Marvel family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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 13:39:00 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-08-23 13:40:20 UTC</tt>.<br>

: The original revision id was <tt>~~157894933~~</tt>.<br>

: The original revision id was <tt>157895167</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>

<h4>Original Wikitext content:</h4>

<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 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.

<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 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.

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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.</pre></div>

<h4>Original HTML content:</h4>

<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 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 />

<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 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 &lt;1204 1907 2793 3380| or &lt;1329 2105 3083 3731| may be employed.<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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 13:39:00 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-08-23 13:40:20 UTC</tt>.<br>
-: The original revision id was <tt>157894933</tt>.<br>
+: The original revision id was <tt>157895167</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>
 <h4>Original Wikitext content:</h4>
-<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 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.
+<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 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 &lt;1204 1907 2793 3380| or &lt;1329 2105 3083 3731| may be employed.
@@ Line 13: / Line 13: @@
 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.</pre></div>
 <h4>Original HTML content:</h4>
-<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Marvel family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The head of the marvel family is marvel, which tempers out 225/224, the septimal kleisma or marvel comma. Marvel has a &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal list basis&lt;/a&gt; of [2, 3, 5]; hence a &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;5-limit&lt;/a&gt; scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by &lt;a class="wiki_link" href="/197edo"&gt;197edo&lt;/a&gt;. 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.&lt;br /&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Marvel family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The head of the marvel family is marvel, which tempers out 225/224, the septimal kleisma or marvel comma. Marvel has a &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal list basis&lt;/a&gt; of [2, 3, 5]; hence a &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;5-limit&lt;/a&gt; scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by &lt;a class="wiki_link" href="/197edo"&gt;197edo&lt;/a&gt;. 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.&lt;br /&gt;
 &lt;br /&gt;
 Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic temperament&lt;/a&gt;. 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 &amp;lt;1204 1907 2793 3380| or &amp;lt;1329 2105 3083 3731| may be employed.&lt;br /&gt;