User:Dummy index/3rd-tritave temperaments: Difference between revisions

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 == "Threedie family" start from 3.5.7.13 ==
-=== BPS III (b30 & b9, b39 & b9) ===
+=== BPS III (b30 &amp; b9, b39 &amp; b9) ===
-: ''Proposed names: [[User:Recentlymaterialized/Miscellaneous rank-2 temperaments #Tripierce (b30 & b39)]]''
+: ''Proposed names: [[User:Recentlymaterialized/Miscellaneous rank-2 temperaments #Tripierce (b30 &amp; b39)]]''
 [[Subgroup]]: 3.5.7.13
@@ Line 23: / Line 23: @@
 Badness (Dirichlet): 0.269
+* {{mos scalesig|3L 6s<3/1>|link=1}}
+* {{mos scalesig|9L 3s<3/1>|link=1}} – This has 5:7:9:13.
 ==== 3.5.7.11.13 ====
@@ Line 43: / Line 46: @@
 Badness (Dirichlet): 0.525
-==== strong extension 3.5.7.11.13 (b39 & b30e) ====
+==== strong extension 3.5.7.11.13 (b39 &amp; b30e) ====
 Subgroup: 3.5.7.11.13
@@ Line 61: / Line 64: @@
 Badness (Dirichlet): 0.713
-==== weak extension 3.5.7.11.13 (b39 & b60) ====
+==== weak extension 3.5.7.11.13 (b39 &amp; b60) ====
 Subgroup: 3.5.7.11.13
@@ Line 79: / Line 82: @@
 Badness (Dirichlet): 0.447
-=== Sirius III (b39 & b6, b39 & b45) ===
+* {{mos scalesig|3L 15s<3/1>|link=1}}
+* {{mos scalesig|18L 3s<3/1>|link=1}} – This has 5:7:9:11:13.
+=== Sirius III (b39 &amp; b6, b39 &amp; b45) ===
 [[Subgroup]]: 3.5.7.13
@@ Line 96: / Line 102: @@
 Badness (Dirichlet): 0.832
+* {{mos scalesig|3L 3s<3/1>|link=1}}
+* {{mos scalesig|6L 3s<3/1>|link=1}}
 ==== 3.5.7.11.13 (also deneb III) ====
@@ Line 116: / Line 125: @@
 Badness (Dirichlet): 0.551
-=== Canopus III (b39 & b36, b39 & b75) ===
+=== Canopus III (b39 &amp; b36, b39 &amp; b75) ===
 [[Subgroup]]: 3.5.7.13
@@ Line 135: / Line 144: @@
 {{main|Suhail}}
-=== b9 & b6 ===
+=== b9 &amp; b6 ===
 [[Subgroup]]: 3.5.7.13
@@ Line 154: / Line 163: @@
 == "Threedie family" start from 3.7.11.13 ==
-=== Mintaka III (b39 & b66) ===
+=== Mintaka III (b39 &amp; b66) ===
+[[Subgroup]]: 3.7.11.13
+[[Comma list]]: 1331/1323, 2197/2187
+[[Sval]] [[mapping]]: {{mapping| 3 0 3 7 | 0 3 2 0 }}
+Sval mapping ([[mingen]]): {{mapping| 3 6 7 7 | 0 -3 -2 0 }}
-Subgroup: 3.7.11.13
+Sval mapping generators: ~13/9, ~21/11
+[[Optimal tuning]] ([[CWE]]): ~13/9 = 1\3edt, ~21/11 = 1122.959
+[[Support]]ing [[ET]]s: 39, 27, 12, 66, 105, 15, 144, 51, 93, 183, 171, 90, 42[+7], 222[-11]
-Comma list: 1331/1323, 2197/2187
+Badness (Dirichlet): 0.237
-Sval mapping: {{mapping| 3 6 7 7 | 0 -3 -2 0 }}
+* {{mos scalesig|3L 9s<3/1>|link=1}} – This and the following have 7:9:11:13.
+* {{mos scalesig|12L 3s<3/1>|link=1}}
 ==== 3.5.7.11.13 (also procyon III) ====
@@ Line 167: / Line 189: @@
 Subgroup: 3.5.7.11.13
-Comma list: 823543/820125, 1331/1323, 2197/2187
+Comma list: 4459/4455, 11011/10935, 847/845
 Sval mapping: {{mapping| 3 6 6 7 7 | 0 -7 -3 -2 0 }}
-==== weak extension 3.5.7.11.13 (b39 & b15, also arcturus III) ====
+Sval mapping generators: ~13/9, ~49/45
+Optimal tuning (CWE): ~13/9 = 1\3edt, ~49/45 = 145.470
+Supporting ETs: 39, 144, 105, 183, 66, 27, 12[-5], 222[-11], 261[-11], 51[-5], 249, 327[-11], 300[-11], 171
+Badness (Dirichlet): 0.459
+==== Weak extension 3.5.7.11.13 (b39 &amp; b15, also arcturus III) ====
+: ''See also: [[Tetrahanson #b39 &amp; b15]]''
 Subgroup: 3.5.7.11.13
-Comma list: 15625/15309, 1331/1323, 2197/2187
+Comma list: 275/273, 1575/1573, 8125/8019
+Sval mapping: {{mapping| 3 3 -3 1 7 | 0 1 6 4 0 }}
+Sval mapping (mingen): {{mapping| 3 4 3 5 7 | 0 1 6 4 0 }}
+Sval mapping generators: ~13/9, ~5/3
+Optimal tuning (CWE): ~13/9 = 1\3edt, ~5/3 = 878.361
+Supporting ETs: 39, 15, 24[-7], 54, 93, 63[-7, -11], 132, 102[-7, -11], 171[-5], 69[+7], 141[-5, -7, -11], 210[-5], 147[+7], 180[-5, -7, -11]
+Badness (Dirichlet): 0.588
+* {{mos scalesig|6L 3s<3/1>|link=1}}
+* {{mos scalesig|9L 6s<3/1>|link=1}} – This has 5:9:11:13.
+* {{mos scalesig|15L 9s<3/1>|link=1}} – This has 5:7:9:11:13.
+=== b27 &amp; b21 ===
+Subgroup: 3.7.11.13
+Comma list: 9477/9317, 2197/2187
+Sval mapping: {{mapping| 3 1 8 7 | 0 3 -1 0 }}
+Sval mapping (mingen): {{mapping| 3 4 7 7 | 0 3 -1 0 }}
+Sval mapping generators: ~13/9, ~243/143
+Optimal tuning (CWE): ~13/9 = 1\3edt, ~243/143 = 912.556
+Supporting ETs: 27, 6, 21, 48, 75, 15[-7], 33[+7], 69, 102, 123[+11], 60[+7], 129[+7], 90[+11], 117[+11]
-Sval mapping: {{mapping| 3 4 3 5 7 | 0 1 6 4 0 }}
+Badness (Dirichlet): 0.830
 == External links ==
-*[https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_13&error=6.2]
+* [https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_13&error=6.2]
-*[https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_11_13&error=4.0]
+* [https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_11_13&error=4.0]
 <!-- b30 & b6, b30 & b45, b9 & b45 -->
-{{stub}}