@@ Line 1: / Line 1: @@
-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;">
+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}}.)
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5
+== Wizard ==
+{{Main| Wizard }}
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Wizard]].''
-[[Comma list]]: 16875/16384
+Wizard has a [[semi-octave]] period and is generated by an interval that can be treated as [[~]][[17/15]]. The semi-octave complement of this interval is ~[[5/4]]. Wizard can be described as {{nowrap| 22 & 72 }}. Its [[ploidacot]] is diploid alpha-hexacot, so six generator steps plus a semi-octave period gives the [[3/1|perfect twelfth]]. [[72edo]], [[94edo]], and especially [[166edo]] are good tunings for it.
-[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
+[[Subgroup]]: 2.3.5.7
-[[Wedgie]]: {{wedgie| 4 -3 -14 }}
+[[Comma list]]: 225/224, 118098/117649
-{{Val list|legend=1| 9, 10, 19, 67c, 86c, 105c }}
+{{Mapping|legend=1| 2 1 5 2 | 0 6 -1 10 }}
+: mapping generators: ~1225/864, ~245/216
-</div></div>
+[[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 }}
-== 7-limit ==
+{{Optimal ET sequence|legend=1| 22, 50, 72, 238c, 310c, 382c, 454bccd }}
-Period: 1\1
-Optimal ([[POTE]]) generator: ~15/14 = 125.608
+[[Badness]] (Sintel): 1.03
-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;">
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-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):
-<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: 2.3.5.7.13
-[[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):
-<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: 45/44, 49/48, 56/55
-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 ===
-Period: 1\1
-Optimal ([[POTE]]) generator: ~14/13 = 126.431
-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;">
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7.11.13
-Comma list: 45/44, 49/48, 56/55, 78/77
-[[POTE generator]]: ~14/13 = 126.431
-Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}]
-{{Val list|legend=1| 9, 10, 19 }}
-</div></div>
-== Negril ==
-Period: 1\1
-Optimal ([[POTE]]) generator: ~15/14 = 124.767
-EDO generators: [[19edo|2\19]], [[29edo|3\29]]
-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: 49/48, 100/99, 225/224
-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 ===
-Period: 1\1
-Optimal ([[POTE]]) generator: ~14/13 = 124.716
-EDO generators: [[19edo|2\19]], [[29edo|3\29]]
-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: 49/48, 65/64, 91/90, 875/858
-Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]
-{{Val list|legend=1| 19, 29, 48df, 77cddf }}
-Badness: 0.0244
-</div></div>
-== Negric ==
-Period: 1\1
-Optimal ([[POTE]]) generator: ~15/14 = 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;">
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7.11
-Comma list: 33/32, 49/48, 77/75
-Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}]
-{{Val list|legend=1| 9, 19e, 47…, 66…, 85… }}
-Badness: 0.0306
-</div></div>
-=== 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;">
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-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;">
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7.11
-Comma list: 49/48, 55/54, 225/224
-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;">
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7.11.13
-Comma list: 49/48, 55/54, 65/64, 91/90
-Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]
-{{Val list|legend=1| 10, 19e, 29, 77cddeef }}
-Badness: 0.0216
-</div></div>
-== Wilsec ==
-Period: 1\1
-Optimal ([[POTE]]) generator: ~11/8 = 537.186
-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">
-Subgroup: 2.3.5.7.11
-Comma list: 49/48, 121/120, 225/224
-Mapping: [{{val| 1 6 -1 5 4 }}, {{val| 0 -8 6 -4 -1 }}]
-{{Val list|legend=1| 9, 20, 29, 38d, 67cdde }}
-Badness: 0.0419
-</div></div>
-=== 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;">
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7.11.13
-Comma list: 49/48, 65/64, 91/90, 121/120
-Mapping: [{{val| 1 6 -1 5 4 7 }}, {{val| 0 -8 6 -4 -1 -6 }}]
-{{Val list|legend=1| 9, 20, 29, 38df, 67cddef }}
-Badness: 0.0252
-</div></div>
-=== 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;">
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 49/48, 65/64, 91/90, 121/120, 154/153
-Mapping: [{{val| 1 6 -1 5 4 7 -2 }}, {{val| 0 -8 6 -4 -1 -6 11 }}]
-{{Val list|legend=1| 9, 20g, 29g, 38df, 67cddefg }}
-Badness: 0.0218
-</div></div>
-=== 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">
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153
-Mapping: [{{val| 1 6 -1 5 4 7 -2 7 }}, {{val| 0 -8 6 -4 -1 -6 11 -5 }}]
-{{Val list|legend=1| 9, 20g, 29g, 38df, 67cddefgh }}
-Badness: 0.0168
-</div></div>
-= Passive =
-{{see also | Archytas clan #Passion }}
-Period: 1\1
-Optimal ([[POTE]]) generator: ~16/15 = 98.809
-EDO generators: [[12edo|1\12]], [[13edo|1\13]]
-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, 256/245
-Mapping: [{{val| 1 2 2 3 }}, {{val| 0 -5 4 -2 }}]
-{{Val list|legend=1| 12, 49dd }}
-Badness: 0.0751
-</div></div>
-= Wizard =
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Wizard]].''
