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Landscape microtemperaments: Difference between revisions

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Landscape rank-two temperaments include sextile, septichrome, pnict, and domain. Considered elsewhere are [[Mirwomo temperaments|caleb]], [[Ragismic microtemperaments #Ennealimmal|ennealimmal]], [[Hemimean clan #Misty|misty]], [[Horwell temperaments #Mutt|mutt]], [[Porwell temperaments #Nessafof|nessafof]], and [[Hemimage temperaments #Chromat|chromat]].
Landscape rank-two temperaments include sextile, septichrome, pnict, and domain. Considered elsewhere are [[Mirwomo temperaments|caleb]], [[Ragismic microtemperaments #Ennealimmal|ennealimmal]], [[Hemimean clan #Misty|misty]], [[Horwell temperaments #Mutt|mutt]], [[Porwell temperaments #Nessafof|nessafof]], and [[Hemimage temperaments #Chromat|chromat]].


= Sextile =
== Sextile ==
[[Comma list]]: 250047/250000, 33554432/33480783
[[Comma list]]: 250047/250000, 33554432/33480783


[[Mapping]]: [<6 0 71 150|, <0 1 -6 -14|]
[[Mapping]]: [{{val|6 0 71 150}}, {{val|0 1 -6 -14}}]


[[Wedgie]]: <<6 -36 -84 -71 -150 -94||
[[Wedgie]]: {{Multival|6 -36 -84 -71 -150 -94}}


[[POTE tuning|POTE generator]]: ~3/2 = 702.212
[[POTE generator]]: ~3/2 = 702.212


{{Val list|legend=1| 12, 258, 270, 1362c, 1632c, 1902c, 2172c }}
{{Val list|legend=1| 12, 258, 270, 1362c, 1632c, 1902c, 2172c }}
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[[Badness]]: 0.070097
[[Badness]]: 0.070097


== 11-limit ==
=== 11-limit ===
Comma list: 5632/5625, 9801/9800, 151263/151250
Comma list: 5632/5625, 9801/9800, 151263/151250


Mapping: [<6 0 71 150 230|, <0 1 -6 -14 -22|]
Mapping: [{{val|6 0 71 150 230}}, {{val|0 1 -6 -14 -22}}]


POTE generator: ~3/2 = 702.202
POTE generator: ~3/2 = 702.202
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Badness: 0.029677
Badness: 0.029677


= Septichrome =
== Septichrome ==
[[Comma list]]: 250047/250000, 2460375/2458624
[[Comma list]]: 250047/250000, 2460375/2458624


[[Mapping]]: [<3 3 1 0|, <0 5 17 24|]
[[Mapping]]: [{{val|3 3 1 0}}, {{val|0 5 17 24}}]


[[Wedgie]]: <<15 51 72 46 72 24||
[[Wedgie]]: {{Multival|15 51 72 46 72 24}}


[[POTE tuning|POTE generator]]: ~243/224 = 140.367
[[POTE generator]]: ~243/224 = 140.367


{{Val list|legend=1| 60, 111, 171, 795, 966, 1137, 1308, 5403b, 6711b }}
{{Val list|legend=1| 60, 111, 171, 795, 966, 1137, 1308, 5403b, 6711b }}
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[[Badness]]: 0.016814
[[Badness]]: 0.016814


= Pnict =
== Pnict ==
[[Comma list]]: 250047/250000, 2100875/2097152
[[Comma list]]: 250047/250000, 2100875/2097152


[[Mapping]]: [<3 10 11 6|, <0 -13 -10 6|]
[[Mapping]]: [{{val|3 10 11 6}}, {{val|0 -13 -10 6}}]


[[Wedgie]]: <<39 30 -18 -43 -138 -126||
[[Wedgie]]: {{Multival|39 30 -18 -43 -138 -126}}


[[POTE tuning|POTE generator]]: ~192/175 = 161.399
[[POTE generator]]: ~192/175 = 161.399


{{Val list|legend=1| 15, 141, 156, 171 }}
{{Val list|legend=1| 15, 141, 156, 171 }}
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[[Badness]]: 0.045660
[[Badness]]: 0.045660


= Domain =
== Domain ==
{{see also|Minortonic family}}
{{see also|Minortonic family}}


[[Comma list]]: 250047/250000, 645700815/645657712
[[Comma list]]: 250047/250000, 645700815/645657712


[[Mapping]]: [<3 -3 -9 -8|, <0 17 35 36|]
[[Mapping]]: [{{val|3 -3 -9 -8}}, {{val|0 17 35 36}}]


[[Wedgie]]: <<-51 -105 -108 -48 -28 44||
[[Wedgie]]: {{Multival| 51 105 108 48 28 -44}}


