@@ Line 3: / Line 3: @@
 Temperaments considered in families and clans are:
-* ''[[Pelogic]]'' → [[Mavila family #Pelogic|Mavila family]] (+21/20 or 135/128, generated by the fifth with 5/4 mapped to the m3)
+* ''[[Pelogic]]'' (+21/20 or 135/128) → [[Mavila family #Pelogic|Mavila family]]
-* [[Meantone]] → [[Meantone family #Septimal meantone|Meantone family]] (+81/80 or 126/125, generated by the fifth with 5/4 mapped to the M3)
+* [[Meantone]] (+81/80 or 126/125) → [[Meantone family #Septimal meantone|Meantone family]]
-* [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]] (+3125/3087, generated by the fifth with 5/4 mapped to the d4)
+* [[Garibaldi]] (+3125/3087) → [[Schismatic family #Garibaldi|Schismatic family]]
-* [[Pajara]] → [[Diaschismic family #Pajara|Diaschismic family]] (+50/49 or 64/63, generated by the fifth with a semioctave period)
+* [[Pajara]] (+50/49 or 64/63) → [[Diaschismic family #Pajara|Diaschismic family]]
-* ''[[Sharpie]]'' → [[Dicot family #Sharpie|Dicot family]] (+25/24 or 28/27, fifth sliced in two)
+* ''[[Sharpie]]'' (+25/24 or 28/27) → [[Dicot family #Sharpie|Dicot family]]
-* ''[[Immune]]'' → [[Immunity family #Immune|Immunity family]] (+781250/750141, twelfth sliced in two)
+* ''[[Immune]]'' (+781250/750141) → [[Immunity family #Immune|Immunity family]]
-* ''[[August]]'' → [[Augmented family #August|Augmented family]] (+36/35 or 128/125, generated by the fifth with a 1/3-octave period)
+* ''[[August]]'' (+36/35 or 128/125) → [[Augmented family #August|Augmented family]]
-* ''[[Fog]]'' → [[Misty family #Fog|Misty family]] (+156250/151263, generated by the fifth with a 1/3-octave period)
+* ''[[Fog]]'' (+156250/151263) → [[Misty family #Fog|Misty family]]
-* [[Negri]] → [[Slendro clan #Negri|Slendro clan]] (+49/48, fourth sliced in four)
+* [[Bunya]] (+15625/15309) → [[Tetracot family #Bunya|Tetracot family]]
-* [[Magic]] → [[Magic family #Magic|Magic family]] (+245/243, twelfth sliced in five)
+* [[Negri]] (+49/48) → [[Semaphoresmic clan #Negri|Semaphoresmic clan]]
-* ''[[Passive]]'' → [[Passion family #Passive|Passion family]] (+256/245, fourth sliced in five)
+* [[Magic]] (+245/243) → [[Magic family #Magic|Magic family]]
-* ''[[Quintapole]]'' → [[Quintaleap family #Quintapole|Quintaleap family]] (+7812500/7411887, fourth sliced in five)
+* ''[[Passive]]'' (+256/245) → [[Passion family #Passive|Passion family]]
-* ''[[Houborizic]]'' → [[Amity family #Houborizic|Amity family]] (+1250000/1240029, eleventh sliced in five)
+* ''[[Houborizic]]'' (+1250000/1240029) → [[Amity family #Houborizic|Amity family]]
-* ''[[Qintosec]]'' → [[Quintosec family #Qintosec|Quintosec family]] (+2560000/2470629, generated by the classical minor second with a 1/5-octave period)
+* ''[[Qintosec]]'' (+2560000/2470629) → [[Quintosec family #Qintosec|Quintosec family]]
-* [[Miracle]] → [[Gamelismic clan #Miracle|Gamelismic clan]] (+1029/1024, fifth sliced in six)
+* [[Miracle]] (+1029/1024) → [[Gamelismic clan #Miracle|Gamelismic clan]]
-* [[Catakleismic]] → [[Kleismic family #Catakleismic|Kleismic family]] (+4375/4374, twelfth sliced in six)
+* [[Catakleismic]] (+4375/4374) → [[Kleismic family #Catakleismic|Kleismic family]]
