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Quartismic family: Difference between revisions

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{{todo|inline=1| discuss title | comment= This doesn't follow the definition of temperament family }}
{{todo|inline=1| discuss title | comment= This doesn't follow the definition of temperament family }}


The '''quartismic family''' is built up from temperaments of various ranks that temper out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo|24 -6 0 1 -5}}. Among the members of this family are Quartismatic, Altierran, Meanquarter, Coin, Escapismic, Dietismic, Kleirtismic, and Doublefour.
The '''quartismic family''' is built up from temperaments of various ranks that temper out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo|24 -6 0 1 -5}}. Among the members of this family are quartismatic, altierran, meanquarter, coin, escapismic, dietismic, kleirtismic, and doublefour.


== Quartismic ==
== Quartismic ==


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


Comma: 117440512/117406179
Subgroup: 2.3.5.7.11


POTE generators: ~3/2 = 701.9826, ~5/4 = 386.3427, ~33/32 = 53.3748
[[Comma list]]: 117440512/117406179


Map: [<1 0 0 1 5|, <0 1 0 1 -1|, <0 0 1 0 0|, <0 0 0 5 1|]
[[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 }}]


Wedgie: <<<<5 1 0 -6 -24||||
{{Multival|legend=1|rank=4| 5 1 0 -6 -24 }}


EDOs: {{EDOs| 21, 22, 24, 25, 43, 45, 46, 67, 68, 89, 90, 91, 92, 110, 111, 113, 114, 132, 134, 135, 138, 156, 157, 159, 178, 179, 180, 181, 202, 224, 270, 313, 359, 494, 629, 653, 742, 877, 1012, 1236, 1506, 2159, 2248, 2383, 2518, 3125, 7419 }}
[[POTE generator]]s: ~3/2 = 701.9826, ~5/4 = 386.3427, ~33/32 = 53.3748


Badness: 0.274 × 10<sup>-6</sup>
{{Val list|legend=1| 21, 22, 24, 25, 43, 45, 46, 67, 68, 89, 90, 91, 92, 110, 111, 113, 114, 132, 134, 135, 138, 156, 157, 159, 178, 179, 180, 181, 202, 224, 270, 313, 359, 494, 629, 653, 742, 877, 1012, 1236, 1506, 2159, 2248, 2383, 2518, 3125, 7419 }}


=== 13-limit ===
[[Badness]]: 0.274 × 10<sup>-6</sup>
 
Commas:
 
POTE generator:
 
Map:
 
Wedgie:
 
EDOs:
 
Badness:
 
=== 17-limit ===
 
Commas:
 
POTE generator:
 
Map:
 
Wedgie:
 
EDOs:
 
Badness:


== Quartismatic ==
== Quartismatic ==


There are some temperaments in the quartismic family in which the quartisma is tempered out, but without any sort of five-limit representation. This particular temperament is the parent temperament of all such no-fives children, and is referred to as '''Saquinlu-azo temperament''' in color notation.
There are some temperaments in the quartismic family in which the quartisma is tempered out, but without any sort of five-limit representation. This particular temperament is the parent temperament of all such no-fives children, and is referred to as '''Saquinlu-azo temperament''' in color notation.


Comma: 117440512/117406179
Subgroup: 2.3.7.11


POTE generators: ~3/2 = 701.9826, ~33/32 = 53.3748
[[Comma list]]: 117440512/117406179


Map: [<1 0 1 5|, <0 1 1 -1|, <0 0 5 1|]
[[Sval]] [[mapping]]: [{{val| 1 0 1 5 }}, {{val| 0 1 1 -1 }}, {{val| 0 0 5 1 }}]


