edo|26\81]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
Mapping: {{mapping| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}


Comma list: 225/224, 40353607/40310784
Optimal tunings:  
* WE: ~2 = 1200.4078{{c}}, ~10/7 = 611.5536{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3392{{c}}


Mapping: [{{val| 9 0 28 11 }}, {{val| 0 2 -1 2 }}]
{{Optimal ET sequence|legend=0| 51f, 53 }}


Wedgie: {{wedgie| 18 -9 18 -56 -22 67 }}
Badness (Sintel): 1.96


{{Val list|legend=1| 63, 72, 495bcd }}
== Naiadical ==
Named by [[Xenllium]] in 2026, naiadical may be described as the {{nowrap| 21 & 29 }} temperament.


Badness: 0.0937
[[Subgroup]]: 2.3.5.7


</div></div>
[[Comma list]]: 225/224, 823543/800000


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


Period: 1\9
[[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 }}


Optimal ([[POTE]]) generator: ~5/4 = 383.146
{{Optimal ET sequence|legend=1| 21, 29, 50, 79d, 129cdd, 179bcddd }}


EDO generators: [[63edo|20\63]], [[72edo|23\72]], [[81edo|26\81]]
[[Badness]] (Sintel): 3.67
 
Scales (Scala files):  
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 225/224, 385/384, 12005/11979
Comma list: 225/224, 245/242, 1617/1600


Mapping: [{{val| 9 0 28 11 24 }}, {{val| 0 2 -1 2 1 }}]
Mapping: {{Mapping| 1 -4 11 9 14 | 0 9 -14 -10 -17 }}


{{Val list|legend=1| 63, 72, 423cd, 495bcd }}
Optimal tunings:
* WE: ~2 = 1201.9008{{c}}, ~21/16 = 745.3867{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~32/21 = 744.1777{{c}}


Badness: 0.0304
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}


</div></div>
Badness (Sintel): 2.00
 
== 13-limit ==
 
Period: 1\9
 
Optimal ([[POTE]]) generator: ~5/4 = 383.047
 
EDO generators: [[63edo|20\63]], [[72edo|23\72]], [[81edo|26\81]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


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


Comma list: 169/168, 225/224, 364/363, 1716/1715
Comma list: 105/104, 196/195, 245/242, 1001/1000


Mapping: [{{val| 9 0 28 11 24 19 }}, {{val| 0 2 -1 2 1 2 }}]
Mapping: {{Mapping| 1 -4 11 9 14 13 | 0 9 -14 -10 -17 -15 }}


{{Val list|legend=1| 63, 72, 279cf }}
Optimal tunings:
* WE: ~2 = 1201.7863{{c}}, ~20/13 = 745.3344{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1931{{c}}


Badness: 0.0223
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}


</div></div>
Badness (Sintel): 1.43


= Submajor =
=== 17-limit ===
== 5-limit ==
Subgroup: 2.3.5.7.11.13.17
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~10125/8192 = 362.321
 
EDO generators: [[43edo|13\43]], [[53edo|16\53]], [[63edo|19\63]], [[96edo|29\96]], [[116edo|35\116]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5
 
Comma list: 69198046875/68719476736
 
Mapping: [{{val| 1 4 -1 }}, {{val| 0 -8 11 }}]
 
{{Val list|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}}
 
Badness: 0.1302
 
</div></div>
 
== 7-limit ==
 
Period: 1\1


Optimal ([[POTE]]) generator: ~49/40 = 362.255
Comma list: 105/104, 170/169, 196/195, 221/220, 245/242


EDO generators: [[43edo|13\43]], [[53edo|16\53]], [[63edo|19\63]], [[96edo|29\96]], [[116edo|35\116]]
Mapping: {{Mapping| 1 -4 11 9 14 13 14 | 0 9 -14 -10 -17 -15 -16 }}


Scales (Scala files):  
Optimal tunings:  
* WE: ~2 = 1201.9208{{c}}, ~20/13 = 745.3976{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1669{{c}}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
{{Optimal ET sequence|legend=0| 21, 29g, 50, 79dg }}
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
Badness (Sintel): 1.26


Comma list: 225/224, 51200/50421
== Quintannic ==
Named by [[Scott Dakota]], quintannic may be described as the {{nowrap| 43 & 60 }} temperament.


Mapping: [{{val| 1 4 -1 1 }}, {{val| 0 -8 11 6 }}]
[[Subgroup]]: 2.3.5.7


Wedgie: {{wedgie| 8 -11 -6 -36 -32 17 }}
[[Comma list]]: 225/224, 9805926501/9765625000


{{Val list|legend=1| 10, 33, 43, 53 }}
{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
: mapping generators: ~2, ~10000/9261


Badness: 0.0605
[[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 }}


</div></div>
{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}


== 11-limit ==
[[Badness]] (Sintel): 3.81
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~27/22 = 362.101
 
EDO generators: [[53edo|16\53]], [[63edo|19\63]], [[116edo|35\116]]
 
Scales (Scala files):  
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


=== 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, 441/440, 43923/43750


Mapping: [{{val| 1 4 -1 1 11 }}, {{val| 0 -8 11 6 -25 }}]
Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}