-Period: 1\2
-Optimal ([[POTE]]) generator: ~5/4 = 383.256
-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">
-Subgroup: 2.3.5.7
-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
 Comma list: 225/224, 385/384, 4000/3993
-Mapping: [{{val| 2 1 5 2 8 }}, {{val| 0 6 -1 10 -3 }}]
+Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}
-Mapping generators: ~99/70, ~25/22
-{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c }}
-Badness: 0.0185
-</div></div>
-=== Lizard ===
-Period: 1\2
-Optimal ([[POTE]]) generator: ~5/4 = 383.389
-EDO generators: [[50edo|16\50]], [[72edo|23\72]]
+Optimal tunings:
+* WE: ~99/70 = 600.3051{{c}}, ~25/22 = 216.8782{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.7961{{c}}
-Scales (Scala files):
+{{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+Badness (Sintel): 0.613
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
+==== Lizard ====
 Subgroup: 2.3.5.7.11.13
 Comma list: 225/224, 351/350, 364/363, 385/384
-Mapping: [{{val| 2 1 5 2 8 11 }}, {{val| 0 6 -1 10 -3 -10 }}]
+Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}
-Mapping generators: ~99/70, ~25/22
-{{Val list|legend=1| 22, 50, 72, 122, 194df }}
+Optimal tunings:
+* WE: ~55/39 = 600.4824{{c}}, ~25/22 = 216.7852{{c}}
+* CWE: ~55/39 = 600.0000{{c}}, ~25/22 = 216.6247{{c}}
-Badness: 0.0218
+{{Optimal ET sequence|legend=0| 22, 50, 72 }}
-</div></div>
+Badness (Sintel): 0.900
-==== 17-limit ====
-Period: 1\2
-Optimal ([[POTE]]) generator: ~5/4 = 383.381
-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">
+===== 17-limit =====
 Subgroup: 2.3.5.7.11.13.17
 Comma list: 221/220, 273/272, 289/288, 351/350, 375/374
-Mapping: [{{val| 2 1 5 2 8 11 6 }}, {{val| 0 6 -1 10 -3 -10 6 }}]
+Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}
-Mapping generators: ~17/12, ~17/15
-{{Val list|legend=1| 22, 50, 72, 122g, 194dfg }}
-Badness: 0.0145
-</div></div>
-==== 19-limit ====
-Period: 1\2
-Optimal ([[POTE]]) generator: ~5/4 = 383.477
+Optimal tunings:
+* WE: ~17/12 = 600.5032{{c}}, ~17/15 = 216.8002{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.6361{{c}}
-EDO generators: [[50edo|16\50]], [[72edo|23\72]]
+{{Optimal ET sequence|legend=0| 22, 50, 72 }}
-Scales (Scala files):
+Badness (Sintel): 0.741
-<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
 Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
-Mapping: [{{val| 2 1 5 2 8 11 6 2 }}, {{val| 0 6 -1 10 -3 -10 6 18 }}]
+Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}
-Mapping generators: ~17/12, ~17/15
-{{Val list|legend=1| 22h, 50, 72, 122g, 194dfg }}
-Badness: 0.0157
-</div></div>
-=== Gizzard ===
-Period: 1\2
-Optimal ([[POTE]]) generator: ~5/4 = 383.170
+Optimal tunings:
+* WE: ~17/12 = 600.4698{{c}}, ~17/15 = 216.6925{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.5434{{c}}
-EDO generators: [[72edo|23\72]], [[94edo|30\94]]
+{{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}
-Scales (Scala files):
+Badness (Sintel): 0.955
-<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">
+==== Gizzard ====
 Subgroup: 2.3.5.7.11.13
 Comma list: 225/224, 325/324, 385/384, 1573/1568
-Mapping: [{{val| 2 1 5 2 8 -2 }}, {{val| 0 6 -1 10 -3 26 }}]
+Mapping: {{mapping| 2 1 5 2 8 -2 | 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
+Optimal tunings:
+* WE: ~99/70 = 600.2896{{c}}, ~25/22 = 216.9343{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.8501{{c}}
-EDO generators: [[72edo|23\72]], [[94edo|30\94]]
+{{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}
-Scales (Scala files):
+Badness (Sintel): 0.837
-<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">
+===== 17-limit =====
 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: {{mapping| 2 1 5 2 8 -2 6 | 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 ====
-Period: 1\2
+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 ([[POTE]]) generator: ~5/4 = 383.138
+{{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}
-EDO generators: [[72edo|23\72]], [[94edo|30\94]]
+Badness (Sintel): 0.694
-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
 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 }}]
+Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}
-Mapping generators: ~17/12, ~17/15
-{{Val list|legend=1| 72, 94, 166g }}
-Badness: 0.0148
-</div></div>
-== Mage ==
+Optimal tunings:
+* WE: ~17/12 = 600.2637{{c}}, ~17/15 = 216.9570{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8687{{c}}
-Period: 1\2
+{{Optimal ET sequence|legend=0| 72, 94, 166g }}
-Optimal ([[POTE]]) generator: ~5/4 = 383.124
+Badness (Sintel): 0.901
-EDO generators: [[22edo|7\22]], [[50edo|16\50]], [[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">
+=== Mage ===
 Subgroup: 2.3.5.7.11
 Comma list: 99/98, 176/175, 1331/1296
-Mapping: [{{val| 2 1 5 2 4 }}, {{val| 0 6 -1 10 8 }}]
+Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }}
-Mapping generators: ~77/54, ~55/48
+Optimal tunings:
+* WE: ~77/54 = 600.6486{{c}}, ~55/48 = 217.1099{{c}}
+* CWE: ~77/54 = 600.0000{{c}}, ~55/48 = 216.9841{{c}}
-{{Val list|legend=1| 22, 50e, 72ee, 94ee }}
+{{Optimal ET sequence|legend=0| 22, 50e, 72ee }}
-Badness: 0.0578
+Badness (Sintel): 1.91
-</div></div>
+== Tritonic ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tritonic]].''
-= Triton =
+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.
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Stump]].''
+[[Subgroup]]: 2.3.5.7
-Period: 1\1
+[[Comma list]]: 225/224, 50421/50000
-Optimal ([[POTE]]) generator: ~7/5 = 568.865
+{{Mapping|legend=1| 1 -1 8 9 | 0 5 -11 -12 }}
+: mapping generators: ~2, ~10/7
-EDO generators: [[19edo|9\19]], [[21edo|10\21]]
+[[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 }}
-Scales (Scala files):
+{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+[[Badness]] (Sintel): 1.20
-<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, 1029/1000
+Comma list: 121/120, 225/224, 441/440
-Mapping: [{{val| 1 0 6 7 }}, {{val| 0 3 -7 -8 }}]
+Mapping: {{mapping| 1 -1 8 9 5 | 0 5 -11 -12 -3 }}
-Wedgie: {{wedgie| 3 -7 -8 -18 -21 1 }}
+Optimal tunings:
+* WE: ~2 = 1201.7116{{c}}, ~10/7 = 620.6166{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6890{{c}}
-{{Val list|legend=1| 19, 78bd, 97bd }}
+{{Optimal ET sequence|legend=0| 29, 31, 60e, 91e, 213bcdeee }}
-Badness: 0.0592
+Badness (Sintel): 0.782
-</div></div>
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
-== 11-limit ==
+Comma list: 105/104, 121/120, 196/195, 275/273
-Period: 1\1
+Mapping: {{mapping| 1 -1 8 9 5 13 | 0 5 -11 -12 -3 -18 }}
-Optimal ([[POTE]]) generator: ~7/5 = 569.144
+Optimal tunings:
+* WE: ~2 = 1201.5355{{c}}, ~10/7 = 620.6855{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8469{{c}}