-* ''[[Marvo]]'' → [[Gravity family #Marvo|Gravity family]] (+78125000/78121827, two octaves and a fifth sliced in six)
+* ''[[Marvo]]'' (+78125000/78121827) → [[Gravity family #Marvo|Gravity family]]
-* [[Orwell]] → [[Semicomma family #Orwell|Semicomma family]] (+1728/1715, twelfth sliced in seven)
+* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell|Semicomma family]]
-* ''[[Snipes]]''  → [[Wesley family #Snipes|Wesley family]] (+6125/5832, two octaves and a fourth sliced in seven)
+* ''[[Snipes]]'' (+6125/5832)  → [[Wesley family #Snipes|Wesley family]]
-* ''[[Submajor]]'' → [[Buzzardsmic clan #Submajor|Buzzardsmic clan]] (+65536/64827, two octaves and a fourth sliced in eight)
+* ''[[Demibuzzard]]'' (+65536/64827) → [[Buzzardsmic clan #Demibuzzard|Buzzardsmic clan]]
-* ''[[Escapist]]'' → [[Escapade family #Escapist|Escapade family]] (+65625/65536, fourth sliced in nine)
+* ''[[Escapist]]'' (+65625/65536) → [[Escapade family #Escapist|Escapade family]]
-* ''[[Decic]]'' → [[Cloudy clan #Decic|Cloudy clan]] (+16807/16384, generated by the fifth with a 1/10-octave period)
+* ''[[Amavil]]'' (+17496/16807) → [[Mabila family #Amavil|Mabila family]]
-* ''[[Amavil]]'' → [[Mabila family #Amavil|Mabila family]] (+17496/16807, four octaves and a fourth sliced in ten)
+* ''[[Betic]]'' (+1071875/1062882) → [[Sycamore family #Betic|Sycamore family]]
-* ''[[Betic]]'' → [[Sycamore family #Betic|Sycamore family]] (+1071875/1062882, fifth sliced in eleven)
+* [[Wizard]] (+118098/117649) → [[Stearnsmic clan #Wizard|Stearnsmic clan]]
-* ''[[Hendeca]]'' → [[11th-octave temperaments #Hendeca|11th-octave temperaments]] (+122880/117649, generated by the fifth with a 1/11-octave period)
+* ''[[Raccoon]]'' (+41943040/40353607) → [[Vavoom family #Raccoon|Vavoom family]]
-* ''[[Compton]]'' → [[Compton family #Compton|Compton family]] (+250047/250000, generated by the classical major third with a 1/12-octave period)
+* ''[[Maquila]]'' (+30233088/28824005) → [[Maquila family #Septimal maquila|Maquila family]]
-* ''[[Raccoon]]'' → [[Vavoom family #Raccoon|Vavoom family]] (+41943040/40353607, twelfth sliced in seventeen)
+* ''[[Gammy]]'' (+94143178827/91913281250) → [[Gammic family #Gammy|Gammic family]]
-* ''[[Maquila]]'' → [[Maquila family #Septimal maquila|Maquila family]] (+30233088/28824005, seven octaves and a fifth sliced in seventeen)
+* [[Compton]] (+250047/250000) → [[Compton family #Compton|Compton family]]
-* ''[[Gammy]]'' → [[Gammic family #Gammy|Gammic family]] (+94143178827/91913281250, fifth sliced in twenty)
-Considered below are wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, alphorn, tertiosec, gwazy, and gracecordial.
+Considered below are tritonic, septimin, merman, slender, triton, marvolo, decic, enneaportent, gracecordial, alphorn, misneb, untriton, naiadical, quintannic, hendeca, gwazy, and tertiosec, in the order of increasing [[badness]].
 Since {{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.
@@ Line 40: / Line 39: @@
 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}}.)
-== Wizard ==
-{{Main| Wizard }}
-: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Wizard]].''
