Orwell: Difference between revisions

Revision as of 13:43, 23 August 2011

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This revision was by author genewardsmith and made on 2011-08-23 13:43:55 UTC.

The original revision id was 247962941.

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Original Wikitext content:

Orwell — so named because 19 steps of [[84edo]], or 19\84, is a possible generator — is an excellent 7-limit temperament and an amazing (because of the low complexity of 11) 11-limit temperament. The "perfect twelfth" 3/1 is divided into 7 equal steps. One of these steps represents 7/6; three represent 8/5. It's a member of the [[Semicomma family]].

In the 11 limit, two generators are equated to 11/8 (meaning 99/98 is tempered out). This means that three stacked generators makes the [[orwell tetrad|guanyin tetrad]] 1/1-7/6-11/8-8/5, a chord in which every interval is a (tempered) 11-limit consonance. Other such chords in orwell are the [[keenanismic tetrads]] and the [[swetismic chords]].

Compatible equal temperaments include [[22edo]], [[31edo]], [[53edo]], and [[84edo]]. Orwell is in better tune in lower limits than higher ones; the [[optimal patent val]] is [[296edo]] in the 5-limit, [[137edo]] in the 7-limit, and [[53edo]] in the 11-limit. It tempers out the semicomma in the 5-limit, 225/224, 1728/1715, 2430/2401 and 6144/6125 in the 7-limit, and 99/98, 121/120, 176/175, 385/384 and 540/539 in the 11-limit. By adding 275/273 to the list of commas it can be extended to the 13-limit as [[Semicomma family#Julia|julia temperament]], and by adding instead 66/65, [[Semicomma family#Winston|winston temperament]].

==Interval chain== 
|| 0. || 271.43 || 542.85 || 814.28 || 1085.71 || 157.13 || 428.56 || 699.98 || 971.41 || 42.84 || 314.26 || 585.69 || 857.12 || 1128.54 || 199.97 || 471.40 || 742.82 || 1014.25 ||
|| 1/1 || 7/6 || 11/8 || 8/5 || 28/15~15/8 || 12/11~11/10 || 14/11~9/7 || 3/2 || 7/4 ||   || 6/5 || 7/5 || 18/11 ||   || 9/8 ||   ||   || 9/5 ||
==MOSes== 
===9-note (LsLsLsLss, proper)=== 
|| Small ("minor") interval || 114.29 || 228.59 || 385.72 || 500.02 || 657.15 || 771.44 || 928.57 || 1042.87 ||
|| JI intervals represented || 15/14~16/15 || 8/7 || 5/4 || 4/3 || 16/11 || 14/9~11/7 || 12/7 || 11/6 ||
|| Large ("major") interval || 157.13 || 271.43 || 428.56 || 542.85 || 699.98 || 814.28 || 971.41 || 1085.71 ||
|| JI intervals represented || 12/11~11/10 || 7/6 || 14/11~9/7 || 11/8 || 3/2 || 8/5 || 7/4 || 15/8 ||
===13-note (LLLsLLsLLsLLs, improper)=== 
|| Small ("minor") interval || 42.84 || 157.13 || 271.43 || 314.26 || 428.56 || 542.85 || 585.69 || 699.98 || 814.28 || 857 || 971.41 || 1085.71 ||
|| JI intervals represented ||   || 12/11~11/10 || 7/6 || 6/5 || 14/11~9/7 || 11/8 || 7/5 || 3/2 || 8/5 || 18/11 || 7/4 || 15/8 ||
|| Large ("major") interval || 114.29 || 228.59 || 342.88 || 385.72 || 500.02 || 614.31 || 657.15 || 771.44 || 885.74 || 928.57 || 1042.87 || 1157.16 ||
|| JI intervals represented || 15/14~16/15 || 8/7 || 11/9 || 5/4 || 4/3 || 10/7 || 16/11 || 14/9~11/7 || 5/3 || 12/7 || 11/6 ||   ||

Original HTML content:

<html><head><title>Orwell</title></head><body>Orwell — so named because 19 steps of <a class="wiki_link" href="/84edo">84edo</a>, or 19\84, is a possible generator — is an excellent 7-limit temperament and an amazing (because of the low complexity of 11) 11-limit temperament. The &quot;perfect twelfth&quot; 3/1 is divided into 7 equal steps. One of these steps represents 7/6; three represent 8/5. It's a member of the <a class="wiki_link" href="/Semicomma%20family">Semicomma family</a>.<br />
<br />
In the 11 limit, two generators are equated to 11/8 (meaning 99/98 is tempered out). This means that three stacked generators makes the <a class="wiki_link" href="/orwell%20tetrad">guanyin tetrad</a> 1/1-7/6-11/8-8/5, a chord in which every interval is a (tempered) 11-limit consonance. Other such chords in orwell are the <a class="wiki_link" href="/keenanismic%20tetrads">keenanismic tetrads</a> and the <a class="wiki_link" href="/swetismic%20chords">swetismic chords</a>.<br />
<br />
Compatible equal temperaments include <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/53edo">53edo</a>, and <a class="wiki_link" href="/84edo">84edo</a>. Orwell is in better tune in lower limits than higher ones; the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> is <a class="wiki_link" href="/296edo">296edo</a> in the 5-limit, <a class="wiki_link" href="/137edo">137edo</a> in the 7-limit, and <a class="wiki_link" href="/53edo">53edo</a> in the 11-limit. It tempers out the semicomma in the 5-limit, 225/224, 1728/1715, 2430/2401 and 6144/6125 in the 7-limit, and 99/98, 121/120, 176/175, 385/384 and 540/539 in the 11-limit. By adding 275/273 to the list of commas it can be extended to the 13-limit as <a class="wiki_link" href="/Semicomma%20family#Julia">julia temperament</a>, and by adding instead 66/65, <a class="wiki_link" href="/Semicomma%20family#Winston">winston temperament</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Interval chain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Interval chain</h2>
 

<table class="wiki_table">
    <tr>
        <td>0.<br />
</td>
        <td>271.43<br />
</td>
        <td>542.85<br />
</td>
        <td>814.28<br />
</td>
        <td>1085.71<br />
</td>
        <td>157.13<br />
</td>
        <td>428.56<br />
</td>
        <td>699.98<br />
</td>
        <td>971.41<br />
</td>
        <td>42.84<br />
</td>
        <td>314.26<br />
</td>
        <td>585.69<br />
</td>
        <td>857.12<br />
</td>
        <td>1128.54<br />
</td>
        <td>199.97<br />
</td>
        <td>471.40<br />
</td>
        <td>742.82<br />
</td>
        <td>1014.25<br />
</td>
    </tr>
    <tr>
        <td>1/1<br />
</td>
        <td>7/6<br />
</td>
        <td>11/8<br />
</td>
        <td>8/5<br />
</td>
        <td>28/15~15/8<br />
</td>
        <td>12/11~11/10<br />
</td>
        <td>14/11~9/7<br />
</td>
        <td>3/2<br />
</td>
        <td>7/4<br />
</td>
        <td><br />
</td>
        <td>6/5<br />
</td>
        <td>7/5<br />
</td>
        <td>18/11<br />
</td>
        <td><br />
</td>
        <td>9/8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9/5<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-MOSes"></a><!-- ws:end:WikiTextHeadingRule:2 -->MOSes</h2>
 <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-MOSes-9-note (LsLsLsLss, proper)"></a><!-- ws:end:WikiTextHeadingRule:4 -->9-note (LsLsLsLss, proper)</h3>
 