-EDO generators: [[19edo|9\19]], [[21edo|10\21]]
+{{Optimal ET sequence|legend=0| 29, 31, 60e }}
-Scales (Scala files):
+Badness (Sintel): 0.950
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+==== 17-limit ====
-<div style="line-height:1.6;">Technical data</div>
+Subgroup: 2.3.5.7.11.13.17
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7.11
-Comma list: 45/44, 56/55, 1029/1000
+Comma list: 105/104, 121/120, 154/153, 196/195, 273/272
-Mapping: [{{val| 1 0 6 7 4 }}, {{val| 0 3 -7 -8 -1 }}]
+Mapping: {{mapping| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}
-{{Val list|legend=1| 19, 59bde, 78bde, 97bde }}
+Optimal tunings:
+* WE: ~2 = 1201.5260{{c}}, ~10/7 = 620.7330{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8986{{c}}
-Badness: 0.0457
+{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
-</div></div>
+Badness (Sintel): 0.973
-= Tritonic =
+==== 19-limit ====
+Subgroup: 2.3.5.7.11.13.17.19
-: ''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
+Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272
-Mapping: [{{val| 1 4 -3 -3 }}, {{val| 0 -5 11 12 }}]
+Mapping: {{mapping| 1 -1 8 9 5 13 17 12 | 0 5 -11 -12 -3 -18 -25 -15 }}
-Wedgie: {{wedgie| 5 -11 -12 -29 -33 3 }}
+Optimal tunings:
+* WE: ~2 = 1201.3100{{c}}, ~10/7 = 620.6509{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9328{{c}}
-{{Val list|legend=1| 29, 31, 60, 91, 122, 213bcd }}
+{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
-</div></div>
+Badness (Sintel): 1.03
-== 11-limit ==
+==== 23-limit ====
+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: ~7/5 = 580.267
+Mapping: {{mapping| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}
-EDO generators: [[29edo|14\29]], [[31edo|15\31]], [[60edo|29\60]]
+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">
+=== Tritoni ===
 Subgroup: 2.3.5.7.11
-Comma list: 121/120, 225/224, 441/440
+Comma list: 225/224, 385/384, 27783/27500
-Mapping: [{{val| 1 4 -3 -3 2 }}, {{val| 0 -5 11 12 3 }}]
-{{Val list|legend=1| 29, 31, 60e }}
-Badness: 0.0237
-</div></div>
-=== 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
+Mapping: {{mapping| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}
-Comma list: 105/104, 121/120, 196/195, 275/273
+Optimal tunings:
+* WE: ~2 = 1201.0888{{c}}, ~10/7 = 620.1733{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6146{{c}}
-Mapping: [{{val| 1 4 -3 -3 2 -5 }}, {{val| 0 -5 11 12 3 18 }}]
+{{Optimal ET sequence|legend=0| 31, 91, 122, 153d }}
-{{Val list|legend=1| 29, 31, 60e, 151cde }}
+Badness (Sintel): 1.50
-Badness: 0.0230
+== Septimin ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Septimin]].''
-</div></div>
+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.
-== Tritoni ==
+[[Subgroup]]: 2.3.5.7
-Period: 1\1
+[[Comma list]]: 225/224, 84035/82944
-Optimal ([[POTE]]) generator: ~7/5 = 580.389
+{{Mapping|legend=1| 1 -7 7 -5 | 0 11 -6 10 }}
+: mapping generators: ~2, ~12/7
-EDO generators: [[31edo|15\31]], [[91edo|44\91]], [[122edo|59\122]]
+[[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 }}
-Scales (Scala files):
+{{Optimal ET sequence|legend=1| 41, 91, 132d }}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+[[Badness]] (Sintel): 1.38
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 225/224, 385/384, 27783/27500
+Comma list: 225/224, 245/242, 385/384
-Mapping: [{{val| 1 4 -3 -3 17 }}, {{val| 0 -5 11 12 -28 }}]
+Mapping: {{mapping| 1 -7 7 -5 -2 | 0 11 -6 10 7 }}
-{{Val list|legend=1| 31, 91, 122, 153d }}
+Optimal tunings:
+* WE: ~2 = 1200.8059{{c}}, ~12/7 = 936.9952{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3906{{c}}
-Badness: 0.0455
+{{Optimal ET sequence|legend=0| 41, 91, 223cdef }}
-</div></div>
+Badness (Sintel): 1.04
-= Merman =
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Merman]].''
+Comma list: 105/104, 144/143, 196/195, 245/242
-Period: 1\1
-Optimal ([[POTE]]) generator: ~7/5 = 585.585
-EDO generators: [[41edo|20\41]], [[43edo|21\43]], [[84edo|41\84]]
+Mapping: {{mapping| 1 -7 7 -5 -2 -8 | 0 11 -6 10 7 15 }}
-Scales (Scala files):
+Optimal tunings:
+* WE: ~2 = 1200.5990{{c}}, ~12/7 = 936.7670{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3196{{c}}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+{{Optimal ET sequence|legend=0| 41, 91 }}
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7
+Badness (Sintel): 0.955
-Comma list: 225/224, 2500000/2470629
+== Merman ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Merman]].''
-Mapping: [{{val| 1 5 -5 -5 }}, {{val| 0 -7 15 16 }}]
+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.
-Wedgie: {{wedgie| 7 -15 -16 -40 -45 5 }}
+The name was likely derived from {{w|Triton (mythology)|''Triton''}}, which was in turn derived from ''tritonic''.
-{{Val list|legend=1| 41, 84, 125 }}
+[[Subgroup]]: 2.3.5.7
-Badness: 0.0551
+[[Comma list]]: 225/224, 2500000/2470629
-</div></div>
+{{Mapping|legend=1| 1 -2 10 11 | 0 7 -15 -16 }}
+: mapping generators: ~2, ~10/7
-== 11-limit ==
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.3898{{c}}, ~10/7 = 614.6413{{c}}
+: [[error map]]: {{val| +0.390 -0.435 -1.630 +1.634 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 614.4073{{c}}
+: error map: {{val| 0.000 -1.104 -2.423 +0.657 }}
-Period: 1\1
+{{Optimal ET sequence|legend=1| 41, 84, 125 }}
-Optimal ([[POTE]]) generator: ~7/5 = 585.606
+[[Badness]] (Sintel): 1.39
-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">
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
 Comma list: 225/224, 441/440, 1344/1331
-Mapping: [{{val| 1 5 -5 -5 2 }}, {{val| 0 -7 15 16 3 }}]
+Mapping: {{mapping| 1 -2 10 11 5 | 0 7 -15 -16 -3 }}
-{{Val list|legend=1| 41, 84, 125e }}
-Badness: 0.0364
-</div></div>
-== 13-limit ==
-Period: 1\1
+Optimal tunings:
+* WE: ~2 = 1199.9578{{c}}, ~10/7 = 614.3720{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3943{{c}}
-Optimal ([[POTE]]) generator: ~7/5 = 585.657
+{{Optimal ET sequence|legend=0| 41, 84, 125e }}
-EDO generators: [[41edo|20\41]], [[43edo|21\43]], [[84edo|41\84]]
+Badness (Sintel): 1.20
-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
 Comma list: 144/143, 225/224, 364/363, 441/440
-Mapping: [{{val| 1 5 -5 -5 2 12 }}, {{val| 0 -7 15 16 3 -17 }}]
+Mapping: {{mapping| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}
-{{Val list|legend=1| 41, 84, 125e, 209ef, 293ef }}
+Optimal tunings:
+* WE: ~2 = 1199.7422{{c}}, ~10/7 = 614.2110{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3442{{c}}
-Badness: 0.0275
+{{Optimal ET sequence|legend=0| 41, 84, 125e, 209ef, 293ef }}
-</div></div>
+Badness (Sintel): 1.14
+=== Mermaid ===
+Subgroup: 2.3.5.7.11
-= Septimin =
+Comma list: 225/224, 385/384, 532400/531441
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Septimin]].''