Wedgie:
[[POTE generator]]s: ~3/2 = 701.9826, ~33/32 = 53.3748


EDOs: {{EDOs| 21, 22, 24, 43, 46, 89, 135, 270, 359, 494, 629, 653, 742, 877, 1012, 1236, 1506, 2159, 2248, 2383, 2518, 7419 }}
{{Val list|legend=1| 21, 22, 24, 43, 46, 89, 135, 270, 359, 494, 629, 653, 742, 877, 1012, 1236, 1506, 2159, 2248, 2383, 2518, 7419 }}
 
Badness:


The following unnamed rank-2 quartismic temperament MOS scales have been found
The following unnamed rank-2 quartismic temperament MOS scales have been found
* [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&ampenv=organ Rank 2 scale (106.71461627796054, 1200.0), 5|5]   
* [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&ampenv=organ Rank 2 scale (106.71461627796054, 1200.0), 5|5]   
* The following scale tree has been found:  [http://www.microtonalsoftware.com/scale-tree.html?left=12&right=11&rr=1200&ioi=106.71461627796054 1200-106.71461627796054-12-11 Scale Tree]
* The following scale tree has been found:  [http://www.microtonalsoftware.com/scale-tree.html?left=12&right=11&rr=1200&ioi=106.71461627796054 1200-106.71461627796054-12-11 Scale Tree]
=== 13-limit ===
Commas:
POTE generator:
Map:
Wedgie:
EDOs:
Badness:
=== 17-limit ===
Commas:
POTE generator:
Map:
Wedgie:
EDOs:
Badness:


== Altierran ==
== Altierran ==


The Altierran clan is the temperament clan consisting of those temperaments in which both the schisma and the quartisma are tempered out.
In altierran, both the schisma and the quartisma are tempered out.


Commas: 32805/32768, 117440512/117406179
Subgroup: 2.3.5.7.11


POTE generators: ~3/2 = 701.7299, ~33/32 = 53.3889
[[Comma list]]: 32805/32768, 161280/161051


Map: [<1 0 15 1 5|, <0 1 -8 1 -1|, <0 0 0 5 1|]  
[[Mapping]]: [{{val| 1 0 15 1 5 }}, {{val| 0 1 -8 1 -1 }}, {{val| 0 0 0 5 1 }}]  


Wedgie: <<-102 24 -15 75 6 -8 40 1 -5 0||
{{Multival|legend=1|rank=3| -102 24 -15 75 6 -8 40 1 -5 0 }}


EDOs: {{EDOs| 135, 159, 224, 248, 313, 472 }}
[[POTE generator]]s: ~3/2 = 701.7299, ~33/32 = 53.3889


Badness:
{{Val list|legend=1| 135, 159, 224, 248, 313, 472 }}


=== 13-limit ===
=== 13-limit ===


Commas: 10985/10976, 32805/32768, 117440512/117406179
{{todo|inline=1| rename | comment = Not an immediate extension, must be renamed }}


POTE generators: ~11/10 = 166.0628, ~33/32 = 53.4151
Subgroup: 2.3.5.7.11.13


Map: [<1 2 -1 3 3 5|, <0 -3 24 -3 3 -11|, <0 0 0 5 1 5|]
[[Comma list]]: 10985/10976, 32805/32768, 161280/161051


Wedgie:  
[[Mapping]]: [{{val| 1 2 -1 3 3 5 }}, {{val| 0 -3 24 -3 3 -11 }}, {{val| 0 0 0 5 1 5 }}]


EDOs: {{EDOs}}
[[POTE generator]]s: ~11/10 = 166.0628, ~33/32 = 53.4151
 
Badness:
 
=== 17-limit ===
 
Commas:
 
POTE generator:
 
Map:
 
Wedgie:
 
EDOs:
 
Badness:


== Meanquarter ==
== Meanquarter ==


The Meanquarter clan is the temperament clan consisting of those temperaments in which both the meantone comma and the quartisma are tempered out.  Meanquarter can easily be extended to a form of [[Semaphore_and_Godzilla|godzilla]], though not all possible tunings for Meanquarter lend themselves to this sort of thing.
In meanquarter, both the meantone comma and the quartisma are tempered out.  


