Varunismic temperaments: Difference between revisions

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This is a collection of rank-2 temperaments tempering out the [[varunisma]], 321489/320000 = {{monzo| -9 8 -4 2 }}.

Temperaments discussed elsewhere are:

* ''[[Injera]]''~~, {~~50/49, 81/80} → [[Meantone family #Injera|Meantone family]]

* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]]

* ''[[Diaschismic]]''~~, {~~126/125~~, 2048/2025}~~ → [[Diaschismic family #~~Diaschismic~~|Diaschismic family]]

* ''[[Diaschismic]]'' (+126/125) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]

* ''[[Compton]]''~~, {~~225/224~~, 250047/250000}~~ → [[Compton family #Compton|Compton family]]

* ''[[Compton]]'' (+225/224) → [[Compton family #Compton|Compton family]]

* ''[[Bamity]]''~~, {~~245/243~~, 64827/64000}~~ → [[Amity family #Bamity|Amity family]]

* ''[[Bamity]]'' (+245/243) → [[Amity family #Bamity|Amity family]]

* [[Unidec]]~~, {~~1029/1024~~, 4375/4374}~~ → [[Gamelismic clan #Unidec|Gamelismic clan]]

* [[Unidec]] (+1029/1024) → [[Gamelismic clan #Unidec|Gamelismic clan]]

* [[Harry]]~~, {~~2401/2400~~, 19683/19600}~~ → [[Gravity family #Harry|Gravity family]] and [[Breedsmic temperaments #Harry|Breedsmic temperaments]]

* [[Harry]] (+2401/2400) → [[Gravity family #Harry|Gravity family]] and [[Breedsmic temperaments #Harry|Breedsmic temperaments]]

* ''[[Bischismic]]''~~, {~~3136/3125~~, 32805/32768}~~ → [[Schismatic family #Bischismic|Schismatic family]]

* ''[[Bischismic]]'' (+3136/3125) → [[Schismatic family #Bischismic|Schismatic family]]

* ''[[Bison]]''~~, {~~6144/6125~~, 78732/78125}~~ → [[Sensipent family #Bison|Sensipent family]]

* ''[[Bison]]'' (+6144/6125) → [[Sensipent family #Bison|Sensipent family]]

* ''[[~~Commatic~~]]''~~, {~~10976/10935~~, 50421/50000}~~ → [[Hemimage temperaments #~~Commatic~~|Hemimage temperaments]]

* ''[[Bicommatic]]'' (+10976/10935) → [[Hemimage temperaments #Bicommatic|Hemimage temperaments]]

* ''[[Narayana]]''~~, {~~65625/65536~~, 321489/320000}~~ → [[Vishnuzmic family #Narayana|Vishnuzmic family]]

* ''[[Narayana]]'' (+65625/65536) → [[Vishnuzmic family #Narayana|Vishnuzmic family]]

* ''[[Decal]]''~~, {~~235298/234375~~, 321489/320000}~~ → [[Pental family #Decal|Pental family]]

* ''[[Decal]]'' (+235298/234375) → [[Pental family #Decal|Pental family]]

* ''[[Bosonic]]''~~, {321489/320000,~~ 589824/588245} → [[26th-octave temperaments #Bosonic|26th-octave temperaments]]

* ''[[Bosonic]]'' (+589824/588245) → [[26th-octave temperaments #Bosonic|26th-octave temperaments]]

== Essence ==

Essence is of interest because of the abundant supply of essentially tempered ~~chords~~. Specifically, [[werckismic chords]], [[squbemic chords]], [[cuthbert chords]], [[sinbadmic chords]], and [[petrmic chords]] in the 13-odd-limit, in addition to [[nicolic chords]] in the 15-odd-limit.

Essence is of interest because of the abundant supply of [[essentially tempered chord]]s. Specifically, [[werckismic chords]], [[squbemic chords]], [[cuthbert chords]], [[sinbadmic chords]], and [[petrmic chords]] in the 13-odd-limit, in addition to [[nicolic chords]] in the 15-odd-limit.