+Mapping: {{mapping| 1 -2 10 11 -16 | 0 7 -15 -16 38 }}
-Period: 1\1
+Optimal tunings:
+* WE: ~2 = 1199.4973{{c}}, ~10/7 = 614.7004{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4470{{c}}
-Optimal ([[POTE]]) generator: ~7/6 = 263.632
+{{Optimal ET sequence|legend=0| 41, 84e, 125, 166 }}
-EDO generators: [[41edo|9\41]], [[50edo|11\50]], [[91edo|20\91]]
+Badness (Sintel): 1.46
-Scales (Scala files):
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+Comma list: 225/224, 325/324, 385/384, 10648/10647
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7
+Mapping: {{mapping| 1 -2 10 11 22 32 | 0 7 -15 -16 38 58 }}
-Comma list: 225/224, 84035/82944
+Optimal tunings:
+* WE: ~2 = 1200.5126{{c}}, ~10/7 = 614.7152{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4562{{c}}
-Mapping: [{{val| 1 4 1 5 }}, {{val| 0 -11 6 -10 }}]
+{{Optimal ET sequence|legend=0| 41, 84ef, 125f, 166 }}
-Wedgie: {{wedgie| 11 -6 10 -35 -15 40 }}
+Badness (Sintel): 1.47
-{{Val list|legend=1| 41, 91, 132 }}
+== 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.
-== 11-limit ==
+[[Subgroup]]: 2.3.5.7
-Period: 1\1
+[[Comma list]]: 225/224, 589824/588245
-Optimal ([[POTE]]) generator: ~7/6 = 263.634
+{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
+: mapping generators: ~2, ~49/48
-EDO generators: [[41edo|9\41]], [[50edo|11\50]], [[91edo|20\91]]
+[[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
-Comma list: 225/224, 385/384, 2401/2376
+Comma list: 225/224, 385/384, 1331/1323
-Mapping: [{{val| 1 4 1 5 5 }}, {{val| 0 -11 6 -10 -7 }}]
+Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
-{{Val list|legend=1| 41, 91, 223cdef }}
+Optimal tunings:
+* WE: ~2 = 1199.4983{{c}}, ~49/48 = 38.4030{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3775{{c}}
-</div></div>
+{{Optimal ET sequence|legend=0| 31, 63, 94, 125 }}
-== 13-limit ==
+Badness (Sintel): 0.838
-Period: 1\1
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-Optimal ([[POTE]]) generator: ~7/6 = 263.700
+Comma list: 225/224, 275/273, 385/384, 1331/1323
-EDO generators: [[41edo|9\41]], [[50edo|11\50]], [[91edo|20\91]]
-Scales (Scala files):
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}
-<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 = 1200.1728{{c}}, ~49/48 = 38.3192{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3129{{c}}
-Comma list: 105/104, 144/143, 196/195, 245/242
+{{Optimal ET sequence|legend=0| 31, 63, 94 }}
-Mapping: [{{val| 1 4 1 5 5 7 }}, {{val| 0 -11 6 -10 -7 -15 }}]
+Badness (Sintel): 1.07
-{{Val list|legend=1| 41, 91 }}
+== Triton ==
+: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''
-</div></div>
+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.
-= Slender =
+[[Subgroup]]: 2.3.5.7
-Period: 1\1
+[[Comma list]]: 225/224, 1029/1000
-Optimal ([[POTE]]) generator: ~49/48 = 38.413
+{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}
+: mapping generators: ~2, ~10/7
-EDO generators: [[31edo|1\31]], [[32edo|1\32]], [[63edo|2\63]], [[94edo|3\94]]
+[[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 }}
-Scales (Scala files):
+{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+[[Badness]] (Sintel): 1.50
-<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, 589824/588245
+Comma list: 45/44, 56/55, 1029/1000
-Mapping: [{{val| 1 2 2 3 }}, {{val| 0 -13 10 -6 }}]
+Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}
-Wedgie: {{wedgie| 13 -10 6 -46 -27 42 }}
+Optimal tunings:
+* WE: ~2 = 1201.3875{{c}}, ~10/7 = 631.5852{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 630.8007{{c}}
-{{Val list|legend=1| 31, 94, 125 }}
+{{Optimal ET sequence|legend=0| 2, 17d, 19 }}
-Badness: 0.0569
+Badness (Sintel): 1.51
-</div></div>
+== Marvolo ==
+[[Subgroup]]: 2.3.5.7
-== 11-limit ==
+[[Comma list]]: 225/224, 156250000/155649627
-Period: 1\1
+{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
+: mapping generators: ~2, ~21/20
-Optimal ([[POTE]]) generator: ~49/48 = 38.387
+[[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 }}
-EDO generators: [[31edo|1\31]], [[32edo|1\32]], [[63edo|2\63]], [[94edo|3\94]]
+{{Optimal ET sequence|legend=1| 29, 43, 72, 619bbccd, 691bbccd }}
-Scales (Scala files):
+[[Badness]] (Sintel): 2.11
-<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
-Comma list: 225/224, 385/384, 1331/1323
+Comma list: 225/224, 441/440, 4000/3993
-Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -13 10 -6 -17 }}]
+Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}
-{{Val list|legend=1| 31, 63, 94, 125 }}
+Optimal tunings:
+* WE: ~2 = 1200.7075{{c}}, ~21/20 = 83.3888{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3564{{c}}
-Badness: 0.02534
+{{Optimal ET sequence|legend=0| 29, 43, 72 }}
-</div></div>
+Badness (Sintel): 0.958
-== 13-limit ==
-Period: 1\1
-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
-Comma list: 225/224, 275/273, 385/384, 1331/1323
+Comma list: 169/168, 225/224, 364/363, 441/440
-Mapping: [{{val| 1 2 2 3 4 3 }}, {{val| 0 -13 10 -6 -17 22 }}]
+Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}
-{{Val list|legend=1| 31, 63, 94 }}
+Optimal tunings:
+* WE: ~2 = 1200.9467{{c}}, ~21/20 = 83.3956{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3516{{c}}
-Badness: 0.02591
+{{Optimal ET sequence|legend=0| 29, 43, 72 }}
-</div></div>
+Badness (Sintel): 0.887
-= Marvo =
+=== 17-limit ===
-{{see also| Gravity family }}
+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: ~27/20 = 516.694
+Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}
-EDO generators: [[65edo|28\65]], [[72edo|31\72]], [[137edo|59\137]]
