EDT: Difference between revisions
Wikispaces>keenanpepper **Imported revision 251460354 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 251460534 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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 02:27:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>251460534</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"> | <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. | ||
| Line 27: | Line 27: | ||
[[39edt]] Triple Bohlen-Pierce (Erlich) | [[39edt]] Triple Bohlen-Pierce (Erlich) | ||
=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]] || | ||
| Line 60: | Line 60: | ||
[Also, the way I see it, as 4edt and 9edt are comparable to 5edo and 7edo, then the "counterparts" of Blackwood and Whitewood would be found in multiples therein and would be octatonic and octadecatonic, eg. 12edt and 27edt. Alas, Ryan has priority ;) ] | [Also, the way I see it, as 4edt and 9edt are comparable to 5edo and 7edo, then the "counterparts" of Blackwood and Whitewood would be found in multiples therein and would be octatonic and octadecatonic, eg. 12edt and 27edt. Alas, Ryan has priority ;) ] | ||
=EDO-EDT correspondence= | |||
||~ EDO ||~ EDT ||~ Comments || | ||~ EDO ||~ EDT ||~ Comments || | ||
|| [[5edo]] || [[8edt]] || 8edt is equivalent to 5edo with ~11 cent octave compression. | || [[5edo]] || [[8edt]] || 8edt is equivalent to 5edo with ~11 cent octave compression. | ||
| Line 126: | Line 126: | ||
|| || [[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!) || | Patent vals match through the 89 limit. (Really! I checked!) ||</pre></div> | ||
</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;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> | ||
<br /> | <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 /> | 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 /> | ||
<br /> | <br /> | ||
| Line 150: | Line 149: | ||
<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;h1&gt; --><h1 id="toc1"><a name="Individual pages for EDT's"></a><!-- ws:end:WikiTextHeadingRule:2 -->Individual pages for EDT's</h1> | ||
<br /> | <br /> | ||
| Line 288: | Line 287: | ||
[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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt; | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="EDO-EDT correspondence"></a><!-- ws:end:WikiTextHeadingRule:4 -->EDO-EDT correspondence</h1> | ||