Marvel family
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- This revision was by author genewardsmith and made on 2010-08-23 13:40:20 UTC.
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Original Wikitext content:
The head of the marvel family is marvel, which tempers out 225/224, the septimal kleisma or marvel comma. Marvel has a [[Normal lists|normal list basis]] of [2, 3, 5]; hence a [[Harmonic Limit|5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo]]. Another is 1/4-kleismic tuning, where the fifth is flattened by (225/224)^(1/4), 1/4 of a septimal kleisma. This leads to just 5/4 and 7/4 intervals, with other elements of the 7-limit tonality diamond sharp or flat by 1/4 septimal kleisma, or 1.93 cents. Another possibility, which also has a claim to being an optimal tuning, is to tune the fifth flat by 1/6 septimal kleisma, the major third flat by 1/3 septimal kleisma, and again to keep 7/4 pure. This leads to a maximum error over the 9-limit tonality diamond of 1/3 septimal kleisma, which is as small as possible. Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[Kleismic family|catakleismic temperament]]. However, if that isn't of interest a tuning map which does not temper the ragisma out, for example via the 1/4 or 1/6 kleismic tunings defined above, or via such vals as <1204 1907 2793 3380| or <1329 2105 3083 3731| may be employed. ==Eleven limit children== The second comma of the [[Normal lists|normal comma list]] defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.
Original HTML content:
<html><head><title>Marvel family</title></head><body>The head of the marvel family is marvel, which tempers out 225/224, the septimal kleisma or marvel comma. Marvel has a <a class="wiki_link" href="/Normal%20lists">normal list basis</a> of [2, 3, 5]; hence a <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by <a class="wiki_link" href="/197edo">197edo</a>. Another is 1/4-kleismic tuning, where the fifth is flattened by (225/224)^(1/4), 1/4 of a septimal kleisma. This leads to just 5/4 and 7/4 intervals, with other elements of the 7-limit tonality diamond sharp or flat by 1/4 septimal kleisma, or 1.93 cents. Another possibility, which also has a claim to being an optimal tuning, is to tune the fifth flat by 1/6 septimal kleisma, the major third flat by 1/3 septimal kleisma, and again to keep 7/4 pure. This leads to a maximum error over the 9-limit tonality diamond of 1/3 septimal kleisma, which is as small as possible.<br /> <br /> Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to <a class="wiki_link" href="/Kleismic%20family">catakleismic temperament</a>. However, if that isn't of interest a tuning map which does not temper the ragisma out, for example via the 1/4 or 1/6 kleismic tunings defined above, or via such vals as <1204 1907 2793 3380| or <1329 2105 3083 3731| may be employed.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Eleven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Eleven limit children</h2> The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.</body></html>