Varunismic temperaments: Difference between revisions

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Revision as of 10:49, 11 June 2021

This is a collection of rank-2 temperaments tempering out the varunisma, 321489/320000 = [-9 8 -4 2⟩.

Temperaments discussed elsewhere are:

injera, {50/49, 81/80} → Meantone family #Injera
diaschismic, {126/125, 2048/2025} → Diaschismic family #Diaschismic
compton, {225/224, 250047/250000} → Compton family #Compton
bamity, {245/243, 64827/64000} → Amity family #Bamity
unidec, {1029/1024, 4375/4374} → Gamelismic clan #Unidec
harry, {2401/2400, 19683/19600} → Breedsmic temperaments #Harry
bischismic, {3136/3125, 32805/32768} → Schismatic family #Bischismic
bison, {6144/6125, 78732/78125} → Sensipent family #Bison
commatic, {10976/10935, 50421/50000} → Hemimage temperaments #Commatic
decal, {235298/234375, 321489/320000} → Pental family #Decal
bosonic, {321489/320000, 589824/588245} → 26th-octave temperaments #Bosonic

Essence

Essence is of interest because of the abundant supply of essentially tempered chords.

Subgroup: 2.3.5.7

Comma list: 321489/320000, 823543/820125

Mapping: [⟨2 10 27 23], ⟨0 -11 -36 -28]]

Wedgie: ⟨⟨ 22 72 56 63 27 -72 ]]

POTE generator: ~243/196 = 372.597

Template:Val list

Badness: 0.1736

11-limit

Subgroup: 2.3.5.7.11

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

POTE generator: ~243/196 = 372.599

Mapping: [⟨2 10 27 23 33], ⟨0 -11 -36 -28 -42]]

Vals: Template:Val list

Badness: 0.0464

13-limit

Subgroup: 2.3.5.7.11.13

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

POTE generator: ~243/196 = 372.602

Mapping: [⟨2 10 27 23 33 31], ⟨0 -11 -36 -28 -42 -38]]

Vals: Template:Val list

Badness: 0.0261

Octowerck

Subgroup: 2.3.5.7

Comma list: 321489/320000, 420175/419904

Mapping: [⟨8 0 -11 14], ⟨0 3 7 2]]

POTE generator: ~350/243 = 633.738

Template:Val list

Badness: 0.1023

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨8 0 -11 14 15], ⟨0 3 7 2 3]]

POTE generator: ~121/84 = 633.355

Vals: Template:Val list

Badness: 0.0302

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨8 0 -11 14 15 -38], ⟨0 3 7 2 3 16]]

