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Landscape microtemperaments: Difference between revisions

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{{Technical data page}}<br><br>
{{Technical data page}}
'''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]]
* [[Augene]] (+64/63 or 126/125) → [[Augmented family #Augene|Augmented family]]
* ''[[Compton]]'' (+225/224) → [[Compton family #Compton|Compton family]]
* ''[[Compton]]'' (+225/224) → [[Compton family #Compton|Compton family]]
* ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic|Kleismic family]]
* ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic|Kleismic family]]
* ''[[Trisensory]]'' (+1728/1715) → [[Sensipent family #Trisensory|Sensipent 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]]
* ''[[Misty]]'' (+3136/3125 or 5120/5103) → [[Misty family]]
* ''[[Nessafof]]'' (+6144/6125) → [[Porwell temperaments #Nessafof|Porwell temperaments]]
* ''[[Nessafof]]'' (+6144/6125) → [[Porwell temperaments #Nessafof|Porwell temperaments]]
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* ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart|Quartonic family]]
* ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart|Quartonic family]]
* ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape|Stearnsmic clan]]
* ''[[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]]
* ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments#Aemilic|159th-octave temperaments]]


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: mapping generators: ~4096/3645, ~3
: mapping generators: ~4096/3645, ~3
{{Multival|legend=1| 6 -36 -84 -71 -150 -94 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
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{{Mapping|legend=1| 3 3 1 0 | 0 5 17 24 }}
{{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
[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~243/224 = 140.367
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{{Mapping|legend=1| 3 10 11 6 | 0 -13 -10 6 }}
{{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
[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~192/175 = 161.399
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{{Mapping|legend=1| 3 -3 -9 -8 | 0 17 35 36 }}
{{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
[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 182.467
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{{Mapping|legend=1| 3 2 8 16 | 0 8 -3 -22 }}
{{Mapping|legend=1| 3 2 8 16 | 0 8 -3 -22 }}
{{Multival|legend=1| 24 -9 -66 -70 -172 -128 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
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== Slendscape ==
== 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
[[Subgroup]]: 2.3.5.7
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: Mapping generators: ~8575/8192, ~1152/875
: 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 }}
{{Optimal ET sequence|legend=1| 255, 270, 525, 795, 1065 }}
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Mapping: {{Mapping| 15 0 17 54 40 | 0 4 3 -2 2 }}
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 }}
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 }}
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 }}
Optimal ET sequence: {{EDOs| 255, 270, 795, 1065 }}
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Badness: 0.00921
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:Temperament collections]]
[[Category:Pages with mostly numerical content]]
[[Category:Landscape microtemperaments| ]] <!-- main article -->
[[Category:Landscape microtemperaments| ]] <!-- main article -->
[[Category:Landscape| ]] <!-- key article -->
[[Category:Landscape| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Microtemperaments]]
[[Category:Microtemperaments]]
Retrieved from "https://en.xen.wiki/w/Landscape_microtemperaments"