-Wizard has a [[semi-octave]] period and is generated by an interval that can be treated as [[~]][[17/15]]. The semi-octave complement of this interval is ~[[5/4]]. Wizard can be described as {{nowrap| 22 & 72 }}. Its [[ploidacot]] is diploid alpha-hexacot, so six generator steps plus a semi-octave period gives the [[3/1|perfect twelfth]]. [[72edo]], [[94edo]], and especially [[166edo]] are good tunings for it.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 225/224, 118098/117649
-{{Mapping|legend=1| 2 1 5 2 | 0 6 -1 10 }}
-: mapping generators: ~1225/864, ~245/216
-[[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 ET sequence|legend=1| 22, 50, 72, 238c, 310c, 382c, 454bccd }}
-[[Badness]] (Sintel): 1.03
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 225/224, 385/384, 4000/3993
-Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}
-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 ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}
-Badness (Sintel): 0.613
-==== Lizard ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 225/224, 351/350, 364/363, 385/384
-Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}
-Optimal tunings:
-* WE: ~55/39 = 600.4824{{c}}, ~25/22 = 216.7852{{c}}
-* CWE: ~55/39 = 600.0000{{c}}, ~25/22 = 216.6247{{c}}
-{{Optimal ET sequence|legend=0| 22, 50, 72 }}
-Badness (Sintel): 0.900
-===== 17-limit =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 221/220, 273/272, 289/288, 351/350, 375/374
-Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}
-Optimal tunings:
-* WE: ~17/12 = 600.5032{{c}}, ~17/15 = 216.8002{{c}}
-* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.6361{{c}}
-{{Optimal ET sequence|legend=0| 22, 50, 72 }}
-Badness (Sintel): 0.741
-===== 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: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}
-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 ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}
-Badness (Sintel): 0.955
-==== Gizzard ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 225/224, 325/324, 385/384, 1573/1568
-Mapping: {{mapping| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }}
-Optimal tunings:
-* WE: ~99/70 = 600.2896{{c}}, ~25/22 = 216.9343{{c}}
-* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.8501{{c}}
-{{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}
-Badness (Sintel): 0.837
-===== 17-limit =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 225/224, 289/288, 325/324, 375/374, 385/384
-Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}
-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 ET sequence|legend=0| 22f, 72, 166g, 238cfg }}
-Badness (Sintel): 0.694
-===== 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: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}
-Optimal tunings:
-* WE: ~17/12 = 600.2637{{c}}, ~17/15 = 216.9570{{c}}
-* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8687{{c}}
-{{Optimal ET sequence|legend=0| 72, 94, 166g }}
-Badness (Sintel): 0.901
-=== Mage ===
-Subgroup: 2.3.5.7.11
-Comma list: 99/98, 176/175, 1331/1296
-Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }}
-Optimal tunings:
-* WE: ~77/54 = 600.6486{{c}}, ~55/48 = 217.1099{{c}}
-* CWE: ~77/54 = 600.0000{{c}}, ~55/48 = 216.9841{{c}}
-{{Optimal ET sequence|legend=0| 22, 50e, 72ee }}
-Badness (Sintel): 1.91
 == Tritonic ==
@@ Line 211: / Line 67: @@
 Comma list: 121/120, 225/224, 441/440
-Mapping: {{mapping| 1 -1 8 9 5 | 0 5 -11 -12 -3 }}
+{{Mapping|legend=0| 1 -1 8 9 5 | 0 5 -11 -12 -3 }}
 Optimal tunings:
@@ Line 226: / Line 82: @@
 Comma list: 105/104, 121/120, 196/195, 275/273
-Mapping: {{mapping| 1 -1 8 9 5 13 | 0 5 -11 -12 -3 -18 }}
+{{Mapping|legend=0| 1 -1 8 9 5 13 | 0 5 -11 -12 -3 -18 }}
 Optimal tunings:
@@ Line 241: / Line 97: @@
 Comma list: 105/104, 121/120, 154/153, 196/195, 273/272
-Mapping: {{mapping| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}
+{{Mapping|legend=0| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}
 Optimal tunings:
@@ Line 256: / Line 112: @@
 Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272
-Mapping: {{mapping| 1 -1 8 9 5 13 17 12 | 0 5 -11 -12 -3 -18 -25 -15 }}
+{{Mapping|legend=0| 1 -1 8 9 5 13 17 12 | 0 5 -11 -12 -3 -18 -25 -15 }}
 Optimal tunings:
@@ Line 271: / Line 127: @@
 Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195
-Mapping: {{mapping| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}
+{{Mapping|legend=0| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}
 Optimal tunings:
@@ Line 286: / Line 142: @@
 Comma list: 225/224, 385/384, 27783/27500
-Mapping: {{mapping| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}
