Quartismic family: Difference between revisions
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The '''quartisma''' or '''Saquinlu-azo comma''' is a comma with a ratio of '''117440512/117406179''' and a [[monzo]] of {{monzo|24 -6 0 1 -5}}. It is an [[11-limit]] | The '''quartisma''' or '''Saquinlu-azo comma''' is a comma with a ratio of '''117440512/117406179''' and a [[monzo]] of {{monzo|24 -6 0 1 -5}}. It is an [[unnoticeable comma]] of the [[11-limit]]- specifically one of the the 2.9.7.11 subgroup- with a value of approximately 0.50619 cents. It is significant on account of being 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 [[22edo]], [[24edo]], [[44edo]], [[68edo]], [[90edo]], [[91edo]], [[92edo]], [[159edo]], and [[3125edo]]. | ||
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 04:51, 9 September 2020
The quartisma or Saquinlu-azo comma is a comma with a ratio of 117440512/117406179 and a monzo of [24 -6 0 1 -5⟩. It is an unnoticeable comma of the 11-limit- specifically one of the the 2.9.7.11 subgroup- with a value of approximately 0.50619 cents. It is significant on account of being 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 22edo, 24edo, 44edo, 68edo, 90edo, 91edo, 92edo, 159edo, and 3125edo.
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: