@@ Line 75: / Line 75: @@
 Comma list: 1331/1323, 19712/19683
-Subgroup-val mapping: {{mapping| 1 1 0 1 | 0 5 24 21 }}
+{{Mapping|legend=2| 1 1 0 1 | 0 5 24 21 }}
 Optimal tunings:
@@ Line 90: / Line 90: @@
 Comma list: 352/351, 729/728, 1331/1323
-Subgroup-val mapping: {{mapping| 1 1 0 1 3 | 0 5 24 21 6 }}
+{{Mapping|legend=2| 1 1 0 1 3 | 0 5 24 21 6 }}
 Optimal tunings:
@@ Line 124: / Line 124: @@
 === Hemif ===
-Hemif is the no-5 [[restriction]] of [[hemififths]], and the add-7 [[extension]] of [[namo]].
+Hemif tempers out the [[parahemif comma]], equating a [[Pythagorean apotome]] with a stack of two septimal third-tones of [[28/27]], and splits the fifth in two. In this temperament, the interval class of [[7/1|7]] is found at +13 steps, as a semi-augmented sixth (C–A{{demisharp2}}). It also equates the large septimal diesis of [[49/48]] with the [[Pythagorean comma]]. This means the fifth should be tuned sharp and the septimal third-tone should be flattened to a somewhat large quartertone which can be used as the undecimal quartertone of [[33/32]], leading to a natural 11-limit extension where [[243/242]] and [[896/891]] are tempered out.
+Hemif is the common [[restriction]] of [[hemififths]] (41 & 58) and [[salsa]] (24 & 41), and the add-7 [[extension]] of [[namo]]. A [[weak extension]] of it is [[sruti]] (24 & 34d).
 [[Subgroup]]: 2.3.7
@@ Line 150: / Line 152: @@
 Comma list: 243/242, 896/891
-Subgroup-val mapping: {{mapping| 1 1 -1 2 | 0 2 13 5 }}
+{{Mapping|legend=2| 1 1 -1 2 | 0 2 13 5 }}
 {{Mapping|legend=4| 1 1 0 -1 2 | 0 2 0 13 5 }}
@@ Line 188: / Line 190: @@
 Comma list: 243/242, 896/891, 1083/1078
-Subgroup-val mapping: {{mapping| 1 1 -1 2 0 | 0 4 26 10 29 }}
+{{Mapping|legend=2| 1 1 -1 2 0 | 0 4 26 10 29 }}
 : mapping generators: ~2, ~21/19
@@ Line 226: / Line 228: @@
 Comma list: 243/242, 65536/65219
-Subgroup-val mapping: {{mapping| 1 1 5 2 | 0 4 -15 10 }}
+{{Mapping|legend=2| 1 1 5 2 | 0 4 -15 10 }}
 Optimal tunings:
@@ Line 241: / Line 243: @@
 Comma list: 243/242, 513/512, 1083/1078
-Subgroup-val mapping: {{mapping| 1 1 5 2 6 | 0 4 -15 10 -12 }}
+{{Mapping|legend=2| 1 1 5 2 6 | 0 4 -15 10 -12 }}
 Optimal tunings:
@@ Line 276: / Line 278: @@
 Comma list: 896/891, 26411/26244
-Subgroup-val mapping: {{mapping| 1 0 -1 6 | 0 5 12 -8 }}
+{{Mapping|legend=2| 1 0 -1 6 | 0 5 12 -8 }}
 Optimal tunings:
@@ Line 291: / Line 293: @@
 Comma list: 144/143, 343/338, 729/728
-Subgroup-val mapping: {{mapping| 1 0 -1 6 -2 | 0 5 12 -8 18 }}
+{{Mapping|legend=2| 1 0 -1 6 -2 | 0 5 12 -8 18 }}
 Optimal tunings:
@@ Line 306: / Line 308: @@
 Comma list: 144/143, 232/231, 343/338, 729/728
-Subgroup-val mapping: {{mapping| 1 0 -1 6 -2 2 | 0 5 12 -8 18 9 }}