[[POTE tuning|POTE generator]]: ~10/9 = 182.467
[[POTE generator]]: ~10/9 = 182.467


{{Val list|legend=1| 171, 1335, 1506, 1677, 1848, 2019, 2190 }}
{{Val list|legend=1| 171, 1335, 1506, 1677, 1848, 2019, 2190 }}
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[[Badness]]: 0.013979
[[Badness]]: 0.013979


= Avicenna =
== Avicenna ==
[[Comma list]]: 250047/250000, 29360128/29296875
[[Comma list]]: 250047/250000, 29360128/29296875


[[Mapping]]: [<3 2 8 16|, <0 8 -3 -22|]
[[Mapping]]: [{{val|3 2 8 16}}, {{val|0 8 -3 -22}}]


[[Wedgie]]: <<24 -9 -66 -70 -172 -128||
[[Wedgie]]: {{Multival|24 -9 -66 -70 -172 -128}}


[[POTE tuning|POTE generator]]: ~1024/945 = 137.768
[[POTE generator]]: ~1024/945 = 137.768


{{Val list|legend=1| 87, 183, 270, 723, 993, 1263, 2796cd, 4059bccd }}
{{Val list|legend=1| 87, 183, 270, 723, 993, 1263, 2796cd, 4059bccd }}
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[[Badness]]: 0.062187
[[Badness]]: 0.062187


== 11-limit ==
=== 11-limit ===
Comma list: 3025/3024, 5632/5625, 102487/102400
Comma list: 3025/3024, 5632/5625, 102487/102400


Mapping: [<3 2 8 16 9|, <0 8 -3 -22 4|]
Mapping: [{{val|3 2 8 16 9}}, {{val|0 8 -3 -22 4}}]


POTE generator: ~693/640 = 137.771
POTE generator: ~693/640 = 137.771
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Badness: 0.023085
Badness: 0.023085


== 13-limit ==
=== 13-limit ===
Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095
Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095


Mapping: [<3 2 8 16 9 8|, <0 8 -3 -22 4 9|]
Mapping: [{{val|3 2 8 16 9 8}}, {{val|0 8 -3 -22 4 9}}]


POTE generator: ~13/12 = 137.777
POTE generator: ~13/12 = 137.777
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Badness: 0.015557
Badness: 0.015557


== Terture ==
{{see also| Vulture family }}
[[Comma list]]: 250047/250000, 359661568/358722675
[[Mapping]]: [{{val|3 4 3 2}}, {{val|0 4 21 34}}]
[[POTE generator]]: ~392/375 = 75.555
{{Val list|legend=1| 111, 159, 270 }}
[[Badness]]: 0.087156
=== 11-limit ===
Comma list: 3025/3024, 19712/19683, 102487/102400
Mapping: [{{val|3 4 3 2 10}}, {{val|0 4 21 34 2}}]
POTE generator: ~392/375 = 75.550
Vals: {{Val list| 111, 159, 270, 1239, 1509, 1779, 2049, 2319 }}
Badness: 0.029326
=== 13-limit ===
Comma list: 676/675, 1001/1000, 3025/3024, 10985/10976
Mapping: [{{val|3 4 3 2 10 6}}, {{val|0 4 21 34 2 27}}]
POTE generator: ~117/112 = 75.553
Vals: {{Val list| 111, 159, 270 }}
Badness: 0.018647
=== 17-limit ===
Comma list: 676/675, 715/714, 936/935, 1001/1000, 4928/4913
Mapping: [{{val|3 4 3 2 10 6 10}}, {{val|0 4 21 34 2 27 12}}]
POTE generator: ~117/112 = 75.560
Vals: {{Val list| 111, 159, 270 }}
Badness: 0.018705
=== 19-limit ===
Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1617/1615
Mapping: [{{val|3 4 3 2 10 6 10 5}}, {{val|0 4 21 34 2 27 12 41}}]
POTE generator: ~95/91 = 75.560
Vals: {{Val list| 111, 159, 270 }}
Badness: 0.013902
=== 23-limit ===
Comma list: 460/459, 529/528, 676/675, 715/714, 936/935, 1001/1000, 1216/1215
Mapping: [{{val|3 4 3 2 10 6 10 5 13}}, {{val|0 4 21 34 2 27 12 41 3}}]
POTE generator: ~24/23 = 75.548
Vals: {{Val list| 111, 159, 270 }}
Badness: 0.014915
[[Category:Temperament collection]]
[[Category:Microtemperament]]
[[Category:Microtemperament]]
[[Category:Landscape]]
[[Category:Landscape]]
Retrieved from "https://en.xen.wiki/w/Landscape_microtemperaments"