Garischismic clan: Difference between revisions

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 * ''[[Gariwizmic]]'' (+420175/419904) → [[Wizmic microtemperaments #Gariwizmic|Wizmic microtemperaments]]
 * ''[[Sextile]]'' (+250047/250000) → [[Landscape microtemperaments #Sextile|Landscape microtemperaments]]
-* ''[[Satin]]'' (+2100875/2097152) → [[Canousmic temperaments #Satin|Canousmic temperaments]]
 * ''[[Alphatrident]]'' (+6144/6125) → [[Alphatricot family #Alphatrident|Alphatricot family]]
 * ''[[Vulture]]'' (+4375/4374) → [[Vulture family #Vulture|Vulture family]]
@@ Line 41: / Line 40: @@
 * ''[[Garistearn]]'' (+118098/117649) → [[Stearnsmic clan #Garistearn|Stearnsmic clan]]
-Considered below are cotoneum and world calendar.
+Considered below are cotoneum, satin, and world calendar.
 === 2.3.7.11 subgroup ===
@@ Line 138: / Line 137: @@
 Badness (Sintel): 1.33
+== Satin ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Satin]].''
+Satin tempers out the [[rainy comma]] and the [[canousma]] in addition to the garischisma, and may be described as the {{nowrap| 94 & 217 }} temperament. It uses [[~]][[11/10]] as a generator, three of which gives a [[4/3|perfect fourth]], tempering out [[4000/3993]] in the 11-limit and onwards. Its [[ploidacot]] is omega-tricot.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2100875/2097152, 4802000/4782969
+{{Mapping|legend=1| 1 2 12 -3 | 0 -3 -70 42 }}
+: mapping generators: ~2, ~8575/7776
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0198{{c}}, ~8575/7776 = 165.9161{{c}}
+: [[error map]]: {{val| +0.020 +0.336 -0.200 -0.411 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~8575/7776 = 165.9133{{c}}
+: error map: {{val| 0.000 +0.305 -0.241 -0.469 }}
+{{Optimal ET sequence|legend=1| 94, 217, 311, 839, 1150 }}
+[[Badness]] (Sintel): 4.99
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 4000/3993, 19712/19683, 41503/41472
+Mapping: {{mapping| 1 2 12 -3 13 | 0 -3 -70 42 -69 }}
+Optimal tunings:
+* WE: ~2 = 1199.9931{{c}}, ~11/10 = 165.9145{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9155{{c}}
+{{Optimal ET sequence|legend=0| 94, 217, 311 }}
+Badness (Sintel): 1.92
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 1575/1573, 2080/2079, 4096/4095, 13720/13689
+Mapping: {{mapping| 1 2 12 -3 13 -1 | 0 -3 -70 42 -69 34 }}
+Optimal tunings:
+* WE: ~2 = 1199.9607{{c}}, ~11/10 = 165.9085{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9141{{c}}
+{{Optimal ET sequence|legend=0| 94, 217, 311, 839e }}
+Badness (Sintel): 1.25
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 595/594, 833/832, 1156/1155, 1575/1573, 4096/4095
+Mapping: {{mapping| 1 2 12 -3 13 -1 11 | 0 -3 -70 42 -69 34 -50 }}
+Optimal tunings:
+* WE: ~2 = 1199.9843{{c}}, ~11/10 = 165.9110{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9132{{c}}
+{{Optimal ET sequence|legend=0| 94, 217, 311, 839e }}
+Badness (Sintel): 1.02
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 595/594, 833/832, 969/968, 1156/1155, 1216/1215, 1575/1573
+Mapping: {{mapping| 1 2 12 -3 13 -1 11 16 | 0 -3 -70 42 -69 34 -50 -85 }}
+Optimal tunings:
+* WE: ~2 = 1199.9875{{c}}, ~11/10 = 165.9111{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9129{{c}}
+{{Optimal ET sequence|legend=0| 94, 217, 311, 839e }}
+Badness (Sintel): 0.881
+=== 23-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 595/594, 760/759, 833/832, 875/874, 969/968, 1105/1104, 1156/1155
+Mapping: {{mapping| 1 2 12 -3 13 -1 11 16 16 | 0 -3 -70 42 -69 34 -50 -85 -83 }}
+Optimal tunings:
+* WE: ~2 = 1199.9745{{c}}, ~11/10 = 165.9103{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9140{{c}}
+{{Optimal ET sequence|legend=0| 94, 217, 311 }}
+Badness (Sintel): 0.871
 == World calendar ==