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: | ||