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 Badness: 0.022036
+== Trinity ==
+The ''trinity'' temperament (152&amp;159) tempers out the [[meter comma]], 703125/702464. It splits the interval of acute minor tenth (~243/100, an octave plus acute minor third) in three. It was so named for the following reason - 133\311 (133 steps of 311edo) is a possible generator, which is placed around 3\7 (1.1¢ flat), three of which makes acute minor third of ~243/200 with octave reduction.
+Subgroup: 2.3.5.7
+[[Comma list]]: 703125/702464, 1600000/1594323
+[[Mapping]]: [{{val|1 8 19 46}}, {{val|0 -15 -39 -101}}]
+{{Multival|legend=1| 15 39 101 27 118 125 }}
+[[POTE generator]]: ~168/125 = 513.178
+{{Val list|legend=1| 152, 311, 463, 774 }}
+[[Badness]]: 0.119453
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 3025/3024, 4000/3993, 19712/19683
+Mapping: [{{val|1 8 19 46 18}}, {{val|0 -15 -39 -101 -34}}]
+POTE generator: ~121/90 = 513.177
+Optimal GPV sequence: {{Val list| 152, 311, 463, 774, 1237e }}
+Badness: 0.031296
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 625/624, 1575/1573, 2080/2079, 13720/13689
+Mapping: [{{val|1 8 19 46 18 64}}, {{val|0 -15 -39 -101 -34 -141}}]
+POTE generator: ~35/26 = 513.182
+Optimal GPV sequence: {{Val list| 152f, 311 }}
+Badness: 0.026418
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 595/594, 625/624, 833/832, 1575/1573, 8624/8619
+Mapping: [{{val|1 8 19 46 18 64 -22}}, {{val|0 -15 -39 -101 -34 -141 61}}]
+POTE generator: ~35/26 = 513.186
+Optimal GPV sequence: {{Val list| 152f, 159, 311, 1092cdg, 1403cdg, 1714cdeg }}
+Badness: 0.025588
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 595/594, 625/624, 833/832, 969/968, 1216/1215, 1575/1573
+Mapping: [{{val|1 8 19 46 18 64 -22 53}}, {{val|0 -15 -39 -101 -34 -141 61 -114}}]
+POTE generator: ~35/26 = 513.185
+Optimal GPV sequence: {{Val list| 152f, 159, 311, 1403cdgh, 1714cdegh, 2025cdefgghh, 2336bccdefgghh }}
+Badness: 0.018412
+=== 23-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 595/594, 625/624, 760/759, 833/832, 875/874, 969/968, 1105/1104
+Mapping: [{{val|1 8 19 46 18 64 -22 53 49}}, {{val|0 -15 -39 -101 -34 -141 61 -114 -104}}]
+POTE generator: ~35/26 = 513.185
+Optimal GPV sequence: {{Val list| 152f, 159, 311, 1092cdgh, 1403cdgh, 1714cdeghi }}
+Badness: 0.014343
+=== 29-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29
+Comma list: 595/594, 625/624, 760/759, 784/783, 833/832, 875/874, 969/968, 1045/1044
+Mapping: [{{val|1 8 19 46 18 64 -22 53 49 72}}, {{val|0 -15 -39 -101 -34 -141 61 -114 -104 -157}}]
+POTE generator: ~35/26 = 513.186
+Optimal GPV sequence: {{Val list| 152fj, 159, 311, 781dh, 1092cdgh, 1403cdgh }}
+Badness: 0.012038
 == Familia ==