Maximal harmony epimorphic scales: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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.
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>2013-12-13 16:13:59 UTC</tt>.<br>
: The original revision id was <tt>477287794</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">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=
=5-limit=
==Five notes==
==Five notes==
[[semilim2]]
[[semilim2|semilim2]]
[[semilim3]]
 
[[semilim3|semilim3]]


==Six notes, 6b val==
==Six notes, 6b val==
[[dwarf6_5]]
[[dwarf6_5|dwarf6_5]]
[[cluster6e]]
 
[[x-wing1]]
[[cluster6e|cluster6e]]
[[x-wing2]]
 
[[x-wing1|x-wing1]]
 
[[x-wing2|x-wing2]]


==Seven notes==
==Seven notes==
[[zarlino]]
[[zarlino|zarlino]]
[[mavchrome6]]
 
[[mavchrome6|mavchrome6]]


==Eight notes==
==Eight notes==
[[semimaj1]]
[[semimaj1|semimaj1]]
[[semimaj2]]
 
[[semimaj2|semimaj2]]


==Nine notes==
==Nine notes==
[[mavdie1]]
[[mavdie1|mavdie1]]


==Ten notes==
==Ten notes==
[[blackchrome1]]
[[blackchrome1|blackchrome1]]
[[blackchrome2]]
 
[[blackchrome2|blackchrome2]]


=7 odd limit=
=7 odd limit=
==Seven notes==
==Seven notes==
[[maxsev1]]
[[maxsev1|maxsev1]]
[[maxsev2]]
 
[[maxsev2|maxsev2]]


=Seven limit marvel=
=Seven limit marvel=
==Seven notes==
==Seven notes==
[[Gypsy scale]]
[[Gypsy_scale|Gypsy scale]]


=Eleven limit marvel=
=Eleven limit marvel=
==Seven notes==
==Seven notes==
[[marvel11max7a]]
[[marvel11max7a|marvel11max7a]]
[[marvel11max7b]]</pre></div>
 
<h4>Original HTML content:</h4>
[[marvel11max7b|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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Maximal harmony epimorphic scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;If we look at all periodic scales &lt;a class="wiki_link" href="/Periodic%20scale#Epimorphic"&gt;epimorphic&lt;/a&gt; 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 &lt;a class="wiki_link" href="/Graph-theoretic%20properties%20of%20scales"&gt;graph of the scale&lt;/a&gt; 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.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5-limit&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x5-limit-Five notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Five notes&lt;/h2&gt;
&lt;a class="wiki_link" href="/semilim2"&gt;semilim2&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/semilim3"&gt;semilim3&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x5-limit-Six notes, 6b val"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Six notes, 6b val&lt;/h2&gt;
&lt;a class="wiki_link" href="/dwarf6_5"&gt;dwarf6_5&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/cluster6e"&gt;cluster6e&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/x-wing1"&gt;x-wing1&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/x-wing2"&gt;x-wing2&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x5-limit-Seven notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Seven notes&lt;/h2&gt;
&lt;a class="wiki_link" href="/zarlino"&gt;zarlino&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/mavchrome6"&gt;mavchrome6&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x5-limit-Eight notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Eight notes&lt;/h2&gt;
&lt;a class="wiki_link" href="/semimaj1"&gt;semimaj1&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/semimaj2"&gt;semimaj2&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x5-limit-Nine notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Nine notes&lt;/h2&gt;
&lt;a class="wiki_link" href="/mavdie1"&gt;mavdie1&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x5-limit-Ten notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Ten notes&lt;/h2&gt;
&lt;a class="wiki_link" href="/blackchrome1"&gt;blackchrome1&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/blackchrome2"&gt;blackchrome2&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="x7 odd limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;7 odd limit&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x7 odd limit-Seven notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Seven notes&lt;/h2&gt;
&lt;a class="wiki_link" href="/maxsev1"&gt;maxsev1&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/maxsev2"&gt;maxsev2&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Seven limit marvel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Seven limit marvel&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Seven limit marvel-Seven notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Seven notes&lt;/h2&gt;
&lt;a class="wiki_link" href="/Gypsy%20scale"&gt;Gypsy scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Eleven limit marvel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Eleven limit marvel&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Eleven limit marvel-Seven notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Seven notes&lt;/h2&gt;
&lt;a class="wiki_link" href="/marvel11max7a"&gt;marvel11max7a&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/marvel11max7b"&gt;marvel11max7b&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

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 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