EDT: Difference between revisions
Wikispaces>genewardsmith **Imported revision 250559574 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 251459550 - Original comment: ** |
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| 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: | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-09-07 02:20:23 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>251459550</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> | ||
| Line 58: | Line 58: | ||
L=7 s=6 58 5sharp1 7sharp10 (Schism*) | L=7 s=6 58 5sharp1 7sharp10 (Schism*) | ||
*Schism, by which I mean, the most accurate value for 5/3 and-or 7/3 is found outside the 4L+5s MOS. | *Schism, by which I mean, the most accurate value for 5/3 and-or 7/3 is found outside the 4L+5s MOS. | ||
[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 ;) ]</pre></div> | [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 || | |||
|| [[5edo]] || [[8edt]] || 8edt is equivalent to 5edo with ~11 cent octave compression. | |||
Equivalently, 5edo is 8edt with ~18 cent stretched tritaves. | |||
[[Patent val|Patent vals]] match through the 13 limit. || | |||
|| || [[9edt]] || || | |||
|| [[6edo]] || || || | |||
|| || [[10edt]] || || | |||
|| [[7edo]] || [[11edt]] || 11edt is equivalent to 7edo with ~10 cent stretched octaves. | |||
Patent vals differ in the 7 limit, but neither can really be said | |||
to represent the 7th harmonic with a straight face. || | |||
|| || [[12edt]] || || | |||
|| [[8edo]] || || || | |||
|| || [[13edt]] || The equal-tempered BP scale cannot be considered equivalent to 8edo. || | |||
|| [[9edo]] || [[14edt]] || There is a lot of mismatch between the pure-octave and pure-tritave tunings, | |||
but the patent vals match through the 13 limit. || | |||
|| || [[15edt]] || || | |||
|| [[10edo]] || [[16edt]] || Similar situation to 5edo~8edt. Patent vals match through the 17 limit. || | |||
|| || [[17edt]] || || | |||
|| [[11edo]] || || || | |||
|| || [[18edt]] || || | |||
|| [[12edo]] || [[19edt]] || 19edt is 12edo with ~1.2 cent octave stretch. Patent vals match | |||
only through the 7 limit, but neither can be said to include 11 at all. || | |||
|| || [[20edt]] || || | |||
|| [[13edo]] || || || | |||
|| || [[21edt]] || || | |||
|| || [[22edt]] || || | |||
|| [[14edo]] || || || | |||
|| || [[23edt]] || || | |||
|| [[15edo]] || [[24edt]] || This is only a rough correspondence, as the (5n)edo ~ (8n)edt sequence | |||
begins to break down. The patent vals match only through the 5 limit. || | |||
|| [[16edo]] || [[25edt]] || Also only a rough correspondence; 25edt corresponds to 16edo | |||
with ~17 cent octave stretch. Patent vals match through the 5 limit. || | |||
|| || [[26edt]] || Double BP || | |||
|| [[17edo]] || [[27edt]] || 27edt is 17edo with ~2.5 cent compressed octaves. With the exception of | |||
5 (which neither represents well), patent vals match through the 13 limit. || | |||
|| || [[28edt]] || || | |||
|| [[18edo]] || || || | |||
|| || [[29edt]] || || | |||
|| [[19edo]] || [[30edt]] || 30edt is 19edo with ~5 cent stretched octaves. | |||
Patent vals match through the 7 limit. || | |||
|| || [[31edt]] || || | |||
|| [[20edo]] || || || | |||
|| || [[32edt]] || || | |||
|| || [[33edt]] || || | |||
|| [[21edo]] || || || | |||
|| || [[34edt]] || || | |||
|| [[22edo]] || [[35edt]] || 35edt is 22edo with ~4 cent compressed octaves. | |||
Patent vals match through the 11 limit. || | |||
|| || [[36edt]] || || | |||
|| [[23edo]] || || || | |||
|| || [[37edt]] || || | |||
|| [[24edo]] || [[38edt]] || Same ~1.2 cent octave stretch as 12edo~19edt. | |||
Patent vals match through the 19 limit. || | |||
|| || [[39edt]] || [[Triple BP]] || | |||
|| [[25edo]] || || || | |||
|| || [[40edt]] || || | |||
|| [[26edo]] || [[41edt]] || 41edt is 26edo with ~6 cent stretched octaves. | |||
Patent vals match through the 7 limit. || | |||
|| || [[42edt]] || || | |||
|| [[27edo]] || [[43edt]] || 43edt is 27edo with ~6 cent compressed octaves. | |||
Patent vals match through the 7 limit. || | |||
|| || [[44edt]] || || | |||
|| [[28edo]] || || || | |||
|| || [[45edt]] || || | |||
|| [[29edo]] || [[46edt]] || 46edt is 29edo with ~0.9 cent compressed octaves. | |||
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;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: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> | ||
| Line 217: | Line 285: | ||
L=7 s=6 58 5sharp1 7sharp10 (Schism*)<br /> | L=7 s=6 58 5sharp1 7sharp10 (Schism*)<br /> | ||
*Schism, by which I mean, the most accurate value for 5/3 and-or 7/3 is found outside the 4L+5s MOS.<br /> | *Schism, by which I mean, the most accurate value for 5/3 and-or 7/3 is found outside the 4L+5s MOS.<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 ;) ]</body></html></pre></div> | [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 /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Individual pages for EDT's-EDO-EDT correspondence"></a><!-- ws:end:WikiTextHeadingRule:4 -->EDO-EDT correspondence</h2> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>EDO<br /> | |||
</th> | |||
<th>EDT<br /> | |||
</th> | |||
<th>Comments<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/5edo">5edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/8edt">8edt</a><br /> | |||
</td> | |||
<td>8edt is equivalent to 5edo with ~11 cent octave compression.<br /> | |||
Equivalently, 5edo is 8edt with ~18 cent stretched tritaves.<br /> | |||
<a class="wiki_link" href="/Patent%20val">Patent vals</a> match through the 13 limit.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/9edt">9edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/6edo">6edo</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/10edt">10edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/7edo">7edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/11edt">11edt</a><br /> | |||
</td> | |||
<td>11edt is equivalent to 7edo with ~10 cent stretched octaves.<br /> | |||
