Orwell
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2011-08-23 13:41:47 UTC.
- The original revision id was 247962391.
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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]] 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 "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 <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">orwell 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:<h2> --><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:<h2> --><h2 id="toc1"><a name="x-MOSes"></a><!-- ws:end:WikiTextHeadingRule:2 -->MOSes</h2>
<!-- ws:start:WikiTextHeadingRule:4:<h3> --><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 ("minor") 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 ("major") 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:<h3> --><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 ("minor") 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 ("major") 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>