Landscape microtemperaments: Difference between revisions
now both pages link, there will be no confusion over accidentally already documenting aemilic |
→Sextile: restore POTE tuning; one-liner intro |
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== Sextile == | == Sextile == | ||
Sextile tempers out the [[garischisma]] with a 1/6-octave period and is the 12 & 270 temperament. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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{{Multival|legend=1| 6 -36 -84 -71 -150 -94 }} | {{Multival|legend=1| 6 -36 -84 -71 -150 -94 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~4096/3645 = 1\6, ~3/2 = 702.2347 | |||
* [[POTE]]: ~4096/3645 = 1\6, ~3/2 = 702.212 | |||
{{Optimal ET sequence|legend=1| 12, 234d, 246d, 258, 270, 1362c, 1632c, 1902c, 2172c, 2442bc, 2712bc }} | {{Optimal ET sequence|legend=1| 12, 234d, 246d, 258, 270, 1362c, 1632c, 1902c, 2172c, 2442bc, 2712bc }} | ||
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Mapping: {{mapping| 6 0 71 150 230 | 0 1 -6 -14 -22 }} | Mapping: {{mapping| 6 0 71 150 230 | 0 1 -6 -14 -22 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~55/49 = 1\6, ~3/2 = 702.2225 | |||
* POTE: ~55/49 = 1\6, ~3/2 = 702.202 | |||
{{Optimal ET sequence|legend=1| 12, 246dee, 258e, 270, 822, 1092, 1362c }} | {{Optimal ET sequence|legend=1| 12, 246dee, 258e, 270, 822, 1092, 1362c }} | ||
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Mapping: {{mapping| 6 0 71 150 230 279 | 0 1 -6 -14 -22 -27 }} | Mapping: {{mapping| 6 0 71 150 230 279 | 0 1 -6 -14 -22 -27 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~55/49 = 1\6, ~3/2 = 702.2141 | |||
* CWE: ~55/49 = 1\6, ~3/2 = 702.2001 | |||
{{Optimal ET sequence|legend=1| 12f, 258ef, 270, 552, 822, 1092, 1914cde }} | {{Optimal ET sequence|legend=1| 12f, 258ef, 270, 552, 822, 1092, 1914cde }} | ||
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Mapping: {{mapping| 6 0 71 150 230 279 -4 | 0 1 -6 -14 -22 -27 3 }} | Mapping: {{mapping| 6 0 71 150 230 279 -4 | 0 1 -6 -14 -22 -27 3 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~55/49 = 1\6, ~3/2 = 702.2117 | |||
* CWE: ~55/49 = 1\6, ~3/2 = 702.1869 | |||
{{Optimal ET sequence|legend=1| 12f, 270, 552g }} | {{Optimal ET sequence|legend=1| 12f, 270, 552g }} | ||
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Mapping: {{mapping| 6 0 71 150 230 279 -4 35 | 0 1 -6 -14 -22 -27 3 -1 }} | Mapping: {{mapping| 6 0 71 150 230 279 -4 35 | 0 1 -6 -14 -22 -27 3 -1 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~55/49 = 1\6, ~3/2 = 702.2118 | |||
* CWE: ~55/49 = 1\6, ~3/2 = 702.1890 | |||
{{Optimal ET sequence|legend=1| 12f, 270, 552g, 822gg }} | {{Optimal ET sequence|legend=1| 12f, 270, 552g, 822gg }} | ||
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Mapping: {{mapping| 6 0 71 150 230 -149 | 0 1 -6 -14 -22 18 }} | Mapping: {{mapping| 6 0 71 150 230 -149 | 0 1 -6 -14 -22 18 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~55/49 = 1\6, ~3/2 = 702.2296 | |||
* CWE: ~55/49 = 1\6, ~3/2 = 702.2285 | |||
{{Optimal ET sequence|legend=1| 12, 258e, 270 }} | {{Optimal ET sequence|legend=1| 12, 258e, 270 }} | ||
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Mapping: {{mapping| 6 0 71 150 230 -149 -4 | 0 1 -6 -14 -22 18 3 }} | Mapping: {{mapping| 6 0 71 150 230 -149 -4 | 0 1 -6 -14 -22 18 3 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~55/49 = 1\6, ~3/2 = 702.2264 | |||
* CWE: ~55/49 = 1\6, ~3/2 = 702.2207 | |||
{{Optimal ET sequence|legend=1| 12, 258e, 270 }} | {{Optimal ET sequence|legend=1| 12, 258e, 270 }} | ||
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Mapping: {{mapping| 6 0 71 150 230 -149 -4 35 | 0 1 -6 -14 -22 18 3 -1 }} | Mapping: {{mapping| 6 0 71 150 230 -149 -4 35 | 0 1 -6 -14 -22 18 3 -1 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~55/49 = 1\6, ~3/2 = 702.2266 | |||
* CWE: ~55/49 = 1\6, ~3/2 = 702.2208 | |||
{{Optimal ET sequence|legend=1| 12, 258e, 270 }} | {{Optimal ET sequence|legend=1| 12, 258e, 270 }} | ||