Marvel family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 157897141 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 157900639 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-08-23 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-08-23 14:06:43 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>157900639</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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 and major third are flattened by (225/224)^(1/4), 1/4 of a septimal kleisma, and 7/4 is kept just. This leads to other elements of the 7-limit tonality diamond sharp or flat by 1/4 septimal kleisma, or 1.93 cents, which is as small as possible. 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. | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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 and major third are flattened by (225/224)^(1/4), 1/4 of a septimal kleisma, and 7/4 is kept just. This leads to other elements of the 7-limit tonality diamond sharp or flat by 1/4 septimal kleisma, or 1.93 cents, which is as small as possible. 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 | Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[Kleismic family|catakleismic temperament]]. Another temperament which does little damage to tuning accuracy is [[Pythagorean family|compton temperament]], for which [[240edo]] may be used. However, if this isn't of interest a tuning map which does not temper other commas out, for example via the 1/4 or 1/6 kleismic tunings defined above, or vals as <1204 1907 2793 3380| or <1329 2105 3083 3731| which have no other usable commas may be employed. | ||
==Eleven limit children== | ==Eleven limit children== | ||
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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 and major third are flattened by (225/224)^(1/4), 1/4 of a septimal kleisma, and 7/4 is kept just. This leads to other elements of the 7-limit tonality diamond sharp or flat by 1/4 septimal kleisma, or 1.93 cents, which is as small as possible. 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 /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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 and major third are flattened by (225/224)^(1/4), 1/4 of a septimal kleisma, and 7/4 is kept just. This leads to other elements of the 7-limit tonality diamond sharp or flat by 1/4 septimal kleisma, or 1.93 cents, which is as small as possible. 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 /> | <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 | 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>. Another temperament which does little damage to tuning accuracy is <a class="wiki_link" href="/Pythagorean%20family">compton temperament</a>, for which <a class="wiki_link" href="/240edo">240edo</a> may be used. However, if this isn't of interest a tuning map which does not temper other commas out, for example via the 1/4 or 1/6 kleismic tunings defined above, or vals as &lt;1204 1907 2793 3380| or &lt;1329 2105 3083 3731| which have no other usable commas may be employed.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Eleven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Eleven limit children</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><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></pre></div> | 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></pre></div> | ||