Landscape microtemperaments: Difference between revisions
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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]]. | |||
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) → [[ | * [[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 }}) → [[ | * ''[[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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== Slendscape == | == Slendscape == | ||
Slendscape tempers out the [[ | 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 = | [[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 = | 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 = | 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 }} | ||