Sensamagic clan: Difference between revisions

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@@ Line 19: / Line 19: @@
 The full 7-limit extensions' relation to BPS is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are
 * [[#Sensi]]
+* [[#Cohemiripple]]
 * ''[[Hedgehog]]'', {50/49, 245/243} → [[Porcupine family #Hedgehog|Porcupine family]]
 * ''[[Fourfives]]'', {245/243, 235298/234375} → [[Fifive family #Fourfives|Fifive family]]
@@ Line 36: / Line 37: @@
 * ''[[Pental]]'', {245/243, 16807/16384} → [[Pental family #Septimal pental|Pental family]]
 * ''[[Bamity]]'', {245/243, 64827/64000} → [[Amity family #Bamity|Amity family]]
+* ''[[Escaped]]'', {245/243, 65625/65536} → [[Escapade family #Escaped|Escapade family]]
-as well as sensi, bohpier, escaped, salsa, pycnic, cohemiripple, superthird, magus and leapweek discussed below.
+as well as bohpier, salsa, pycnic, superthird, magus and leapweek discussed below.
 == Sensi ==
@@ Line 258: / Line 260: @@
 Badness: 0.026339
+== Cohemiripple ==
+{{See also| Ripple family }}
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 245/243, 1323/1250
+[[Mapping]]: [{{val| 1 -3 -5 -5 }}, {{val| 0 10 16 17 }}]
+{{Multival|legend=1| 10 16 17 2 -1 -5 }}
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 549.944
+{{Val list|legend=1| 11cd, 13cd, 24 }}
+[[Badness]]: 0.190208
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 77/75, 243/242, 245/242
+Mapping: [{{val| 1 -3 -5 -5 -8 }}, {{val| 0 10 16 17 25 }}]
+Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.945
+Optimal GPV sequence: {{Val list| 11cdee, 13cdee, 24 }}
+Badness: 0.082716
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 66/65, 77/75, 147/143, 243/242
+Mapping: [{{val| 1 -3 -5 -5 -8 -5 }}, {{val| 0 -10 -16 -17 -25 -19 }}]
+Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.958
+Optimal GPV sequence: {{Val list| 11cdeef, 13cdeef, 24 }}
+Badness: 0.049933
 == Bohpier ==
@@ Line 351: / Line 396: @@
 Badness: 0.082158
-== Escaped ==
-{{See also| Escapade family #Escaped }}
-This temperament is also known as "sensa" because it tempers out 245/243, 352/351, and 385/384 as a sensamagic temperament. ''Not to be confused with the 19e &amp; 27 temperament (sensi extension).''
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 245/243, 65625/65536
-[[Mapping]]: [{{val| 1 2 2 4 }}, {{val| 0 -9 7 -26 }}]
-{{Multival|legend=1| 9 -7 26 -32 16 80 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 55.122
-{{Val list|legend=1| 22, 65, 87, 196, 283 }}
-[[Badness]]: 0.088746
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 245/243, 385/384, 4000/3993
-Mapping: [{{val| 1 2 2 4 3 }}, {{val| 0 -9 7 -26 10 }}]
-Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 55.126
-Optimal GPV sequence: {{Val list| 22, 65, 87, 196, 283 }}
-Badness: 0.035844
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 245/243, 352/351, 385/384, 625/624
-Mapping: [{{val| 1 2 2 4 3 2 }}, {{val| 0 -9 7 -26 10 37 }}]
-Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 55.138
-Optimal GPV sequence: {{Val list| 22, 65, 87, 283 }}
-Badness: 0.031366
 == Salsa ==
@@ Line 458: / Line 458: @@
 [[Badness]]: 0.073735
-== Cohemiripple ==
-{{See also| Ripple family }}
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 245/243, 1323/1250
-[[Mapping]]: [{{val| 1 -3 -5 -5 }}, {{val| 0 10 16 17 }}]
-{{Multival|legend=1| 10 16 17 2 -1 -5 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 549.944
-{{Val list|legend=1| 11cd, 13cd, 24 }}
-[[Badness]]: 0.190208
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 77/75, 243/242, 245/242
-Mapping: [{{val| 1 -3 -5 -5 -8 }}, {{val| 0 10 16 17 25 }}]
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.945
-Optimal GPV sequence: {{Val list| 11cdee, 13cdee, 24 }}
-Badness: 0.082716
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 66/65, 77/75, 147/143, 243/242
-Mapping: [{{val| 1 -3 -5 -5 -8 -5 }}, {{val| 0 -10 -16 -17 -25 -19 }}]
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.958
-Optimal GPV sequence: {{Val list| 11cdeef, 13cdeef, 24 }}
-Badness: 0.049933
 == Superthird ==