Trisedodge family: Difference between revisions
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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 }}. | ||
Named by [[Petr Pařízek]] in 2011, ''trisedodge'' (originally spelt ''trisedoge'') means that three semidiminished [[octave]]s add up to [[7/1]], and that an octave is made of 5 [[period]]s<ref name="naming">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. | Named by [[Petr Pařízek]] in 2011, ''trisedodge'' (originally spelt ''trisedoge'') means that three semidiminished [[octave]]s add up to [[7/1]], and that an octave is made of 5 [[period]]s<ref name="naming">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. | ||
Temperaments discussed elsewhere include [[ | Temperaments discussed elsewhere include [[15th-octave temperaments #Quindecic|quindecic]] and [[Stearnsmic clan #Decistearn|decistearn]]. Considered below are trisedodge and coblack. | ||
== Trisedodge == | == Trisedodge == | ||
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{{Mapping|legend=1| 5 1 7 21 | 0 3 2 -3 }} | {{Mapping|legend=1| 5 1 7 21 | 0 3 2 -3 }} | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
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Badness: ? | Badness: ? | ||
Badness ( | Badness (Sintel): 1.609 | ||
==== 19-limit ==== | ==== 19-limit ==== | ||
| Line 126: | Line 125: | ||
Badness: ? | Badness: ? | ||
Badness ( | Badness (Sintel): 1.542 | ||
==== 23-limit ==== | ==== 23-limit ==== | ||
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Badness: ? | Badness: ? | ||
Badness ( | Badness (Sintel): 1.463 | ||
==== 29-limit ==== | ==== 29-limit ==== | ||
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Badness: ? | Badness: ? | ||
Badness ( | Badness (Sintel): 1.380 | ||
==== Trisey ==== | ==== Trisey ==== | ||
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{{See also| Cloudy clan #Coblack }} | {{See also| Cloudy clan #Coblack }} | ||
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. Coblack was also named by Petr Pařízek, who considered it a counterpart of [[ | 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. Coblack was also named by Petr Pařízek, who considered it a counterpart of [[blackwood]]<ref name="naming"/>. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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{{Mapping|legend=1| 5 1 7 14 | 0 3 2 0 }} | {{Mapping|legend=1| 5 1 7 14 | 0 3 2 0 }} | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
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Badness: 0.045070 | Badness: 0.045070 | ||
== | == References == | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||