+{{Mapping|legend=2| 1 0 -1 6 -2 2 | 0 5 12 -8 18 9 }}
 Optimal tunings:
@@ Line 321: / Line 323: @@
 Comma list: 352/351, 364/363, 26411/26244
-Subgroup-val mapping: {{mapping| 1 0 -1 6 11 | 0 5 12 -8 -23 }}
+{{Mapping|legend=2| 1 0 -1 6 11 | 0 5 12 -8 -23 }}
 Optimal tunings:
@@ Line 336: / Line 338: @@
 Comma list: 169/168, 896/891, 26411/26244
-Subgroup-val mapping: {{mapping| 1 0 -1 6 1 | 0 10 24 -16 17 }}
+{{Mapping|legend=2| 1 0 -1 6 1 | 0 10 24 -16 17 }}
 : mapping generators: ~2, ~143/128
@@ Line 352: / Line 354: @@
 Comma list: 784/783, 5887/5832
-Subgroup-val mapping: {{mapping| 1 0 -1 2 | 0 5 12 9 }}
+{{Mapping|legend=2| 1 0 -1 2 | 0 5 12 9 }}
 Optimal tunings:
@@ Line 391: / Line 393: @@
 Comma list: 99/98, 243/242
-Subgroup-val mapping: {{mapping| 1 -1 -3 -3 | 0 4 9 10 }}
+{{Mapping|legend=2| 1 -1 -3 -3 | 0 4 9 10 }}
 {{Mapping|legend=4| 1 -1 0 -3 -3 | 0 4 0 9 10 }}
@@ Line 408: / Line 410: @@
 Comma list: 78/77, 99/98, 243/242
-Subgroup-val mapping: {{mapping| 1 -1 -3 -3 -6 | 0 4 9 10 15 }}
+{{Mapping|legend=2| 1 -1 -3 -3 -6 | 0 4 9 10 15 }}
 {{Mapping|legend=4| 1 -1 0 -3 -3 -6 | 0 4 0 9 10 15}}
@@ Line 425: / Line 427: @@
 Comma list: 99/98, 144/143, 243/242
-Subgroup-val mapping: {{mapping| 1 -1 -3 -3 5 | 0 4 9 10 -2 }}
+{{Mapping|legend=2| 1 -1 -3 -3 5 | 0 4 9 10 -2 }}
 {{Mapping|legend=4| 1 -1 0 -3 -3 5 | 0 4 0 9 10 -2 }}
@@ Line 444: / Line 446: @@
 Comma list: 99/98, 243/242, 363/361
-Subgroup-val mapping: {{mapping| 2 2 3 4 5 | 0 4 9 10 12 }}
+{{Mapping|legend=2| 2 2 3 4 5 | 0 4 9 10 12 }}
 : mapping generators: ~209/147, ~21/19
@@ Line 504: / Line 506: @@
 Comma list: 99/98, 864/847
-Subgroup-val mapping: {{mapping| 1 1 2 3 | 0 5 7 4 }}
+{{Mapping|legend=2| 1 1 2 3 | 0 5 7 4 }}
 {{Mapping|legend=4| 1 1 0 2 3 | 0 5 0 7 4 }}
@@ Line 521: / Line 523: @@
 Comma list: 78/77, 99/98, 144/143
-Subgroup-val mapping: {{mapping| 1 1 2 3 3 | 0 5 7 4 6 }}
+{{Mapping|legend=2| 1 1 2 3 3 | 0 5 7 4 6 }}
 {{Mapping|legend=4| 1 1 0 2 3 3 | 0 5 0 7 4 6 }}
@@ Line 563: / Line 565: @@
 Comma list: 243/242, 2401/2376
-Subgroup-val mapping: {{mapping| 1 1 2 2 | 0 8 11 20 }}
+{{Mapping|legend=2| 1 1 2 2 | 0 8 11 20 }}
 Optimal tunings:
@@ Line 578: / Line 580: @@
 Comma list: 133/132, 243/242, 343/342
-Subgroup-val mapping: {{mapping| 1 1 2 2 3 | 0 8 11 20 17 }}
+{{Mapping|legend=2| 1 1 2 2 3 | 0 8 11 20 17 }}
 Optimal tunings:
@@ Line 633: / Line 635: @@
 Comma list: 43923/43904, 5767168/5764801
-Subgroup-val mapping: {{mapping| 1 -4 3 5 | 0 29 -1 -8 }}
+{{Mapping|legend=2| 1 -4 3 5 | 0 29 -1 -8 }}
 Optimal tunings:
@@ Line 676: / Line 678: @@
 Comma list: 896/891, 1331/1323
-Subgroup-val mapping: {{mapping| 1 0 -21 -14 | 0 1 15 11 }}
+{{Mapping|legend=2| 1 0 -21 -14 | 0 1 15 11 }}