+{{Mapping|legend=0| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}
 Optimal tunings:
@@ Line 314: / Line 170: @@
 : error map: {{val| 0.000 -1.516 -4.735 -4.790 }}
-{{Optimal ET sequence|legend=1| 41, 91, 132d }}
+{{Optimal ET sequence|legend=1| 9, 23, 32, 41, 91, 132d }}
 [[Badness]] (Sintel): 1.38
@@ Line 323: / Line 179: @@
 Comma list: 225/224, 245/242, 385/384
-Mapping: {{mapping| 1 -7 7 -5 -2 | 0 11 -6 10 7 }}
+{{Mapping|legend=0| 1 -7 7 -5 -2 | 0 11 -6 10 7 }}
 Optimal tunings:
@@ Line 329: / Line 185: @@
 * CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3906{{c}}
-{{Optimal ET sequence|legend=0| 41, 91, 223cdef }}
+{{Optimal ET sequence|legend=0| 9, 23, 32, 41, 91, 223cdef }}
 Badness (Sintel): 1.04
@@ Line 338: / Line 194: @@
 Comma list: 105/104, 144/143, 196/195, 245/242
-Mapping: {{mapping| 1 -7 7 -5 -2 -8 | 0 11 -6 10 7 15 }}
+{{Mapping|legend=0| 1 -7 7 -5 -2 -8 | 0 11 -6 10 7 15 }}
 Optimal tunings:
@@ Line 344: / Line 200: @@
 * CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3196{{c}}
-{{Optimal ET sequence|legend=0| 41, 91 }}
+{{Optimal ET sequence|legend=0| 9, 32f, 41, 91 }}
 Badness (Sintel): 0.955
@@ Line 377: / Line 233: @@
 Comma list: 225/224, 441/440, 1344/1331
-Mapping: {{mapping| 1 -2 10 11 5 | 0 7 -15 -16 -3 }}
+{{Mapping|legend=0| 1 -2 10 11 5 | 0 7 -15 -16 -3 }}
 Optimal tunings:
@@ Line 387: / Line 243: @@
 Badness (Sintel): 1.20
-=== 13-limit ===
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
 Comma list: 144/143, 225/224, 364/363, 441/440
-Mapping: {{mapping| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}
+{{Mapping|legend=0| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}
 Optimal tunings:
@@ Line 401: / Line 257: @@
 Badness (Sintel): 1.14
+=== Mermaid ===
+Subgroup: 2.3.5.7.11
+Comma list: 225/224, 385/384, 532400/531441
+{{Mapping|legend=0| 1 -2 10 11 -16 | 0 7 -15 -16 38 }}
+Optimal tunings:
+* WE: ~2 = 1199.4973{{c}}, ~10/7 = 614.7004{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4470{{c}}
+{{Optimal ET sequence|legend=0| 41, 84e, 125, 166 }}
+Badness (Sintel): 1.46
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 225/224, 325/324, 385/384, 10648/10647
+{{Mapping|legend=0| 1 -2 10 11 22 32 | 0 7 -15 -16 38 58 }}
+Optimal tunings:
+* WE: ~2 = 1200.5126{{c}}, ~10/7 = 614.7152{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4562{{c}}
+{{Optimal ET sequence|legend=0| 41, 84ef, 125f, 166 }}
+Badness (Sintel): 1.47
 == Slender ==
@@ Line 429: / Line 315: @@
 Comma list: 225/224, 385/384, 1331/1323
-Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
+{{Mapping|legend=0| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
 Optimal tunings:
@@ Line 444: / Line 330: @@
 Comma list: 225/224, 275/273, 385/384, 1331/1323
-Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}
+{{Mapping|legend=0| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}
 Optimal tunings:
@@ Line 455: / Line 341: @@
 == Triton ==
-: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Stump]].''
+: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''
 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.
@@ Line 481: / Line 367: @@
 Comma list: 45/44, 56/55, 1029/1000
-Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}
+{{Mapping|legend=0| 1 0 6 7 4 | 0 3 -7 -8 -1 }}
 Optimal tunings:
@@ Line 514: / Line 400: @@
 Comma list: 225/224, 441/440, 4000/3993
-Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}
+{{Mapping|legend=0| 1 2 1 1 2 | 0 -6 19 26 21 }}
 Optimal tunings:
@@ Line 529: / Line 415: @@
 Comma list: 169/168, 225/224, 364/363, 441/440
-Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}
+{{Mapping|legend=0| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}
 Optimal tunings:
@@ Line 544: / Line 430: @@
 Comma list: 169/168, 221/220, 225/224, 364/363, 441/440
-Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}
+{{Mapping|legend=0| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}
 Optimal tunings:
@@ Line 559: / Line 445: @@
 Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440
-Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}
+{{Mapping|legend=0| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}
 Optimal tunings:
@@ Line 568: / Line 454: @@
 Badness (Sintel): 0.895
+== Decic ==
+{{Main| Decic }}
+Named by [[Xenllium]] in 2021, decic tempers out 16807/16384, the [[cloudy comma]], and {{monzo| 11 -10 -10 10 }}, the [[linus comma]], in addition to the marvel comma. It may be described as the {{nowrap| 50 & 60 }} temperament, with a period of 1/10 octave and a [[ploidacot]] signature of decaploid monocot. It is [[support]]ed by [[10edo|10-]], [[50edo|50-]], and [[60edo]].
