Wedgie/Archived version: Difference between revisions

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In the particular case of the 11-limit in rank three, we have that {{nowrap|(W ∨ 2) ∧ K}} gives the full wedgie, which has ten coefficents, in terms of the first six upon rounding off. Using this for a search is less difficult than it sounds, since the complexity numbers for rank three are so much lower. If the relative error E satisifes {{nowrap|E ≤ {{frac|1|2√(5)''q''5''q''7''q''11}}}}, then the rounding off is guaranteed to lead to the correct result. This amount, 0.0099, is again easily met.

== Using wedgies to find temperaments ==

The links to the page were not anchored to a subsection of the page; they were simply directed to the page. However, the page is not itself a dedicated explanation of such a temperament-finding method, and does not clearly appear to include an explanation of such a method anywhere within it. In 2012, when this page and the several pages linking to it for an explanation of this temperament-finding method were first created, still no such explanation existed, and it does not appear to exist in an easy-to-find place in page edit histories. Furthermore, the original author of these pages, [[Gene Ward Smith]], has unfortunately passed away, so he cannot be consulted on the matter. And so for now this page here is intended to serve as a placeholder for this missing information, in case anyone is eventually able to fill it in.

For now, one possible explanation of this method could be: iterate through all temperaments by complexity using wedgies, and filter out those which are non-temperaments and/or are of high badness.

{{Todo|add definition|update|inline=1|comment=Document this method via [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_17912.html Temperament seaches using wedgies only].}}

== See also ==

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 In the particular case of the 11-limit in rank three, we have that {{nowrap|(W ∨ 2) ∧ K}} gives the full wedgie, which has ten coefficents, in terms of the first six upon rounding off. Using this for a search is less difficult than it sounds, since the complexity numbers for rank three are so much lower. If the relative error E satisifes {{nowrap|E ≤ {{frac|1|2√(5)''q''<sub>5</sub>''q''<sub>7</sub>''q''<sub>11</sub>}}}}, then the rounding off is guaranteed to lead to the correct result. This amount, 0.0099, is again easily met.
+== Using wedgies to find temperaments ==
+The links to the page were not anchored to a subsection of the page; they were simply directed to the page. However, the page is not itself a dedicated explanation of such a temperament-finding method, and does not clearly appear to include an explanation of such a method anywhere within it. In 2012, when this page and the several pages linking to it for an explanation of this temperament-finding method were first created, still no such explanation existed, and it does not appear to exist in an easy-to-find place in page edit histories. Furthermore, the original author of these pages, [[Gene Ward Smith]], has unfortunately passed away, so he cannot be consulted on the matter. And so for now this page here is intended to serve as a placeholder for this missing information, in case anyone is eventually able to fill it in.
+For now, one possible explanation of this method could be: iterate through all temperaments by complexity using wedgies, and filter out those which are non-temperaments and/or are of high badness.
+{{Todo|add definition|update|inline=1|comment=Document this method via [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_17912.html Temperament seaches using wedgies only].}}
 == See also ==