41edo: Difference between revisions
Wikispaces>TallKite **Imported revision 599968232 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 601503962 - 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: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-06 08:42:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>601503962</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> | ||
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=Commas= | =Commas= | ||
41 EDO tempers out the following commas using its patent val, < 41 65 95 115 142 152 168 174 185 199 203 |. | 41 EDO tempers out the following commas using its patent val, < 41 65 95 115 142/1 152 168 174 185 199/1 203 |. | ||
||~ Name ||~ Monzo ||~ Ratio ||~ Cents || | ||~ Name ||~ Monzo ||~ Ratio ||~ Cents || | ||
|| odiheim || | -1 2 -4 5 -2 > ||= | || odiheim || | -1 2 -4 5 -2 > ||= || 0.15 || | ||
|| harmonisma || | 3 -2 0 -1 3 -2 > ||= 10648/10647 || 0.16 || | || harmonisma || | 3 -2 0 -1 3 -2 > ||= 10648/10647 || 0.16 || | ||
|| tridecimal schisma, Sagittal schismina || | 12 -2 -1 -1 0 -1 > ||= 4096/4095 || 0.42 || | || tridecimal schisma, Sagittal schismina || | [[tel:12 -2 -1 -1 0 -1|12 -2 -1 -1 0 -1]] > ||= 4096/4095 || 0.42 || | ||
|| Lehmerisma || | -4 -3 2 -1 2 > ||= 3025/3024 || 0.57 || | || Lehmerisma || | -4 -3 2 -1 2 > ||= 3025/3024 || 0.57 || | ||
|| Breedsma || | -5 -1 -2 4 > ||= 2401/2400 || 0.72 || | || Breedsma || | -5 -1 -2 4 > ||= 2401/2400 || 0.72 || | ||
| Line 35: | Line 35: | ||
|| undevicesimal comma, Boethius' comma || | -9 3 0 0 0 0 0 1 > ||= 513/512 || 3.38 || | || undevicesimal comma, Boethius' comma || | -9 3 0 0 0 0 0 1 > ||= 513/512 || 3.38 || | ||
|| moctdel || | -2 0 3 -3 1 > ||= 1375/1372 || 3.78 || | || moctdel || | -2 0 3 -3 1 > ||= 1375/1372 || 3.78 || | ||
|| Beta 2, septimal schisma, garischisma || | 25 -14 0 -1 > ||= | || Beta 2, septimal schisma, garischisma || | 25 -14 0 -1 > ||= || 3.80 || | ||
|| Werckmeister's undecimal septenarian schisma, werckisma || | -3 2 -1 2 -1 > ||= 441/440 || 3.93 || | || Werckmeister's undecimal septenarian schisma, werckisma || | -3 2 -1 2 -1 > ||= 441/440 || 3.93 || | ||
|| cuthbert || | 0 0 -1 1 2 -2 > ||= 847/845 || 4.09 || | || cuthbert || | 0 0 -1 1 2 -2 > ||= 847/845 || 4.09 || | ||
| Line 55: | Line 55: | ||
|| septendecimal comma || | -7 7 0 0 0 0 -1 > ||= 2187/2176 || 8.73 || | || septendecimal comma || | -7 7 0 0 0 0 -1 > ||= 2187/2176 || 8.73 || | ||
|| mynucuma || | 2 -1 -1 2 0 -1 > ||= 196/195 || 8.86 || | || mynucuma || | 2 -1 -1 2 0 -1 > ||= 196/195 || 8.86 || | ||
|| quince || | -15 0 -2 7 > ||= | || quince || | -15 0 -2 7 > ||= || 9.15 || | ||
|| undecimal semicomma, pentacircle (minthma * gentle) || | 7 -4 0 1 -1 > ||= 896/891 || 9.69 || | || undecimal semicomma, pentacircle (minthma * gentle) || | 7 -4 0 1 -1 > ||= 896/891 || 9.69 || | ||
|| 29th-partial chroma || | -4 -2 1 0 0 0 0 0 0 1 > ||= 145/144 || 11.98 || | || 29th-partial chroma || | -4 -2 1 0 0 0 0 0 0 1 > ||= 145/144 || 11.98 || | ||
| Line 62: | Line 62: | ||
|| septimal semicomma, octagar || | 5 -4 3 -2 > ||= 4000/3969 || 13.47 || | || septimal semicomma, octagar || | 5 -4 3 -2 > ||= 4000/3969 || 13.47 || | ||
|| minor BP diesis, sensamagic || | 0 -5 1 2 > ||= 245/243 || 14.19 || | || minor BP diesis, sensamagic || | 0 -5 1 2 > ||= 245/243 || 14.19 || | ||
|| secorian || | 12 -7 0 1 0 -1 > ||= 28672/28431 || 14.61 || | || secorian || | [[tel:12 -7 0 1 0 -1|12 -7 0 1 0 -1]] > ||= 28672/28431 || 14.61 || | ||
|| mirwomo comma || | -15 3 2 2 > ||= 33075/32768 || 16.14 || | || mirwomo comma || | -15 3 2 2 > ||= 33075/32768 || 16.14 || | ||
|| vicesimotertial comma || | 5 -6 0 0 0 0 0 0 1 > ||= 736/729 || 16.54 || | || vicesimotertial comma || | 5 -6 0 0 0 0 0 0 1 > ||= 736/729 || 16.54 || | ||