POTE generator: ~75/52 = 633.742

Vals: Template:Val list

Badness: 0.0276

@@ Line 1: / Line 1: @@
-This is a collection of temperaments tempering out the [[varunisma]], 321489/320000 = {{monzo| -9 8 -4 2 }}.
+This is a collection of rank-2 temperaments tempering out the [[varunisma]], 321489/320000 = {{monzo| -9 8 -4 2 }}.
 Temperaments discussed elsewhere are:
@@ Line 14: / Line 14: @@
 * ''[[bosonic]]'', {321489/320000, 589824/588245} → [[26th-octave temperaments #Bosonic]]
-= Essence =
+== Essence ==
 Essence is of interest because of the abundant supply of essentially tempered chords.
-Commas: 321489/320000, 823543/820125
+Subgroup: 2.3.5.7
-POTE generator: ~243/196 = 372.597
+[[Comma list]]: 321489/320000, 823543/820125
-Map: [&lt;2 10 27 23|, &lt;0 -11 -36 -28|]
+[[Mapping]]: [{{val| 2 10 27 23 }}, {{val| 0 -11 -36 -28 }}]
-Wedgie: &lt;&lt;22 72 56 63 27 -72||
+{{Multival|legend=1| 22 72 56 63 27 -72 }}
-EDOs: 58, 190, 248, 438d, 686d
+[[POTE generator]]: ~243/196 = 372.597
-Badness: 0.1736
+{{Val list|legend=1| 58, 132d, 190, 248, 438d, 686d }}
-== 11-limit ==
+[[Badness]]: 0.1736
-Commas: 441/440, 8019/8000, 456533/455625
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 441/440, 8019/8000, 456533/455625
 POTE generator: ~243/196 = 372.599
-Map: [&lt;2 10 27 23 33|, &lt;0 -11 -36 -28 -42|]
+Mapping: [{{val| 2 10 27 23 33 }}, {{val| 0 -11 -36 -28 -42 }}]
-EDOs: 58, 190, 248, 438d
+Vals: {{Val list| 58, 132de, 190, 248, 438d }}
 Badness: 0.0464
-== 13-limit ==
+=== 13-limit ===
-Commas: 441/440, 729/728, 847/845, 1001/1000
+Subgroup: 2.3.5.7.11.13
+Comma list: 441/440, 729/728, 847/845, 1001/1000
 POTE generator: ~243/196 = 372.602
-Map: [&lt;2 10 27 23 33 31|, &lt;0 -11 -36 -28 -42 -38|]
+Mapping: [{{val| 2 10 27 23 33 31 }}, {{val| 0 -11 -36 -28 -42 -38 }}]
-EDOs: 58, 190, 248, 438d
+Vals: {{Val list| 58, 132de, 190, 248, 438d }}
 Badness: 0.0261
-= Octowerck =
+== Octowerck ==
-Commas: 321489/320000, 420175/419904
+Subgroup: 2.3.5.7
+[[Comma list]]: 321489/320000, 420175/419904
-POTE generator: ~350/243 = 633.738
+[[Mapping]]: [{{val| 8 0 -11 14 }}, {{val| 0 3 7 2 }}]
-Map: [&lt;8 0 -11 14|, &lt;0 3 7 2|]
+[[POTE generator]]: ~350/243 = 633.738
-EDOs: 72, 176, 248, 320
+{{Val list|legend=1| 72, 176, 248, 320 }}
-Badness: 0.1023
+[[Badness]]: 0.1023
-== 11-limit ==
+=== 11-limit ===
-Commas: 441/440, 8019/8000, 41503/41472
+Subgroup: 2.3.5.7.11
+Comma list: 441/440, 8019/8000, 41503/41472
+Mapping: [{{val| 8 0 -11 14 15 }}, {{val| 0 3 7 2 3 }}]
 POTE generator: ~121/84 = 633.355
-Map: [&lt;8 0 -11 14 15|, &lt;0 3 7 2 3|]
+Vals: {{Val list| 72, 176, 248, 320 }}
-EDOs: 72, 176, 248, 320
+Badness: 0.0302
-Badness: 0.0302
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 441/440, 729/728, 1001/1000, 6656/6655
-== 13-limit ==
+Mapping: [{{val| 8 0 -11 14 15 -38 }}, {{val| 0 3 7 2 3 16 }}]
-Commas: 441/440, 729/728, 1001/1000, 6656/6655
 POTE generator: ~75/52 = 633.742
-Map: [&lt;8 0 -11 14 15 -38|, &lt;0 3 7 2 3 16|]
+Vals: {{Val list| 72, 176f, 248, 320 }}
-EDOs: 72, 248, 320
 Badness: 0.0276
@@ Line 87: / Line 99: @@
 [[Category:Temperament collection]]
 [[Category:Varunismic temperaments| ]] <!-- main article -->
-[[Category:Varuna]]
 [[Category:Rank 2]]
-{{todo| cleanup }}

Varunismic temperaments: Difference between revisions

Revision as of 10:49, 11 June 2021

Contents

Essence

11-limit

13-limit

Octowerck

11-limit

13-limit

Navigation menu

Varunismic temperaments: Difference between revisions

Revision as of 10:49, 11 June 2021

Essence

11-limit

13-limit

Octowerck

11-limit

13-limit

Navigation menu

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