[[Subgroup]]: 2.3.5.7

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[[Comma list]]: 321489/320000, 823543/820125

~~[[Mapping]]: [~~{{~~val~~| 2 10 27 23 ~~}}, {{val~~| 0 -11 -36 -28 }}]

~~{{Multival|legend=1| 22 72 56 63 27 -72 }}~~

: mapping generators: ~567/400, ~243/196

[[POTE ~~generator~~]]: ~243/196 = 372.597

[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~243/196 = 372.597 (~343/300 = 227.403)

{{Optimal ET sequence|legend=1| 58, 132d, 190, 248, 438d, 686d }}

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Comma list: 441/440, 8019/8000, 456533/455625

~~POTE generator~~: ~~~150/121 = 372.599~~

Mapping: {{mapping| 2 10 27 23 33 | 0 -11 -36 -28 -42 }}

~~Mapping~~: ~~[{{val|~~ 2 ~~10 27 23 33 }}~~, ~~{{val| 0 -11 -36 -28 -42 }}]~~

Optimal tuning (POTE): ~99/70 = 1\2, ~150/121 = 372.599 (~154/135 = 227.401)

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Comma list: 441/440, 729/728, 847/845, 1001/1000

~~POTE generator~~: ~~~26/21 = 372.602~~

Mapping: {{mapping| 2 10 27 23 33 31 | 0 -11 -36 -28 -42 -38 }}

~~Mapping~~: ~~[{{val|~~ 2 ~~10 27 23 33 31 }}~~, ~~{{val| 0 -11 -36 -28 -42 -38 }}]~~

Optimal tuning (POTE): ~99/70 = 1\2, ~26/21 = 372.602 (~154/135 = 227.398)

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== Octowerck ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 321489/320000, 420175/419904

~~[[Mapping]]: [~~{{~~val~~| 8 0 -11 14 ~~}}, {{val~~| 0 3 7 2 }}]

~~Mapping~~ generators: ~160/147, ~350/243

: mapping generators: ~160/147, ~350/243

[[POTE ~~generator~~]]: ~350/243 = 633.738

[[Optimal tuning]] ([[POTE]]): ~160/147 = 1\8, ~350/243 = 633.738 (~49/48 = 33.738)

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Comma list: 441/440, 8019/8000, 41503/41472

Mapping: [{{~~val~~| 8 0 -11 14 15 ~~}}, {{val~~| 0 3 7 2 3 }}]

Mapping: {{mapping| 8 0 -11 14 15 | 0 3 7 2 3 }}

POTE ~~generator~~: ~121/84 = 633.755

Optimal tuning (POTE): ~12/11 = 1\8, ~121/84 = 633.755 (~49/48 = 33.755)

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Comma list: 441/440, 729/728, 1001/1000, 6656/6655

Mapping: [{{~~val~~| 8 0 -11 14 15 -38 ~~}}, {{val~~| 0 3 7 2 3 16 }}]

Mapping: {{mapping| 8 0 -11 14 15 -38 | 0 3 7 2 3 16 }}

POTE ~~generator~~: ~75/52 = 633.742

Optimal tuning (POTE): ~12/11 = 1\8, ~75/52 = 633.742 (~49/48 = 33.742)

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Comma list: 351/350, 364/363, 441/440, 2197/2187

Mapping: [{{~~val~~| 8 0 -11 14 15 0 ~~}}, {{val~~| 0 3 7 2 3 7 }}]

Mapping: {{mapping| 8 0 -11 14 15 0 | 0 3 7 2 3 7 }}

POTE ~~generator~~: ~13/9 = 633.8370

Optimal tuning (POTE): ~12/11 = 1\8, ~13/9 = 633.8370 (~49/48 = 33.8370)

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[[Category:Temperament collections]]

[[Category:Pages with mostly numerical content]]

[[Category:Varunismic temperaments| ]]

[[Category:Varuna| ]]

[[Category:Rank 2]]

