Schismatic family: Difference between revisions

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 Temperaments discussed elsewhere include:
-* ''[[Sensamagic clan #Salsa|Salsa]]'' (+245/243) → [[Sensamagic clan #Salsa|Sensamagic clan]]
+* ''[[Guiron]]'' (+1029/1024) → [[Gamelismic clan #Guiron|Gamelismic clan]]
-* ''[[Gamelismic clan #Guiron|Guiron]]'' (+1029/1024) → [[Gamelismic clan #Guiron|Gamelismic clan]]
+* ''[[Pogo]]'' (+118098/117649) → [[Stearnsmic clan #Pogo|Stearnsmic clan]]
 The schismatic family boasts a variety of remarkable extensions to subgroups in high prime limits. These are listed at the bottom of this page, in [[#Subgroup extensions]].
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 Badness (Smith): 0.024734
+== Salsa ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 245/243, 32805/32768
+{{Mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }}
+: mapping generators: ~2, ~128/105
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.7707{{c}}, ~128/105 = 351.2748{{c}}
+: [[error map]]: {{val| +0.771 +1.365 -1.315 -3.024 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 351.0471{{c}}
+: error map: {{val| 0.000 +0.139 -3.068 -5.213 }}
+{{Optimal ET sequence|legend=1| 17, 24, 41, 106d, 147d, 188cd }}
+[[Badness]] (Sintel): 2.03
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 243/242, 245/242, 385/384
+Mapping: {{mapping| 1 1 7 -1 2 | 0 2 -16 13 5 }}
+Optimal tunings:
+* WE: ~2 = 1200.3891{{c}}, ~11/9 = 351.1275{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.0141{{c}}
+{{Optimal ET sequence|legend=0| 17, 24, 41, 106d }}
+Badness (Sintel): 1.30
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 105/104, 144/143, 243/242, 245/242
+Mapping: {{mapping| 1 1 7 -1 2 4 | 0 2 -16 13 5 -1 }}
+Optimal tunings:
+* WE: ~2 = 1199.9362{c}}, ~11/9 = 351.0061{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.0247{{c}}
+{{Optimal ET sequence|legend=0| 17, 24, 41 }}
+Badness (Sintel): 1.27
 == Hemischis ==
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 Badness (Smith): 0.024506
-== Pogo ==
-{{See also| Stearnsmic clan #Pogo }}
-The pogo temperament ({{nowrap| 94 & 130 }}) splits the period in two to address the difference between [[#Tertiaschis]] and [[#Countertertiaschis]]. The schismic tempering of the fifth is just about right for tempering out the stearnsma.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 32805/32768, 118098/117649
-{{Mapping|legend=1| 2 1 22 2 | 0 3 -24 5 }}
-: mapping generators: ~343/243, ~9/7
-[[Optimal tuning]] ([[POTE]]): ~343/243 = 600.000{{c}}, ~9/7 = 433.901{{c}}
-{{Optimal ET sequence|legend=1| 36, 94, 130, 224, 354 }}
-[[Badness]] (Smith): 0.079635
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 4000/3993, 32805/32768
-Mapping: {{mapping| 2 1 22 2 25 | 0 3 -24 5 -25 }}
-Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 433.911{{c}}
-{{Optimal ET sequence|legend=0| 36, 94, 130, 224, 354, 578 }}
-Badness (Smith): 0.031857
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 540/539, 729/728, 1575/1573, 4096/4095
-Mapping: {{mapping| 2 1 22 2 25 -2 | 0 3 -24 5 -25 13 }}
-Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 433.911{{c}}
-{{Optimal ET sequence|legend=0| 36, 94, 130, 224, 354, 578 }}
-Badness (Smith): 0.017514
 == Term ==