+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
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 225/224, 78125000/78121827
-Mapping: [{{val| 1 5 12 29 }}, {{val| 0 -6 -17 -46 }}]
+Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440
-Wedgie: {{wedgie| 6 17 46 13 56 59 }}
+Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}
-{{Val list|legend=1| 65d, 72, 137, 209, 281, 569bcc }}
+Optimal tunings:
+* WE: ~2 = 1200.7625{{c}}, ~21/20 = 83.3895{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3551{{c}}
-Badness: 0.0976
+{{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: ~27/20 = 516.699
+{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
+: mapping generators: ~2592/2401, ~12005/6912
-EDO generators: [[65edo|28\65]], [[72edo|31\72]], [[137edo|59\137]]
+[[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
-Comma list: 225/224, 243/242, 4000/3993
+Comma list: 225/224, 385/384, 12005/11979
-Mapping: [{{val| 1 5 12 29 12 }}, {{val| 0 -6 -17 -46 -15 }}]
+Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}
-{{Val list|legend=1| 65d, 72, 281, 353c, 425bc, 497bc }}
+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: 0.0317
+{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}
-</div></div>
+Badness (Sintel): 1.01
-== 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">
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 225/224, 243/242, 351/350, 1625/1617
+Comma list: 169/168, 225/224, 364/363, 1716/1715
-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
-</div></div>
-= Marvolo =
-Period: 1\1
-Optimal ([[POTE]]) generator: ~21/20 = 83.348
-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">
-Subgroup: 2.3.5.7
-Comma list: 225/224, 156250000/155649627
-Mapping: [{{val| 1 2 1 1 }}, {{val| 0 -6 19 26 }}]
+Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}
-Wedgie: {{wedgie| 6 -19 -26 -44 -58 -7 }}
+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}})
-{{Val list|legend=1| 29, 43, 72, 619bcd, 691bcd }}
+{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}
-Badness: 0.0833
+Badness (Sintel): 0.922
-</div></div>
+== Gracecordial ==
+: ''For the 5-limit version, see [[Schismic–Pythagorean equivalence continuum #Gracecordial (5-limit)]].''
-== 11-limit ==
+[[Subgroup]]: 2.3.5.7
-Period: 1\1
+[[Comma list]]: 225/224, 781250000/771895089
-Optimal ([[POTE]]) generator: ~21/20 = 83.340
+{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
+: mapping generators: ~2, ~3
-EDO generators: [[29edo|2\29]], [[43edo|3\43]], [[72edo|5\72]]
+[[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">
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 225/224, 441/440, 4000/3993
+Comma list: 225/224, 385/384, 236328125/234365481
-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 0 34 63 -90 | 0 1 -20 -38 59 }}
-EDO generators: [[29edo|2\29]], [[43edo|3\43]], [[72edo|5\72]]
+Optimal tunings:
+* WE: ~2 = 1200.5571{{c}}, ~3/2 = 701.1589{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8328{{c}}
-Scales (Scala files):
+{{Optimal ET sequence|legend=0| 12e, 113, 125, 238c }}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+Badness (Sintel): 2.96
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 169/168, 225/224, 364/363, 441/440
+Comma list: 225/224, 325/324, 385/384, 831875/830466
-Mapping: [{{val| 1 2 1 1 2 3 }}, {{val| 0 -6 19 26 21 10 }}]
+Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}
-{{Val list|legend=1| 29, 43, 72, 115f }}
+Optimal tunings:
+* WE: ~2 = 1200.6282{{c}}, ~3/2 = 701.2080{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8421{{c}}
-Badness: 0.0215
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
-</div></div>
+Badness (Sintel): 2.16
-= Amavil =
+==== 17-limit ====
-== 5-limit (mabila) ==
+Subgroup: 2.3.5.7.11.13.17
-Period: 1\1
+Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913
-Optimal ([[POTE]]) generator: ~512/375 = 529.6849
+Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}
-EDO generators: [[34edo|15\34]], [[43edo|19\43]], [[77edo|34\77]], [[111edo|49\111]]
+Optimal tunings:
+* WE: ~2 = 1200.5058{{c}}, ~3/2 = 701.1360{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8414{{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): 1.96
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5
+==== 19-limit ====
+Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 268435456/263671875
+Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444
-Mapping: [{{val| 1 6 1 }}, {{val| 0 -10 3 }}]
+Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}
-{{Val list|legend=1| 9, 25, 34, 77, 111, 145, 256c }}
+Optimal tunings:
+* WE: ~2 = 1200.4418{{c}}, ~3/2 = 701.0999{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8425{{c}}
-Badness: 0.2325
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
-</div></div>
+Badness (Sintel): 1.71
-== 7-limit ==
+==== 23-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23
-Period: 1\1
+Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528
-Optimal ([[POTE]]) generator: ~48/35 = 529.979
+Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}
-EDO generators: [[34edo|15\34]], [[43edo|19\43]]
+Optimal tunings:
+* WE: ~2 = 1200.4641{{c}}, ~3/2 = 701.1145{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8444{{c}}
-Scales (Scala files):
+{{Optimal ET sequence|legend=0| 12e, 113, 238cfi }}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+Badness (Sintel): 1.57
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7
+==== 29-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23.29
-Comma list: 225/224, 17496/16807
+Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493
-Mapping: [{{val| 1 6 1 9 }}, {{val| 0 -10 3 -14 }}]
+Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}
-Wedgie: {{wedgie| 10 -3 14 -28 -6 41 }}
+Optimal tunings:
+* WE: ~2 = 1200.4400{{c}}, ~3/2 = 701.0986{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8428{{c}}
-{{Val list|legend=1| 9, 25d, 34d, 43, 77d }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
-Badness: 0.1096
+Badness (Sintel): 1.50
-</div></div>
+==== 31-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23.29.31
-== 11-limit ==
+Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493
-Period: 1\1
+Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}
-Optimal ([[POTE]]) generator: ~15/11 = 529.974
+Optimal tunings:
+* WE: ~2 = 1200.4178{{c}}, ~3/2 = 701.0822{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8396{{c}}
-EDO generators: [[34edo|15\34]], [[43edo|19\43]]
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
-Scales (Scala files):
+Badness (Sintel): 1.53
-<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
-Comma list: 99/98, 176/175, 864/847
+Comma list: 225/224, 441/440, 109375/107811
-Mapping: [{{val| 1 6 1 9 7 }}, {{val| 0 -10 3 -14 -8 }}]
-{{Val list|legend=1| 9, 34d, 43, 77de }}
-Badness: 0.0426
-</div></div>
-== 13-limit ==
+Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}
-Period: 1\1
+Optimal tunings:
+* WE: ~2 = 1200.6064{{c}}, ~3/2 = 701.2398{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8718{{c}}
-Optimal ([[POTE]]) generator: ~15/11 = 529.951
+{{Optimal ET sequence|legend=0| 12, …, 101cd, 113 }}
-EDO generators: [[34edo|15\34]], [[43edo|19\43]]
+Badness (Sintel): 2.21
-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">
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 78/77, 99/98, 144/143, 176/175
+Comma list: 225/224, 364/363, 441/440, 6125/6084
-Mapping: [{{val| 1 6 1 9 7 9 }}, {{val| 0 -10 3 -14 -8 -12 }}]
+Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}
-{{Val list|legend=1| 9, 34d, 43, 77de }}
+Optimal tunings:
+* WE: ~2 = 1200.6225{{c}}, ~3/2 = 701.2539{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8781{{c}}
-Badness: 0.0258
+{{Optimal ET sequence|legend=0| 12f, …, 101cdf, 113 }}
-</div></div>
+Badness (Sintel): 1.83
-= Enneaportent =
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
-Period: 1\9
+Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989
-Optimal ([[POTE]]) generator: ~5/4 = 383.165
+Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}
-EDO generators: [[63edo|20\63]], [[72edo|23\72]], [[81edo|26\81]]
+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, 40353607/40310784
-Mapping: [{{val| 9 0 28 11 }}, {{val| 0 2 -1 2 }}]
+Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663
-Wedgie: {{wedgie| 18 -9 18 -56 -22 67 }}
+Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}
-{{Val list|legend=1| 63, 72, 495bcd }}
+Optimal tunings:
+* WE: ~2 = 1200.2658{{c}}, ~3/2 = 701.0213{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8629{{c}}
-Badness: 0.0937
+{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}
-</div></div>
+Badness (Sintel): 1.68
-== 11-limit ==
+== Alphorn ==
+[[Subgroup]]: 2.3.5.7
-Period: 1\9
+[[Comma list]]: 225/224, 5764801/5668704
-Optimal ([[POTE]]) generator: ~5/4 = 383.146
+{{Mapping|legend=1| 1 -7 5 -9 | 0 16 -5 22 }}
+: mapping generators: ~2, ~35/24
-EDO generators: [[63edo|20\63]], [[72edo|23\72]], [[81edo|26\81]]
+[[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 }}
-Scales (Scala files):
+{{Optimal ET sequence|legend=1| 13d, 28d, 41, 151cd, 192cdd, 233ccdd }}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+[[Badness]] (Sintel): 3.27
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 225/224, 385/384, 12005/11979
+Comma list: 225/224, 385/384, 12250/11979
-Mapping: [{{val| 9 0 28 11 24 }}, {{val| 0 2 -1 2 1 }}]
+Mapping: {{mapping| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}
-{{Val list|legend=1| 63, 72, 423cd, 495bcd }}
+Optimal tunings:
+* WE: ~2 = 1200.5123{{c}}, ~16/11 = 644.1307{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 643.8662{{c}}
-Badness: 0.0304
+{{Optimal ET sequence|legend=0| 13d, 28d, 41 }}
-</div></div>
+Badness (Sintel): 2.43
-== 13-limit ==
+== Misneb ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Misneb]].''
-Period: 1\9
+[[Subgroup]]: 2.3.5.7
-Optimal ([[POTE]]) generator: ~5/4 = 383.047
+[[Comma list]]: 225/224, 4194304/4117715
-EDO generators: [[63edo|20\63]], [[72edo|23\72]], [[81edo|26\81]]
+{{Mapping|legend=1| 1 -12 15 1 | 0 15 -14 2 }}
+: mapping generators: ~2, ~15/8
-Scales (Scala files):
+[[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 }}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+{{Optimal ET sequence|legend=1| 21, 32, 53 }}
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7.11.13
+[[Badness]] (Sintel): 3.57
-Comma list: 169/168, 225/224, 364/363, 1716/1715
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-Mapping: [{{val| 9 0 28 11 24 19 }}, {{val| 0 2 -1 2 1 2 }}]
+Comma list: 99/98, 176/175, 1310720/1294139
-{{Val list|legend=1| 63, 72, 279cf }}
+Mapping: {{mapping| 1 -12 15 1 27 | 0 15 -14 2 -26 }}
-Badness: 0.0223
+Optimal tunings:
+* WE: ~2 = 1200.1654{{c}}, ~15/8 = 1086.8269{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6766{{c}}
-</div></div>
+{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}
-= Submajor =
+Badness (Sintel): 2.82
-== 5-limit ==
-Period: 1\1
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
-Optimal ([[POTE]]) generator: ~10125/8192 = 362.321
+Comma list: 99/98, 176/175, 640/637, 847/845
