Minortonic family: Difference between revisions
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== Mitonic == | == Mitonic == | ||
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. | 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. | ||
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=== Mineral === | === Mineral === | ||
Extending mitonic to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: ''mineral'' (46&171) and ''ore'' (46&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). | Extending mitonic to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: ''mineral'' (46&171) and ''ore'' (46&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). In the 17-limit, both mineral and ore temper out 833/832, 1225/1224, 1701/1700, and 4096/4095 (2.3.5.7.13.17 commas). | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||