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+{{Technical data page}}
 This is a collection of rank-2 temperaments tempering out the [[varunisma]], 321489/320000 = {{monzo| -9 8 -4 2 }}.
 Temperaments discussed elsewhere are:
-* ''[[Injera]]'', {50/49, 81/80} → [[Meantone family #Injera|Meantone family]]
+* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]]
-* ''[[Diaschismic]]'', {126/125, 2048/2025} → [[Diaschismic family #Diaschismic|Diaschismic family]]
+* ''[[Diaschismic]]'' (+126/125) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]
-* ''[[Compton]]'', {225/224, 250047/250000} → [[Compton family #Compton|Compton family]]
+* ''[[Compton]]'' (+225/224) → [[Compton family #Compton|Compton family]]
-* ''[[Bamity]]'', {245/243, 64827/64000} → [[Amity family #Bamity|Amity family]]
+* ''[[Bamity]]'' (+245/243) → [[Amity family #Bamity|Amity family]]
-* [[Unidec]], {1029/1024, 4375/4374} → [[Gamelismic clan #Unidec|Gamelismic clan]]
+* [[Unidec]] (+1029/1024) → [[Gamelismic clan #Unidec|Gamelismic clan]]
-* [[Harry]], {2401/2400, 19683/19600} → [[Gravity family #Harry|Gravity family]] and [[Breedsmic temperaments #Harry|Breedsmic temperaments]]
+* [[Harry]] (+2401/2400) → [[Gravity family #Harry|Gravity family]] and [[Breedsmic temperaments #Harry|Breedsmic temperaments]]
-* ''[[Bischismic]]'', {3136/3125, 32805/32768} → [[Schismatic family #Bischismic|Schismatic family]]
+* ''[[Bischismic]]'' (+3136/3125) → [[Schismatic family #Bischismic|Schismatic family]]
-* ''[[Bison]]'', {6144/6125, 78732/78125} → [[Sensipent family #Bison|Sensipent family]]
+* ''[[Bison]]'' (+6144/6125) → [[Sensipent family #Bison|Sensipent family]]
-* ''[[Commatic]]'', {10976/10935, 50421/50000} → [[Hemimage temperaments #Commatic|Hemimage temperaments]]
+* ''[[Bicommatic]]'' (+10976/10935) → [[Hemimage temperaments #Bicommatic|Hemimage temperaments]]
-* ''[[Narayana]]'', {65625/65536, 321489/320000} → [[Vishnuzmic family #Narayana|Vishnuzmic family]]
+* ''[[Narayana]]'' (+65625/65536) → [[Vishnuzmic family #Narayana|Vishnuzmic family]]
-* ''[[Decal]]'', {235298/234375, 321489/320000} → [[Pental family #Decal|Pental family]]
+* ''[[Decal]]'' (+235298/234375) → [[Pental family #Decal|Pental family]]
-* ''[[Bosonic]]'', {321489/320000, 589824/588245} → [[26th-octave temperaments #Bosonic|26th-octave temperaments]]
+* ''[[Bosonic]]'' (+589824/588245) → [[26th-octave temperaments #Bosonic|26th-octave temperaments]]
 == Essence ==
-Essence is of interest because of the abundant supply of essentially tempered chords. Specifically, [[werckismic chords]], [[squbemic chords]], [[cuthbert chords]], [[sinbadmic chords]], and [[petrmic chords]] in the 13-odd-limit, in addition to [[nicolic chords]] in the 15-odd-limit.
+Essence is of interest because of the abundant supply of [[essentially tempered chord]]s. Specifically, [[werckismic chords]], [[squbemic chords]], [[cuthbert chords]], [[sinbadmic chords]], and [[petrmic chords]] in the 13-odd-limit, in addition to [[nicolic chords]] in the 15-odd-limit.
