Minortonic family: Difference between revisions

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 As a 5-limit temperament, mitonic becomes minortonic, a super-accurate microtemperament tempering out the minortone comma, {{Monzo|-16 35 -17}}. Flipping that gives the 5-limit wedgie {{Multival|17 35 16}}, which tells us that 10/9 can be taken as the generator, with 17 of them giving a 6, 18 of them a 20/3, and 35 of them giving a 40. The generator should be tuned about 1/16 of a cent flat, with 6^(1/17) being 0.06423 cents flat and 40^(1/35) being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.
-However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171&nbsp;EDO]]. The wedgie is now {{Multival|17 35 -21 16 -81 -147}}, with 21 10/9 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.
+However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171edo|171 EDO]]. The wedgie is now {{Multival|17 35 -21 16 -81 -147}}, with 21 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.
 Subgroup: 2.3.5.7
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 [[Badness]]: 0.025184
+=== Mineral ===
+Extending mitonic to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: ''mineral'' (46&amp;171) and ''ore'' (46&amp;125). The mineral temperament tempers out 441/440 and 16384/16335 in the 11-limit (equating 10/9 with 49/44 and 21/20 with 22/21).
+Subgroup: 2.3.5.7.11
+Comma list: 441/440, 4375/4374, 16384/16335
+Mapping: [{{val|1 -1 -3 6 10}}, {{val|0 17 35 -21 -43}}]
+POTE generator: ~10/9 = 182.482
+Vals: {{Val list| 46, 125e, 171, 217, 605ee, 822dee }}
+Badness: 0.059060
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 364/363, 441/440, 3584/3575, 4375/4374
+Mapping: [{{val|1 -1 -3 6 10 11}}, {{val|0 17 35 -21 -43 -48}}]
+POTE generator: ~10/9 = 182.481
+Vals: {{Val list| 46, 125e, 171, 217, 605ee, 822dee }}
+Badness: 0.033140
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 364/363, 441/440, 595/594, 1156/1155, 3584/3575
+Mapping: [{{val|1 -1 -3 6 10 11 5}}, {{val|0 17 35 -21 -43 -48 -6}}]
+POTE generator: ~10/9 = 182.481
+Vals: {{Val list| 46, 125e, 171, 217, 605ee, 822dee }}
+Badness: 0.019792
+=== Ore ===
+The ore temperament tempers out 385/384 and 1331/1323 in the 11-limit, and maps [[11/8]] to three generators.
+Subgroup: 2.3.5.7.11
+Comma list: 385/384, 1331/1323, 4375/4374
+Mapping: [{{val|1 -1 -3 6 3}}, {{val|0 17 35 -21 3}}]
+POTE generator: ~10/9 = 182.449
+Vals: {{Val list| 46, 125, 171e }}
+Badness: 0.053662
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 352/351, 385/384, 1331/1323, 3267/3250
+Mapping: [{{val|1 -1 -3 6 3 11}}, {{val|0 17 35 -21 3 -48}}]
+POTE generator: ~10/9 = 182.470
+Vals: {{Val list| 46, 125, 171e, 388ee }}
+Badness: 0.046170
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 352/351, 385/384, 561/560, 715/714, 1452/1445
+Mapping: [{{val|1 -1 -3 6 3 11 5}}, {{val|0 17 35 -21 3 -48 -6}}]
+POTE generator: ~10/9 = 182.471
+Vals: {{Val list| 46, 125, 171e, 388ee }}
+Badness: 0.028423
 == Domain ==