<table class="wiki_table">
    <tr>
        <td>Small (&quot;minor&quot;) interval<br />
</td>
        <td>114.29<br />
</td>
        <td>228.59<br />
</td>
        <td>385.72<br />
</td>
        <td>500.02<br />
</td>
        <td>657.15<br />
</td>
        <td>771.44<br />
</td>
        <td>928.57<br />
</td>
        <td>1042.87<br />
</td>
    </tr>
    <tr>
        <td>JI intervals represented<br />
</td>
        <td>15/14~16/15<br />
</td>
        <td>8/7<br />
</td>
        <td>5/4<br />
</td>
        <td>4/3<br />
</td>
        <td>16/11<br />
</td>
        <td>14/9~11/7<br />
</td>
        <td>12/7<br />
</td>
        <td>11/6<br />
</td>
    </tr>
    <tr>
        <td>Large (&quot;major&quot;) interval<br />
</td>
        <td>157.13<br />
</td>
        <td>271.43<br />
</td>
        <td>428.56<br />
</td>
        <td>542.85<br />
</td>
        <td>699.98<br />
</td>
        <td>814.28<br />
</td>
        <td>971.41<br />
</td>
        <td>1085.71<br />
</td>
    </tr>
    <tr>
        <td>JI intervals represented<br />
</td>
        <td>12/11~11/10<br />
</td>
        <td>7/6<br />
</td>
        <td>14/11~9/7<br />
</td>
        <td>11/8<br />
</td>
        <td>3/2<br />
</td>
        <td>8/5<br />
</td>
        <td>7/4<br />
</td>
        <td>15/8<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-MOSes-13-note (LLLsLLsLLsLLs, improper)"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-note (LLLsLLsLLsLLs, improper)</h3>
 

<table class="wiki_table">
    <tr>
        <td>Small (&quot;minor&quot;) interval<br />
</td>
        <td>42.84<br />
</td>
        <td>157.13<br />
</td>
        <td>271.43<br />
</td>
        <td>314.26<br />
</td>
        <td>428.56<br />
</td>
        <td>542.85<br />
</td>
        <td>585.69<br />
</td>
        <td>699.98<br />
</td>
        <td>814.28<br />
</td>
        <td>857<br />
</td>
        <td>971.41<br />
</td>
        <td>1085.71<br />
</td>
    </tr>
    <tr>
        <td>JI intervals represented<br />
</td>
        <td><br />
</td>
        <td>12/11~11/10<br />
</td>
        <td>7/6<br />
</td>
        <td>6/5<br />
</td>
        <td>14/11~9/7<br />
</td>
        <td>11/8<br />
</td>
        <td>7/5<br />
</td>
        <td>3/2<br />
</td>
        <td>8/5<br />
</td>
        <td>18/11<br />
</td>
        <td>7/4<br />
</td>
        <td>15/8<br />
</td>
    </tr>
    <tr>
        <td>Large (&quot;major&quot;) interval<br />
</td>
        <td>114.29<br />
</td>
        <td>228.59<br />
</td>
        <td>342.88<br />
</td>
        <td>385.72<br />
</td>
        <td>500.02<br />
</td>
        <td>614.31<br />
</td>
        <td>657.15<br />
</td>
        <td>771.44<br />
</td>
        <td>885.74<br />
</td>
        <td>928.57<br />
</td>
        <td>1042.87<br />
</td>
        <td>1157.16<br />
</td>
    </tr>
    <tr>
        <td>JI intervals represented<br />
</td>
        <td>15/14~16/15<br />
</td>
        <td>8/7<br />
</td>
        <td>11/9<br />
</td>
        <td>5/4<br />
</td>
        <td>4/3<br />
</td>
        <td>10/7<br />
</td>
        <td>16/11<br />
</td>
        <td>14/9~11/7<br />
</td>
        <td>5/3<br />
</td>
        <td>12/7<br />
</td>
        <td>11/6<br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>

