Landscape microtemperaments: Difference between revisions

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~~'''Landscape microtemperaments''' are~~ [[~~Rank~~-2 temperament|rank-2]] ~~[[temperament]]s~~ [[tempering out]] the [[landscape comma]] ({{monzo| -4 6 -6 3 }} = 250047/250000).

This is a collection of [[rank-2 temperament|rank-2]] '''landscape microtemperaments''', which [[tempering out|temper out]] the [[landscape comma]] ({{monzo|legend=1| -4 6 -6 3 }}, [[ratio]]: 250047/250000). For the [[rank-3 temperament]], see [[Landscape family #Landscape]].

~~Landscape rank-2 temperaments~~ discussed elsewhere are:

Temperaments discussed elsewhere are:

* [[Augene]] (+64/63 or 126/125) → [[Augmented family #Augene|Augmented family]]

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

* ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic|Kleismic family]]

* ''[[Trisensory]]'' (+1728/1715) → [[Sensipent family #Trisensory|Sensipent family]]

* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[~~Ragismic microtemperaments~~ #Ennealimmal|~~Ragismic microtemperaments~~]]

* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]

* ''[[Misty]]'' (+3136/3125 or 5120/5103) → [[Misty family]]

* ''[[Nessafof]]'' (+6144/6125) → [[Porwell temperaments #Nessafof|Porwell temperaments]]

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* ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart|Quartonic family]]

* ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape|Stearnsmic clan]]

* ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[~~Tricot~~ family #Tritricot|~~Tricot~~ family]]

* ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]]

* ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments#Aemilic|159th-octave temperaments]]

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: mapping generators: ~4096/3645, ~3

~~{{Multival|legend=1| 6 -36 -84 -71 -150 -94 }}~~

[[Optimal tuning]]s:

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~~{{Multival|legend=1| 15 51 72 46 72 24 }}~~

[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~243/224 = 140.367

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~~{{Multival|legend=1| 39 30 -18 -43 -138 -126 }}~~

[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~192/175 = 161.399

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~~{{Multival|legend=1| 51 105 108 48 28 -44 }}~~

[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 182.467

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~~{{Multival|legend=1| 24 -9 -66 -70 -172 -128 }}~~

[[Optimal tuning]]s:

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== Slendscape ==

Slendscape tempers out the [[~~slendrisma~~]] (68719476736/68641485507) in addition to landscape comma, and thereby features a period of ~~1＼15~~.

Slendscape tempers out the [[slendroschisma]] (68719476736/68641485507) in addition to landscape comma, and thereby features a period of 1\15.

[[Subgroup]]: 2.3.5.7

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: Mapping generators: ~8575/8192, ~1152/875

[[Optimal tuning]] ([[CTE]]): ~8575/8192 = ~~1＼15~~, ~1152/875 = 475.4847 (~6/5 = 315.4847 or ~21/20 = 84.5153)

[[Optimal tuning]] ([[CTE]]): ~8575/8192 = 80.0000, ~1152/875 = 475.4847 (~6/5 = 315.4847 or ~21/20 = 84.5153)

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Mapping: {{Mapping| 15 0 17 54 40 | 0 4 3 -2 2 }}

Optimal tuning (CTE): ~22/21 = ~~1＼15~~, ~968/735 = 475.4912 (~6/5 = 315.4912 or ~21/20 = 84.5088)

Optimal tuning (CTE): ~22/21 = 80.0000, ~968/735 = 475.4912 (~6/5 = 315.4912 or ~21/20 = 84.5088)

Optimal ET sequence: {{EDOs| 255, 270, 525, 795, 1065 }}

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Mapping: {{Mapping| 15 0 17 54 40 109 | 0 4 3 -2 2 -9 }}

Optimal tuning (CTE): ~22/21 = ~~1＼15~~, ~154/117 = 475.4935 (~6/5 = 315.4935 or ~21/20 = 84.5065)

Optimal tuning (CTE): ~22/21 = 80.0000, ~154/117 = 475.4935 (~6/5 = 315.4935 or ~21/20 = 84.5065)

