Quartismic family: Difference between revisions

Revision as of 12:26, 7 June 2021

Todo: discuss title

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 [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.

Subgroup: 2.3.5.7.11

Comma list: 117440512/117406179

Mapping: [⟨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 ]]]]

POTE generators: ~3/2 = 701.9826, ~5/4 = 386.3427, ~33/32 = 53.3748

Template:Val list

Badness: 0.274 × 10^-6

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.

Subgroup: 2.3.7.11

Comma list: 117440512/117406179

Sval mapping: [⟨1 0 1 5], ⟨0 1 1 -1], ⟨0 0 5 1]]

POTE generators: ~3/2 = 701.9826, ~33/32 = 53.3748

Template:Val list

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

Altierran

In altierran, both the schisma and the quartisma are tempered out.

Subgroup: 2.3.5.7.11

Comma list: 32805/32768, 161280/161051

Mapping: [⟨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 ]]]

POTE generators: ~3/2 = 701.7299, ~33/32 = 53.3889

Template:Val list

13-limit

Todo: rename

Not an immediate extension, must be renamed

Subgroup: 2.3.5.7.11.13

Comma list: 10985/10976, 32805/32768, 161280/161051

Mapping: [⟨1 2 -1 3 3 5], ⟨0 -3 24 -3 3 -11], ⟨0 0 0 5 1 5]]

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

Meanquarter

In meanquarter, both the meantone comma and the quartisma are tempered out.

Subgroup: 2.3.5.7.11

Comma list: 81/80, 4128768/4026275

Mapping: [⟨1 0 -4 1 5], ⟨0 1 4 1 -1], ⟨0 0 5 1]]

POTE generators: ~3/2 = 697.3325, ~33/32 = 54.1064

Template:Val list

Coin

In coin, both the magic comma and the quartisma are tempered out.

Subgroup: 2.3.5.7.11

Comma list: 3125/3072, 117440512/117406179

Mapping: [⟨1 0 2 1 5], ⟨0 5 1 0 -6], ⟨0 0 0 5 1]]

POTE generators: ~5/4 = 380.3623, ~9/7 = 433.3120

Template:Val list

Escapismic

In escapisimic, both the escapade comma and the quartisma are tempered out, thus, it is essentially an Escapade expansion.

Subgroup: 2.3.5.7.11

Comma list: 117440512/117406179, 4294967296/4271484375

Mapping: [⟨1 2 2 3 3], ⟨0 -9 7 -4 10], ⟨0 0 0 5 1]]

POTE generators: ~33/32 = 55.3538

Template:Val list

Dietismic

In dietismic, both the diaschisma and the quartisma are tempered out. Dietismic can easily be further tempered to shrutar, and in fact, it is rather unusual to find a different tempering option.

Subgroup: 2.3.5.7.11

Comma list: 2048/2025, 117440512/117406179

POTE generators: ~3/2 = 704.5238, ~33/32 = 53.4408

Mapping: [⟨2 3 5 5 7], ⟨0 2 -4 7 -1]]

Template:Val list

Scales:

Rank 2 scale (52.6800, 2/1), 13|9

Rank 2 scale (53.3742, 2/1), 13|9

Kleirtismic

In kleirtismic, both the kleisma and the quartisma are tempered out. The "kleir-" in "kleirtismic" is pronounced the same as "Clair".

Subgroup: 2.3.5.7.11

Comma list: 15625/15552, 117440512/117406179

Mapping: [⟨1 0 1 1 5], ⟨0 6 5 1 -7], ⟨0 0 0 5 1]]

POTE generators: ~6/5 = 317.0291, ~68/55 = 370.2940

Template:Val list

Doublefour

In doublefour, both the tetracot comma and the quartisma are tempered out.

Subgroup: 2.3.5.7.11

Comma list: 20000/19683, 100656875/99090432

Mapping: [⟨1 1 1 2 4], ⟨0 4 9 4 -4], ⟨0 0 0 5 1]]

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

Template:Val list

Quartismic family: Difference between revisions

Revision as of 12:26, 7 June 2021

Contents

Quartismic

Quartismatic

Altierran

13-limit

Meanquarter

Coin

Escapismic

Dietismic

Kleirtismic

Doublefour

Navigation menu

@@ Line 1: / Line 1: @@
 {{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 ==
-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 ==
-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
 * [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]
-=== 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.
+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 ===
-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 ==
-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 ==
-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 ==
-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 ==
-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]
@@ Line 207: / Line 131: @@
 == 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 ==
-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:Microtemperament]]
 [[Category:Quartismic]]
 [[Category:Rank 4]]

Quartismic family: Difference between revisions

Revision as of 12:26, 7 June 2021

Quartismic

Quartismatic

Altierran

13-limit

Meanquarter

Coin

Escapismic

Dietismic

Kleirtismic

Doublefour

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