33ed4: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:jauernig|jauernig]] and made on <tt>2015-01-09 19:15:15 UTC</tt>.<br>

: This revision was by author [[User:jauernig|jauernig]] and made on <tt>2015-01-09 19:17:30 UTC</tt>.<br>

: The original revision id was <tt>~~536807712~~</tt>.<br>

: The original revision id was <tt>536807766</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>

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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">**33ed4** is the [[ED4|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[xenharmonic/cent|cent]]s. It takes out every second step of [[33edo]] and falls between [[16edo]] and [[17edo]]. So even degree 16 or degree 17 can play the role of the [[octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of <span style="color: #00cc00;">equivocal tuning</span>.

It has a [[9_5|9/5]] which is 0.6 cents sharp, a [[7_5|7/5]] which is 0.7 cents flat, and a [[9_7|9/7]] which is 1.3 cents sharp. Therefore it is closely related to [[13edt]], the [[Bohlen-Pierce]] scale, although it has no pure [[3_1|3/1]], which is 11.1 cents flat.

It has a [[9_5|9/5]] which is 0.6 cents sharp, a [[7_5|7/5]] which is 0.7 cents flat, and a [[9_7|9/7]] which is 1.3 cents sharp. Therefore it is closely related to [[13edt]], the [[Bohlen-Pierce]] scale, although it has no pure [[3_1|3/1]], which is 11.1 cents flat. The lack of a [[3_2|pure fifth]] makes it also interesting.

Furthermore it has some [[11-limit]], [[13-limit]], [[17-limit]] and even [[23-limit]] which are very close (most of them under or nearby 1 cent).

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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>33ed4</title></head><body><strong>33ed4</strong> is the <a class="wiki_link" href="/ED4">Equal Divisions of the Double Octave</a> into 33 narrow chromatic semitones each of 72.727 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s. It takes out every second step of <a class="wiki_link" href="/33edo">33edo</a> and falls between <a class="wiki_link" href="/16edo">16edo</a> and <a class="wiki_link" href="/17edo">17edo</a>. So even degree 16 or degree 17 can play the role of the <a class="wiki_link" href="/octave">octave</a>, depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of <span style="color: #00cc00;">equivocal tuning</span>.<br />

<br />

It has a <a class="wiki_link" href="/9_5">9/5</a> which is 0.6 cents sharp, a <a class="wiki_link" href="/7_5">7/5</a> which is 0.7 cents flat, and a <a class="wiki_link" href="/9_7">9/7</a> which is 1.3 cents sharp. Therefore it is closely related to <a class="wiki_link" href="/13edt">13edt</a>, the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, although it has no pure <a class="wiki_link" href="/3_1">3/1</a>, which is 11.1 cents flat.<br />

It has a <a class="wiki_link" href="/9_5">9/5</a> which is 0.6 cents sharp, a <a class="wiki_link" href="/7_5">7/5</a> which is 0.7 cents flat, and a <a class="wiki_link" href="/9_7">9/7</a> which is 1.3 cents sharp. Therefore it is closely related to <a class="wiki_link" href="/13edt">13edt</a>, the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, although it has no pure <a class="wiki_link" href="/3_1">3/1</a>, which is 11.1 cents flat. The lack of a <a class="wiki_link" href="/3_2">pure fifth</a> makes it also interesting.<br />

<br />

Furthermore it has some <a class="wiki_link" href="/11-limit">11-limit</a>, <a class="wiki_link" href="/13-limit">13-limit</a>, <a class="wiki_link" href="/17-limit">17-limit</a> and even <a class="wiki_link" href="/23-limit">23-limit</a> which are very close (most of them under or nearby 1 cent).<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:jauernig|jauernig]] and made on <tt>2015-01-09 19:15:15 UTC</tt>.<br>
+: This revision was by author [[User:jauernig|jauernig]] and made on <tt>2015-01-09 19:17:30 UTC</tt>.<br>
-: The original revision id was <tt>536807712</tt>.<br>
+: The original revision id was <tt>536807766</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>
@@ Line 8: / Line 8: @@
 <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">**33ed4** is the [[ED4|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[xenharmonic/cent|cent]]s. It takes out every second step of [[33edo]] and falls between [[16edo]] and [[17edo]]. So even degree 16 or degree 17 can play the role of the [[octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of &lt;span style="color: #00cc00;"&gt;equivocal tuning&lt;/span&gt;.
-It has a [[9_5|9/5]] which is 0.6 cents sharp, a [[7_5|7/5]] which is 0.7 cents flat, and a [[9_7|9/7]] which is 1.3 cents sharp. Therefore it is closely related to [[13edt]], the [[Bohlen-Pierce]] scale, although it has no pure [[3_1|3/1]], which is 11.1 cents flat.
+It has a [[9_5|9/5]] which is 0.6 cents sharp, a [[7_5|7/5]] which is 0.7 cents flat, and a [[9_7|9/7]] which is 1.3 cents sharp. Therefore it is closely related to [[13edt]], the [[Bohlen-Pierce]] scale, although it has no pure [[3_1|3/1]], which is 11.1 cents flat. The lack of a [[3_2|pure fifth]] makes it also interesting.
 Furthermore it has some [[11-limit]], [[13-limit]], [[17-limit]] and even [[23-limit]] which are very close (most of them under or nearby 1 cent).
@@ Line 55: / Line 55: @@
 <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;33ed4&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;33ed4&lt;/strong&gt; is the &lt;a class="wiki_link" href="/ED4"&gt;Equal Divisions of the Double Octave&lt;/a&gt; into 33 narrow chromatic semitones each of 72.727 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent"&gt;cent&lt;/a&gt;s. It takes out every second step of &lt;a class="wiki_link" href="/33edo"&gt;33edo&lt;/a&gt; and falls between &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt; and &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;. So even degree 16 or degree 17 can play the role of the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt;, depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of &lt;span style="color: #00cc00;"&gt;equivocal tuning&lt;/span&gt;.&lt;br /&gt;
 &lt;br /&gt;
-It has a &lt;a class="wiki_link" href="/9_5"&gt;9/5&lt;/a&gt; which is 0.6 cents sharp, a &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt; which is 0.7 cents flat, and a &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt; which is 1.3 cents sharp. Therefore it is closely related to &lt;a class="wiki_link" href="/13edt"&gt;13edt&lt;/a&gt;, the &lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt; scale, although it has no pure &lt;a class="wiki_link" href="/3_1"&gt;3/1&lt;/a&gt;, which is 11.1 cents flat.&lt;br /&gt;
+It has a &lt;a class="wiki_link" href="/9_5"&gt;9/5&lt;/a&gt; which is 0.6 cents sharp, a &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt; which is 0.7 cents flat, and a &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt; which is 1.3 cents sharp. Therefore it is closely related to &lt;a class="wiki_link" href="/13edt"&gt;13edt&lt;/a&gt;, the &lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt; scale, although it has no pure &lt;a class="wiki_link" href="/3_1"&gt;3/1&lt;/a&gt;, which is 11.1 cents flat. The lack of a &lt;a class="wiki_link" href="/3_2"&gt;pure fifth&lt;/a&gt; makes it also interesting.&lt;br /&gt;
 &lt;br /&gt;
 Furthermore it has some &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;, &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;, &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt; and even &lt;a class="wiki_link" href="/23-limit"&gt;23-limit&lt;/a&gt; which are very close (most of them under or nearby 1 cent).&lt;br /&gt;