Quartismic family: Difference between revisions
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The '''quartismic family''' is built up from temperaments 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 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 [24 -6 0 1 -5⟩. As the quartisma is an unnoticeable comma, this rank-4 temperament is a [[Microtempering|microtemperament]]. | ||
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Wedgie: <<<<5 1 0 -6 -24|||| | Wedgie: <<<<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}} | 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 }} | ||
Badness: 0.274 × 10<sup>-6</sup> | Badness: 0.274 × 10<sup>-6</sup> | ||
== 13-limit == | === 13-limit === | ||
Commas: | Commas: | ||
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Badness: | Badness: | ||
== 17-limit == | === 17-limit === | ||
Commas: | Commas: | ||
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Badness: | 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. | ||
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Wedgie: | Wedgie: | ||
EDOs: {{EDOs|21, 22, 24, 43, 46, 89, 135, 270, 359, 494, 629, 653, 742, 877, 1012, 1236, 1506, 2159, 2248, 2383, 2518, 7419}} | EDOs: {{EDOs| 21, 22, 24, 43, 46, 89, 135, 270, 359, 494, 629, 653, 742, 877, 1012, 1236, 1506, 2159, 2248, 2383, 2518, 7419 }} | ||
Badness: | Badness: | ||
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* 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 == | === 13-limit === | ||
Commas: | Commas: | ||
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Badness: | Badness: | ||
== 17-limit == | === 17-limit === | ||
Commas: | Commas: | ||
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Badness: | 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. | The Altierran clan is the temperament clan consisting of those temperaments in which both the schisma and the quartisma are tempered out. | ||
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Wedgie: <<-102 24 -15 75 6 -8 40 1 -5 0|| | Wedgie: <<-102 24 -15 75 6 -8 40 1 -5 0|| | ||
EDOs: {{EDOs|135, 159, 224, 248, 313, 472}} | EDOs: {{EDOs| 135, 159, 224, 248, 313, 472 }} | ||
Badness: | Badness: | ||
== 13-limit == | === 13-limit === | ||
Commas: 10985/10976, 32805/32768, 117440512/117406179 | Commas: 10985/10976, 32805/32768, 117440512/117406179 | ||
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Badness: | Badness: | ||
== 17-limit == | === 17-limit === | ||
Commas: | Commas: | ||
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Badness: | 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. | 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. | ||
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Wedgie: | Wedgie: | ||
EDOs: {{EDOs|24, 43, 45, 67}} | EDOs: {{EDOs| 24, 43, 45, 67 }} | ||
Badness: | 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. | The Coin clan is the temperament clan consisting of those temperaments in which both the magic comma and the quartisma are tempered out. | ||
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Map: [<1 0 2 1 5|, <0 5 1 0 -6|, <0 0 0 5 1|] | Map: [<1 0 2 1 5|, <0 5 1 0 -6|, <0 0 0 5 1|] | ||
EDOs: {{EDOs|22, 25, 139cdd}} | EDOs: {{EDOs| 22, 25, 139cdd }} | ||
Badness: | Badness: | ||
= 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]]. | 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]]. | ||
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Wedgie: | Wedgie: | ||
EDOs: {{EDOs|21, 22, 43}} | EDOs: {{EDOs| 21, 22, 43 }} | ||
Badness: | 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. | 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. | ||
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Wedgie: | Wedgie: | ||
EDOs: {{EDOs|22, 24, 38cdde, 46, 68, 114}} | EDOs: {{EDOs| 22, 24, 38cdde, 46, 68, 114 }} | ||
Badness: | Badness: | ||
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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=9&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white%20white%20black%20white%20black&waveform=triangle&env=organ Rank 2 scale (53.3742, 2/1), 13|9] | [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=9&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white%20white%20black%20white%20black&waveform=triangle&env=organ Rank 2 scale (53.3742, 2/1), 13|9] | ||
= 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" | 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" | ||
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Wedgie: | Wedgie: | ||
EDOs: {{EDOs|159, 178, 246}} | EDOs: {{EDOs| 159, 178, 246 }} | ||
Badness: | 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. | The Doublefour clan is the temperament clan consisting of those temperaments in which both the tetracot comma and the quartisma are tempered out. | ||
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Wedgie: | Wedgie: | ||
EDOs: {{EDOs|48d, 68, 89c}} | EDOs: {{EDOs| 48d, 68, 89c }} | ||
Badness: | Badness: | ||
Revision as of 19:27, 13 October 2020
The quartismic family is built up from temperaments that temper out the quartisma- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of [24 -6 0 1 -5⟩. Among the members of this family are Quartismatic, Altierran, Meanquarter, Coin, Escapismic, Dietismic, Kleirtismic, and Doublefour.