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|| Ptolemy's comma, ptolemisma || | 2 -2 2 0 -1 > ||= 100/99 || 17.40 || | || Ptolemy's comma, ptolemisma || | 2 -2 2 0 -1 > ||= 100/99 || 17.40 || | ||
|| '41-tone' comma || | 65 -41 > ||= || 19.84 || | || '41-tone' comma || | 65 -41 > ||= || 19.84 || | ||
|| tolerma || | 10 -11 2 1 > ||= | || tolerma || | 10 -11 2 1 > ||= || 19.95 || | ||
|| major BP diesis, gariboh || | 0 -2 5 -3 > ||= 3125/3087 || 21.18 || | || major BP diesis, gariboh || | 0 -2 5 -3 > ||= 3125/3087 || 21.18 || | ||
|| cassacot || | -1 0 1 2 -2 > ||= 245/242 || 21.33 || | || cassacot || | -1 0 1 2 -2 > ||= 245/242 || 21.33 || | ||
|| keema || | -5 -3 3 1 > ||= 875/864 || 21.90 || | || keema || | -5 -3 3 1 > ||= 875/864 || 21.90 || | ||
|| blackjackisma || | -10 7 8 -7 > ||= | || blackjackisma || | -10 7 8 -7 > ||= || 22.41 || | ||
|| roda || | 20 -17 3 > ||= | || roda || | 20 -17 3 > ||= || 25.71 || | ||
|| minimal diesis, tetracot comma || | 5 -9 4 > ||= 20000/19683 || 27.66 || | || minimal diesis, tetracot comma || | 5 -9 4 > ||= 20000/19683 || 27.66 || | ||
|| small diesis, magic comma || | -10 -1 5 > ||= 3125/3072 || 29.61 || | || small diesis, magic comma || | -10 -1 5 > ||= 3125/3072 || 29.61 || | ||
|| thuja comma || | 15 0 1 0 -5 > ||= | || thuja comma || | 15 0 1 0 -5 > ||= || 29.72 || | ||
|| Ampersand's comma || | -25 7 6 > ||= || 31.57 || | || Ampersand's comma || | -25 7 6 > ||= || 31.57 || | ||
|| great BP diesis || | 0 -7 6 -1 > ||= 15625/15309 || 35.37 || | || great BP diesis || | 0 -7 6 -1 > ||= 15625/15309 || 35.37 || | ||
|| shibboleth || | -5 -10 9 > ||= | || shibboleth || | -5 -10 9 > ||= || 57.27 || | ||
=Temperaments= | =Temperaments= | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc1"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:11 -->Commas</h1> | <!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc1"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:11 -->Commas</h1> | ||
41 EDO tempers out the following commas using its patent val, &lt; 41 65 95 115 142 152 168 174 185 199 203 |.<br /> | 41 EDO tempers out the following commas using its patent val, &lt; 41 65 95 115 142/1 152 168 174 185 199/1 203 |.<br /> | ||
| Line 319: | Line 319: | ||
<td>| -1 2 -4 5 -2 &gt;<br /> | <td>| -1 2 -4 5 -2 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>0.15<br /> | <td>0.15<br /> | ||
| Line 337: | Line 337: | ||
<td>tridecimal schisma, Sagittal schismina<br /> | <td>tridecimal schisma, Sagittal schismina<br /> | ||
</td> | </td> | ||
<td>| 12 -2 -1 -1 0 -1 &gt;<br /> | <td>| <a class="wiki_link" href="http://tel.wikispaces.com/12%20-2%20-1%20-1%200%20-1">12 -2 -1 -1 0 -1</a> &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">4096/4095<br /> | <td style="text-align: center;">4096/4095<br /> | ||
| Line 439: | Line 439: | ||
<td>| 25 -14 0 -1 &gt;<br /> | <td>| 25 -14 0 -1 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>3.80<br /> | <td>3.80<br /> | ||
| Line 639: | Line 639: | ||
<td>| -15 0 -2 7 &gt;<br /> | <td>| -15 0 -2 7 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>9.15<br /> | <td>9.15<br /> | ||
| Line 707: | Line 707: | ||
<td>secorian<br /> | <td>secorian<br /> | ||
</td> | </td> | ||
<td>| 12 -7 0 1 0 -1 &gt;<br /> | <td>| <a class="wiki_link" href="http://tel.wikispaces.com/12%20-7%200%201%200%20-1">12 -7 0 1 0 -1</a> &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">28672/28431<br /> | <td style="text-align: center;">28672/28431<br /> | ||
| Line 779: | Line 779: | ||
<td>| 10 -11 2 1 &gt;<br /> | <td>| 10 -11 2 1 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>19.95<br /> | <td>19.95<br /> | ||
