Landscape microtemperaments: Difference between revisions

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== Sextile ==
== Sextile ==
Subgroup: 2.3.5.7
[[Comma list]]: 250047/250000, 33554432/33480783
[[Comma list]]: 250047/250000, 33554432/33480783


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


[[Wedgie]]: {{Multival|6 -36 -84 -71 -150 -94}}
{{Multival|legend=1| 6 -36 -84 -71 -150 -94 }}


[[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, 234d, 246d, 258, 270, 1362c, 1632c, 1902c, 2172c }}


[[Badness]]: 0.070097
[[Badness]]: 0.070097


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800, 151263/151250
Comma list: 5632/5625, 9801/9800, 151263/151250


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


Vals: {{Val list| 12, 270, 822, 1092 }}
Vals: {{Val list| 12, 246dee, 258e, 270, 822, 1092 }}


Badness: 0.029677
Badness: 0.029677


== Septichrome ==
== Septichrome ==
Subgroup: 2.3.5.7
[[Comma list]]: 250047/250000, 2460375/2458624
[[Comma list]]: 250047/250000, 2460375/2458624


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


[[Wedgie]]: {{Multival|15 51 72 46 72 24}}
{{Multival|legend=1| 15 51 72 46 72 24 }}


[[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, 8019bc }}


[[Badness]]: 0.016814
[[Badness]]: 0.016814


== Pnict ==
== Pnict ==
Subgroup: 2.3.5.7
[[Comma list]]: 250047/250000, 2100875/2097152
[[Comma list]]: 250047/250000, 2100875/2097152


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


[[Wedgie]]: {{Multival|39 30 -18 -43 -138 -126}}
{{Multival|legend=1| 39 30 -18 -43 -138 -126 }}


[[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, 2409cd, 2580cd, …, 4461bccddd, 4632bccddd }}


[[Badness]]: 0.045660
[[Badness]]: 0.045660


== Domain ==
== Domain ==
{{see also|Minortonic family}}
{{see also| Minortonic family }}
 
Subgroup: 2.3.5.7


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


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


[[Wedgie]]: {{Multival| 51 105 108 48 28 -44}}
{{Multival|legend=1| 51 105 108 48 28 -44 }}


[[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, 1164, 1335, 1506, 1677, 1848, 2019, 2190, 11943, 13962, 15981, 18000, 20019, 22038 }}


[[Badness]]: 0.013979
[[Badness]]: 0.013979


== Avicenna ==
== Avicenna ==
Subgroup: 2.3.5.7
[[Comma list]]: 250047/250000, 29360128/29296875
[[Comma list]]: 250047/250000, 29360128/29296875


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


[[Wedgie]]: {{Multival|24 -9 -66 -70 -172 -128}}
{{Multival|legend=1| 24 -9 -66 -70 -172 -128 }}


[[POTE generator]]: ~1024/945 = 137.768
[[POTE generator]]: ~1024/945 = 137.768
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=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 5632/5625, 102487/102400
Comma list: 3025/3024, 5632/5625, 102487/102400


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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095
Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095


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== Terture ==
== Terture ==
{{see also| Vulture family }}
{{see also| Vulture family }}
Subgroup: 2.3.5.7


[[Comma list]]: 250047/250000, 359661568/358722675
[[Comma list]]: 250047/250000, 359661568/358722675


[[Mapping]]: [{{val|3 4 3 2}}, {{val|0 4 21 34}}]
[[Mapping]]: [{{val| 3 4 3 2 }}, {{val| 0 4 21 34 }}]


[[POTE generator]]: ~392/375 = 75.555
[[POTE generator]]: ~392/375 = 75.555
Line 117: Line 135:


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 19712/19683, 102487/102400
Comma list: 3025/3024, 19712/19683, 102487/102400


Mapping: [{{val|3 4 3 2 10}}, {{val|0 4 21 34 2}}]
Mapping: [{{val| 3 4 3 2 10 }}, {{val| 0 4 21 34 2 }}]


POTE generator: ~392/375 = 75.550
POTE generator: ~392/375 = 75.550
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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 3025/3024, 10985/10976
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}}]
Mapping: [{{val| 3 4 3 2 10 6 }}, {{val| 0 4 21 34 2 27 }}]


POTE generator: ~117/112 = 75.553
POTE generator: ~117/112 = 75.553
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=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 676/675, 715/714, 936/935, 1001/1000, 4928/4913
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}}]
Mapping: [{{val| 3 4 3 2 10 6 10 }}, {{val| 0 4 21 34 2 27 12 }}]


POTE generator: ~117/112 = 75.560
POTE generator: ~117/112 = 75.560
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=== 19-limit ===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1617/1615
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}}]
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
POTE generator: ~95/91 = 75.560
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=== 23-limit ===
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 460/459, 529/528, 676/675, 715/714, 936/935, 1001/1000, 1216/1215
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}}]
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
POTE generator: ~24/23 = 75.548
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Badness: 0.014915
Badness: 0.014915


[[Category:Regular temperament theory]]
[[Category:Temperament collection]]
[[Category:Temperament collection]]
[[Category:Landscape microtemperaments| ]] <!-- main article -->
[[Category:Microtemperament]]
[[Category:Microtemperament]]
[[Category:Landscape]]
[[Category:Rank 2]]

Revision as of 16:18, 4 July 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, chromat, ennealimmal, misty, mutt, nessafof, and term.

Sextile

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7.11.13.17

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

Subgroup: 2.3.5.7.11.13.17.19

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

Subgroup: 2.3.5.7.11.13.17.19.23

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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