Minimum-ambiguity DE scales: Difference between revisions

Wikispaces>keenanpepper
**Imported revision 279763906 - Original comment: **
 
Wikispaces>keenanpepper
**Imported revision 279769642 - 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:keenanpepper|keenanpepper]] and made on <tt>2011-11-28 13:34:01 UTC</tt>.<br>
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-11-28 13:45:21 UTC</tt>.<br>
: The original revision id was <tt>279763906</tt>.<br>
: The original revision id was <tt>279769642</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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* 1 2 1 2 1 2 2 ([[orgone]]-like)
* 1 2 1 2 1 2 2 ([[orgone]]-like)
* 1 1 1 3 1 1 3
* 1 1 1 3 1 1 3
* 1 1 1 1 1 1 5</pre></div>
* 1 1 1 1 1 1 5
 
==8 notes==
Minimum ambiguity between intervals:
* 4 periods per octave in [[12edo]]
** 1 2 1 2 1 2 1 2 (familiar [[diminished]]-like octatonic scale)
* 2 periods per octave in [[14edo]]
** 1 2 2 2 1 2 2 2 ([[hedgehog]]-like)
** 1 1 1 4 1 1 1 4
* 1 period per octave in [[15edo]]
** 1 2 2 2 2 2 2 2 ([[porcupine]]-like)
** 1 1 1 1 1 1 1 8
One ambiguous interval allowed:
* 1 period per octave in [[14edo]]
** 1 1 3 1 1 3 1 3
** 1 1 1 1 1 1 1 7
Two ambiguous intervals allowed:
* 2 periods per octave in [[12edo]]
** 1 1 1 3 1 1 1 3 ([[pajara]]-like)
* 1 period per octave in [[13edo]]
** 1 2 1 2 2 1 2 2 ([[13edo#Igliashon%27s%2013-EDO%20diatonic%20approaches|oneirotonic]])
** 1 1 1 1 1 1 1 6</pre></div>
<h4>Original HTML content:</h4>
<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;Minimum-ambiguity DE scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;These &lt;a class="wiki_link" href="/distributionally%20even"&gt;distributionally even&lt;/a&gt; scales have maximum distinguishability, where &amp;quot;distinguishability&amp;quot; is defined as the minimum separation between different notes or intervals. If &amp;quot;ambiguity&amp;quot; (confusability) is defined as the inverse of distinguishability, then they have minimum ambiguity.&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;Minimum-ambiguity DE scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;These &lt;a class="wiki_link" href="/distributionally%20even"&gt;distributionally even&lt;/a&gt; scales have maximum distinguishability, where &amp;quot;distinguishability&amp;quot; is defined as the minimum separation between different notes or intervals. If &amp;quot;ambiguity&amp;quot; (confusability) is defined as the inverse of distinguishability, then they have minimum ambiguity.&lt;br /&gt;
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&lt;ul&gt;&lt;li&gt;1 2 2 2 2 2 2 (&lt;a class="wiki_link" href="/13edo#Igliashon%27s%2013-EDO%20diatonic%20approaches"&gt;archeotonic&lt;/a&gt;)&lt;/li&gt;&lt;li&gt;1 1 3 1 3 1 3&lt;/li&gt;&lt;li&gt;1 1 1 4 1 1 4&lt;/li&gt;&lt;li&gt;1 1 1 1 1 1 7&lt;/li&gt;&lt;/ul&gt;One ambiguous interval allowed: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;1 2 2 2 2 2 2 (&lt;a class="wiki_link" href="/13edo#Igliashon%27s%2013-EDO%20diatonic%20approaches"&gt;archeotonic&lt;/a&gt;)&lt;/li&gt;&lt;li&gt;1 1 3 1 3 1 3&lt;/li&gt;&lt;li&gt;1 1 1 4 1 1 4&lt;/li&gt;&lt;li&gt;1 1 1 1 1 1 7&lt;/li&gt;&lt;/ul&gt;One ambiguous interval allowed: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;1 2 2 1 2 2 2 (familiar &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;-like diatonic scale)&lt;/li&gt;&lt;li&gt;1 1 1 1 1 1 6&lt;/li&gt;&lt;/ul&gt;Two ambiguous intervals allowed: &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;)&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;1 2 2 1 2 2 2 (familiar &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;-like diatonic scale)&lt;/li&gt;&lt;li&gt;1 1 1 1 1 1 6&lt;/li&gt;&lt;/ul&gt;Two ambiguous intervals allowed: &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;)&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;1 2 1 2 1 2 2 (&lt;a class="wiki_link" href="/orgone"&gt;orgone&lt;/a&gt;-like)&lt;/li&gt;&lt;li&gt;1 1 1 3 1 1 3&lt;/li&gt;&lt;li&gt;1 1 1 1 1 1 5&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;ul&gt;&lt;li&gt;1 2 1 2 1 2 2 (&lt;a class="wiki_link" href="/orgone"&gt;orgone&lt;/a&gt;-like)&lt;/li&gt;&lt;li&gt;1 1 1 3 1 1 3&lt;/li&gt;&lt;li&gt;1 1 1 1 1 1 5&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-8 notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;8 notes&lt;/h2&gt;
Minimum ambiguity between intervals:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;4 periods per octave in &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;ul&gt;&lt;li&gt;1 2 1 2 1 2 1 2 (familiar &lt;a class="wiki_link" href="/diminished"&gt;diminished&lt;/a&gt;-like octatonic scale)&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;2 periods per octave in &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt;&lt;ul&gt;&lt;li&gt;1 2 2 2 1 2 2 2 (&lt;a class="wiki_link" href="/hedgehog"&gt;hedgehog&lt;/a&gt;-like)&lt;/li&gt;&lt;li&gt;1 1 1 4 1 1 1 4&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;1 period per octave in &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;&lt;ul&gt;&lt;li&gt;1 2 2 2 2 2 2 2 (&lt;a class="wiki_link" href="/porcupine"&gt;porcupine&lt;/a&gt;-like)&lt;/li&gt;&lt;li&gt;1 1 1 1 1 1 1 8&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;One ambiguous interval allowed:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;1 period per octave in &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt;&lt;ul&gt;&lt;li&gt;1 1 3 1 1 3 1 3&lt;/li&gt;&lt;li&gt;1 1 1 1 1 1 1 7&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;Two ambiguous intervals allowed:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;2 periods per octave in &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;ul&gt;&lt;li&gt;1 1 1 3 1 1 1 3 (&lt;a class="wiki_link" href="/pajara"&gt;pajara&lt;/a&gt;-like)&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;1 period per octave in &lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt;&lt;ul&gt;&lt;li&gt;1 2 1 2 2 1 2 2 (&lt;a class="wiki_link" href="/13edo#Igliashon%27s%2013-EDO%20diatonic%20approaches"&gt;oneirotonic&lt;/a&gt;)&lt;/li&gt;&lt;li&gt;1 1 1 1 1 1 1 6&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>