Minimum-ambiguity DE scales: Difference between revisions
Wikispaces>keenanpepper **Imported revision 279769642 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 279783254 - 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 | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-11-28 14:12:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>279783254</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 period per octave in [[13edo]] | * 1 period per octave in [[13edo]] | ||
** 1 2 1 2 2 1 2 2 ([[13edo#Igliashon%27s%2013-EDO%20diatonic%20approaches|oneirotonic]]) | ** 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> | ** 1 1 1 1 1 1 1 6 | ||
==9 notes== | |||
Minimum ambiguity between intervals: | |||
* 3 periods per octave in [[15edo]] | |||
** 1 2 2 1 2 2 1 2 2 ([[triforce]]-like) | |||
** 1 1 3 1 1 3 1 1 3 | |||
* 1 period per octave in [[17edo]] | |||
** 1 2 2 2 2 2 2 2 2 ([[bleu]]-like) | |||
** 1 1 3 1 3 1 3 1 3 | |||
** 1 1 1 1 6 1 1 1 6 | |||
** 1 1 1 1 1 1 1 1 9 | |||
One ambiguous interval allowed: | |||
* 1 period per octave in [[16edo]] | |||
** 1 2 2 2 2 1 2 2 2 ([[mavila]]-like) | |||
** 1 1 1 1 1 1 1 1 8 | |||
Two ambiguous intervals allowed: | |||
* 1 period per octave in [[15edo]] | |||
** 1 1 1 1 4 1 1 1 4 | |||
** 1 1 1 1 1 1 1 1 7 | |||
</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"><html><head><title>Minimum-ambiguity DE scales</title></head><body>These <a class="wiki_link" href="/distributionally%20even">distributionally even</a> scales have maximum distinguishability, where &quot;distinguishability&quot; is defined as the minimum separation between different notes or intervals. If &quot;ambiguity&quot; (confusability) is defined as the inverse of distinguishability, then they have minimum ambiguity.<br /> | <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>Minimum-ambiguity DE scales</title></head><body>These <a class="wiki_link" href="/distributionally%20even">distributionally even</a> scales have maximum distinguishability, where &quot;distinguishability&quot; is defined as the minimum separation between different notes or intervals. If &quot;ambiguity&quot; (confusability) is defined as the inverse of distinguishability, then they have minimum ambiguity.<br /> | ||
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<ul><li>4 periods per octave in <a class="wiki_link" href="/12edo">12edo</a><ul><li>1 2 1 2 1 2 1 2 (familiar <a class="wiki_link" href="/diminished">diminished</a>-like octatonic scale)</li></ul></li><li>2 periods per octave in <a class="wiki_link" href="/14edo">14edo</a><ul><li>1 2 2 2 1 2 2 2 (<a class="wiki_link" href="/hedgehog">hedgehog</a>-like)</li><li>1 1 1 4 1 1 1 4</li></ul></li><li>1 period per octave in <a class="wiki_link" href="/15edo">15edo</a><ul><li>1 2 2 2 2 2 2 2 (<a class="wiki_link" href="/porcupine">porcupine</a>-like)</li><li>1 1 1 1 1 1 1 8</li></ul></li></ul>One ambiguous interval allowed:<br /> | <ul><li>4 periods per octave in <a class="wiki_link" href="/12edo">12edo</a><ul><li>1 2 1 2 1 2 1 2 (familiar <a class="wiki_link" href="/diminished">diminished</a>-like octatonic scale)</li></ul></li><li>2 periods per octave in <a class="wiki_link" href="/14edo">14edo</a><ul><li>1 2 2 2 1 2 2 2 (<a class="wiki_link" href="/hedgehog">hedgehog</a>-like)</li><li>1 1 1 4 1 1 1 4</li></ul></li><li>1 period per octave in <a class="wiki_link" href="/15edo">15edo</a><ul><li>1 2 2 2 2 2 2 2 (<a class="wiki_link" href="/porcupine">porcupine</a>-like)</li><li>1 1 1 1 1 1 1 8</li></ul></li></ul>One ambiguous interval allowed:<br /> | ||
<ul><li>1 period per octave in <a class="wiki_link" href="/14edo">14edo</a><ul><li>1 1 3 1 1 3 1 3</li><li>1 1 1 1 1 1 1 7</li></ul></li></ul>Two ambiguous intervals allowed:<br /> | <ul><li>1 period per octave in <a class="wiki_link" href="/14edo">14edo</a><ul><li>1 1 3 1 1 3 1 3</li><li>1 1 1 1 1 1 1 7</li></ul></li></ul>Two ambiguous intervals allowed:<br /> | ||
<ul><li>2 periods per octave in <a class="wiki_link" href="/12edo">12edo</a><ul><li>1 1 1 3 1 1 1 3 (<a class="wiki_link" href="/pajara">pajara</a>-like)</li></ul></li><li>1 period per octave in <a class="wiki_link" href="/13edo">13edo</a><ul><li>1 2 1 2 2 1 2 2 (<a class="wiki_link" href="/13edo#Igliashon%27s%2013-EDO%20diatonic%20approaches">oneirotonic</a>)</li><li>1 1 1 1 1 1 1 6</li></ul></li></ul></body></html></pre></div> | <ul><li>2 periods per octave in <a class="wiki_link" href="/12edo">12edo</a><ul><li>1 1 1 3 1 1 1 3 (<a class="wiki_link" href="/pajara">pajara</a>-like)</li></ul></li><li>1 period per octave in <a class="wiki_link" href="/13edo">13edo</a><ul><li>1 2 1 2 2 1 2 2 (<a class="wiki_link" href="/13edo#Igliashon%27s%2013-EDO%20diatonic%20approaches">oneirotonic</a>)</li><li>1 1 1 1 1 1 1 6</li></ul></li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-9 notes"></a><!-- ws:end:WikiTextHeadingRule:12 -->9 notes</h2> | |||
Minimum ambiguity between intervals:<br /> | |||
<ul><li>3 periods per octave in <a class="wiki_link" href="/15edo">15edo</a><ul><li>1 2 2 1 2 2 1 2 2 (<a class="wiki_link" href="/triforce">triforce</a>-like)</li><li>1 1 3 1 1 3 1 1 3</li></ul></li><li>1 period per octave in <a class="wiki_link" href="/17edo">17edo</a><ul><li>1 2 2 2 2 2 2 2 2 (<a class="wiki_link" href="/bleu">bleu</a>-like)</li><li>1 1 3 1 3 1 3 1 3</li><li>1 1 1 1 6 1 1 1 6</li><li>1 1 1 1 1 1 1 1 9</li></ul></li></ul>One ambiguous interval allowed:<br /> | |||
<ul><li>1 period per octave in <a class="wiki_link" href="/16edo">16edo</a><ul><li>1 2 2 2 2 1 2 2 2 (<a class="wiki_link" href="/mavila">mavila</a>-like)</li><li>1 1 1 1 1 1 1 1 8</li></ul></li></ul>Two ambiguous intervals allowed:<br /> | |||
<ul><li>1 period per octave in <a class="wiki_link" href="/15edo">15edo</a><ul><li>1 1 1 1 4 1 1 1 4</li><li>1 1 1 1 1 1 1 1 7</li></ul></li></ul></body></html></pre></div> | |||