25edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 244898861 - Original comment: ** |
Wikispaces>igliashon **Imported revision 248696827 - 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:igliashon|igliashon]] and made on <tt>2011-08-26 15:33:17 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>248696827</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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|| Degrees || Cents value ||= Approximate | || Degrees || Cents value ||= Approximate | ||
Ratios* || | Ratios* ||= Armodue | ||
|| 0 || 0 ||= 1/1 || | Notation || | ||
|| 1 || 48 ||= 33/32, 39/38, 34/33 || | || 0 || 0 ||= 1/1 ||= 1 || | ||
|| 2 || 96 ||= 17/16, 20/19, 18/17 || | || 1 || 48 ||= 33/32, 39/38, 34/33 ||= 1# || | ||
|| 3 || 144 ||= 12/11, 38/35 || | || 2 || 96 ||= 17/16, 20/19, 18/17 ||= 2b || | ||
|| 4 || 192 ||= 9/8, 10/9, 19/17 || | || 3 || 144 ||= 12/11, 38/35 ||= 2 || | ||
|| 5· || 240 ||= 8/7 || | || 4 || 192 ||= 9/8, 10/9, 19/17 ||= 2# || | ||
|| 6 || 288 ||= 19/16, 20/17 || | || 5· || 240 ||= 8/7 ||= 3b || | ||
|| 7 || 336 ||= 39/32, 17/14, 40/33 || | || 6 || 288 ||= 19/16, 20/17 ||= 3 || | ||
|| 8· || 384 ||= 5/4 || | || 7 || 336 ||= 39/32, 17/14, 40/33 ||= 3# || | ||
|| 9 || 432 ||= 9/7, 32/25, 50/39 || | || 8· || 384 ||= 5/4 ||= 4b || | ||
|| 10 || 480 ||= 33/25, 25/19 || | || 9 || 432 ||= 9/7, 32/25, 50/39 ||= 4 || | ||
|| 11· || 528 ||= 31/21, 34/25 || | || 10 || 480 ||= 33/25, 25/19 ||= 4#/5b || | ||
|| 12 || 576 ||= 7/5, 39/28 || | || 11· || 528 ||= 31/21, 34/25 ||= 5 || | ||
|| 13 || 624 ||= 10/7, 56/39 || | || 12 || 576 ||= 7/5, 39/28 ||= 5# || | ||
|| 14· || 672 ||= 42/31, 25/17 || | || 13 || 624 ||= 10/7, 56/39 ||= 6b || | ||
|| 15 || 720 ||= 50/33, 38/25 || | || 14· || 672 ||= 42/31, 25/17 ||= 6 || | ||
|| 16 || 768 ||= 14/9, 25/16, 39/25 || | || 15 || 720 ||= 50/33, 38/25 ||= 6# || | ||
|| 17· || 816 ||= 8/5 || | || 16 || 768 ||= 14/9, 25/16, 39/25 ||= 7b || | ||
|| 18 || 864 ||= 64/39, 28/17, 33/20 || | || 17· || 816 ||= 8/5 ||= 7 || | ||
|| 19 || 912 ||= 32/19, 17/10 || | || 18 || 864 ||= 64/39, 28/17, 33/20 ||= 7# || | ||
|| 20· || 960 ||= 7/4 || | || 19 || 912 ||= 32/19, 17/10 ||= 8b || | ||
|| 21 || 1008 ||= 16/9, 9/5, 34/19 || | || 20· || 960 ||= 7/4 ||= 8 || | ||
|| 22 || 1056 ||= 11/6, 35/19 || | || 21 || 1008 ||= 16/9, 9/5, 34/19 ||= 8# || | ||
|| 23 || 1104 ||= 32/17, 17/9, 19/10 || | || 22 || 1056 ||= 11/6, 35/19 ||= 9b || | ||
|| 24 || 1152 ||= 33/17, 64/33, 76/39 || | || 23 || 1104 ||= 32/17, 17/9, 19/10 ||= 9 || | ||
|| | || 24 || 1152 ||= 33/17, 64/33, 76/39 ||= 9#/1b || | ||
|| 25 || 1200 ||= 2/1 ||= 1 || | |||
*based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible. | *based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible. | ||
=Relationship to Armodue= | |||
Like 16-EDO and 23-EDO, 25-EDO contains the 9-note "Superdiatonic" scale of 7L2s (LLLsLLLLs) that is generated by a circle of heavily-flattened 3/2s (ranging in size from 5\9-EDO or 666.67 cents, to 4\7-EDO or 685.71 cents). The 25-EDO generator for this scale is the 672-cent interval. This allows 25-EDO to be used with the Armodue notation system in much the same way that 19-EDO is used with the standard diatonic notation; see the above interval chart for the Armodue names. Because the 25-EDO Armodue 6th is flatter than that of 16-EDO (the middle of the Armodue spectrum), sharps are lower in pitch than enharmonic flats. | |||
=Commas= | =Commas= | ||
25 EDO tempers out the following commas. (Note: This assumes the val < 25 40 58 70 86 93 |.) | 25 EDO tempers out the following commas. (Note: This assumes the val < 25 40 58 70 86 93 |.) | ||
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[[image:mm25.PNG]]</pre></div> | [[image:mm25.PNG]]</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>25edo</title></head><body><!-- ws:start:WikiTextTocRule: | <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>25edo</title></head><body><!-- ws:start:WikiTextTocRule:12:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#x25 tone equal temperament">25 tone equal temperament</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Relationship to Armodue">Relationship to Armodue</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#A 25edo keyboard">A 25edo keyboard</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x25 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #006b2e;">25 tone equal temperament</span></h1> | ||
