EDT: Difference between revisions
Wikispaces>Kosmorsky **Imported revision 287102944 - Original comment: ** |
Wikispaces>hstraub **Imported revision 295467160 - 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: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2012-01-26 03:50:08 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>295467160</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> | ||
<h4>Original Wikitext content:</h4> | <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">=Division of the tritave (3/1) into n equal parts= | <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">[[toc|flat]] | ||
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=Division of the tritave (3/1) into n equal parts= | |||
Western music generally revolves around the principle of **octave equivalence**: notes an octave apart are often perceived in western music as being the same //chroma// but differing in pitch height. As the octave corresponds to a 2/1 frequency ratio, it has been proposed that the next-simplest after the octave, the 3/1, can also be used to evoke a sense of chroma equivalence. This interval corresponds to a perfect twelfth in the diatonic scale, but when used to refer to an equivalence interval it is often called the "tritave". | Western music generally revolves around the principle of **octave equivalence**: notes an octave apart are often perceived in western music as being the same //chroma// but differing in pitch height. As the octave corresponds to a 2/1 frequency ratio, it has been proposed that the next-simplest after the octave, the 3/1, can also be used to evoke a sense of chroma equivalence. This interval corresponds to a perfect twelfth in the diatonic scale, but when used to refer to an equivalence interval it is often called the "tritave". | ||
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Also, on the topic of multiples of 13edt, 26 (double) and 39 (triple) offer very good harmonic approximations, the former of the 8th, 13th and 17th partials, and the latter of the 11th and 13th. However, quadruple and quintuple, ie. 52 and 65edt, also exist offering good approximations of the octave. 52edt is very nearly [[33edo]], and 65edt is practically identical to [[41edo]].</pre></div> | Also, on the topic of multiples of 13edt, 26 (double) and 39 (triple) offer very good harmonic approximations, the former of the 8th, 13th and 17th partials, and the latter of the 11th and 13th. However, quadruple and quintuple, ie. 52 and 65edt, also exist offering good approximations of the octave. 52edt is very nearly [[33edo]], and 65edt is practically identical to [[41edo]].</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>edt</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Division of the tritave (3/1) into n equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 -->Division of the tritave (3/1) into n equal parts</h1> | <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>edt</title></head><body><!-- ws:start:WikiTextTocRule:12:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#Division of the tritave (3/1) into n equal parts">Division of the tritave (3/1) into n equal parts</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Rank two temperaments">Rank two temperaments</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Individual pages for EDT's">Individual pages for EDT's</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#EDO-EDT correspondence">EDO-EDT correspondence</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#toc4"> </a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Multiples of 13EDT which approximate EDO">Multiples of 13EDT which approximate EDO</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | ||
<!-- ws:end:WikiTextTocRule:19 --><br /> | |||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Division of the tritave (3/1) into n equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 -->Division of the tritave (3/1) into n equal parts</h1> | |||
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Western music generally revolves around the principle of <strong>octave equivalence</strong>: notes an octave apart are often perceived in western music as being the same <em>chroma</em> but differing in pitch height. As the octave corresponds to a 2/1 frequency ratio, it has been proposed that the next-simplest after the octave, the 3/1, can also be used to evoke a sense of chroma equivalence. This interval corresponds to a perfect twelfth in the diatonic scale, but when used to refer to an equivalence interval it is often called the &quot;tritave&quot;.<br /> | Western music generally revolves around the principle of <strong>octave equivalence</strong>: notes an octave apart are often perceived in western music as being the same <em>chroma</em> but differing in pitch height. As the octave corresponds to a 2/1 frequency ratio, it has been proposed that the next-simplest after the octave, the 3/1, can also be used to evoke a sense of chroma equivalence. This interval corresponds to a perfect twelfth in the diatonic scale, but when used to refer to an equivalence interval it is often called the &quot;tritave&quot;.<br /> | ||