{{Val list|legend=1| 53, 116, 169de, 285cde }}
Optimal tunings:
* WE: ~2 = 1201.0031{{c}}, ~320/297 = 139.9435{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~320/297 = 139.8053{{c}}


Badness: 0.0506
{{Optimal ET sequence|legend=0| 43, 60e, 103, 369bcdeee, 472bbcddeee }}


</div></div>
Badness (Sintel): 1.74


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~16/13 = 362.105
EDO generators: [[53edo|16\53]], [[63edo|19\63]], [[116edo|35\116]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 169/168, 225/224, 275/273, 385/384
Comma list: 225/224, 441/440, 1001/1000, 1188/1183


Mapping: [{{val| 1 4 -1 1 11 4 }}, {{val| 0 -8 11 6 -25 -1 }}]
Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}


{{Val list|legend=1| 53, 116, 169de, 285cdef }}
Optimal tunings:
* WE: ~2 = 1200.8354{{c}}, ~13/12 = 139.9095{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.7997{{c}}


Badness: 0.0277
{{Optimal ET sequence|legend=0| 43, 60e, 103 }}


</div></div>
Badness (Sintel): 1.35


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


Period: 1\1
Comma list: 225/224, 273/272, 375/374, 441/440, 891/884


Optimal ([[POTE]]) generator: ~49/40 = 362.418
Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}


EDO generators: [[43edo|13\43]], [[53edo|16\53]], [[96edo|29\96]]
Optimal tunings:  
* WE: ~2 = 1200.7402{{c}}, ~13/12 = 139.9015{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.8038{{c}}


Scales (Scala files):
{{Optimal ET sequence|legend=0| 43, 60e, 103 }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Badness (Sintel): 1.17
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11
== Gwazy ==
: ''For the 5-limit version, see [[Very high accuracy temperaments #Kwazy]].''


Comma list: 99/98, 176/175, 51200/50421
Named by [[Petr Pařízek]] in 2011<ref name="petr's long post"/>, gwazy may be described as the {{nowrap| 22 & 74 }} temperament.


POTE generator: ~49/40 = 362.418
[[Subgroup]]: 2.3.5.7


Mapping: [{{val| 1 4 -1 1 -5 }}, {{val| 0 -8 11 6 28 }}]
[[Comma list]]: 225/224, 5971968/5764801


{{Val list|legend=1| 43, 53, 96, 149d }}
{{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}
: mapping generators: ~2401/1728, ~35/32


Badness: 0.0518
[[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 }}


</div></div>
{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}


=== 13-limit ===
[[Badness]] (Sintel): 4.53


Period: 1\1
=== 11-limit ===
Subgroup: 2.3.5.7.11


Optimal ([[POTE]]) generator: ~16/13 = 362.402
Comma list: 99/98, 176/175, 65536/65219


EDO generators: [[43edo|13\43]], [[53edo|16\53]], [[96edo|29\96]]
Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}


Scales (Scala files):  
Optimal tunings:  
* WE: ~363/256 = 599.8517{{c}}, ~11/10 = 162.5518{{c}}
* CWE: ~363/256 = 600.0000{{c}}, ~11/10 = 162.5863{{c}}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
{{Optimal ET sequence|legend=0| 22, 74, 96 }}
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11.13
Badness (Sintel): 2.26


Comma list: 99/98, 169/168, 176/175, 640/637
== Tertiosec ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tertiosec]].''


POTE generator: ~16/13 = 362.402
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 4 -1 1 -5 4 }}, {{val| 0 -8 11 6 28 -1 }}]
[[Subgroup]]: 2.3.5.7


{{Val list|legend=1| 43, 53, 96, 149d }}
[[Comma list]]: 225/224, 14495514624/13841287201


Badness: 0.0297
{{Mapping|legend=1| 3 -1 12 7 | 0 8 -7 2 }}
: mapping generators: ~3072/2401, ~2048/1715


</div></div>
[[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 }}


= Alphorn =
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}


Period: 1\1
[[Badness]] (Sintel): 10.9


Optimal ([[POTE]]) generator: ~48/35 = 556.221
=== 11-limit ===
 
Subgroup: 2.3.5.7.11
EDO generators: [[28edo|13\28]], [[41edo|19\41]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7
 
Comma list: 225/224, 5764801/5668704
 
Mapping: [{{val| 1 9 0 13 }}, {{val| 0 -16 5 -22 }}]
 
Wedgie: {{wedgie| 16 -5 22 -45 -10 65 }}
 
{{Val list|legend=1| 28d, 41, 151cd, 192cd, 233cd }}


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


</div></div>
Mapping: {{mapping| 3 -1 12 7 14 | 0 8 -7 2 -5 }}
 
== 11-limit ==
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~11/8 = 556.144
 
EDO generators: [[28edo|13\28]], [[41edo|19\41]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 12250/11979


Mapping: [{{val| 1 9 0 13 3 }}, {{val| 0 -16 5 -22 1 }}]
Optimal tunings:  
* WE: ~44/35 = 399.6550{{c}}, ~33/28 = 287.5803{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~33/28 = 287.8224{{c}}


{{Val list|legend=1| 28d, 41, 315cde }}
{{Optimal ET sequence|legend=0| 21, 54, 75e }}


Badness: 0.0735
Badness (Sintel): 5.74


</div></div>
== 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"