Mercator family: Difference between revisions

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 == Iodine ==
 Iodine is named after the 53rd chemical element and can be expressed as the 159 & 742 temperament.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: {{monzo| -19 14 -5 3 }}, {{monzo| 8 3 -20 12 }}
+[[Mapping]]: [{{val| 53 84 2 -53 }}, {{val| 0 0 3 5 }}]
+Mapping generators: ~3125/3087, 6075/3584
+[[Optimal tuning]] ([[CTE]]): ~6075/3584 = 913.7347
+{{Val list|legend=1| 159, 424cd, 583, 742, 2385d, 3127d }}
+[[Badness]]: 0.477
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 160083/160000, 820125/819896, 4302592/4296875
+Mapping: [{{val| 53 84 2 -53 143 }}, {{val| 0 0 3 5 1 }}]
+Optimal tuning (CTE): ~6075/3584 = 913.7322
+Optimal GPV sequence: {{Val list| 159, 424cd, 583, 742, 2385d, 3127d }}
+Badness: 0.0875
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 6656/6655, 34398/34375, 43904/43875, 59535/59488
+Mapping: [{{val| 53 84 2 -53 143 -46 }}, {{val| 0 0 3 5 1 6 }}]
+Optimal tuning (CTE): ~441/260 = 913.7115
+Optimal GPV sequence: {{Val list| 159, 424cdff, 583f, 742, 1643 }}
+Badness: 0.0476
 === 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 1701/1700, 8624/8619, 12376/12375, 14400/14399, 14875/14872, 225000/224939
+Comma list: 1701/1700, 6656/6655, 8624/8619, 12376/12375, 14875/14872
+Mapping: [{{val| 53 84 2 -53 143 -46 257 }}, {{val| 0 0 3 5 1 6 -1 }}]
-Mapping: [{{val|53	84	122	147	183	194	217}}, {{val|0	0	3	5	1	6	-1}}]
+Optimal tuning (CTE): ~441/260 = 913.7131
-POTE generator: = 8.0623
+Optimal GPV sequence: {{Val list| 159, 583f, 742 }}
-Optimal GPV sequence: {{EDOs|159, 742}}
+Badness: 0.0328
-Badness: 0.053105
 [[Category:Temperament families]]
-[[Category:Mercator]]
+[[Category:Mercator family]] <!-- main article -->
 [[Category:Rank 2]]