| Line 819: | Line 819: | ||
<td>| -10 7 8 -7 &gt;<br /> | <td>| -10 7 8 -7 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>22.41<br /> | <td>22.41<br /> | ||
| Line 829: | Line 829: | ||
<td>| 20 -17 3 &gt;<br /> | <td>| 20 -17 3 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>25.71<br /> | <td>25.71<br /> | ||
| Line 859: | Line 859: | ||
<td>| 15 0 1 0 -5 &gt;<br /> | <td>| 15 0 1 0 -5 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>29.72<br /> | <td>29.72<br /> | ||
| Line 889: | Line 889: | ||
<td>| -5 -10 9 &gt;<br /> | <td>| -5 -10 9 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>57.27<br /> | <td>57.27<br /> | ||
| Line 2,858: | Line 2,858: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:29:&lt;h1&gt; --><h1 id="toc10"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:29 -->Links</h1> | <!-- ws:start:WikiTextHeadingRule:29:&lt;h1&gt; --><h1 id="toc10"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:29 -->Links</h1> | ||
<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow">Wikipedia article on 41edo</a></li><li><a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis">Magic22 as srutis</a> describes a possible use of 41edo for <a class="wiki_link" href="/indian">indian</a> music.</li><li>see also <a class="wiki_link" href="/Magic%20family">Magic family</a></li><li>Sword, Ron. <a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank">&quot;Tetracontamonophonic Scales for Guitar&quot;</a></li></ul><!-- ws:start:WikiTextReferencesRule: | <ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow">Wikipedia article on 41edo</a></li><li><a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis">Magic22 as srutis</a> describes a possible use of 41edo for <a class="wiki_link" href="/indian">indian</a> music.</li><li>see also <a class="wiki_link" href="/Magic%20family">Magic family</a></li><li>Sword, Ron. <a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank">&quot;Tetracontamonophonic Scales for Guitar&quot;</a></li></ul><!-- ws:start:WikiTextReferencesRule:3838: --><hr class="references" /><ol class="references"> | ||
<li id="cite_note-1"><a href="#cite_ref-1">^</a> <a class="wiki_link_ext" href="http://x31eq.com/schismic.htm" rel="nofollow">&quot;Schismic Temperaments&quot;</a> at x31eq.com the website of <a class="wiki_link" href="/Graham%20Breed">Graham Breed</a></li> | <li id="cite_note-1"><a href="#cite_ref-1">^</a> <a class="wiki_link_ext" href="http://x31eq.com/schismic.htm" rel="nofollow">&quot;Schismic Temperaments&quot;</a> at x31eq.com the website of <a class="wiki_link" href="/Graham%20Breed">Graham Breed</a></li> | ||
<li id="cite_note-2"><a href="#cite_ref-2">^</a> <a class="wiki_link_ext" href="http://x31eq.com/decimal_lattice.htm" rel="nofollow">&quot;Lattices with Decimal Notation&quot;</a> at x31eq.com</li> | <li id="cite_note-2"><a href="#cite_ref-2">^</a> <a class="wiki_link_ext" href="http://x31eq.com/decimal_lattice.htm" rel="nofollow">&quot;Lattices with Decimal Notation&quot;</a> at x31eq.com</li> | ||
<li id="cite_note-3"><a href="#cite_ref-3">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow">Schismatic temperament</a></li> | <li id="cite_note-3"><a href="#cite_ref-3">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow">Schismatic temperament</a></li> | ||
<li id="cite_note-4"><a href="#cite_ref-4">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow">Magic temperament</a></li> | <li id="cite_note-4"><a href="#cite_ref-4">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow">Magic temperament</a></li> | ||
</ol><!-- ws:end:WikiTextReferencesRule: | </ol><!-- ws:end:WikiTextReferencesRule:3838 --></body></html></pre></div> | ||