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 microtemperament.
Comma: 117440512/117406179
POTE generators: ~3/2 = 701.9826, ~5/4 = 386.3427, ~33/32 = 53.3748
Map: [<1 0 0 1 5|, <0 1 0 1 -1|, <0 0 1 0 0|, <0 0 0 5 1|]
Wedgie: <<<<5 1 0 -6 -24||||
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
Badness: 0.274 × 10-6
13-limit
Commas:
POTE generator:
Map:
Wedgie:
EDOs:
Badness:
17-limit
Commas:
POTE generator:
Map:
Wedgie:
EDOs:
Badness:
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.
Comma: 117440512/117406179
POTE generators: ~3/2 = 701.9826, ~33/32 = 53.3748
Map: [<1 0 1 5|, <0 1 1 -1|, <0 0 5 1|]
Wedgie:
EDOs: 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
- Rank 2 scale (106.71461627796054, 1200.0), 5|5
- The following scale tree has been found: 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
The Altierran clan is the temperament clan consisting of those temperaments in which both the schisma and the quartisma are tempered out.
Commas: 32805/32768, 117440512/117406179
POTE generators: ~3/2 = 701.7299, ~33/32 = 53.3889
Map: [<1 0 15 1 5|, <0 1 -8 1 -1|, <0 0 0 5 1|]
Wedgie: <<-102 24 -15 75 6 -8 40 1 -5 0||
EDOs: 135, 159, 224, 248, 313, 472
Badness:
13-limit
Commas: 10985/10976, 32805/32768, 117440512/117406179
POTE generators: ~11/10 = 166.0628, ~33/32 = 53.4151
Map: [<1 2 -1 3 3 5|, <0 -3 24 -3 3 -11|, <0 0 0 5 1 5|]
Wedgie:
EDOs:
Badness:
17-limit
Commas:
POTE generator:
Map:
Wedgie:
EDOs:
Badness:
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 godzilla, though not all possible tunings for Meanquarter lend themselves to this sort of thing.
Commas: 81/80, 117440512/117406179
POTE generators: ~3/2 = 697.3325, ~33/32 = 54.1064
Map: [<1 0 -4 1 5|, <0 1 4 1 -1|, <0 0 5 1|]
Wedgie:
Badness:
Coin
The Coin clan is the temperament clan consisting of those temperaments in which both the magic comma and the quartisma are tempered out.
Commas: 3125/3072, 117440512/117406179
POTE generators: ~5/4 = 380.3623, ~9/7 = 433.3120
Map: [<1 0 2 1 5|, <0 5 1 0 -6|, <0 0 0 5 1|]
Badness:
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 extension.
Commas: 117440512/117406179, 4294967296/4271484375
POTE generators: ~33/32 = 55.3538
Map: [<1 2 2 3 3|, <0 -9 7 -4 10|]
Wedgie:
Badness:
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 shrutar, and in fact, it is rather unusual to find a Dietismic temperament that is not also some form of shrutar.
Commas: 2048/2025, 117440512/117406179
POTE generators: ~33/32 = 52.6800
Map: [<2 3 5 5 7|, <0 2 -4 7 -1|]
Wedgie:
EDOs: 22, 24, 38cdde, 46, 68, 114
Badness:
Rank 2 scale (52.6800, 2/1), 13|9
Rank 2 scale (53.3742, 2/1), 13|9
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"
Commas: 15625/15552, 117440512/117406179
POTE generators: ~6/5 = 317.0291, ~68/55 370.2940
Map: [<1 0 1 1 5|, <0 6 5 1 -7|, <0 0 0 5 1|]
Wedgie:
Badness:
Doublefour
The Doublefour clan is the temperament clan consisting of those temperaments in which 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
Map: [<1 1 1 2 4|, <0 4 9 4 -4|, <0 0 0 5 1|]
Wedgie:
Badness: