Semicanousmic clan: Difference between revisions

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 * ''[[Semicanou]]'', {9801/9800, 14641/14580} → [[Canou family #Semicanou|Canou family]]
-Considered below are deuteromere, the no-7 subgroup temperament, and vonacimes, but we can begin by looking at the rank-4 temperament.
+Considered below are synsem and vonacimes, in addition to deuteromere, the no-7 subgroup temperament, but we can begin by looking at the rank-4 temperament.
 == Semicanousmic ==
 : ''For the full 19-limit extension, see [[Rank-4 temperament #Semicanousmic (14641/14580)]].''
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 14641/14580
@@ Line 19: / Line 19: @@
 Mapping generators: ~2, ~3, ~18/11, ~7
-[[POTE generator]]s: ~3/2 = 702.2503, ~18/11 = 854.5421, ~7/4 = 968.6866
+Optimal tuning ([[POTE]]): ~3/2 = 702.2503, ~18/11 = 854.5421, ~7/4 = 968.6866
 {{Val list|legend=1| 14c, 17c, 24, 31, 63, 80, 87, 111, 118, 198, 212, 292, 323, 410, 851e }}
@@ Line 26: / Line 26: @@
 == Deuteromere ==
-Subgroup: 2.3.5.11
+[[Subgroup]]: 2.3.5.11
 [[Comma list]]: 14641/14580
@@ Line 34: / Line 34: @@
 Sval mapping generators: ~2, ~3, ~18/11
-[[POTE generator]]s: ~3/2 = 702.2503, ~18/11 = 854.5421
+Optimal tuning ([[POTE]]): ~3/2 = 702.2503, ~18/11 = 854.5421
 {{Val list|legend=1| 7, 17c, 24, 31, 56, 73, 80, 87, 118, 205, 323, 528e }}
@@ Line 47: / Line 47: @@
 Sval mapping: [{{val| 1 0 2 1 -4 }}, {{val| 0 1 2 2 6 }}, {{val| 0 0 -4 -1 -2 }}]
-POTE generators: ~3/2 = 702.3162, ~18/11 = 854.5619
+Optimal tuning (POTE): ~3/2 = 702.3162, ~18/11 = 854.5619
 Optimal GPV sequence: {{val list| 24, 31g, 55g, 56gg, 63, 70c, 80gg, 87, 111, 118, 205, 528e, 733e }}
@@ Line 60: / Line 60: @@
 Sval mapping: [{{val| 1 0 2 1 -4 -4 }}, {{val| 0 1 2 2 6 7 }}, {{val| 0 0 -4 -1 -2 -4 }}]
-POTE generators: ~3/2 = 702.2578, ~18/11 = 854.5595
+Optimal tuning (POTE): ~3/2 = 702.2578, ~18/11 = 854.5595
 Optimal GPV sequence: {{val list| 24, 55gh, 63, 70c, 80gghh, 87, 94, 111, 118, 205, 323, 528e }}
 Badness: 0.403 × 10<sup>-3</sup>
+== Synsem ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 14641/14580, 19712/19683
+[[Mapping]]: [{{val| 1 0 2 -9 1 }}, {{val| 0 1 2 7 2 }}, {{val| 0 0 -4 1 -1 }}]
+Mapping generators: ~2, ~3, ~18/11
+Optimal tuning ([[POTE]]): ~3/2 = 702.0109, ~18/11 = 854.4606
+{{Val list|legend=1| 7d, 17c, 24, 77c, 87d, 94, 111, 118, 212, 323, 441e }}
+[[Badness]]: 3.26 × 10<sup>-3</sup>
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 1573/1568, 2080/2079, 14641/14580
+Mapping: [{{val| 1 0 2 -9 1 -15 }}, {{val| 0 1 2 7 2 10 }}, {{val| 0 0 -4 1 -1 4 }}]
+Optimal tuning (POTE): ~3/2 = 702.1049, ~18/11 = 854.5542
+Optimal GPV sequence: {{Val list| 94, 111, 205, 212, 323, 535ef }}
+Badness: 3.01 × 10<sup>-3</sup>
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 442/441, 561/560, 715/714, 14641/14580
+Mapping: [{{val| 1 0 2 -9 1 -15 -4 }}, {{val| 0 1 2 7 2 10 6 }}, {{val| 0 0 -4 1 -1 4 -2 }}]
+Optimal tuning (POTE): ~3/2 = 702.1272, ~18/11 = 854.5224
+Optimal GPV sequence: {{Val list| 94, 111, 205, 212g, 323 }}
+Badness: 1.69 × 10<sup>-3</sup>
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 442/441, 561/560, 715/714, 1216/1215, 1445/1444
+Mapping: [{{val| 1 0 2 -9 1 -15 -4 -4 }}, {{val| 0 1 2 7 2 10 6 7 }}, {{val| 0 0 -4 1 -1 4 -2 -4 }}]
+Optimal tuning (POTE): ~3/2 = 702.1340, ~18/11 = 854.5120
+Optimal GPV sequence: {{Val list| 94, 111, 205, 212gh, 323 }}
+Badness: 1.27 × 10<sup>-3</sup>
 == Vonacimes ==
 Vonacimes (''semicanou'' spelt backwards) is in a certain sense dual to semicanou. It splits the perfect twelfth into two, whereas semicanou splits the octave.
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 14641/14580, 160083/160000
@@ Line 77: / Line 131: @@
 Mapping generators: ~2, ~400/231, ~200/189
-[[POTE generator]]s: ~400/231 = 951.1931, ~200/189 = 96.5791
+Optimal tuning ([[POTE]]): ~400/231 = 951.1931, ~200/189 = 96.5791
 {{Val list|legend=1| 87, 111, 125, 198, 212, 323, 410 }}
-[[Badness]]: 3.946 × 10<sup>-3</sup>
+[[Badness]]: 3.95 × 10<sup>-3</sup>
 === 13-limit ===
@@ Line 90: / Line 144: @@
 Mapping: [{{val| 1 0 2 7 1 1 }}, {{val| 0 2 0 -6 3 3 }}, {{val| 0 0 4 7 1 4 }}]
-POTE generators: ~26/15 = 951.2412, ~55/52 = 96.6292
+Optimal tuning (POTE): ~26/15 = 951.2412, ~55/52 = 96.6292
 Optimal GPV sequence: {{val list| 87, 111, 198, 323, 410 }}
-Badness: 1.893 × 10<sup>-3</sup>
+Badness: 1.89 × 10<sup>-3</sup>
 === 17-limit ===
@@ Line 103: / Line 157: @@
 Mapping: [{{val| 1 0 2 7 1 1 -4 }}, {{val| 0 2 0 -6 3 3 10 }}, {{val| 0 0 4 7 1 4 2 }}]
-POTE generators: ~26/15 = 951.1985, ~55/52 = 96.5941
+Optimal tuning (POTE): ~26/15 = 951.1985, ~55/52 = 96.5941
 Optimal GPV sequence: {{val list| 87, 111, 198g, 212g, 299, 323, 410 }}
-Badness: 1.903 × 10<sup>-3</sup>
+Badness: 1.90 × 10<sup>-3</sup>
 === 19-limit ===
@@ Line 116: / Line 170: @@
 Mapping: [{{val| 1 0 2 7 1 1 -4 -4 }}, {{val| 0 2 0 -6 3 3 10 10 }}, {{val| 0 0 4 7 1 4 2 4 }}]
-POTE generators: ~26/15 = 951.1592, ~55/52 = 96.5502
+Optimal tuning (POTE): ~26/15 = 951.1592, ~55/52 = 96.5502
 Optimal GPV sequence: {{val list| 87, 111, 198gh, 212gh, 299, 323, 410, 622ef }}
-Badness: 1.733 × 10<sup>-3</sup>
+Badness: 1.73 × 10<sup>-3</sup>
 [[Category:Temperament clans]]
 [[Category:Semicanousmic clan| ]] <!-- main article -->
 [[Category:Rank 3]]