+It can be extended to the 11-, 13-, and 17-limit by adding [[385/384]], [[105/104]], and [[170/169]] to the comma list in this order.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 225/224, 16807/16384
+{{Mapping|legend=1| 10 0 39 28 | 0 1 -1 0 }}
+: mapping generators: ~15/14, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~15/14 = 120.1837{{c}}, ~3/2 = 699.7654{{c}} (~49/48 = 21.3366{{c}})
+: [[error map]]: {{val| +1.837 -0.353 -0.753 -3.683 }}
+* [[CWE]]: ~15/14 = 120.0000{{c}}, ~3/2 = 698.8236{{c}} (~49/48 = 21.1764{{c}})
+: error map: {{val| 0.000 -3.131 -5.137 -8.826 }}
+{{Optimal ET sequence|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}
+[[Badness]] (Sintel): 2.26
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 225/224, 385/384, 3087/3025
+{{Mapping|legend=0| 10 0 39 28 3 | 0 1 -1 0 2 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1406{{c}}, ~3/2 = 697.6075{{c}} (~56/55 = 23.2360{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.0142{{c}} (~56/55 = 22.9858{{c}})
+{{Optimal ET sequence|legend=0| 10, 40, 50 }}
+Badness (Sintel): 2.11
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 105/104, 144/143, 196/195, 2200/2197
+{{Mapping|legend=0| 10 0 39 28 3 37 | 0 1 -1 0 2 0 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1166{{c}}, ~3/2 = 697.6705{{c}} (~78/77 = 23.0289{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.1492{{c}} (~78/77 = 22.8508{{c}})
+{{Optimal ET sequence|legend=0| 10, 40, 50 }}
+Badness (Sintel): 1.52
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
+{{Mapping|legend=0| 10 0 39 28 3 37 25 | 0 1 -1 0 2 0 1 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1262{{c}}, ~3/2 = 697.8185{{c}} (~78/77 = 22.9388{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.2757{{c}} (~78/77 = 22.7243{{c}})
+{{Optimal ET sequence|legend=0| 10, 40, 50 }}
+Badness (Sintel): 1.28
+=== Splendecic ===
+Splendecic (50 & 60e) is an alternative extension of decic, tempering out 1617/1600, 2401/2376 and 4375/4356 in the 11-limit. As a temperament of the [[fantastic]] rank-3 temperament, its name is a portmanteau of ''splendid'' and ''decic''.
+Subgroup: 2.3.5.7.11
+Comma list: 225/224, 1617/1600, 2401/2376
+{{Mapping|legend=0| 10 0 39 28 82 | 0 1 -1 0 -3 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1874{{c}}, ~3/2 = 699.6085{{c}} (~99/98 = 21.5156{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.3531{{c}} (~99/98 = 21.6469{{c}})
+{{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de, 170cddee }}
+Badness (Sintel): 1.98
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 105/104, 196/195, 1001/1000, 1188/1183
+{{Mapping|legend=0| 10 0 39 28 82 37 | 0 1 -1 0 -3 0 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1565{{c}}, ~3/2 = 699.2756{{c}} (~91/90 = 21.6631{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.2480{{c}} (~91/90 = 21.7520{{c}})
+{{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de }}
+Badness (Sintel): 1.57
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 105/104, 170/169, 196/195, 289/288, 375/374
+{{Mapping|legend=0| 10 0 39 28 82 37 25 | 0 1 -1 0 -3 0 1 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1571{{c}}, ~3/2 = 699.2892{{c}} (~91/90 = 21.6536{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.3144{{c}} (~91/90 = 21.6856{{c}})
+{{Optimal ET sequence|legend=0| 10e, 50, 60e, 110deg }}
+Badness (Sintel): 1.33
+=== Prodecic ===
+Prodecic (50e & 60e) is an alternative extension of decic, tempering out 441/440, 1375/1372 and 4375/4356 in the 11-limit. As a temperament of the [[prodigy]] rank-3 temperament, its name is a portmanteau of ''prodigy'' and ''decic''.
