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 }}
Line 16: Line 16:
[[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
Line 27: Line 27:
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 }}
Line 40: Line 40:
[[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 }}
Line 53: Line 53:
[[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 }}
Line 68: Line 68:
[[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 }}
Line 81: Line 81:
[[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
Line 92: Line 92:
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
Line 103: Line 103:
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]]

Revision as of 06:16, 27 June 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 caleb, 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

Template:Val list

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

Template:Val list

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

Template:Val list

Badness: 0.045660

Domain

See also: Minortonic family

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

Template:Val list

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

Template:Val list

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

Terture

See also: Vulture family

Comma list: 250047/250000, 359661568/358722675

Mapping: [⟨3 4 3 2], ⟨0 4 21 34]]

POTE generator: ~392/375 = 75.555

Template:Val list

Badness: 0.087156

11-limit

Comma list: 3025/3024, 19712/19683, 102487/102400

Mapping: [⟨3 4 3 2 10], ⟨0 4 21 34 2]]

POTE generator: ~392/375 = 75.550

Vals: Template:Val list

Badness: 0.029326

13-limit

Comma list: 676/675, 1001/1000, 3025/3024, 10985/10976

Mapping: [⟨3 4 3 2 10 6], ⟨0 4 21 34 2 27]]

POTE generator: ~117/112 = 75.553

Vals: Template:Val list

Badness: 0.018647

17-limit

Comma list: 676/675, 715/714, 936/935, 1001/1000, 4928/4913

Mapping: [⟨3 4 3 2 10 6 10], ⟨0 4 21 34 2 27 12]]

POTE generator: ~117/112 = 75.560

Vals: Template:Val list

Badness: 0.018705

19-limit

Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1617/1615

Mapping: [⟨3 4 3 2 10 6 10 5], ⟨0 4 21 34 2 27 12 41]]

POTE generator: ~95/91 = 75.560

Vals: Template:Val list

Badness: 0.013902

23-limit

Comma list: 460/459, 529/528, 676/675, 715/714, 936/935, 1001/1000, 1216/1215

Mapping: [⟨3 4 3 2 10 6 10 5 13], ⟨0 4 21 34 2 27 12 41 3]]

POTE generator: ~24/23 = 75.548

Vals: Template:Val list

Badness: 0.014915

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