Optimal ET sequence: {{EDOs| 255, 270, 795, 1065 }}

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Badness: 0.00921

== Poe ==

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 250047/250000, {{monzo| 15 -16 -4 7 }}

[[Optimal tuning]]s:

* [[CTE]]: ~2240/2187 = 1\30, ~3/2 = 702.141 (~81/80 = 22.141)

* [[CWE]]: ~2240/2187 = 1\30, ~3/2 = 702.166 (~81/80 = 22.166)

=== 11-limit ===

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 19712/19683, 250047/250000

Mapping: {{mapping| 30 0 -73 -106 -134 | 0 1 3 4 5 }}

Optimal tunings:

* CTE: ~45/44 = 1\30, ~3/2 = 702.182 (~81/80 = 22.182)

* CWE: ~45/44 = 1\30, ~3/2 = 702.213 (~81/80 = 22.213)

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 19712/19683, 1001/1000, 4459/4455, 4225/4224

Mapping: {{mapping| 30 0 -73 -106 -134 111 | 0 1 3 4 5 0 }}

Optimal tunings:

* CTE: ~45/44 = 1\30, ~3/2 = 702.182 (~81/80 = 22.182)

* CWE: ~45/44 = 1\30, ~3/2 = 702.170 (~81/80 = 22.170)

[[Category:Temperament collections]]

[[Category:Pages with mostly numerical content]]

[[Category:Landscape microtemperaments| ]]

[[Category:Landscape| ]]

[[Category:Rank 2]]

[[Category:Microtemperaments]]

