Maja family: Difference between revisions

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-__FORCETOC__
+{{Technical data page}}
-=Maja=
+The '''maja family''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] the [[maja comma]], {{monzo| -3 -23 17 }} = 762939453125/753145430616.
-Comma: 762939453125/753145430616
-POTE generator: ~125/81 = 747.198
+Maja was named by [[Petr Pařízek]] in 2011 for 13/10 is a generator and that ''M'' and ''J'' are the 13th letter and the 10th letter, respectively<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. It is unrelated to either the [[interval quality|major quality]] or [[magic|magic temperament]].
-Map: [&lt;1 8 11|, &lt;0 -17 -23|]
+== Maja ==
+[[Subgroup]]: 2.3.5
-EDOs: 45, 53, 432, 485, 538, 591, 644, 697, 750
+[[Comma list]]: 762939453125/753145430616
-Badness: 0.3610
+{{Mapping|legend=1| 1 8 11 | 0 -17 -23 }}
-==7-limit==
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.198
-Commas: 2430/2401, 3125/3087
-POTE generator: ~125/81 = 747.145
+{{Optimal ET sequence|legend=1| 8, 45, 53, 432, 485, 538, 591, 644, 697, 750, 803c }}
-Map: [&lt;1 8 11 13|, &lt;0 -17 -23 -27|]
+[[Badness]]: 0.361013
-EDOs: 45, 53, 469cd
+== Septimal maja ==
+[[Subgroup]]: 2.3.5.7
-Badness: 0.0894
+[[Comma list]]: 2430/2401, 3125/3087
-==11-limit==
+{{Mapping|legend=1| 1 8 11 13 | 0 -17 -23 -27 }}
-Commas: 99/98, 121/120, 3125/3087
-POTE generator: ~125/81 = 747.100
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~54/35 = 747.145
-Map: [&lt;1 8 11 13 11|, &lt;0 -17 -23 -27 -20|]
+{{Optimal ET sequence|legend=1| 8d, 45, 53 }}
-EDOs: 45e, 53
+[[Badness]]: 0.089454
-Badness: 0.0500
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-==13-limit==
+Comma list: 99/98, 121/120, 3125/3087
-Commas: 176/175, 275/273, 325/324, 540/539
-POTE generator: ~125/81 = 747.095
+Mapping: {{mapping| 1 8 11 13 11 | 0 -17 -23 -27 -20 }}
-Map: [&lt;1 8 11 13 11 12|, &lt;0 -17 -23 -27 -20 -22|]
+Optimal tuning (POTE): ~2 = 1\1, ~54/35 = 747.100
-EDOs: 45ef, 53
+{{Optimal ET sequence|legend=1| 8d, 45e, 53 }}
-Badness: 0.0275
+Badness: 0.049991
-=Majo=
+=== 13-limit ===
-Commas: 6144/6125, 1250000/1240029
+Subgroup: 2.3.5.7.11.13
-POTE generator: ~125/81 = 747.264
+Comma list: 99/98, 121/120, 169/168, 275/273
-Map: [&lt;1 8 11 -7|, &lt;0 -17 -23 26|]
+Mapping: {{mapping| 1 8 11 13 11 12 | 0 -17 -23 -27 -20 -22 }}
-Wedgie: &lt;&lt;17 23 -26 -3 -89 -125||
+Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.095
-EDOs: 53, 167, 220
+{{Optimal ET sequence|legend=1| 8d, 45ef, 53 }}
-Badness: 0.1405
+Badness: 0.027532
+== Majo ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 6144/6125, 1250000/1240029
+{{Mapping|legend=1| 1 8 11 -7 | 0 -17 -23 26 }}
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.264
+{{Optimal ET sequence|legend=1| 53, 167, 220, 493bd, 713bdd }}
+[[Badness]]: 0.140489
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 2200/2187, 3388/3375, 6144/6125
+Mapping: {{mapping| 1 8 11 -7 31 | 0 -17 -23 26 -73 }}
+Optimal tuning (POTE): ~2 = 1\1, ~77/50 = 747.287
+{{Optimal ET sequence|legend=1| 53, 114e, 167, 220, 387bd }}
+Badness: 0.081931
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 325/324, 352/351, 1001/1000, 2704/2695
+Mapping: {{mapping| 1 8 11 -7 31 12 | 0 -17 -23 26 -73 -22 }}
+Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.286
+{{Optimal ET sequence|legend=1| 53, 114e, 167, 220, 387bd }}
+Badness: 0.043128
+== Notes ==
+[[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Maja family| ]] <!-- main article -->
+[[Category:Maja| ]] <!-- key article -->
+[[Category:Rank 2]]