 [[Subgroup]]: 2.3.5.7
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 [[Comma list]]: 321489/320000, 823543/820125
-[[Mapping]]: [{{val| 2 10 27 23 }}, {{val| 0 -11 -36 -28 }}]
+{{Mapping|legend=1| 2 10 27 23 | 0 -11 -36 -28 }}
-{{Multival|legend=1| 22 72 56 63 27 -72 }}
+: mapping generators: ~567/400, ~243/196
-[[POTE generator]]: ~243/196 = 372.597
+[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~243/196 = 372.597 (~343/300 = 227.403)
 {{Optimal ET sequence|legend=1| 58, 132d, 190, 248, 438d, 686d }}
@@ Line 37: / Line 38: @@
 Comma list: 441/440, 8019/8000, 456533/455625
-POTE generator: ~150/121 = 372.599
+Mapping: {{mapping| 2 10 27 23 33 | 0 -11 -36 -28 -42 }}
-Mapping: [{{val| 2 10 27 23 33 }}, {{val| 0 -11 -36 -28 -42 }}]
+Optimal tuning (POTE): ~99/70 = 1\2, ~150/121 = 372.599 (~154/135 = 227.401)
 {{Optimal ET sequence|legend=1| 58, 132de, 190, 248, 438d }}
@@ Line 50: / Line 51: @@
 Comma list: 441/440, 729/728, 847/845, 1001/1000
-POTE generator: ~26/21 = 372.602
+Mapping: {{mapping| 2 10 27 23 33 31 | 0 -11 -36 -28 -42 -38 }}
-Mapping: [{{val| 2 10 27 23 33 31 }}, {{val| 0 -11 -36 -28 -42 -38 }}]
+Optimal tuning (POTE): ~99/70 = 1\2, ~26/21 = 372.602 (~154/135 = 227.398)
 {{Optimal ET sequence|legend=1| 58, 132de, 190, 248, 438d }}
@@ Line 59: / Line 60: @@
 == Octowerck ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 321489/320000, 420175/419904
-[[Mapping]]: [{{val| 8 0 -11 14 }}, {{val| 0 3 7 2 }}]
+{{Mapping|legend=1| 8 0 -11 14 | 0 3 7 2 }}
-Mapping generators: ~160/147, ~350/243
+: mapping generators: ~160/147, ~350/243
-[[POTE generator]]: ~350/243 = 633.738
+[[Optimal tuning]] ([[POTE]]): ~160/147 = 1\8, ~350/243 = 633.738 (~49/48 = 33.738)
 {{Optimal ET sequence|legend=1| 32c, 72, 176, 248, 320 }}
@@ Line 78: / Line 79: @@
 Comma list: 441/440, 8019/8000, 41503/41472
-Mapping: [{{val| 8 0 -11 14 15 }}, {{val| 0 3 7 2 3 }}]
+Mapping: {{mapping| 8 0 -11 14 15 | 0 3 7 2 3 }}
-POTE generator: ~121/84 = 633.755
+Optimal tuning (POTE): ~12/11 = 1\8, ~121/84 = 633.755 (~49/48 = 33.755)
 {{Optimal ET sequence|legend=1| 32c, 72, 176, 248, 320 }}
@@ Line 91: / Line 92: @@
 Comma list: 441/440, 729/728, 1001/1000, 6656/6655
-Mapping: [{{val| 8 0 -11 14 15 -38 }}, {{val| 0 3 7 2 3 16 }}]
+Mapping: {{mapping| 8 0 -11 14 15 -38 | 0 3 7 2 3 16 }}
-POTE generator: ~75/52 = 633.742
+Optimal tuning (POTE): ~12/11 = 1\8, ~75/52 = 633.742 (~49/48 = 33.742)
 {{Optimal ET sequence|legend=1| 72, 176f, 248, 320 }}
@@ Line 104: / Line 105: @@
 Comma list: 351/350, 364/363, 441/440, 2197/2187
-Mapping: [{{val| 8 0 -11 14 15 0 }}, {{val| 0 3 7 2 3 7 }}]
+Mapping: {{mapping| 8 0 -11 14 15 0 | 0 3 7 2 3 7 }}
-POTE generator: ~13/9 = 633.8370
+Optimal tuning (POTE): ~12/11 = 1\8, ~13/9 = 633.8370 (~49/48 = 33.8370)
 {{Optimal ET sequence|legend=1| 32cf, 72, 176, 248f }}
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 [[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Varunismic temperaments| ]] <!-- main article -->
+[[Category:Varuna| ]] <!-- key article -->
 [[Category:Rank 2]]