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-'''Landscape microtemperaments''' are [[Rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the [[landscape comma]] ({{monzo| -4 6 -6 3 }} = 250047/250000).
+{{Technical data page}}
+This is a collection of [[rank-2 temperament|rank-2]] '''landscape microtemperaments''', which [[tempering out|temper out]] the [[landscape comma]] ({{monzo|legend=1| -4 6 -6 3 }}, [[ratio]]: 250047/250000). For the [[rank-3 temperament]], see [[Landscape family #Landscape]].
-Landscape rank-2 temperaments discussed elsewhere are:
+Temperaments discussed elsewhere are:
 * [[Augene]] (+64/63 or 126/125) → [[Augmented family #Augene|Augmented family]]
 * ''[[Compton]]'' (+225/224) → [[Compton family #Compton|Compton family]]
 * ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic|Kleismic family]]
 * ''[[Trisensory]]'' (+1728/1715) → [[Sensipent family #Trisensory|Sensipent family]]
-* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Ragismic microtemperaments #Ennealimmal|Ragismic microtemperaments]]
+* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]
 * ''[[Misty]]'' (+3136/3125 or 5120/5103) → [[Misty family]]
 * ''[[Nessafof]]'' (+6144/6125) → [[Porwell temperaments #Nessafof|Porwell temperaments]]
@@ Line 15: / Line 16: @@
 * ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart|Quartonic family]]
 * ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape|Stearnsmic clan]]
-* ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Tricot family #Tritricot|Tricot family]]
+* ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]]
 * ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments#Aemilic|159th-octave temperaments]]
@@ Line 30: / Line 31: @@
 : mapping generators: ~4096/3645, ~3
-{{Multival|legend=1| 6 -36 -84 -71 -150 -94 }}
 [[Optimal tuning]]s:
@@ Line 152: / Line 151: @@
 {{Mapping|legend=1| 3 3 1 0 | 0 5 17 24 }}
-{{Multival|legend=1| 15 51 72 46 72 24 }}
 [[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~243/224 = 140.367
@@ Line 234: / Line 231: @@
 {{Mapping|legend=1| 3 10 11 6 | 0 -13 -10 6 }}
-{{Multival|legend=1| 39 30 -18 -43 -138 -126 }}
 [[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~192/175 = 161.399
@@ Line 251: / Line 246: @@
 {{Mapping|legend=1| 3 -3 -9 -8 | 0 17 35 36 }}
-{{Multival|legend=1| 51 105 108 48 28 -44 }}
 [[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 182.467
@@ Line 266: / Line 259: @@
 {{Mapping|legend=1| 3 2 8 16 | 0 8 -3 -22 }}
-{{Multival|legend=1| 24 -9 -66 -70 -172 -128 }}
 [[Optimal tuning]]s:
@@ Line 418: / Line 409: @@
 == Slendscape ==
-Slendscape tempers out the [[slendrisma]] (68719476736/68641485507) in addition to landscape comma, and thereby features a period of 1＼15.
+Slendscape tempers out the [[slendroschisma]] (68719476736/68641485507) in addition to landscape comma, and thereby features a period of 1\15.
 [[Subgroup]]: 2.3.5.7
@@ Line 428: / Line 419: @@
 : Mapping generators: ~8575/8192, ~1152/875
-[[Optimal tuning]] ([[CTE]]): ~8575/8192 = 1＼15, ~1152/875 = 475.4847 (~6/5 = 315.4847 or ~21/20 = 84.5153)
+[[Optimal tuning]] ([[CTE]]): ~8575/8192 = 80.0000, ~1152/875 = 475.4847 (~6/5 = 315.4847 or ~21/20 = 84.5153)
 {{Optimal ET sequence|legend=1| 255, 270, 525, 795, 1065 }}
@@ Line 441: / Line 432: @@
 Mapping: {{Mapping| 15 0 17 54 40 | 0 4 3 -2 2 }}
-Optimal tuning (CTE): ~22/21 = 1＼15, ~968/735 = 475.4912 (~6/5 = 315.4912 or ~21/20 = 84.5088)
+Optimal tuning (CTE): ~22/21 = 80.0000, ~968/735 = 475.4912 (~6/5 = 315.4912 or ~21/20 = 84.5088)
 Optimal ET sequence: {{EDOs| 255, 270, 525, 795, 1065 }}
@@ Line 454: / Line 445: @@
 Mapping: {{Mapping| 15 0 17 54 40 109 | 0 4 3 -2 2 -9 }}
-Optimal tuning (CTE): ~22/21 = 1＼15, ~154/117 = 475.4935 (~6/5 = 315.4935 or ~21/20 = 84.5065)
+Optimal tuning (CTE): ~22/21 = 80.0000, ~154/117 = 475.4935 (~6/5 = 315.4935 or ~21/20 = 84.5065)
 Optimal ET sequence: {{EDOs| 255, 270, 795, 1065 }}
@@ Line 687: / Line 678: @@
 Badness: 0.00921
+== Poe ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 250047/250000, {{monzo| 15 -16 -4 7 }}
+{{Mapping|legend=1| 30 0 -73 -106 | 0 1 3 4 }}
+[[Optimal tuning]]s:
+* [[CTE]]: ~2240/2187 = 1\30, ~3/2 = 702.141 (~81/80 = 22.141)
+* [[CWE]]: ~2240/2187 = 1\30, ~3/2 = 702.166 (~81/80 = 22.166)
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 9801/9800, 19712/19683, 250047/250000
+Mapping: {{mapping| 30 0 -73 -106 -134 | 0 1 3 4 5 }}
+Optimal tunings:
+* CTE: ~45/44 = 1\30, ~3/2 = 702.182 (~81/80 = 22.182)
+* CWE: ~45/44 = 1\30, ~3/2 = 702.213 (~81/80 = 22.213)
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 19712/19683, 1001/1000, 4459/4455, 4225/4224
+Mapping: {{mapping| 30 0 -73 -106 -134 111 | 0 1 3 4 5 0 }}
+Optimal tunings:
+* CTE: ~45/44 = 1\30, ~3/2 = 702.182 (~81/80 = 22.182)
+* CWE: ~45/44 = 1\30, ~3/2 = 702.170 (~81/80 = 22.170)
 [[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Landscape microtemperaments| ]] <!-- main article -->
 [[Category:Landscape| ]] <!-- key article -->
 [[Category:Rank 2]]
 [[Category:Microtemperaments]]