Trisedodge family: Difference between revisions
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{{Technical data page}} | |||
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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In the 11-limit the generator can be taken to be ~11/10, reached as a period minus 25/24, that is, (55/48)/(25/24) = 11/10. Therefore, since a period plus a gen is 6/5 and a period minus a gen is 11/10, we reach 12/11 at 2 gens. | In the 11-limit the generator can be taken to be ~11/10, reached as a period minus 25/24, that is, (55/48)/(25/24) = 11/10. Therefore, since a period plus a gen is 6/5 and a period minus a gen is 11/10, we reach 12/11 at 2 gens. | ||
Remarkably, trisedodge admits an extension to the full [[29-limit]] which, except for prime 13, is surprisingly obvious/simple a way to extend the 11-limit representation. | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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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 ==== | ||
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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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Optimal tunings: | Optimal tunings: | ||
* CTE: ~ | * CTE: ~23/20 = 1\5, ~11/8 = 554.673 (~24/23 = 74.673) | ||
* CWE: ~ | * CWE: ~23/20 = 1\5, ~11/8 = 554.684 (~24/23 = 74.684) | ||
Optimal ET sequence: {{Optimal ET sequence| 15f, 65d, 80 }} | Optimal ET sequence: {{Optimal ET sequence| 15f, 65d, 80 }} | ||
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Badness: ? | Badness: ? | ||
Badness ( | Badness (Sintel): 1.380 | ||
==== Trisey ==== | ==== Trisey ==== | ||
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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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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Trisedodge family| ]] <!-- main article --> | [[Category:Trisedodge family| ]] <!-- main article --> | ||
[[Category:Trisedodge| ]] <!-- key article --> | [[Category:Trisedodge| ]] <!-- key article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||