<br /> | <br /> | ||
25EDO divides the <a class="wiki_link" href="/octave">octave</a> in 25 equal steps of exact size 48 <a class="wiki_link" href="/cent">cent</a>s each. It is a good way to tune the <a class="wiki_link" href="/Blackwood%20temperament">Blackwood temperament</a>, which takes the very sharp fifths of <a class="wiki_link" href="/5EDO">5EDO</a> as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 (<a class="wiki_link" href="/5_4">5/4</a>) and 7 (<a class="wiki_link" href="/7_4">7/4</a>?).<br /> | 25EDO divides the <a class="wiki_link" href="/octave">octave</a> in 25 equal steps of exact size 48 <a class="wiki_link" href="/cent">cent</a>s each. It is a good way to tune the <a class="wiki_link" href="/Blackwood%20temperament">Blackwood temperament</a>, which takes the very sharp fifths of <a class="wiki_link" href="/5EDO">5EDO</a> as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 (<a class="wiki_link" href="/5_4">5/4</a>) and 7 (<a class="wiki_link" href="/7_4">7/4</a>?).<br /> | ||
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<td style="text-align: center;">Approximate<br /> | <td style="text-align: center;">Approximate<br /> | ||
Ratios*<br /> | Ratios*<br /> | ||
</td> | |||
<td style="text-align: center;">Armodue<br /> | |||
Notation<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 104: | Line 113: | ||
</td> | </td> | ||
<td style="text-align: center;">1/1<br /> | <td style="text-align: center;">1/1<br /> | ||
</td> | |||
<td style="text-align: center;">1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 112: | Line 123: | ||
</td> | </td> | ||
<td style="text-align: center;">33/32, 39/38, 34/33<br /> | <td style="text-align: center;">33/32, 39/38, 34/33<br /> | ||
</td> | |||
<td style="text-align: center;">1#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 120: | Line 133: | ||
</td> | </td> | ||
<td style="text-align: center;">17/16, 20/19, 18/17<br /> | <td style="text-align: center;">17/16, 20/19, 18/17<br /> | ||
</td> | |||
<td style="text-align: center;">2b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 128: | Line 143: | ||
</td> | </td> | ||
<td style="text-align: center;">12/11, 38/35<br /> | <td style="text-align: center;">12/11, 38/35<br /> | ||
</td> | |||
<td style="text-align: center;">2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 136: | Line 153: | ||
</td> | </td> | ||
<td style="text-align: center;">9/8, 10/9, 19/17<br /> | <td style="text-align: center;">9/8, 10/9, 19/17<br /> | ||
</td> | |||
<td style="text-align: center;">2#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 144: | Line 163: | ||
</td> | </td> | ||
<td style="text-align: center;">8/7<br /> | <td style="text-align: center;">8/7<br /> | ||
</td> | |||
<td style="text-align: center;">3b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 152: | Line 173: | ||
</td> | </td> | ||
<td style="text-align: center;">19/16, 20/17<br /> | <td style="text-align: center;">19/16, 20/17<br /> | ||
</td> | |||
<td style="text-align: center;">3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 160: | Line 183: | ||
</td> | </td> | ||
<td style="text-align: center;">39/32, 17/14, 40/33<br /> | <td style="text-align: center;">39/32, 17/14, 40/33<br /> | ||
</td> | |||
<td style="text-align: center;">3#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 168: | Line 193: | ||
</td> | </td> | ||
<td style="text-align: center;">5/4<br /> | <td style="text-align: center;">5/4<br /> | ||
</td> | |||
<td style="text-align: center;">4b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 176: | Line 203: | ||
</td> | </td> | ||
<td style="text-align: center;">9/7, 32/25, 50/39<br /> | <td style="text-align: center;">9/7, 32/25, 50/39<br /> | ||
</td> | |||
<td style="text-align: center;">4<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 184: | Line 213: | ||
</td> | </td> | ||
<td style="text-align: center;">33/25, 25/19<br /> | <td style="text-align: center;">33/25, 25/19<br /> | ||
</td> | |||
<td style="text-align: center;">4#/5b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 192: | Line 223: | ||
</td> | </td> | ||
<td style="text-align: center;">31/21, 34/25<br /> | <td style="text-align: center;">31/21, 34/25<br /> | ||
</td> | |||