@@ 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:genewardsmith|genewardsmith]] and made on <tt>2011-08-23 13:41:47 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-23 13:43:55 UTC</tt>.<br>
-: The original revision id was <tt>247962391</tt>.<br>
+: The original revision id was <tt>247962941</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">Orwell — so named because 19 steps of [[84edo]], or 19\84, is a possible generator — is an excellent 7-limit temperament and an amazing (because of the low complexity of 11) 11-limit temperament. The "perfect twelfth" 3/1 is divided into 7 equal steps. One of these steps represents 7/6; three represent 8/5. It's a member of the [[Semicomma family]].
-In the 11 limit, two generators are equated to 11/8 (meaning 99/98 is tempered out). This means that three stacked generators makes the [[orwell tetrad]] 1/1-7/6-11/8-8/5, a chord in which every interval is a (tempered) 11-limit consonance. Other such chords in orwell are the [[keenanismic tetrads]] and the [[swetismic chords]].
+In the 11 limit, two generators are equated to 11/8 (meaning 99/98 is tempered out). This means that three stacked generators makes the [[orwell tetrad|guanyin tetrad]] 1/1-7/6-11/8-8/5, a chord in which every interval is a (tempered) 11-limit consonance. Other such chords in orwell are the [[keenanismic tetrads]] and the [[swetismic chords]].
 Compatible equal temperaments include [[22edo]], [[31edo]], [[53edo]], and [[84edo]]. Orwell is in better tune in lower limits than higher ones; the [[optimal patent val]] is [[296edo]] in the 5-limit, [[137edo]] in the 7-limit, and [[53edo]] in the 11-limit. It tempers out the semicomma in the 5-limit, 225/224, 1728/1715, 2430/2401 and 6144/6125 in the 7-limit, and 99/98, 121/120, 176/175, 385/384 and 540/539 in the 11-limit. By adding 275/273 to the list of commas it can be extended to the 13-limit as [[Semicomma family#Julia|julia temperament]], and by adding instead 66/65, [[Semicomma family#Winston|winston temperament]].
@@ Line 29: / Line 29: @@
 <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;Orwell&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Orwell — so named because 19 steps of &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;, or 19\84, is a possible generator — is an excellent 7-limit temperament and an amazing (because of the low complexity of 11) 11-limit temperament. The &amp;quot;perfect twelfth&amp;quot; 3/1 is divided into 7 equal steps. One of these steps represents 7/6; three represent 8/5. It's a member of the &lt;a class="wiki_link" href="/Semicomma%20family"&gt;Semicomma family&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-In the 11 limit, two generators are equated to 11/8 (meaning 99/98 is tempered out). This means that three stacked generators makes the &lt;a class="wiki_link" href="/orwell%20tetrad"&gt;orwell tetrad&lt;/a&gt; 1/1-7/6-11/8-8/5, a chord in which every interval is a (tempered) 11-limit consonance. Other such chords in orwell are the &lt;a class="wiki_link" href="/keenanismic%20tetrads"&gt;keenanismic tetrads&lt;/a&gt; and the &lt;a class="wiki_link" href="/swetismic%20chords"&gt;swetismic chords&lt;/a&gt;.&lt;br /&gt;
+In the 11 limit, two generators are equated to 11/8 (meaning 99/98 is tempered out). This means that three stacked generators makes the &lt;a class="wiki_link" href="/orwell%20tetrad"&gt;guanyin tetrad&lt;/a&gt; 1/1-7/6-11/8-8/5, a chord in which every interval is a (tempered) 11-limit consonance. Other such chords in orwell are the &lt;a class="wiki_link" href="/keenanismic%20tetrads"&gt;keenanismic tetrads&lt;/a&gt; and the &lt;a class="wiki_link" href="/swetismic%20chords"&gt;swetismic chords&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 Compatible equal temperaments include &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;, and &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;. Orwell is in better tune in lower limits than higher ones; the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; is &lt;a class="wiki_link" href="/296edo"&gt;296edo&lt;/a&gt; in the 5-limit, &lt;a class="wiki_link" href="/137edo"&gt;137edo&lt;/a&gt; in the 7-limit, and &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; in the 11-limit. It tempers out the semicomma in the 5-limit, 225/224, 1728/1715, 2430/2401 and 6144/6125 in the 7-limit, and 99/98, 121/120, 176/175, 385/384 and 540/539 in the 11-limit. By adding 275/273 to the list of commas it can be extended to the 13-limit as &lt;a class="wiki_link" href="/Semicomma%20family#Julia"&gt;julia temperament&lt;/a&gt;, and by adding instead 66/65, &lt;a class="wiki_link" href="/Semicomma%20family#Winston"&gt;winston temperament&lt;/a&gt;.&lt;br /&gt;

Orwell: Difference between revisions

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IMPORTED REVISION FROM WIKISPACES

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