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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | If we look at all periodic scales [[Periodic_scale#Epimorphism|epimorphic]] with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the [[Graph-theoretic_properties_of_scales|graph of the scale]] is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-02-14 12:08:22 UTC</tt>.<br>
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| : The original revision id was <tt>407006390</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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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">If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the [[Graph-theoretic properties of scales|graph of the scale]] is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.
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| =5-limit= | | = 5-limit = |
| ==Five notes== | | == Five notes == |
| [[semilim2]] | | [[semilim2]] |
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| [[semilim3]] | | [[semilim3]] |
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| ==Six notes, 6b val== | | == Six notes, 6b val == |
| [[dwarf6_5]] | | [[dwarf6_5]] |
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| [[cluster6e]] | | [[cluster6e]] |
| [[x-wing1]]
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| [[x-wing2]]
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| ==Seven notes== | | [[x-wing1|x-wing1]] |
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| | [[x-wing2|x-wing2]] |
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| | == Seven notes == |
| [[zarlino]] | | [[zarlino]] |
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| [[mavchrome6]] | | [[mavchrome6]] |
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| ==Eight notes== | | == Eight notes == |
| [[semimaj1]] | | [[semimaj1]] |
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| [[semimaj2]] | | [[semimaj2]] |
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| ==Nine notes== | | == Nine notes == |
| [[mavdie1]] | | [[mavdie1]] |
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| ==Ten notes== | | == Ten notes == |
| [[blackchrome1]] | | [[blackchrome1]] |
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| [[blackchrome2]] | | [[blackchrome2]] |
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| =7 odd limit= | | = 7 odd limit = |
| ==Seven notes== | | == Seven notes == |
| [[maxsev1]] | | [[maxsev1]] |
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| [[maxsev2]] | | [[maxsev2]] |
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| =Seven limit marvel= | | = Seven limit marvel = |
| ==Seven notes== | | == Seven notes == |
| [[Gypsy scale]] | | [[Gypsy_scale|Gypsy scale]] |
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| =Eleven limit marvel= | | = Eleven limit marvel = |
| ==Seven notes== | | == Seven notes == |
| [[marvel11max7a]] | | [[marvel11max7a]] |
| [[marvel11max7b]]</pre></div> | | |
| <h4>Original HTML content:</h4>
| | [[marvel11max7b]] |
| <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>Maximal harmony epimorphic scales</title></head><body>If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the <a class="wiki_link" href="/Graph-theoretic%20properties%20of%20scales">graph of the scale</a> is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.<br />
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| | {{Navbox scale gallery}} |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5-limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit</h1>
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x5-limit-Five notes"></a><!-- ws:end:WikiTextHeadingRule:2 -->Five notes</h2>
| | [[Category:Lists of scales]] |
| <a class="wiki_link" href="/semilim2">semilim2</a><br />
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| <a class="wiki_link" href="/semilim3">semilim3</a><br />
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| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x5-limit-Six notes, 6b val"></a><!-- ws:end:WikiTextHeadingRule:4 -->Six notes, 6b val</h2>
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| <a class="wiki_link" href="/dwarf6_5">dwarf6_5</a><br />
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| <a class="wiki_link" href="/cluster6e">cluster6e</a><br />
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| <a class="wiki_link" href="/x-wing1">x-wing1</a><br />
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| <a class="wiki_link" href="/x-wing2">x-wing2</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x5-limit-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:6 -->Seven notes</h2>
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| <a class="wiki_link" href="/zarlino">zarlino</a><br />
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| <a class="wiki_link" href="/mavchrome6">mavchrome6</a><br />
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| <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x5-limit-Eight notes"></a><!-- ws:end:WikiTextHeadingRule:8 -->Eight notes</h2>
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| <a class="wiki_link" href="/semimaj1">semimaj1</a><br />
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| <a class="wiki_link" href="/semimaj2">semimaj2</a><br />
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| <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x5-limit-Nine notes"></a><!-- ws:end:WikiTextHeadingRule:10 -->Nine notes</h2>
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| <a class="wiki_link" href="/mavdie1">mavdie1</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x5-limit-Ten notes"></a><!-- ws:end:WikiTextHeadingRule:12 -->Ten notes</h2>
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| <a class="wiki_link" href="/blackchrome1">blackchrome1</a><br />
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| <a class="wiki_link" href="/blackchrome2">blackchrome2</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="x7 odd limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->7 odd limit</h1>
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| <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x7 odd limit-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:16 -->Seven notes</h2>
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| <a class="wiki_link" href="/maxsev1">maxsev1</a><br />
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| <a class="wiki_link" href="/maxsev2">maxsev2</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Seven limit marvel"></a><!-- ws:end:WikiTextHeadingRule:18 -->Seven limit marvel</h1>
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| <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Seven limit marvel-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:20 -->Seven notes</h2>
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| <a class="wiki_link" href="/Gypsy%20scale">Gypsy scale</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Eleven limit marvel"></a><!-- ws:end:WikiTextHeadingRule:22 -->Eleven limit marvel</h1>
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| <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Eleven limit marvel-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:24 -->Seven notes</h2>
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| <a class="wiki_link" href="/marvel11max7a">marvel11max7a</a><br />
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| <a class="wiki_link" href="/marvel11max7b">marvel11max7b</a></body></html></pre></div>
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