<td style="text-align: center;">5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">7/5, 39/28<br /> | <td style="text-align: center;">7/5, 39/28<br /> | ||
</td> | |||
<td style="text-align: center;">5#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">10/7, 56/39<br /> | <td style="text-align: center;">10/7, 56/39<br /> | ||
</td> | |||
<td style="text-align: center;">6b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">42/31, 25/17<br /> | <td style="text-align: center;">42/31, 25/17<br /> | ||
</td> | |||
<td style="text-align: center;">6<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">50/33, 38/25<br /> | <td style="text-align: center;">50/33, 38/25<br /> | ||
</td> | |||
<td style="text-align: center;">6#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">14/9, 25/16, 39/25<br /> | <td style="text-align: center;">14/9, 25/16, 39/25<br /> | ||
</td> | |||
<td style="text-align: center;">7b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">8/5<br /> | <td style="text-align: center;">8/5<br /> | ||
</td> | |||
<td style="text-align: center;">7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">64/39, 28/17, 33/20<br /> | <td style="text-align: center;">64/39, 28/17, 33/20<br /> | ||
</td> | |||
<td style="text-align: center;">7#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">32/19, 17/10<br /> | <td style="text-align: center;">32/19, 17/10<br /> | ||
</td> | |||
<td style="text-align: center;">8b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">7/4<br /> | <td style="text-align: center;">7/4<br /> | ||
</td> | |||
<td style="text-align: center;">8<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">16/9, 9/5, 34/19<br /> | <td style="text-align: center;">16/9, 9/5, 34/19<br /> | ||
</td> | |||
<td style="text-align: center;">8#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">11/6, 35/19<br /> | <td style="text-align: center;">11/6, 35/19<br /> | ||
</td> | |||
<td style="text-align: center;">9b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">32/17, 17/9, 19/10<br /> | <td style="text-align: center;">32/17, 17/9, 19/10<br /> | ||
</td> | |||
<td style="text-align: center;">9<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">33/17, 64/33, 76/39<br /> | <td style="text-align: center;">33/17, 64/33, 76/39<br /> | ||
</td> | |||
<td style="text-align: center;">9#/1b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>25<br /> | ||
</td> | </td> | ||
<td>1200<br /> | <td>1200<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">2/1<br /> | <td style="text-align: center;">2/1<br /> | ||
</td> | |||
<td style="text-align: center;">1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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*based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible.<br /> | *based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible.<br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule: | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Relationship to Armodue"></a><!-- ws:end:WikiTextHeadingRule:6 -->Relationship to Armodue</h1> | |||
<br /> | |||
Like 16-EDO and 23-EDO, 25-EDO contains the 9-note &quot;Superdiatonic&quot; scale of 7L2s (LLLsLLLLs) that is generated by a circle of heavily-flattened 3/2s (ranging in size from 5\9-EDO or 666.67 cents, to 4\7-EDO or 685.71 cents). The 25-EDO generator for this scale is the 672-cent interval. This allows 25-EDO to be used with the Armodue notation system in much the same way that 19-EDO is used with the standard diatonic notation; see the above interval chart for the Armodue names. Because the 25-EDO Armodue 6th is flatter than that of 16-EDO (the middle of the Armodue spectrum), sharps are lower in pitch than enharmonic flats.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->Commas</h1> | |||
25 EDO tempers out the following commas. (Note: This assumes the val &lt; 25 40 58 70 86 93 |.)<br /> | 25 EDO tempers out the following commas. (Note: This assumes the val &lt; 25 40 58 70 86 93 |.)<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="A 25edo keyboard"></a><!-- ws:end:WikiTextHeadingRule:10 -->A 25edo keyboard</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:518:&lt;img src=&quot;/file/view/mm25.PNG/179204243/mm25.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/mm25.PNG/179204243/mm25.PNG" alt="mm25.PNG" title="mm25.PNG" /><!-- ws:end:WikiTextLocalImageRule:518 --></body></html></pre></div> | ||