Trisedodge family: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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The '''trisedodge family''' tempers out the trisedodge comma, 30958682112/30517578125 = {{monzo| 19 10 -15 }}. | The '''trisedodge family''' tempers out the [[trisedodge comma]], 30958682112/30517578125 = {{monzo| 19 10 -15 }}. | ||
Temperaments discussed elsewhere include [[Trienstonic clan #Quindecic|quindecic]] and [[Stearnsmic clan #Decistearn|decistearn]]. | Temperaments discussed elsewhere include [[Trienstonic clan #Quindecic|quindecic]] and [[Stearnsmic clan #Decistearn|decistearn]]. | ||
== Trisedodge == | == Trisedodge == | ||
Subgroup: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
[[Comma list]]: 30958682112/30517578125 | [[Comma list]]: 30958682112/30517578125 | ||
{{Mapping|legend=1| 5 1 7 | 0 3 2 }} | |||
: mapping generators: ~144/125, ~864/625 | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~144/125 = 1\5, ~25/24 = 74.0077 | ||
{{Optimal ET sequence|legend=1| 15, 50, 65, 340c, 405c, 470c, 535c, 600c }} | {{Optimal ET sequence|legend=1| 15, 50, 65, 340c, 405c, 470c, 535c, 600c }} | ||
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Comma list: 4000/3993, 6912/6875 | Comma list: 4000/3993, 6912/6875 | ||
Sval mapping: | Sval mapping: {{mapping| 5 1 7 15 | 0 3 2 1 }} | ||
POTE | Optimal tuning (POTE): ~55/48 = 1\5, ~25/24 = 74.1247 | ||
{{Optimal ET sequence|legend=1| 15, 35, 50, 65, 210e, 275e, 340ce }} | {{Optimal ET sequence|legend=1| 15, 35, 50, 65, 210e, 275e, 340ce }} | ||
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== Septimal trisedodge == | == Septimal trisedodge == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 4000/3969, 110592/109375 | [[Comma list]]: 4000/3969, 110592/109375 | ||
{{Mapping|legend=1| 5 1 7 21 | 0 3 2 -3 }} | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~144/125 = 1\5, ~25/24 = 74.9480 | ||
{{Optimal ET sequence|legend=1| 15, 50d, 65d, 80 }} | {{Optimal ET sequence|legend=1| 15, 50d, 65d, 80 }} | ||
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Comma list: 176/175, 1331/1323, 2560/2541 | Comma list: 176/175, 1331/1323, 2560/2541 | ||
Mapping: | Mapping: {{mapping| 5 1 7 21 15 | 0 3 2 -3 1 }} | ||
POTE | Optimal tuning (POTE): ~55/48 = 1\5, ~25/24 = 74.9401 | ||
{{Optimal ET sequence|legend=1| 15, 50d, 65d, 80 }} | {{Optimal ET sequence|legend=1| 15, 50d, 65d, 80 }} | ||
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In addition to 126/125, the coblack temperament tempers out the [[cloudy comma]], 16807/16384, which is the amount by which five septimal supermajor seconds ([[8/7]]) fall short of an octave. | In addition to 126/125, the coblack temperament tempers out the [[cloudy comma]], 16807/16384, which is the amount by which five septimal supermajor seconds ([[8/7]]) fall short of an octave. | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 126/125, 16807/16384 | [[Comma list]]: 126/125, 16807/16384 | ||
{{Mapping|legend=1| 5 1 7 14 | 0 3 2 0 }} | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~8/7 = 1\5, ~21/20 = 73.044 | ||
{{Optimal ET sequence|legend=1| 15, 35, 50, 65, 115d }} | {{Optimal ET sequence|legend=1| 15, 35, 50, 65, 115d }} | ||
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Comma list: 126/125, 245/242, 385/384 | Comma list: 126/125, 245/242, 385/384 | ||
Mapping: | Mapping: {{mapping| 5 1 7 14 15 | 0 3 2 0 1 }} | ||
POTE | Optimal tuning (POTE): ~8/7 = 1\5, ~21/20 = 73.264 | ||
{{Optimal ET sequence|legend=1| 15, 35, 50, 65, 115d }} | {{Optimal ET sequence|legend=1| 15, 35, 50, 65, 115d }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Trisedodge family| ]] <!-- main article --> | [[Category:Trisedodge family| ]] <!-- main article --> | ||
[[Category:Trisedodge| ]] <!-- key article --> | |||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||