Stearnsmic clan: Difference between revisions

← Older edit

VisualWikitext

@@ Line 1: / Line 1: @@
-The '''stearnsmic clan''' tempers out the stearnsma, the no-fives comma {{monzo| 1 10 0 -6 }} = 118098/117649.
+{{Technical data page}}
+The '''stearnsmic clan''' tempers out the [[stearnsma]], the no-fives comma {{monzo| 1 10 0 -6 }} = 118098/117649.
 == No-five stearnsmic ==
@@ Line 39: / Line 40: @@
 {{Mapping|legend=1| 2 1 22 2 | 0 3 -24 5 }}
-{{Multival|legend=1| 6 -48 10 -90 -1 158 }}
 [[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~9/7 = 433.901
@@ Line 80: / Line 79: @@
 {{Mapping|legend=1| 2 1 -12 2 | 0 3 23 5 }}
-{{Multival|legend=1| 6 46 10 59 -1 -106 }}
 [[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~9/7 = 434.218
@@ Line 137: / Line 134: @@
 : mapping generators: ~2450/2187, ~567/500
-{{Multival|legend=1| 36 66 60 21 -6 -46 }}
+[[Optimal tuning]] ([[CTE]]): ~2450/2187 = 1\6, ~567/500 = 216.9394 (~245/243 = 16.9394)
-[[Optimal tuning]] ([[POTE]]): ~2450/2187 = 1\6, ~567/500 = 216.942
 {{Optimal ET sequence|legend=1| 72, 210, 282, 354 }}
@@ Line 152: / Line 147: @@
 Mapping: {{mapping| 6 3 2 6 11 | 0 6 11 10 9 }}
-Optimal tuning (POTE): ~121/108 = 1\6, ~567/500 = 216.950
+Optimal tuning (CTE): ~55/49 = 1\6, ~567/500 = 216.9242 (~100/99 = 16.9242)
-{{Optimal ET sequence|legend=1| 72, 282, 354 }}
+{{Optimal ET sequence|legend=1| 72, 210e, 282, 354 }}
 Badness: 0.032096
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 540/539, 729/728, 1575/1573, 34398/34375
+Mapping: {{mapping| 6 3 2 6 11 -6 | 0 6 11 10 9 26 }}
+Optimal tuning (CTE): ~55/49 = 1\6, ~312/275 = 216.9332 (~105/104 = 16.9332)
+{{Optimal ET sequence|legend=1| 72, 210ef, 282, 354 }}
+Badness: 0.0258
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 540/539, 729/728, 936/935, 1156/1155, 1575/1573
+Mapping: {{mapping| 6 3 2 6 11 -6 5 | 0 6 11 10 9 26 18 }}
+Optimal tuning (CTE): ~55/49 = 1\6, ~17/15 = 216.9345 (~105/104 = 16.9345)
+{{Optimal ET sequence|legend=1| 72, 210efg, 282, 354 }}
+Badness: 0.0154
 == Garistearn ==
@@ Line 166: / Line 187: @@
 {{Mapping|legend=1| 94 149 0 264 | 0 0 1 0 }}
-{{Multival|legend=1| 0 94 0 149 0 -264 }}
 [[Optimal tuning]] ([[POTE]]): ~1029/1024 = 1\94, ~5/4 = 386.7805
@@ Line 226: / Line 245: @@
 : mapping generators: ~15/14, ~135/98
-{{Multival|legend=1| 30 20 50 -38 -5 60 }}
 [[Optimal tuning]] ([[CTE]]): ~15/14 = 1\10, ~135/98 = 553.810 (~36/35 = 46.190)
@@ Line 286: / Line 303: @@
 Badness: 0.018232
+=== 23-limit ===
+By equating 16/13 with 69/56 and 85/69 (enabling 56:69:85 chords), we find [[23/16]] at 2 generators underneath 6 periods (which is the [[5edo]] fifth, [[10edo|6\10]]).
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 221/220, 289/288, 351/350, 361/360, 456/455, 476/475, 897/896
+Mapping: {{mapping| 10 2 14 5 30 37 27 24 36 | 0 3 2 5 1 0 3 4 2 }}
+Optimal tuning (CTE): ~161/150 = 1\10, ~11/8 = 553.918 (~36/35 = 46.082)
+{{Optimal ET sequence|legend=1| 30dh, 50, 80, 130 }}
+Badness: 0.016719
 [[Category:Temperament clans]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Stearnsmic clan| ]] <!-- main article -->
 [[Category:Hades]] <!-- key article -->
 [[Category:Rank 2]]