Commas: 81/80, 117440512/117406179
Subgroup: 2.3.5.7.11


POTE generators: ~3/2 = 697.3325, ~33/32 = 54.1064
[[Comma list]]: 81/80, 4128768/4026275


Map: [<1 0 -4 1 5|, <0 1 4 1 -1|, <0 0 5 1|]
[[Mapping]]: [{{val| 1 0 -4 1 5 }}, {{val| 0 1 4 1 -1 }}, {{val| 0 0 5 1 }}]


Wedgie:
[[POTE generator]]s: ~3/2 = 697.3325, ~33/32 = 54.1064


EDOs: {{EDOs| 24, 43, 45, 67 }}
{{Val list|legend=1| 24, 43, 45, 67 }}
 
Badness:


== Coin ==
== Coin ==


The Coin clan is the temperament clan consisting of those temperaments in which both the magic comma and the quartisma are tempered out.
In coin, both the magic comma and the quartisma are tempered out.


Commas: 3125/3072, 117440512/117406179
Subgroup: 2.3.5.7.11


POTE generators: ~5/4 = 380.3623, ~9/7 = 433.3120
[[Comma list]]: 3125/3072, 117440512/117406179


Map: [<1 0 2 1 5|, <0 5 1 0 -6|, <0 0 0 5 1|]
[[Mapping]]: [{{val| 1 0 2 1 5 }}, {{val| 0 5 1 0 -6 }}, {{val| 0 0 0 5 1 }}]


EDOs: {{EDOs| 22, 25, 139cdd }}
[[POTE generator]]s: ~5/4 = 380.3623, ~9/7 = 433.3120


Badness:
{{Val list|legend=1| 22, 25, 139cdd }}


== Escapismic ==
== Escapismic ==


The Escapisimic clan is the temperament clan consisting of those temperaments in which both the escapade comma and the quartisma are tempered out, thus, it is essentially an [[Escapade_family|Escapade extension]].
In escapisimic, both the escapade comma and the quartisma are tempered out, thus, it is essentially an [[Escapade family|Escapade expansion]].


Commas: 117440512/117406179, 4294967296/4271484375
Subgroup: 2.3.5.7.11


POTE generators: ~33/32 = 55.3538
[[Comma list]]: 117440512/117406179, 4294967296/4271484375


Map: [<1 2 2 3 3|, <0 -9 7 -4 10|]
[[Mapping]]: [{{val| 1 2 2 3 3 }}, {{val| 0 -9 7 -4 10 }}, {{val| 0 0 0 5 1 }}]


Wedgie:
[[POTE generator]]s: ~33/32 = 55.3538


EDOs: {{EDOs| 21, 22, 43 }}
{{Val list|legend=1| 21, 22, 43 }}
 
Badness:


== Dietismic ==
== Dietismic ==


The Dietismic clan is the temperament clan consisting of those temperaments in which both the diaschisma and the quartisma are tempered out. Dietismic can easily be extended to a form of [[Diaschismic_family#Shrutar|shrutar]], and in fact, it is rather unusual to find a Dietismic temperament that is not also some form of shrutar.
In dietismic, both the diaschisma and the quartisma are tempered out. Dietismic can easily be further tempered to [[Diaschismic family #Shrutar|shrutar]], and in fact, it is rather unusual to find a different tempering option.


