Quartismic family: Difference between revisions
23edo removed from the list of EDOs that temper out the quartisma due to failing the monzo test despite seeming to have the telltale patent val relations- a sign of inconsistency. |
Added 44edo to the list of examples of EDOs that temper out the quartisma- it's surprising that none of the computer checks run by Flora have caught this one in light of the mathematical confirmation |
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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]], [[46edo]] and [[159edo]]. | 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 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. | ||
Revision as of 18:50, 8 September 2020
The quartisma or Saquinlu-azo comma is an 11-limit comma with a ratio of 117440512/117406179 and a monzo of [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 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.
No-five map: [<1 0 1 5], <0 1 1 -1], <0 0 5 1]]
No-five POTE generators: ~3/2 = 701.9826, ~33/32 = 53.3748
No-five 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 quartismic MOS scales have been found: