EDT: Difference between revisions
Wikispaces>keenanpepper **Imported revision 251459550 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 251460354 - 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>2011-09-07 02: | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-09-07 02:26:25 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>251460354</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">==Division of the tritave (3/1) into n equal parts== | ||
After the octave (roughly 2:1 but it has been tuned sharp and flat for various reasons), the next simple "frame interval" available is the ratio 3:1. Among other names, the third harmonic has been called the "perfect twelfth" "triple" or "tritave". There has been argument whether pitches a tritave apart can be heard as equivalent, but with proper context and/or experience, at least some people find that they can. Arguably that is the single criterion for calling the tritave a true frame interval. Some put a great emphasis on timbre, claiming that a lack of even harmonics (octaves) emphasizes the property of tritave equivalence, or at least enhances the perception of [[BP]] harmonies, though the necessity of this claim is arguable. It is certain that musically valuable organizations of pitch can arise through the equal division of non-octave intervals regardless of equivalence, and either way, the multitude of equal divisions of the tritave are rich and ripe for exploration. | After the octave (roughly 2:1 but it has been tuned sharp and flat for various reasons), the next simple "frame interval" available is the ratio 3:1. Among other names, the third harmonic has been called the "perfect twelfth" "triple" or "tritave". There has been argument whether pitches a tritave apart can be heard as equivalent, but with proper context and/or experience, at least some people find that they can. Arguably that is the single criterion for calling the tritave a true frame interval. Some put a great emphasis on timbre, claiming that a lack of even harmonics (octaves) emphasizes the property of tritave equivalence, or at least enhances the perception of [[BP]] harmonies, though the necessity of this claim is arguable. It is certain that musically valuable organizations of pitch can arise through the equal division of non-octave intervals regardless of equivalence, and either way, the multitude of equal divisions of the tritave are rich and ripe for exploration. | ||
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[[39edt]] Triple Bohlen-Pierce (Erlich) | [[39edt]] Triple Bohlen-Pierce (Erlich) | ||
=Individual pages for EDT's= | ==Individual pages for EDT's== | ||
|| [[edt|1edt]] || [[2edt]] || [[3edt]] || [[4edt]] || [[5edt]] || [[6edt]] || [[7edt]] || [[8edt]] || [[9edt]] || [[10edt]] || [[11edt]] || [[12edt]] || | || [[edt|1edt]] || [[2edt]] || [[3edt]] || [[4edt]] || [[5edt]] || [[6edt]] || [[7edt]] || [[8edt]] || [[9edt]] || [[10edt]] || [[11edt]] || [[12edt]] || | ||
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|| || [[45edt]] || || | || || [[45edt]] || || | ||
|| [[29edo]] || [[46edt]] || 46edt is 29edo with ~0.9 cent compressed octaves. | || [[29edo]] || [[46edt]] || 46edt is 29edo with ~0.9 cent compressed octaves. | ||
Patent vals match through the 89 limit. (Really! I checked!) ||</pre></div> | Patent vals match through the 89 limit. (Really! I checked!) || | ||
</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; | <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;h2&gt; --><h2 id="toc0"><a name="x-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</h2> | ||
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After the octave (roughly 2:1 but it has been tuned sharp and flat for various reasons), the next simple &quot;frame interval&quot; available is the ratio 3:1. Among other names, the third harmonic has been called the &quot;perfect twelfth&quot; &quot;triple&quot; or &quot;tritave&quot;. There has been argument whether pitches a tritave apart can be heard as equivalent, but with proper context and/or experience, at least some people find that they can. Arguably that is the single criterion for calling the tritave a true frame interval. Some put a great emphasis on timbre, claiming that a lack of even harmonics (octaves) emphasizes the property of tritave equivalence, or at least enhances the perception of <a class="wiki_link" href="/BP">BP</a> harmonies, though the necessity of this claim is arguable. It is certain that musically valuable organizations of pitch can arise through the equal division of non-octave intervals regardless of equivalence, and either way, the multitude of equal divisions of the tritave are rich and ripe for exploration.<br /> | After the octave (roughly 2:1 but it has been tuned sharp and flat for various reasons), the next simple &quot;frame interval&quot; available is the ratio 3:1. Among other names, the third harmonic has been called the &quot;perfect twelfth&quot; &quot;triple&quot; or &quot;tritave&quot;. There has been argument whether pitches a tritave apart can be heard as equivalent, but with proper context and/or experience, at least some people find that they can. Arguably that is the single criterion for calling the tritave a true frame interval. Some put a great emphasis on timbre, claiming that a lack of even harmonics (octaves) emphasizes the property of tritave equivalence, or at least enhances the perception of <a class="wiki_link" href="/BP">BP</a> harmonies, though the necessity of this claim is arguable. It is certain that musically valuable organizations of pitch can arise through the equal division of non-octave intervals regardless of equivalence, and either way, the multitude of equal divisions of the tritave are rich and ripe for exploration.<br /> | ||
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<a class="wiki_link" href="/39edt">39edt</a> Triple Bohlen-Pierce (Erlich)<br /> | <a class="wiki_link" href="/39edt">39edt</a> Triple Bohlen-Pierce (Erlich)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt; | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Individual pages for EDT's"></a><!-- ws:end:WikiTextHeadingRule:2 -->Individual pages for EDT's</h2> | ||
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[Also, the way I see it, as 4edt and 9edt are comparable to 5edo and 7edo, then the &quot;counterparts&quot; of Blackwood and Whitewood would be found in multiples therein and would be octatonic and octadecatonic, eg. 12edt and 27edt. Alas, Ryan has priority ;) ]<br /> | [Also, the way I see it, as 4edt and 9edt are comparable to 5edo and 7edo, then the &quot;counterparts&quot; of Blackwood and Whitewood would be found in multiples therein and would be octatonic and octadecatonic, eg. 12edt and 27edt. Alas, Ryan has priority ;) ]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name=" | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-EDO-EDT correspondence"></a><!-- ws:end:WikiTextHeadingRule:4 -->EDO-EDT correspondence</h2> | ||