Commas: 2048/2025, 117440512/117406179
Subgroup: 2.3.5.7.11


POTE generators: ~33/32 = 52.6800
[[Comma list]]: 2048/2025, 117440512/117406179


Map: [<2 3 5 5 7|, <0 2 -4 7 -1|]
[[POTE generator]]s: ~3/2 = 704.5238, ~33/32 = 53.4408


Wedgie:
[[Mapping]]: [{{val| 2 3 5 5 7 }}, {{val| 0 2 -4 7 -1 }}]


EDOs: {{EDOs| 22, 24, 38cdde, 46, 68, 114 }}
{{Val list|legend=1| 22, 24, 38cdde, 46, 68, 114 }}


Badness:
Scales:  


[https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(52.6800%2C%202%2F1)&data=52.680000%0A105.360000%0A158.040000%0A210.720000%0A263.400000%0A316.080000%0A368.760000%0A421.440000%0A474.120000%0A526.800000%0A579.480000%0A632.160000%0A684.840000%0A725.880000%0A778.560000%0A831.240000%0A883.920000%0A936.600000%0A989.280000%0A1041.960000%0A1094.640000%0A1147.320000%0A1200.000000&freq=440&midi=69&vert=9&horiz=1&colors=&waveform=triangle&ampenv=organ Rank 2 scale (52.6800, 2/1), 13|9]
[https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(52.6800%2C%202%2F1)&data=52.680000%0A105.360000%0A158.040000%0A210.720000%0A263.400000%0A316.080000%0A368.760000%0A421.440000%0A474.120000%0A526.800000%0A579.480000%0A632.160000%0A684.840000%0A725.880000%0A778.560000%0A831.240000%0A883.920000%0A936.600000%0A989.280000%0A1041.960000%0A1094.640000%0A1147.320000%0A1200.000000&freq=440&midi=69&vert=9&horiz=1&colors=&waveform=triangle&ampenv=organ Rank 2 scale (52.6800, 2/1), 13|9]
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== Kleirtismic ==
== Kleirtismic ==


The Kleirtismic clan is the temperament clan consisting of those temperaments in which both the kleisma and the quartisma are tempered out. The "kleir-" in "Kleirtismic" is pronounced the same as "Clair"
In kleirtismic, both the kleisma and the quartisma are tempered out. The "kleir-" in "kleirtismic" is pronounced the same as "Clair".


Commas: 15625/15552, 117440512/117406179
Subgroup: 2.3.5.7.11


POTE generators: ~6/5 = 317.0291, ~68/55 370.2940
[[Comma list]]: 15625/15552, 117440512/117406179


Map: [<1 0 1 1 5|, <0 6 5 1 -7|, <0 0 0 5 1|]
[[Mapping]]: [{{val| 1 0 1 1 5 }}, {{val| 0 6 5 1 -7 }}, {{val| 0 0 0 5 1 }}]


Wedgie:
[[POTE generator]]s: ~6/5 = 317.0291, ~68/55 = 370.2940


EDOs: {{EDOs| 159, 178, 246 }}
{{Val list|legend=1| 159, 178, 246 }}
 
Badness:


== Doublefour ==
== Doublefour ==


The Doublefour clan is the temperament clan consisting of those temperaments in which both the tetracot comma and the quartisma are tempered out.
In doublefour, both the tetracot comma and the quartisma are tempered out.
 
Commas: 20000/19683, 117440512/117406179


POTE generators: ~425/384 = 175.9566, ~33/32 = 52.9708
Subgroup: 2.3.5.7.11


Map: [<1 1 1 2 4|, <0 4 9 4 -4|, <0 0 0 5 1|]
[[Comma list]]: 20000/19683, 100656875/99090432


Wedgie:
[[Mapping]]: [{{val| 1 1 1 2 4 }}, {{val| 0 4 9 4 -4 }}, {{val| 0 0 0 5 1 }}]


EDOs: {{EDOs| 48d, 68, 89c }}
[[POTE generator]]s: ~425/384 = 175.9566, ~33/32 = 52.9708


Badness:
{{Val list|legend=1| 48d, 68, 89c }}


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Microtemperament]]
[[Category:Microtemperament]]
[[Category:Quartismic]]
[[Category:Quartismic]]
[[Category:Rank 4]]
[[Category:Rank 4]]
Retrieved from "https://en.xen.wiki/w/Quartismic_family"