15edo: Difference between revisions
Wikispaces>guest **Imported revision 241839323 - Original comment: ** |
Wikispaces>guest **Imported revision 242162119 - 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:guest|guest]] and made on <tt>2011-07- | : This revision was by author [[User:guest|guest]] and made on <tt>2011-07-20 16:35:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>242162119</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">=15 tone equal temperament= | <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">=15 tone equal temperament= | ||
from //wikipedia//: | from //wikipedia//: | ||
""In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the [[octave]] into 15 equal steps. Each step represents a frequency ratio of 2^(1/15), or 80 [[cent]]s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of [[5edo|5 equal divisions of the octave]] (or five scales of [[3edo]])." | ""In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the [[octave]] into 15 equal steps. Each step represents a frequency ratio of 2^(1/15), or 80 [[cent]]s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of [[5edo|5 equal divisions of the octave]] (or five scales of [[3edo]])." | ||
15-edo can be seen as a [[7-limit]] temperament because of its ability to approximate some septimal intervals, but it also contains some fairly obvious approximations to [[11-limit]] intervals, so it can reasonably be described as an 11-limit temperament; however, due to its rather distant approximation of the 3rd harmonic (and therefore the 9th harmonic as well), those seeking to approximate JI with 15-edo would be best advised to avoid chords requiring those harmonics. | |||
==Harmony== | ==Harmony== | ||
|| Degree || Cents || Approximate Ratios* || | || Degree || Cents ||= Approximate Ratios* || | ||
|| 0 || 0 || 1/1 || | || 0 || 0 ||= 1/1 || | ||
|| 1 || 80 || | || 1 || 80 ||= 25/24, 21/20 || | ||
|| 2 || 160 || 11/10 || | || 2 || 160 ||= 11/10, 12/11, 10/9 || | ||
|| 3 || 240 || 8/7, 7/6 || | || 3 || 240 ||= 8/7, 7/6, 9/8 || | ||
|| 4 || 320 || 6/5 || | || 4 || 320 ||= 6/5 || | ||
|| 5 || 400 || 5/4, 14/11 || | || 5 || 400 ||= 5/4, 14/11 || | ||
|| 6 || 480 || 4/3 || | || 6 || 480 ||= 4/3 || | ||
|| 7 || 560 || 11/8, 7/5 || | || 7 || 560 ||= 11/8, 7/5 || | ||
|| 8 || 640 || 16/11, | || 8 || 640 ||= 16/11, 10/7 || | ||
|| 9 || 720 || 3/2 || | || 9 || 720 ||= 3/2 || | ||
|| 10 || 800 || 8/5, 11/7 || | || 10 || 800 ||= 8/5, 11/7 || | ||
|| 11 || 880 || 5/3 || | || 11 || 880 ||= 5/3 || | ||
|| 12 || 960 || 7/4, 12/7 || | || 12 || 960 ||= 7/4, 12/7, 16/9 || | ||
|| 13 || 1040 || 20/11 || | || 13 || 1040 ||= 20/11, 11/6, 9/5 || | ||
|| 14 || 1120 || | || 14 || 1120 ||= 48/25, 40/21 || | ||
|| 15 || 1200 || 2/1 || | || 15 || 1200 ||= 2/1 || | ||
*based on treating 15-EDO as an 11-limit temperament; other approaches are possible | *based on treating 15-EDO as an 11-limit temperament; other approaches are possible | ||
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<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>15edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x15 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->15 tone equal temperament</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>15edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x15 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->15 tone equal temperament</h1> | ||
<br /> | <br /> | ||
from <em>wikipedia</em>:<br /> | from <em>wikipedia</em>:<br /> | ||
&quot;&quot;In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 15 equal steps. Each step represents a frequency ratio of 2^(1/15), or 80 <a class="wiki_link" href="/cent">cent</a>s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of <a class="wiki_link" href="/5edo">5 equal divisions of the octave</a> (or five scales of <a class="wiki_link" href="/3edo">3edo</a>).&quot;<br /> | &quot;&quot;In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 15 equal steps. Each step represents a frequency ratio of 2^(1/15), or 80 <a class="wiki_link" href="/cent">cent</a>s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of <a class="wiki_link" href="/5edo">5 equal divisions of the octave</a> (or five scales of <a class="wiki_link" href="/3edo">3edo</a>).&quot;<br /> | ||
<br /> | |||
15-edo can be seen as a <a class="wiki_link" href="/7-limit">7-limit</a> temperament because of its ability to approximate some septimal intervals, but it also contains some fairly obvious approximations to <a class="wiki_link" href="/11-limit">11-limit</a> intervals, so it can reasonably be described as an 11-limit temperament; however, due to its rather distant approximation of the 3rd harmonic (and therefore the 9th harmonic as well), those seeking to approximate JI with 15-edo would be best advised to avoid chords requiring those harmonics. <br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x15 tone equal temperament-Harmony"></a><!-- ws:end:WikiTextHeadingRule:2 -->Harmony</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x15 tone equal temperament-Harmony"></a><!-- ws:end:WikiTextHeadingRule:2 -->Harmony</h2> | ||
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<td>Cents<br /> | <td>Cents<br /> | ||
</td> | </td> | ||
<td>Approximate Ratios*<br /> | <td style="text-align: center;">Approximate Ratios*<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>0<br /> | <td>0<br /> | ||
</td> | </td> | ||
<td>1/1<br /> | <td style="text-align: center;">1/1<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>80<br /> | <td>80<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">25/24, 21/20<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>160<br /> | <td>160<br /> | ||
</td> | </td> | ||
<td>11/10<br /> | <td style="text-align: center;">11/10, 12/11, 10/9<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>240<br /> | <td>240<br /> | ||
</td> | </td> | ||
<td>8/7, 7/6<br /> | <td style="text-align: center;">8/7, 7/6, 9/8<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>320<br /> | <td>320<br /> | ||
</td> | </td> | ||
<td>6/5<br /> | <td style="text-align: center;">6/5<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>400<br /> | <td>400<br /> | ||
</td> | </td> | ||
<td>5/4, 14/11<br /> | <td style="text-align: center;">5/4, 14/11<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>480<br /> | <td>480<br /> | ||
</td> | </td> | ||
<td>4/3<br /> | <td style="text-align: center;">4/3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>560<br /> | <td>560<br /> | ||
</td> | </td> | ||
<td>11/8, 7/5<br /> | <td style="text-align: center;">11/8, 7/5<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>640<br /> | <td>640<br /> | ||
</td> | </td> | ||
<td>16/11, | <td style="text-align: center;">16/11, 10/7<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>720<br /> | <td>720<br /> | ||
</td> | </td> | ||
<td>3/2<br /> | <td style="text-align: center;">3/2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>800<br /> | <td>800<br /> | ||
</td> | </td> | ||
<td>8/5, 11/7<br /> | <td style="text-align: center;">8/5, 11/7<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>880<br /> | <td>880<br /> | ||
</td> | </td> | ||
<td>5/3<br /> | <td style="text-align: center;">5/3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>960<br /> | <td>960<br /> | ||
</td> | </td> | ||
<td>7/4, 12/7<br /> | <td style="text-align: center;">7/4, 12/7, 16/9<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>1040<br /> | <td>1040<br /> | ||
</td> | </td> | ||
<td>20/11<br /> | <td style="text-align: center;">20/11, 11/6, 9/5<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>1120<br /> | <td>1120<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">48/25, 40/21<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>1200<br /> | <td>1200<br /> | ||
</td> | </td> | ||
<td>2/1<br /> | <td style="text-align: center;">2/1<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||