 {{Mapping|legend=4| 1 0 0 -21 -14 | 0 1 0 15 11 }}
@@ Line 693: / Line 695: @@
 Comma list: 169/168, 352/351, 364/363
-Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 | 0 1 15 11 8 }}
+{{Mapping|legend=2| 1 0 -21 -14 -9 | 0 1 15 11 8 }}
 {{Mapping|legend=4| 1 0 0 -21 -14 -9 | 0 1 0 15 11 8 }}
@@ Line 710: / Line 712: @@
 Comma list: 169/168, 208/207, 352/351, 364/363
-Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 -5 | 0 1 15 11 8 6 }}
+{{Mapping|legend=2| 1 0 -21 -14 -9 -5 | 0 1 15 11 8 6 }}
 {{Mapping|legend=4| 1 0 0 -21 -14 -9 0 0 -5 | 0 1 0 15 11 8 0 0 6 }}
@@ Line 727: / Line 729: @@
 Comma list: 169/168, 208/207, 232/231, 352/351, 364/363
-Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 -5 -38 | 0 1 15 11 8 6 27 }}
+{{Mapping|legend=2| 1 0 -21 -14 -9 -5 -38 | 0 1 15 11 8 6 27 }}
 {{Mapping|legend=4| 1 0 0 -21 -14 -9 -5 0 0 -38 | 0 1 0 15 11 8 0 0 6 27 }}
@@ Line 794: / Line 796: @@
 Comma list: {{monzo| -42 -2 -5 16 }}, {{monzo| 10 -46 29 -5 }}
-Subgroup-val mapping: {{mapping| 1 -126 -214 -80 | 0 439 746 288 }}
+{{Mapping|legend=2| 1 -126 -214 -80 | 0 439 746 288 }}
 Optimal tunings:
@@ Line 809: / Line 811: @@
 Comma list: 39337984/39328497, {{monzo| 0 -14 7 4 -3 }}, {{monzo| -18 -24 14 -1 5 }}
-Subgroup-val mapping: {{mapping| 1 -126 -214 -80 -18 | 0 439 746 288 76 }}
+{{Mapping|legend=2| 1 -126 -214 -80 -18 | 0 439 746 288 76 }}
 Optimal tunings:
@@ Line 824: / Line 826: @@
 Comma list: 10081799/10077696, 10754912/10744731, 39337984/39328497, 480024727/480020256
-Subgroup-val mapping: {{mapping| 1 -126 -214 -80 -18 -171 | 0 439 746 288 76 603 }}
+{{Mapping|legend=2| 1 -126 -214 -80 -18 -171 | 0 439 746 288 76 603 }}
 Optimal tunings:
@@ Line 963: / Line 965: @@
 Comma list: 144/143, 729/704
-Subgroup-val mapping: {{mapping| 1 0 -6 10 | 0 1 6 -4 }}
+{{Mapping|legend=2| 1 0 -6 10 | 0 1 6 -4 }}
 Optimal tunings:
@@ Line 978: / Line 980: @@
 Comma list: 363/361, 729/704
-Subgroup-val mapping: {{mapping| 1 0 -6 -6 | 0 2 12 13 }}
+{{Mapping|legend=2| 1 0 -6 -6 | 0 2 12 13 }}
 : mapping generators: ~2, ~19/11
@@ Line 1,016: / Line 1,018: @@
 Comma list: 512/507, 1352/1331
-Subgroup-val mapping: {{mapping| 1 -3 5 6 | 0 6 -2 -3 }}
+{{Mapping|legend=2| 1 -3 5 6 | 0 6 -2 -3 }}
 : mapping generators: ~2, ~22/13
@@ Line 1,052: / Line 1,054: @@
 Comma list: 352/351, 531674/531441
-Subgroup-val mapping: {{mapping| 1 1 0 3 | 0 5 21 6 }}
+{{Mapping|legend=2| 1 1 0 3 | 0 5 21 6 }}
 Optimal tunings:
@@ Line 1,186: / Line 1,188: @@
 Comma list: 3888/3887, 12168/12167
-Subgroup-val mapping: {{mapping| 1 -5 -7 -7 | 0 8 13 14 }}
+{{Mapping|legend=2| 1 -5 -7 -7 | 0 8 13 14 }}
 Optimal tunings:

No-fives subgroup temperaments: Difference between revisions