+Subgroup: 2.3.5.7.11
+Comma list: 225/224, 441/440, 5929/5832
+{{Mapping|legend=0| 10 0 39 28 -13 | 0 1 -1 0 3 }}
+Optimal tunings:
+* WE: ~15/14 = 120.2024{{c}}, ~3/2 = 701.3908{{c}} (~55/54 = 19.8237{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.5235{{c}} (~55/54 = 19.4765{{c}})
+{{Optimal ET sequence|legend=0| 10, 50e, 60e }}
+Badness (Sintel): 2.20
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 105/104, 196/195, 275/273, 5929/5832
+{{Mapping|legend=0| 10 0 39 28 -13 37 | 0 1 -1 0 3 0 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1654{{c}}, ~3/2 = 701.4683{{c}} (~91/90 = 19.5242{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.7175{{c}} (~91/90 = 19.2825{{c}})
+{{Optimal ET sequence|legend=0| 10, 50e, 60e }}
+Badness (Sintel): 1.73
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 105/104, 154/153, 170/169, 196/195, 289/288
+{{Mapping|legend=0| 10 0 39 28 -13 37 25 | 0 1 -1 0 3 0 1 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1577{{c}}, ~3/2 = 701.3950{{c}} (~91/90 = 19.5514{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.6932{{c}} (~91/90 = 19.3068{{c}})
+{{Optimal ET sequence|legend=0| 10, 50e, 60e }}
+Badness (Sintel): 1.41
 == Enneaportent ==
@@ Line 592: / Line 641: @@
 Comma list: 225/224, 385/384, 12005/11979
-Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}
+{{Mapping|legend=0| 9 0 28 11 24 | 0 2 -1 2 1 }}
 Optimal tunings:
@@ Line 607: / Line 656: @@
 Comma list: 169/168, 225/224, 364/363, 1716/1715
-Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}
+{{Mapping|legend=0| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}
 Optimal tunings:
@@ Line 630: / Line 679: @@
 * [[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}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.8112{{c}}
 : error map: {{val| 0.000 -1.144 -2.537 +0.349 }}
@@ Line 642: / Line 691: @@
 Comma list: 225/224, 385/384, 236328125/234365481
-Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}
+{{Mapping|legend=0| 1 0 34 63 -90 | 0 1 -20 -38 59 }}
 Optimal tunings:
@@ Line 657: / Line 706: @@
 Comma list: 225/224, 325/324, 385/384, 831875/830466
-Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}
+{{Mapping|legend=0| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}
 Optimal tunings:
@@ Line 672: / Line 721: @@
 Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913
-Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}
+{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}
 Optimal tunings:
@@ Line 687: / Line 736: @@
 Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444
-Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}
+{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}
 Optimal tunings:
@@ Line 702: / Line 751: @@
 Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528
-Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}
+{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}
 Optimal tunings:
@@ Line 717: / Line 766: @@
 Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493
-Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}
+{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}
 Optimal tunings:
@@ Line 732: / Line 781: @@
 Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493
-Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}
+{{Mapping|legend=0| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}
 Optimal tunings:
@@ Line 747: / Line 796: @@
 Comma list: 225/224, 441/440, 109375/107811
-Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}
+{{Mapping|legend=0| 1 0 34 63 89 | 0 1 -20 -38 -54 }}
 Optimal tunings:
@@ Line 762: / Line 811: @@
 Comma list: 225/224, 364/363, 441/440, 6125/6084
-Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}
+{{Mapping|legend=0| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}
 Optimal tunings:
@@ Line 777: / Line 826: @@
 Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989
-Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}
+{{Mapping|legend=0| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}
 Optimal tunings:
@@ Line 792: / Line 841: @@
 Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663
-Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}
+{{Mapping|legend=0| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}
 Optimal tunings:
@@ Line 825: / Line 874: @@
 Comma list: 225/224, 385/384, 12250/11979
