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Landscape microtemperaments: Difference between revisions

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→Sextile: tuning, comma basis, badness, keys
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== Sextile ==
== Sextile ==
Subgroup: 2.3.5.7
[[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 }}]
Mapping generators: ~4096/3645, ~3


{{Multival|legend=1| 6 -36 -84 -71 -150 -94 }}
{{Multival|legend=1| 6 -36 -84 -71 -150 -94 }}


[[POTE generator]]: ~3/2 = 702.212
[[Optimal tuning]] ([[CTE]]): ~4096/3645 = 1\6, ~3/2 = 702.2347


{{Val list|legend=1| 12, 234d, 246d, 258, 270, 1362c, 1632c, 1902c, 2172c }}
{{Val list|legend=1| 12, 234d, 246d, 258, 270, 1362c, 1632c, 1902c, 2172c, 2442bc, 2712bc }}


[[Badness]]: 0.070097
[[Badness]]: 0.070097
Line 36: Line 38:
Comma list: 5632/5625, 9801/9800, 151263/151250
Comma list: 5632/5625, 9801/9800, 151263/151250


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


POTE generator: ~3/2 = 702.202
Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2225


Optimal GPV sequence: {{Val list| 12, 246dee, 258e, 270, 822, 1092 }}
Optimal GPV sequence: {{Val list| 12, 246dee, 258e, 270, 822, 1092 }}
Line 47: Line 49:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 1716/1715, 5632/5625, 9801/9800, 151263/151250
Comma list: 1716/1715, 2080/2079, 5632/5625, 10648/10647


Mapping: [{{val|6 0 71 150 230 279}}, {{val|0 1 -6 -14 -22 -27}}]
Mapping: [{{val| 6 0 71 150 230 279 }}, {{val| 0 1 -6 -14 -22 -27 }}]


POTE generator: ~3/2 = 702.202
Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2141


Optimal GPV sequence: {{Val list| 12f, 258ef, 270, 552, 822, 1092 }}
Optimal GPV sequence: {{Val list| 12f, 258ef, 270, 552, 822, 1092 }}


Badness: 0.029677
Badness: 0.0191


==== 17-limit ====
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 936/935, 1716/1715, 5632/5625, 9801/9800, 151263/151250
Comma list: 936/935, 1701/1700, 1716/1715, 5632/5625, 7744/7735


Mapping: [{{val|6 0 71 150 230 279 -4}}, {{val|0 1 -6 -14 -22 -27 3}}]
Mapping: [{{val| 6 0 71 150 230 279 -4 }}, {{val| 0 1 -6 -14 -22 -27 3 }}]


POTE generator: ~3/2 = 702.202
Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2117


Optimal GPV sequence: {{Val list| 12f, 258ef, 270, 552g }}
Optimal GPV sequence: {{Val list| 12f, 258ef, 270, 552g }}


Badness: 0.029677
Badness: 0.0209


==== 19-limit ====
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 936/935, 1216/1215, 1716/1715, 5632/5625, 9801/9800, 151263/151250
Comma list: 936/935, 1216/1215, 1701/1700, 1716/1715, 2376/2375, 4200/4199


Mapping: [{{val|6 0 71 150 230 279 -4 35}}, {{val|0 1 -6 -14 -22 -27 3 -1}}]
Mapping: [{{val| 6 0 71 150 230 279 -4 35 }}, {{val| 0 1 -6 -14 -22 -27 3 -1 }}]


POTE generator: ~3/2 = 702.202
Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2118


Optimal GPV sequence: {{Val list| 12f, 258ef, 270, 552g, }}
Optimal GPV sequence: {{Val list| 12f, 258ef, 270, 552g }}


Badness: 0.029677
Badness: 0.0156


=== Sextilia ===
=== Sextilia ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 1001/1000, 5632/5625, 9801/9800, 151263/151250
Comma list: 1001/1000, 4096/4095, 4459/4455, 20449/20412


Mapping: [⟨6 0 71 150 230 -149], ⟨0 1 -6 -14 -22 18]]
Mapping: [{{val| 6 0 71 150 230 -149 }}, {{val| 0 1 -6 -14 -22 18 }}]


POTE generator: ~3/2 = 702.202
Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2296


Optimal GPV sequence: {{Val list| 12, 246deef, 258e, 270 }}
Optimal GPV sequence: {{Val list| 12, 246deef, 258e, 270 }}


Badness: 0.029677
Badness: 0.0391


==== 17-limit ====
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 715/714, 1001/1000, 5632/5625, 9801/9800, 151263/151250
Comma list: 715/714, 1001/1000, 1701/1700, 4096/4095, 4459/4455


Mapping: [⟨6 0 71 150 230 -149 -4], ⟨0 1 -6 -14 -22 18 3]]
Mapping: [{{val| 6 0 71 150 230 -149 -4 }}, {{val| 0 1 -6 -14 -22 18 3 }}]


POTE generator: ~3/2 = 702.202
Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2264


Optimal GPV sequence: {{Val list| 12, 246deef, 258e, 270 }}
Optimal GPV sequence: {{Val list| 12, 246deef, 258e, 270 }}


Badness: 0.029677
Badness: 0.0384


==== 19-limit ====
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 715/714, 1001/1000, 1216/1215, 5632/5625, 9801/9800, 151263/151250
Comma list: 715/714, 1001/1000, 1216/1215, 1701/1700, 1729/1728, 2912/2907


Mapping: [⟨6 0 71 150 230 -149 -4 35], ⟨0 1 -6 -14 -22 18 3 -1]]
Mapping: [{{val| 6 0 71 150 230 -149 -4 35 }}, {{val| 0 1 -6 -14 -22 18 3 -1 }}]


POTE generator: ~3/2 = 702.202
Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2266


Optimal GPV sequence: {{Val list| 12, 246deef, 258e, 270 }}
Optimal GPV sequence: {{Val list| 12, 246deef, 258e, 270 }}


Badness: 0.029677
Badness: 0.0252


== Septichrome ==
== Septichrome ==
Retrieved from "https://en.xen.wiki/w/Landscape_microtemperaments"