Landscape microtemperaments: Difference between revisions
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= Sextile = | = Sextile = | ||
[[Comma list]]: 250047/250000, 33554432/33480783 | [[Comma list]]: 250047/250000, 33554432/33480783 | ||
[[Mapping]]: [<6 0 71 150|, <0 1 -6 -14|] | [[Mapping]]: [<6 0 71 150|, <0 1 -6 -14|] | ||
[[Wedgie]]: <<6 -36 -84 -71 -150 -94|| | [[Wedgie]]: <<6 -36 -84 -71 -150 -94|| | ||
[[POTE tuning|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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== 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|] | |||
POTE generator: ~3/2 = 702.202 | POTE generator: ~3/2 = 702.202 | ||
Vals: {{Val list| 12, 270, 822, 1092 }} | Vals: {{Val list| 12, 270, 822, 1092 }} | ||
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= Septichrome = | = Septichrome = | ||
[[Comma list]]: 250047/250000, 2460375/2458624 | [[Comma list]]: 250047/250000, 2460375/2458624 | ||
[[Mapping]]: [<3 3 1 0|, <0 5 17 24|] | [[Mapping]]: [<3 3 1 0|, <0 5 17 24|] | ||
[[Wedgie]]: <<15 51 72 46 72 24|| | [[Wedgie]]: <<15 51 72 46 72 24|| | ||
[[POTE tuning|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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= Pnict = | = Pnict = | ||
[[Comma list]]: 250047/250000, 2100875/2097152 | [[Comma list]]: 250047/250000, 2100875/2097152 | ||
[[Mapping]]: [<3 10 11 6|, <0 -13 -10 6|] | [[Mapping]]: [<3 10 11 6|, <0 -13 -10 6|] | ||
[[Wedgie]]: <<39 30 -18 -43 -138 -126|| | [[Wedgie]]: <<39 30 -18 -43 -138 -126|| | ||
[[POTE tuning|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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[[Comma list]]: 250047/250000, 645700815/645657712 | [[Comma list]]: 250047/250000, 645700815/645657712 | ||
[[Mapping]]: [<3 -3 -9 -8|, <0 17 35 36|] | [[Mapping]]: [<3 -3 -9 -8|, <0 17 35 36|] | ||
[[Wedgie]]: <<-51 -105 -108 -48 -28 44|| | [[Wedgie]]: <<-51 -105 -108 -48 -28 44|| | ||
[[POTE tuning|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 }} | ||
[[Badness]]: 0.013979 | [[Badness]]: 0.013979 | ||
= Avicenna = | |||
[[Comma list]]: 250047/250000, 29360128/29296875 | |||
[[Mapping]]: [<3 2 8 16|, <0 8 -3 -22|] | |||
[[Wedgie]]: <<24 -9 -66 -70 -172 -128|| | |||
[[POTE tuning|POTE generator]]: ~1024/945 = 137.768 | |||
{{Val list|legend=1| 87, 183, 270, 723, 993, 1263, 2796cd, 4059bccd }} | |||
[[Badness]]: 0.062187 | |||
== 11-limit == | |||
Comma list: 3025/3024, 5632/5625, 102487/102400 | |||
Mapping: [<3 2 8 16 9|, <0 8 -3 -22 4|] | |||
POTE generator: ~693/640 = 137.771 | |||
Vals: {{Val list| 87, 183, 270, 1263, 1533, 1803c, 2073c }} | |||
Badness: 0.023085 | |||
== 13-limit == | |||
Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095 | |||
Mapping: [<3 2 8 16 9 8|, <0 8 -3 -22 4 9|] | |||
POTE generator: ~13/12 = 137.777 | |||
Vals: {{Val list| 87, 183, 270 }} | |||
Badness: 0.015557 | |||
[[Category:Microtemperament]] | [[Category:Microtemperament]] | ||
[[Category:Landscape]] | [[Category:Landscape]] | ||
Revision as of 15:06, 10 April 2021
Landscape microtemperaments are rank two temperaments tempering out the landscape comma ([-4 6 -6 3⟩ = 250047/250000).
Landscape rank-two temperaments include sextile, septichrome, pnict, and domain. Considered elsewhere are ennealimmal, misty, mutt, nessafof, and chromat.
Sextile
Comma list: 250047/250000, 33554432/33480783
Mapping: [<6 0 71 150|, <0 1 -6 -14|]
Wedgie: <<6 -36 -84 -71 -150 -94||
POTE generator: ~3/2 = 702.212
Badness: 0.070097
11-limit
Comma list: 5632/5625, 9801/9800, 151263/151250
Mapping: [<6 0 71 150 230|, <0 1 -6 -14 -22|]
POTE generator: ~3/2 = 702.202
Vals: Template:Val list
Badness: 0.029677
Septichrome
Comma list: 250047/250000, 2460375/2458624
Mapping: [<3 3 1 0|, <0 5 17 24|]
Wedgie: <<15 51 72 46 72 24||
POTE generator: ~243/224 = 140.367
Badness: 0.016814
Pnict
Comma list: 250047/250000, 2100875/2097152
Mapping: [<3 10 11 6|, <0 -13 -10 6|]
Wedgie: <<39 30 -18 -43 -138 -126||
POTE generator: ~192/175 = 161.399
Badness: 0.045660
Domain
Comma list: 250047/250000, 645700815/645657712
Mapping: [<3 -3 -9 -8|, <0 17 35 36|]
Wedgie: <<-51 -105 -108 -48 -28 44||
POTE generator: ~10/9 = 182.467
Badness: 0.013979
Avicenna
Comma list: 250047/250000, 29360128/29296875
Mapping: [<3 2 8 16|, <0 8 -3 -22|]
Wedgie: <<24 -9 -66 -70 -172 -128||
POTE generator: ~1024/945 = 137.768
Badness: 0.062187
11-limit
Comma list: 3025/3024, 5632/5625, 102487/102400
Mapping: [<3 2 8 16 9|, <0 8 -3 -22 4|]
POTE generator: ~693/640 = 137.771
Vals: Template:Val list
Badness: 0.023085
13-limit
Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095
Mapping: [<3 2 8 16 9 8|, <0 8 -3 -22 4 9|]
POTE generator: ~13/12 = 137.777
Vals: Template:Val list
Badness: 0.015557