Maximal harmony epimorphic scales
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Original Wikitext content:
If we look at all periodic scales [[Periodic scale#Epimorphic|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.
=5-limit=
==Five notes==
[[semilim2]]
[[semilim3]]
==Six notes, 6b val==
[[dwarf6_5]]
[[cluster6e]]
[[x-wing1]]
[[x-wing2]]
==Seven notes==
[[zarlino]]
[[mavchrome6]]
==Eight notes==
[[semimaj1]]
[[semimaj2]]
==Nine notes==
[[mavdie1]]
==Ten notes==
[[blackchrome1]]
[[blackchrome2]]
=7 odd limit=
==Seven notes==
[[maxsev1]]
[[maxsev2]]
=Seven limit marvel=
==Seven notes==
[[Gypsy scale]]
=Eleven limit marvel=
==Seven notes==
[[marvel11max7a]]
[[marvel11max7b]]Original HTML content:
<html><head><title>Maximal harmony epimorphic scales</title></head><body>If we look at all periodic scales <a class="wiki_link" href="/Periodic%20scale#Epimorphic">epimorphic</a> 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 />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x5-limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit</h1>
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x5-limit-Five notes"></a><!-- ws:end:WikiTextHeadingRule:2 -->Five notes</h2>
<a class="wiki_link" href="/semilim2">semilim2</a><br />
<a class="wiki_link" href="/semilim3">semilim3</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x5-limit-Six notes, 6b val"></a><!-- ws:end:WikiTextHeadingRule:4 -->Six notes, 6b val</h2>
<a class="wiki_link" href="/dwarf6_5">dwarf6_5</a><br />
<a class="wiki_link" href="/cluster6e">cluster6e</a><br />
<a class="wiki_link" href="/x-wing1">x-wing1</a><br />
<a class="wiki_link" href="/x-wing2">x-wing2</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x5-limit-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:6 -->Seven notes</h2>
<a class="wiki_link" href="/zarlino">zarlino</a><br />
<a class="wiki_link" href="/mavchrome6">mavchrome6</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="x5-limit-Eight notes"></a><!-- ws:end:WikiTextHeadingRule:8 -->Eight notes</h2>
<a class="wiki_link" href="/semimaj1">semimaj1</a><br />
<a class="wiki_link" href="/semimaj2">semimaj2</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x5-limit-Nine notes"></a><!-- ws:end:WikiTextHeadingRule:10 -->Nine notes</h2>
<a class="wiki_link" href="/mavdie1">mavdie1</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="x5-limit-Ten notes"></a><!-- ws:end:WikiTextHeadingRule:12 -->Ten notes</h2>
<a class="wiki_link" href="/blackchrome1">blackchrome1</a><br />
<a class="wiki_link" href="/blackchrome2">blackchrome2</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="x7 odd limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->7 odd limit</h1>
<!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="x7 odd limit-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:16 -->Seven notes</h2>
<a class="wiki_link" href="/maxsev1">maxsev1</a><br />
<a class="wiki_link" href="/maxsev2">maxsev2</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="Seven limit marvel"></a><!-- ws:end:WikiTextHeadingRule:18 -->Seven limit marvel</h1>
<!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="Seven limit marvel-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:20 -->Seven notes</h2>
<a class="wiki_link" href="/Gypsy%20scale">Gypsy scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:<h1> --><h1 id="toc11"><a name="Eleven limit marvel"></a><!-- ws:end:WikiTextHeadingRule:22 -->Eleven limit marvel</h1>
<!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="Eleven limit marvel-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:24 -->Seven notes</h2>
<a class="wiki_link" href="/marvel11max7a">marvel11max7a</a><br />
<a class="wiki_link" href="/marvel11max7b">marvel11max7b</a></body></html>