-Mapping: {{mapping| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}
+{{Mapping|legend=0| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}
 Optimal tunings:
@@ Line 860: / Line 909: @@
 Comma list: 99/98, 176/175, 1310720/1294139
-Mapping: {{mapping| 1 -12 15 1 27 | 0 15 -14 2 -26 }}
+{{Mapping|legend=0| 1 -12 15 1 27 | 0 15 -14 2 -26 }}
 Optimal tunings:
@@ Line 875: / Line 924: @@
 Comma list: 99/98, 176/175, 640/637, 847/845
-Mapping: {{mapping| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}
+{{Mapping|legend=0| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}
 Optimal tunings:
@@ Line 890: / Line 939: @@
 Comma list: 225/224, 385/384, 66550/64827
-Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}
+{{Mapping|legend=0| 1 3 1 3 6 | 0 -15 14 -2 -27 }}
 Optimal tunings:
@@ Line 927: / Line 976: @@
 Comma list: 121/120, 225/224, 22000/21609
-Mapping: {{mapping| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}
+{{Mapping|legend=0| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}
 Optimal tunings:
@@ Line 942: / Line 991: @@
 Comma list: 121/120, 225/224, 275/273, 1040/1029
-Mapping: {{mapping| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}
+{{Mapping|legend=0| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}
 Optimal tunings:
@@ Line 1,042: / Line 1,091: @@
 Comma list: 225/224, 441/440, 43923/43750
-Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}
+{{Mapping|legend=0| 1 1 5 7 8 | 0 5 -23 -36 -39 }}
 Optimal tunings:
@@ Line 1,057: / Line 1,106: @@
 Comma list: 225/224, 441/440, 1001/1000, 1188/1183
-Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}
+{{Mapping|legend=0| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}
 Optimal tunings:
@@ Line 1,072: / Line 1,121: @@
 Comma list: 225/224, 273/272, 375/374, 441/440, 891/884
-Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}
+{{Mapping|legend=0| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}
 Optimal tunings:
@@ Line 1,081: / Line 1,130: @@
 Badness (Sintel): 1.17
+== Hendeca ==
+{{Distinguish| Hendec }}
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Hendecatonic]].''
+Hendeca tempers out the same 5-limit comma as [[porwell temperaments #Hendecatonic|hendecatonic]], and has a period of 1/11 octave. However, in this temperament, nine periods represent [[7/4]], the same as [[keemic temperaments #Undeka|undeka]]. It can be tuned to [[22edo]] or [[33edo]] using the [[patent val]], or [[55edo]] using the 55d val. It was named by [[Xenllium]] in 2025 as a low-accuracy variant of hendecatonic.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 225/224, 122880/117649
+{{Mapping|legend=1| 11 0 43 31 | 0 1 -1 0 }}
+: mapping generators: ~16/15, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~16/15 = 108.9526{{c}}, ~3/2 = 702.4215{{c}}
+: [[error map]]: {{val| -1.521 -1.055 -2.252 +8.705 }}
+* [[CWE]]: ~16/15 = 109.0909{{c}}, ~3/2 = 703.2071{{c}}
+: error map: {{val| 0.000 +1.252 +1.388 +12.992 }}
+{{Optimal ET sequence|legend=1| 22, 55d, 77d, 99dd }}
+[[Badness]] (Sintel): 4.37
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 121/120, 225/224, 352/343
+{{Mapping|legend=0| 11 0 43 31 38 | 0 1 -1 0 0 }}
+Optimal tunings:
+* WE: ~16/15 = 109.0109{{c}}, ~3/2 = 702.5746{{c}}
+* CWE: ~16/15 = 109.0909{{c}}, ~3/2 = 703.0395{{c}}
+{{Optimal ET sequence|legend=0| 22, 55d }}
+Badness (Sintel): 2.46
 == Gwazy ==
@@ Line 1,109: / Line 1,196: @@
 Comma list: 99/98, 176/175, 65536/65219
-Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}
+{{Mapping|legend=0| 2 1 6 4 8 | 0 8 -5 6 -4 }}
 Optimal tunings:
@@ Line 1,122: / Line 1,209: @@
 : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tertiosec]].''
-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''.
+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>.
 [[Subgroup]]: 2.3.5.7
@@ Line 1,146: / Line 1,233: @@
 Comma list: 225/224, 3840/3773, 12005/11979
-Mapping: {{mapping| 3 -1 12 7 14 | 0 8 -7 2 -5 }}
+{{Mapping|legend=0| 3 -1 12 7 14 | 0 8 -7 2 -5 }}
 Optimal tunings:
@@ Line 1,158: / Line 1,245: @@
 == References ==
+[[Category:Marvel temperaments| ]] <!-- main article -->
 [[Category:Temperament collections]]
-[[Category:Marvel temperaments| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]

Marvel temperaments: Difference between revisions