Vishnu family: Difference between revisions

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 The second comma in the comma list defines which 7-limit family member we are looking at. Septimal vishnu (118 & 152) adds [[4375/4374]]. Narayana (84 & 118) adds [[65625/65536]]. Vishnean (16 & 50) adds [[126/125]]. There is also an unnamed 50 & 84 temperament, which tempers out [[225/224]]. These all use the same generators as classical vishnu.
-Quarvish (68 & 270) adds [[2401/2400]], splitting the generator in four. Decavish adds [[420175/419904]], with a 1/10-octave period.
+Trivish (84 & 186) adds [[250047/250000]], splitting the semi-octave period in three. Quarvish (68 & 270) adds [[2401/2400]], splitting the generator in four. Decavish (50 & 220) adds [[420175/419904]], splitting the semi-octave period in five.
 == Septimal vishnu ==
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 Badness (Sintel): 1.68
+== Trivish ==
+Trivish tempers out 250047/250000, the [[landscape comma]], with a 1/6-octave period. It may be described as the {{nowrap| 84 & 186 }} temperament. It is more significant in the [[11-limit]], where it tempers out the [[kalisma]] and the [[olympia]]. In the [[13-limit]], the generator can be taken as a [[~]][[14/13]]. [[270edo]] is an obvious tuning for it, but it can be tuned to [[354edo]], [[624edo]] or [[894edo]]. It was named by [[Flora Canou]] in 2026 for the fact that it splits the period of vishnu in three.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 250047/250000, 134217728/133984375
+{{Mapping|legend=1| 6 5 12 22 | 0 7 3 -8 }}
+: mapping generators: ~18375/16384, ~2205/2048
+[[Optimal tuning]]s:
+* [[WE]]: ~18375/16384 = 199.9885{{c}}, ~2205/2048 = 128.8583{{c}}
+: [[error map]]: {{val| -0.069 -0.005 +0.123 +0.054 }}
+* [[CWE]]: ~18375/16384 = 200.0000{{c}}, ~2205/2048 = 128.8643{{c}}
+: error map: {{val| 0.000 +0.095 +0.279 +0.256 }}
+{{Optimal ET sequence|legend=1| 84, 186, 270, 624, 894, 1164 }}
+[[Badness]] (Sintel): 1.51
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 9801/9800, 131072/130977, 151263/151250
+Mapping: {{mapping| 6 5 12 22 33 | 0 7 3 -8 -19 }}
+Optimal tunings:
+* WE: ~55/49 = 199.9885{{c}}, ~320/297 = 128.8582{{c}}
+* CWE: ~55/49 = 200.0000{{c}}, ~320/297 = 128.8661{{c}}
+{{Optimal ET sequence|legend=0| 84, 186, 270, 624, 894, 1164 }}
+Badness (Sintel): 0.807
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 1716/1715, 2080/2079, 4096/4095, 34398/34375
+Mapping: {{mapping| 6 5 12 22 33 28 | 0 7 3 -8 -19 -9 }}
+Optimal tunings:
+* WE: ~55/49 = 199.9922{{c}}, ~14/13 = 128.8565{{c}}
+* CWE: ~55/49 = 200.0000{{c}}, ~14/13 = 128.8621{{c}}
+{{Optimal ET sequence|legend=0| 84, 186, 270, 624, 894, 2058f }}
+Badness (Sintel): 0.791
+=== 2.3.5.7.11.13.19 subgroup ===
+Subgroup: 2.3.5.7.11.13.19
+Comma list: 1521/1520, 1716/1715, 2080/2079, 2376/2375, 3250/3249
+Mapping: {{mapping| 6 5 12 22 33 28 30 | 0 7 3 -8 -19 -9 -7 }}
+Optimal tunings:
+* WE: ~55/49 = 199.9909{{c}}, ~14/13 = 128.8564{{c}}
+* CWE: ~55/49 = 200.0000{{c}}, ~14/13 = 128.8630{{c}}
+{{Optimal ET sequence|legend=0| 84, 186, 270, 624, 894 }}
+Badness (Sintel): 0.591
 == Quarvish ==
-Quarvish tempers out 2401/2400, the [[breedsma]], and may be described as the {{nowrap| 68 & 202 }} temperament.
+Quarvish tempers out 2401/2400, the [[breedsma]], and may be described as the {{nowrap| 68 & 270 }} temperament.
 [[Subgroup]]: 2.3.5.7
@@ Line 210: / Line 275: @@
 == Decavish ==
-Decavish tempers out the [[wizma]] as well as the [[linus comma]], and may be described as the {{nowrap| 50 & 270 }} temperament. It was named by [[Xenllium]] in 2021 for the fact that its period is 1/10 octave.
+Decavish tempers out the [[wizma]] as well as the [[linus comma]], and may be described as the {{nowrap| 50 & 220 }} temperament. It was named by [[Xenllium]] in 2021 for the fact that its period is 1/10 octave.
 [[Subgroup]]: 2.3.5.7