-EDO generators: [[43edo|13\43]], [[53edo|16\53]], [[63edo|19\63]], [[96edo|29\96]], [[116edo|35\116]]
+Mapping: {{mapping| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}
-Scales (Scala files):
+Optimal tunings:
+* WE: ~2 = 1200.1687{{c}}, ~15/8 = 1086.8295{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6757{{c}}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5
+Badness (Sintel): 1.88
-Comma list: 69198046875/68719476736
+=== Musneb ===
+Subgroup: 2.3.5.7.11
-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
-EDO generators: [[43edo|13\43]], [[53edo|16\53]], [[63edo|19\63]], [[96edo|29\96]], [[116edo|35\116]]
+Comma list: 225/224, 385/384, 66550/64827
-Scales (Scala files):
+Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+Optimal tunings:
-<div style="line-height:1.6;">Technical data</div>
+* WE: ~2 = 1200.0839{{c}}, ~15/8 = 1086.9343{{c}}
-<div class="mw-collapsible-content">
+* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.8593{{c}}
-Subgroup: 2.3.5.7
+{{Optimal ET sequence|legend=0| 21e, 32, 53 }}
-Comma list: 225/224, 51200/50421
+Badness (Sintel): 2.89
-Mapping: [{{val| 1 4 -1 1 }}, {{val| 0 -8 11 6 }}]
+== Untriton ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''
-Wedgie: {{wedgie| 8 -11 -6 -36 -32 17 }}
+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| 10, 33, 43, 53 }}
+[[Subgroup]]: 2.3.5.7
-Badness: 0.0605
+[[Comma list]]: 225/224, 125000000/121060821
-</div></div>
+{{Mapping|legend=1| 1 -3 12 13 | 0 9 -19 -20 }}
+: mapping generators: ~2, ~10/7
-== 11-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: ~27/22 = 362.101
+[[Badness]] (Sintel): 3.64
-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
-Comma list: 225/224, 385/384, 6655/6561
+Comma list: 121/120, 225/224, 22000/21609
-Mapping: [{{val| 1 4 -1 1 11 }}, {{val| 0 -8 11 6 -25 }}]
+Mapping: {{mapping| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}
-{{Val list|legend=1| 53, 116, 169de, 285cde }}
+Optimal tunings:
+* WE: ~2 = 1200.3591{{c}}, ~10/7 = 611.5569{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3690{{c}}
-Badness: 0.0506
+{{Optimal ET sequence|legend=0| 51, 53 }}
-</div></div>
+Badness (Sintel): 2.46
 === 13-limit ===
+Subgroup: 2.3.5.7.11.13
-Period: 1\1
+Comma list: 121/120, 225/224, 275/273, 1040/1029
-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;">
+Mapping: {{mapping| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}
-<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 = 1200.4078{{c}}, ~10/7 = 611.5536{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3392{{c}}
-Comma list: 169/168, 225/224, 275/273, 385/384
+{{Optimal ET sequence|legend=0| 51f, 53 }}
-Mapping: [{{val| 1 4 -1 1 11 4 }}, {{val| 0 -8 11 6 -25 -1 }}]
+Badness (Sintel): 1.96
-{{Val list|legend=1| 53, 116, 169de, 285cdef }}
+== Naiadical ==
+Named by [[Xenllium]] in 2026, naiadical may be described as the {{nowrap| 21 & 29 }} temperament.
-Badness: 0.0277
+[[Subgroup]]: 2.3.5.7
-</div></div>
+[[Comma list]]: 225/224, 823543/800000
-== Interpental ==
+{{Mapping|legend=1| 1 -4 11 9 | 0 9 -14 -10 }}
+: mapping generators: ~2, ~32/21
-Period: 1\1
+[[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: ~49/40 = 362.418
+{{Optimal ET sequence|legend=1| 21, 29, 50, 79d, 129cdd, 179bcddd }}
-EDO generators: [[43edo|13\43]], [[53edo|16\53]], [[96edo|29\96]]
+[[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
-Comma list: 99/98, 176/175, 51200/50421
+Comma list: 225/224, 245/242, 1617/1600
-POTE generator: ~49/40 = 362.418
-Mapping: [{{val| 1 4 -1 1 -5 }}, {{val| 0 -8 11 6 28 }}]
+Mapping: {{Mapping| 1 -4 11 9 14 | 0 9 -14 -10 -17 }}
-{{Val list|legend=1| 43, 53, 96, 149d }}
+Optimal tunings:
+* WE: ~2 = 1201.9008{{c}}, ~21/16 = 745.3867{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~32/21 = 744.1777{{c}}
-Badness: 0.0518
+{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
-</div></div>
+Badness (Sintel): 2.00
 === 13-limit ===
-Period: 1\1
-Optimal ([[POTE]]) generator: ~16/13 = 362.402
-EDO generators: [[43edo|13\43]], [[53edo|16\53]], [[96edo|29\96]]
-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: 99/98, 169/168, 176/175, 640/637
+Comma list: 105/104, 196/195, 245/242, 1001/1000
-POTE generator: ~16/13 = 362.402
+Mapping: {{Mapping| 1 -4 11 9 14 13 | 0 9 -14 -10 -17 -15 }}
-Mapping: [{{val| 1 4 -1 1 -5 4 }}, {{val| 0 -8 11 6 28 -1 }}]
+Optimal tunings:
+* WE: ~2 = 1201.7863{{c}}, ~20/13 = 745.3344{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1931{{c}}
-{{Val list|legend=1| 43, 53, 96, 149d }}
+{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
-Badness: 0.0297
+Badness (Sintel): 1.43
-</div></div>
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
-= Alphorn =
-Period: 1\1
-Optimal ([[POTE]]) generator: ~48/35 = 556.221
-EDO generators: [[28edo|13\28]], [[41edo|19\41]]
+Comma list: 105/104, 170/169, 196/195, 221/220, 245/242
-Scales (Scala files):
+Mapping: {{Mapping| 1 -4 11 9 14 13 14 | 0 9 -14 -10 -17 -15 -16 }}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+Optimal tunings:
-<div style="line-height:1.6;">Technical data</div>
+* WE: ~2 = 1201.9208{{c}}, ~20/13 = 745.3976{{c}}
-<div class="mw-collapsible-content">
+* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1669{{c}}
-Subgroup: 2.3.5.7
+{{Optimal ET sequence|legend=0| 21, 29g, 50, 79dg }}
-Comma list: 225/224, 5764801/5668704
+Badness (Sintel): 1.26
-Mapping: [{{val| 1 9 0 13 }}, {{val| 0 -16 5 -22 }}]
+== Quintannic ==
+Named by [[Scott Dakota]], quintannic may be described as the {{nowrap| 43 & 60 }} temperament.
