Quartismic family: Difference between revisions
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Looks like I botched the calculations for 46edo- after a second run-though, I got "0", so I restore 46edo to the list, so my mistake for removing 46edo from the lists in the first place |
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The '''quartisma''' or '''Saquinlu-azo comma''' is an 11-limit comma with a ratio of '''117440512/117406179''' and a [[monzo]] of {{monzo|24 -6 0 1 -5}}. It has a value of approximately 0.50619 cents- meaning it is an [[unnoticeable comma]]- and it is the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. Examples of edos that temper out the quartisma are [[21edo]], [[22edo]], [[24edo]], [[43edo]], [[44edo]] and [[159edo]]. The comma is also a comma in the 2.9.7.11 subgroup. | The '''quartisma''' or '''Saquinlu-azo comma''' is an 11-limit comma with a ratio of '''117440512/117406179''' and a [[monzo]] of {{monzo|24 -6 0 1 -5}}. It has a value of approximately 0.50619 cents- meaning it is an [[unnoticeable comma]]- and it is the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. Examples of edos that temper out the quartisma are [[21edo]], [[22edo]], [[24edo]], [[43edo]], [[44edo]], [[46edo]] and [[159edo]]. The comma is also a comma in the 2.9.7.11 subgroup. | ||
The rank-3 '''quartismic or Saquinlu-azo temperament''' is the rank-3 2.3.7.11 temperament that tempers out this comma; equivalently it is the 22&24&159 temperament. This page will also list various rank-2 temperaments that temper out this comma and thus belong in the quartismic family. | The rank-3 '''quartismic or Saquinlu-azo temperament''' is the rank-3 2.3.7.11 temperament that tempers out this comma; equivalently it is the 22&24&159 temperament. This page will also list various rank-2 temperaments that temper out this comma and thus belong in the quartismic family. | ||
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No-five POTE generators: ~3/2 = 701.9826, ~33/32 = 53.3748 | No-five POTE generators: ~3/2 = 701.9826, ~33/32 = 53.3748 | ||
No-five edos: {{EDOs|21, 22, 24, 43, 89, 135, 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518, 7419}} | No-five edos: {{EDOs|21, 22, 24, 43, 46, 89, 135, 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518, 7419}} | ||
The following scale tree has been found: | The following scale tree has been found: | ||