Patent vals differ in the 7 limit, but neither can really be said<br /> | |||
to represent the 7th harmonic with a straight face.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/12edt">12edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/8edo">8edo</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/13edt">13edt</a><br /> | |||
</td> | |||
<td>The equal-tempered BP scale cannot be considered equivalent to 8edo.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/9edo">9edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/14edt">14edt</a><br /> | |||
</td> | |||
<td>There is a lot of mismatch between the pure-octave and pure-tritave tunings,<br /> | |||
but the patent vals match through the 13 limit.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/15edt">15edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/10edo">10edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/16edt">16edt</a><br /> | |||
</td> | |||
<td>Similar situation to 5edo~8edt. Patent vals match through the 17 limit.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/17edt">17edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/11edo">11edo</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/18edt">18edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/12edo">12edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/19edt">19edt</a><br /> | |||
</td> | |||
<td>19edt is 12edo with ~1.2 cent octave stretch. Patent vals match<br /> | |||
only through the 7 limit, but neither can be said to include 11 at all.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/20edt">20edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/13edo">13edo</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/21edt">21edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/22edt">22edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/14edo">14edo</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/23edt">23edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/15edo">15edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/24edt">24edt</a><br /> | |||
</td> | |||
<td>This is only a rough correspondence, as the (5n)edo ~ (8n)edt sequence<br /> | |||
begins to break down. The patent vals match only through the 5 limit.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/16edo">16edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/25edt">25edt</a><br /> | |||
</td> | |||
<td>Also only a rough correspondence; 25edt corresponds to 16edo<br /> | |||
with ~17 cent octave stretch. Patent vals match through the 5 limit.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/26edt">26edt</a><br /> | |||
</td> | |||
<td>Double BP<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/17edo">17edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/27edt">27edt</a><br /> | |||
</td> | |||
<td>27edt is 17edo with ~2.5 cent compressed octaves. With the exception of<br /> | |||
5 (which neither represents well), patent vals match through the 13 limit.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/28edt">28edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/18edo">18edo</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/29edt">29edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/19edo">19edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/30edt">30edt</a><br /> | |||
</td> | |||
<td>30edt is 19edo with ~5 cent stretched octaves.<br /> | |||
Patent vals match through the 7 limit.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/31edt">31edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/20edo">20edo</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/32edt">32edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/33edt">33edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/21edo">21edo</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/34edt">34edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/22edo">22edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/35edt">35edt</a><br /> | |||
</td> | |||
<td>35edt is 22edo with ~4 cent compressed octaves.<br /> | |||
Patent vals match through the 11 limit.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/36edt">36edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/23edo">23edo</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/37edt">37edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/24edo">24edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/38edt">38edt</a><br /> | |||
</td> | |||
<td>Same ~1.2 cent octave stretch as 12edo~19edt.<br /> | |||
Patent vals match through the 19 limit.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/39edt">39edt</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Triple%20BP">Triple BP</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/25edo">25edo</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/40edt">40edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/26edo">26edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/41edt">41edt</a><br /> | |||
</td> | |||
<td>41edt is 26edo with ~6 cent stretched octaves.<br /> | |||
Patent vals match through the 7 limit.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/42edt">42edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/27edo">27edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/43edt">43edt</a><br /> | |||
</td> | |||
<td>43edt is 27edo with ~6 cent compressed octaves.<br /> | |||
Patent vals match through the 7 limit.<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/44edt">44edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/28edo">28edo</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/45edt">45edt</a><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/29edo">29edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/46edt">46edt</a><br /> | |||
</td> | |||
<td>46edt is 29edo with ~0.9 cent compressed octaves.<br /> | |||
Patent vals match through the 89 limit. (Really! I checked!)<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
</body></html></pre></div> | |||