Quartismic family: Difference between revisions

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The '''~~quartisma~~''' is the ratio 117440512/117406179 ~~(in [[~~monzo~~]] form,~~ {{monzo|24 -6 0 1 -5}}), or the ~~difference between six~~ [[~~33/32]] quarter tones and one [[77/64~~]] ~~minor third~~.

The '''quartismic family''' is a family of [[rank-4]] temperaments tempers out the [[quartisma]] – the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo|24 -6 0 1 -5}}, however, most of the members of this rank-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see [[the Quartercache]].

The ~~rank~~-~~3 '''~~quartismic ~~temperament'''~~ is the rank-3 2.3.7.11 ~~temperament that tempers out this comma; equivalently it is the~~ 22~~&24&~~159 ~~temperament~~. ~~The page will also~~ list ~~various rank~~-2 ~~temperaments that temper out this comma and thus belong in the quartismic family~~.

== Quartismic ==

The 11-limit parent comma for the quartismic family is the the quartisma with a ratio of 117440512/117406179 and a monzo of {{monzo| 24 -6 0 1 -5 }}. As the quartisma is an unnoticeable comma, this rank-4 temperament is a [[microtemperament]].

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 117440512/117406179

[[Mapping]]: [{{val| 1 0 0 1 5 }}, {{val| 0 1 0 1 -1 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 5 1 }}]

Mapping generators: ~2, ~3, ~5, ~33/32

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9742, ~5/4 = 386.3137, ~33/32 = 53.3683

{{Optimal ET sequence|legend=1| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}

[[Badness]]: 0.274 × 10<sup>-6</sup>

== Tridecimal quartismic ==

[[Subgroup]]: 2.3.5.7.11.13

[[Comma list]]: 6656/6655, 123201/123200

[[Mapping]]: [{{val| 1 0 0 1 5 6 }}, {{val| 0 1 0 1 -1 -3 }}, {{val| 0 0 1 0 0 1 }}, {{val| 0 0 0 5 1 3 }}]

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9695, ~5/4 = 386.3174, ~33/32 = 53.3698

{{Optimal ET sequence|legend=1| 22, 43f, 46, 65d, 89f, 111, 159, 224, 270, 494, 764, 1012, 1236, 1506, 2901, 3125, 3395, 8026e, 8296e, 11421e, 11691e, 12927e, 13421e, 16322ee, 16816dee }}

[[Badness]]: 1.739 × 10<sup>-6</sup>

[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:Microtemperaments]]

[[Category:Quartismic]]

[[Category:Rank 4]]

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-The '''quartisma''' is the ratio 117440512/117406179 (in [[monzo]] form, {{monzo|24 -6 0 1 -5}}), or the difference between six [[33/32]] quarter tones and one [[77/64]] minor third.
+{{Technical data page}}
+The '''quartismic family''' is a family of [[rank-4]] temperaments tempers out the [[quartisma]] – the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo|24 -6 0 1 -5}}, however, most of the members of this rank-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see [[the Quartercache]].
-The rank-3 '''quartismic temperament''' is the rank-3 2.3.7.11 temperament that tempers out this comma; equivalently it is the 22&24&159 temperament. The page will also list various rank-2 temperaments that temper out this comma and thus belong in the quartismic family.
+== Quartismic ==
+The 11-limit parent comma for the quartismic family is the the quartisma with a ratio of 117440512/117406179 and a monzo of {{monzo| 24 -6 0 1 -5 }}. As the quartisma is an unnoticeable comma, this rank-4 temperament is a [[microtemperament]].
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 117440512/117406179
+[[Mapping]]: [{{val| 1 0 0 1 5 }}, {{val| 0 1 0 1 -1 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 5 1 }}]
+Mapping generators: ~2, ~3, ~5, ~33/32
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9742, ~5/4 = 386.3137, ~33/32 = 53.3683
+{{Optimal ET sequence|legend=1| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}
+[[Badness]]: 0.274 × 10<sup>-6</sup>
+== Tridecimal quartismic ==
+[[Subgroup]]: 2.3.5.7.11.13
+[[Comma list]]: 6656/6655, 123201/123200
+[[Mapping]]: [{{val| 1 0 0 1 5 6 }}, {{val| 0 1 0 1 -1 -3 }}, {{val| 0 0 1 0 0 1 }}, {{val| 0 0 0 5 1 3 }}]
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9695, ~5/4 = 386.3174, ~33/32 = 53.3698
+{{Optimal ET sequence|legend=1| 22, 43f, 46, 65d, 89f, 111, 159, 224, 270, 494, 764, 1012, 1236, 1506, 2901, 3125, 3395, 8026e, 8296e, 11421e, 11691e, 12927e, 13421e, 16322ee, 16816dee }}
+[[Badness]]: 1.739 × 10<sup>-6</sup>
+[[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Microtemperaments]]
+[[Category:Quartismic]]
+[[Category:Rank 4]]