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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 [[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]].
| | #redirect [[Catalog of rank-4 temperaments #Quartismic (117440512/117406179)]] |
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| 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 map: [<1 0 1 5], <0 1 1 -1], <0 0 5 1]]
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| No-five POTE generators: ~3/2 = 701.9826, ~33/32 = 53.3748
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| No-five edos: {{EDOs|21, 22, 24, 43, 46, 89, 135, 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518, 7419}}
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| The following scale tree has been found:
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| * [http://www.microtonalsoftware.com/scale-tree.html?left=12&right=11&rr=1200&ioi=106.71461627796054 1200-106.71461627796054-12-11 Scale Tree]
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| The following quartismic MOS scales have been found:
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| * [https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(53.37418112074753%2C%202%2F1)%2C%2013%7C9&data=53.374181%0A106.748362%0A160.122543%0A213.496724%0A266.870906%0A320.245087%0A373.619268%0A426.993449%0A480.367630%0A533.741811%0A587.115992%0A640.490173%0A693.864355%0A719.632370%0A773.006551%0A826.380732%0A879.754913%0A933.129094%0A986.503276%0A1039.877457%0A1093.251638%0A1146.625819%0A1200.000000&freq=440&midi=69&vert=5&horiz=1&colors=&waveform=triangle&env=organ Rank 2 scale (53.37418112074753, 2/1), 13|9]
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| * [https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(106.71461627796054%2C%201200.0)%2C%205%7C5&data=106.714616%0A213.429233%0A320.143849%0A426.858465%0A533.573081%0A666.426919%0A773.141535%0A879.856151%0A986.570767%0A1093.285384%0A1200.000000&freq=440&midi=69&vert=9&horiz=1&colors=&waveform=triangle&env=organ Rank 2 scale (106.71461627796054, 1200.0), 5|5]
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| [[Category:Quartismic]]
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| [[Category:Rank 2]]
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| [[Category:Temperament]]
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