Gallery of MOS transversals: Difference between revisions
Wikispaces>genewardsmith **Imported revision 247862451 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 248012631 - 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>2011-08-23 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-23 17:36:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>248012631</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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[[miracle21trans511]] | [[miracle21trans511]] | ||
[[miracle31trans511]] | [[miracle31trans511]] | ||
=[[Wuerschmidt family#Hemiwuerschmidt|Hemiwuerschmidt]]= | |||
[[hemiwuerschmidt19trans37]] | |||
[[hemiwuerschmidt25trans37]] | |||
[[hemiwuerschmidt31trans37]] | |||
=[[Starling temperaments#Myna temperament|Myna]]= | =[[Starling temperaments#Myna temperament|Myna]]= | ||
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[[orwell31trans57]]</pre></div> | [[orwell31trans57]]</pre></div> | ||
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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>Gallery of MOS transversals</title></head><body><!-- ws:start:WikiTextTocRule: | <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>Gallery of MOS transversals</title></head><body><!-- ws:start:WikiTextTocRule:18:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><a href="#Introduction">Introduction</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Ennealimmal">Ennealimmal</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Magic">Magic</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Meantone">Meantone</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Miracle">Miracle</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#Hemiwuerschmidt">Hemiwuerschmidt</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Myna">Myna</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Orwell">Orwell</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:28 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:0 -->Introduction</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:0 -->Introduction</h1> | ||
By giving a <a class="wiki_link" href="/transversal">transversal</a> for a <a class="wiki_link" href="/MOSScales">MOS</a> for a particular rank two temperament, we can define the MOS as the tempering, in that temperament, of the scale. This is not very interesting in itself; what is more interesting is that since only three primes--2 and two odd primes--can be used for the transversal, we can put the result into <a class="wiki_link" href="/Scala">Scala</a>, and use its &quot;Lattice and player&quot; command under the Analyze pull-down menu to depict the MOS in terms of a lattice diagram. This can be used to better understand the chord relationships within the MOS. It should be noted that while only chords with two odd primes are depicted, larger chords are associated to them. When 3 and 5 are relatively complex as in miracle, for instance, 7 is likely to be brought along with them, and hence the lattice picture of the 5-limit triads can be used to understand relations between tetrads in miracle and other temperaments of a similar kind. Choosing two primes which bound a chord of interest often works: for instance 3 and 5 bound 7 in miracle, so that the 5-limit transversal shows 7-limit tetrads. On the other hand, in the 11-limit, 5 and 11 bound both 7 and 9, so that the complete 11-limit sextads are represented by the triads of the 2.5.11 transveral.<br /> | By giving a <a class="wiki_link" href="/transversal">transversal</a> for a <a class="wiki_link" href="/MOSScales">MOS</a> for a particular rank two temperament, we can define the MOS as the tempering, in that temperament, of the scale. This is not very interesting in itself; what is more interesting is that since only three primes--2 and two odd primes--can be used for the transversal, we can put the result into <a class="wiki_link" href="/Scala">Scala</a>, and use its &quot;Lattice and player&quot; command under the Analyze pull-down menu to depict the MOS in terms of a lattice diagram. This can be used to better understand the chord relationships within the MOS. It should be noted that while only chords with two odd primes are depicted, larger chords are associated to them. When 3 and 5 are relatively complex as in miracle, for instance, 7 is likely to be brought along with them, and hence the lattice picture of the 5-limit triads can be used to understand relations between tetrads in miracle and other temperaments of a similar kind. Choosing two primes which bound a chord of interest often works: for instance 3 and 5 bound 7 in miracle, so that the 5-limit transversal shows 7-limit tetrads. On the other hand, in the 11-limit, 5 and 11 bound both 7 and 9, so that the complete 11-limit sextads are represented by the triads of the 2.5.11 transveral.<br /> | ||
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<a class="wiki_link" href="/miracle31trans511">miracle31trans511</a><br /> | <a class="wiki_link" href="/miracle31trans511">miracle31trans511</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Myna"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Hemiwuerschmidt"></a><!-- ws:end:WikiTextHeadingRule:12 --><a class="wiki_link" href="/Wuerschmidt%20family#Hemiwuerschmidt">Hemiwuerschmidt</a></h1> | ||
<a class="wiki_link" href="/hemiwuerschmidt19trans37">hemiwuerschmidt19trans37</a><br /> | |||
<a class="wiki_link" href="/hemiwuerschmidt25trans37">hemiwuerschmidt25trans37</a><br /> | |||
<a class="wiki_link" href="/hemiwuerschmidt31trans37">hemiwuerschmidt31trans37</a><br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Myna"></a><!-- ws:end:WikiTextHeadingRule:14 --><a class="wiki_link" href="/Starling%20temperaments#Myna temperament">Myna</a></h1> | |||
<a class="wiki_link" href="/myna19trans">myna19trans</a><br /> | <a class="wiki_link" href="/myna19trans">myna19trans</a><br /> | ||
<a class="wiki_link" href="/myna23trans">myna23trans</a><br /> | <a class="wiki_link" href="/myna23trans">myna23trans</a><br /> | ||
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<a class="wiki_link" href="/myna27trans37">myna27trans37</a><br /> | <a class="wiki_link" href="/myna27trans37">myna27trans37</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Orwell"></a><!-- ws:end:WikiTextHeadingRule:16 --><a class="wiki_link" href="/Semicomma%20family">Orwell</a></h1> | ||
<a class="wiki_link" href="/orwell13trans">orwell13trans</a><br /> | <a class="wiki_link" href="/orwell13trans">orwell13trans</a><br /> | ||
<a class="wiki_link" href="/orwell22trans">orwell22trans</a><br /> | <a class="wiki_link" href="/orwell22trans">orwell22trans</a><br /> | ||