-Wedgie: {{wedgie| 16 -5 22 -45 -10 65 }}
+[[Subgroup]]: 2.3.5.7
-{{Val list|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
+[[Comma list]]: 225/224, 9805926501/9765625000
-Badness: 0.1293
+{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
+: mapping generators: ~2, ~10000/9261
-</div></div>
+[[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 }}
-== 11-limit ==
+{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}
-Period: 1\1
-Optimal ([[POTE]]) generator: ~11/8 = 556.144
+[[Badness]] (Sintel): 3.81
-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">
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 225/224, 385/384, 12250/11979
+Comma list: 225/224, 441/440, 43923/43750
-Mapping: [{{val| 1 9 0 13 3 }}, {{val| 0 -16 5 -22 1 }}]
-{{Val list|legend=1| 28d, 41, 315cde }}
+Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}
-Badness: 0.0735
+Optimal tunings:
+* WE: ~2 = 1201.0031{{c}}, ~320/297 = 139.9435{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~320/297 = 139.8053{{c}}
-</div></div>
+{{Optimal ET sequence|legend=0| 43, 60e, 103, 369bcdeee, 472bbcddeee }}
-= Decic =
+Badness (Sintel): 1.74
-The ''decic'' temperament (10&amp;50, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the [[225/224|marvel comma]], 225/224 in the 7-limit. It can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order.
-== 7-limit ==
+=== 13-limit ===
-Period: 1\10
+Subgroup: 2.3.5.7.11.13
-Optimal ([[POTE]]) generator: ~3/2 = 698.696
+Comma list: 225/224, 441/440, 1001/1000, 1188/1183
-EDO generators: [[50edo|1\50]], [[60edo|1\60]]
+Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}
-Scales (Scala files):
+Optimal tunings:
+* WE: ~2 = 1200.8354{{c}}, ~13/12 = 139.9095{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.7997{{c}}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+{{Optimal ET sequence|legend=0| 43, 60e, 103 }}
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7
+Badness (Sintel): 1.35
-[[Comma list]]: 225/224, 16807/16384
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
-[[Mapping]]: [{{val| 10 0 39 28 }}, {{val| 0 1 -1 0 }}]
+Comma list: 225/224, 273/272, 375/374, 441/440, 891/884
-Mapping generators: ~15/14, ~3
+Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}
-{{Multival|legend=1| 10 -10 0 -39 -28 28 }}
+Optimal tunings:
+* WE: ~2 = 1200.7402{{c}}, ~13/12 = 139.9015{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.8038{{c}}
-[[Tuning ranges]]:
+{{Optimal ET sequence|legend=0| 43, 60e, 103 }}
-* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
-* nice range: ~3/2 = [693.686, 701.955]
-* strict range: ~3/2 = [696.000, 700.000]
-{{Val list|legend=1| 10, 50, 60, 110d }}
+Badness (Sintel): 1.17
-[[Badness]]: 0.089135
+== Gwazy ==
+: ''For the 5-limit version, see [[Very high accuracy temperaments #Kwazy]].''
-</div></div>
+Named by [[Petr Pařízek]] in 2011<ref name="petr's long post"/>, gwazy may be described as the {{nowrap| 22 & 74 }} temperament.
-== 11-limit ==
+[[Subgroup]]: 2.3.5.7
-Period: 1\10
-Optimal (POTE) generator: ~3/2 = 696.791
+[[Comma list]]: 225/224, 5971968/5764801
-EDO generators: [[50edo|1\50]], [[60edo|1\60]]
+{{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}
+: mapping generators: ~2401/1728, ~35/32
-Scales (Scala files):
+[[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 class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
+[[Badness]] (Sintel): 4.53
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 225/224, 385/384, 3087/3025
+Comma list: 99/98, 176/175, 65536/65219
-Mapping: [{{val| 10 0 39 28 3 }}, {{val| 0 1 -1 0 2 }}]
+Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}
-Mapping generators: ~15/14, ~3
+Optimal tunings:
+* WE: ~363/256 = 599.8517{{c}}, ~11/10 = 162.5518{{c}}
+* CWE: ~363/256 = 600.0000{{c}}, ~11/10 = 162.5863{{c}}
-Tuning ranges:
+{{Optimal ET sequence|legend=0| 22, 74, 96 }}
-* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
-* nice range: ~3/2 = [693.686, 701.955]
-* strict range: ~3/2 = [696.000, 700.000]
-{{Val list|legend=1| 10, 50, 60 }}
+Badness (Sintel): 2.26
-Badness: 0.063900
+== Tertiosec ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tertiosec]].''
-</div></div>
+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>.
-== 13-limit ==
+[[Subgroup]]: 2.3.5.7
-Period: 1\10
-Optimal (POTE) generator: ~3/2 = 696.993
+[[Comma list]]: 225/224, 14495514624/13841287201
-EDO generators: [[50edo|1\50]], [[60edo|1\60]]
+{{Mapping|legend=1| 3 -1 12 7 | 0 8 -7 2 }}
+: mapping generators: ~3072/2401, ~2048/1715
-Scales (Scala files):
+[[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 }}
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}
-<div style="line-height:1.6;">Technical data</div>
-<div class="mw-collapsible-content">
-Subgroup: 2.3.5.7.11.13
+[[Badness]] (Sintel): 10.9
-Comma list: 105/104, 144/143, 196/195, 2200/2197
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-Mapping: [{{val| 10 0 39 28 3 37 }}, {{val| 0 1 -1 0 2 0 }}]
-Mapping generators: ~14/13, ~3
-Tuning ranges:
-* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
-* nice range: ~3/2 = [693.686, 701.955]
-* strict range: ~3/2 = [696.000, 700.000]
-{{Val list|legend=1| 10, 50, 60 }}
-Badness: 0.036880
-</div></div>
-== 17-limit ==
-Period: 1\10
-Optimal (POTE) generator: ~3/2 = 697.085
-EDO generators: [[50edo|1\50]], [[60edo|1\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: 2.3.5.7.11.13.17
-Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
-Mapping: [{{val| 10 0 39 28 3 37 25 }}, {{val| 0 1 -1 0 2 0 1 }}]
+Comma list: 225/224, 3840/3773, 12005/11979
-Mapping generators: ~14/13, ~3
+Mapping: {{mapping| 3 -1 12 7 14 | 0 8 -7 2 -5 }}
-Tuning ranges:
+Optimal tunings:
-* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
+* WE: ~44/35 = 399.6550{{c}}, ~33/28 = 287.5803{{c}}
-* nice range: ~3/2 = [693.686, 701.955]
+* CWE: ~44/35 = 400.0000{{c}}, ~33/28 = 287.8224{{c}}
-* strict range: ~3/2 = [696.000, 700.000]
-{{Val list|legend=1| 10, 50, 60 }}
+{{Optimal ET sequence|legend=0| 21, 54, 75e }}
-Badness: 0.025064
+Badness (Sintel): 5.74
-</div></div>
+== References ==
-[[Category:Theory]]
+[[Category:Temperament collections]]
-[[Category:Temperament]]
+[[Category:Marvel temperaments| ]] <!-- main article -->
-[[Category:Marvel]]
 [[Category:Rank 2]]

Marvel temperaments: Difference between revisions