27edt: Difference between revisions

Revision as of 16:25, 6 September 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2011-09-06 16:25:26 UTC.

The original revision id was 251307046.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

=[[#Division of the tritave (3/1) into 12 equal parts]]Division of the tritave (3/1) into 27 equal parts= 

Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 [[cent]]s, corresponding to 17.035 edo, which is nearly identical to one step of [[17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime number]].

27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). See, e.g., [[http://launch.dir.groups.yahoo.com/group/tuning/message/86909]] and [[http://www.klingon.org/smboard/index.php?topic=1810.0]].

==Intervals== 
||~ degrees of 27edt ||~ cents value ||~ approximation in 17edo ||
|| 0 || 0.00 || 0.00 ||
|| 1 || 70.44 || 70.59 ||
|| 2 || 140.89 || 141.18 ||
|| 3 || 211.33 || 211.76 ||
|| 4 || 281.77 || 282.35 ||
|| 5 || 352.21 || 352.94 ||
|| 6 || 422.66 || 423.53 ||
|| 7 || 493.10 || 494.12 ||
|| 8 || 563.54 || 564.71 ||
|| 9 || 633.99 || 635.29 ||
|| 10 || 704.43 || 705.88 ||
|| 11 || 774.87 || 776.47 ||
|| 12 || 845.31 || 847.06 ||
|| 13 || 915.76 || 917.65 ||
|| 14 || 986.20 || 988.24 ||
|| 15 || 1056.64 || 1058.82 ||
|| 16 || 1127.08 || 1129.41 ||
|| 17 || 1197.53 || 1200.00 ||
|| 18 || 1267.97 || 1270.59 ||
|| 19 || 1338.41 || 1341.18 ||
|| 20 || 1408.86 || 1411.76 ||
|| 21 || 1479.30 || 1482.35 ||
|| 22 || 1549.74 || 1551.94 ||
|| 23 || 1620.18 || 1623.53 ||
|| 24 || 1690.63 || 1694.12 ||
|| 25 || 1761.07 || 1764.71 ||
|| 26 || 1831.51 || 1835.29 ||
|| 27 || 1901.96 || 1905.88 ||

Original HTML content:

<html><head><title>27edt</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Division of the tritave (3/1) into 27 equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 --><!-- ws:start:WikiTextAnchorRule:4:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Division of the tritave (3/1) into 12 equal parts&quot; title=&quot;Anchor: Division of the tritave (3/1) into 12 equal parts&quot;/&gt; --><a name="Division of the tritave (3/1) into 12 equal parts"></a><!-- ws:end:WikiTextAnchorRule:4 -->Division of the tritave (3/1) into 27 equal parts</h1>
 <br />
Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 <a class="wiki_link" href="/cent">cent</a>s, corresponding to 17.035 edo, which is nearly identical to one step of <a class="wiki_link" href="/17edo">17edo</a> (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a <a class="wiki_link" href="/prime%20number">prime number</a>.<br />
<br />
27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). See, e.g., <a class="wiki_link_ext" href="http://launch.dir.groups.yahoo.com/group/tuning/message/86909" rel="nofollow">http://launch.dir.groups.yahoo.com/group/tuning/message/86909</a> and <a class="wiki_link_ext" href="http://www.klingon.org/smboard/index.php?topic=1810.0" rel="nofollow">http://www.klingon.org/smboard/index.php?topic=1810.0</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Division of the tritave (3/1) into 27 equal parts-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
 

<table class="wiki_table">
    <tr>
        <th>degrees of 27edt<br />
</th>
        <th>cents value<br />
</th>
        <th>approximation in 17edo<br />
</th>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0.00<br />
</td>
        <td>0.00<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>70.44<br />
</td>
        <td>70.59<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>140.89<br />
</td>
        <td>141.18<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>211.33<br />
</td>
        <td>211.76<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>281.77<br />
</td>
        <td>282.35<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>352.21<br />
</td>
        <td>352.94<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>422.66<br />
</td>
        <td>423.53<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>493.10<br />
</td>
        <td>494.12<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>563.54<br />
</td>
        <td>564.71<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>633.99<br />
</td>
        <td>635.29<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>704.43<br />
</td>
        <td>705.88<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>774.87<br />
</td>
        <td>776.47<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>845.31<br />
</td>
        <td>847.06<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>915.76<br />
</td>
        <td>917.65<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>986.20<br />
</td>
        <td>988.24<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>1056.64<br />
</td>
        <td>1058.82<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>1127.08<br />
</td>
        <td>1129.41<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>1197.53<br />
</td>
        <td>1200.00<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>1267.97<br />
</td>
        <td>1270.59<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>1338.41<br />
</td>
        <td>1341.18<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>1408.86<br />
</td>
        <td>1411.76<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>1479.30<br />
</td>
        <td>1482.35<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>1549.74<br />
</td>
        <td>1551.94<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>1620.18<br />
</td>
        <td>1623.53<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>1690.63<br />
</td>
        <td>1694.12<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>1761.07<br />
</td>
        <td>1764.71<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>1831.51<br />
</td>
        <td>1835.29<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>1901.96<br />
</td>
        <td>1905.88<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:xenwolf|xenwolf]] and made on <tt>2011-06-30 09:15:41 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-06 16:25:26 UTC</tt>.<br>
-: The original revision id was <tt>239487217</tt>.<br>
+: The original revision id was <tt>251307046</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">=[[#Division of the tritave (3/1) into 12 equal parts]]Division of the tritave (3/1) into 27 equal parts=
-Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 [[cent]]s, which is nearly identical to one step of [[17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime number]].
+Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 [[cent]]s, corresponding to 17.035 edo, which is nearly identical to one step of [[17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime number]].
 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). See, e.g., [[http://launch.dir.groups.yahoo.com/group/tuning/message/86909]] and [[http://www.klingon.org/smboard/index.php?topic=1810.0]].
@@ Line 45: / Line 45: @@
 <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;27edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Division of the tritave (3/1) into 27 equal parts"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:4:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Division of the tritave (3/1) into 12 equal parts&amp;quot; title=&amp;quot;Anchor: Division of the tritave (3/1) into 12 equal parts&amp;quot;/&amp;gt; --&gt;&lt;a name="Division of the tritave (3/1) into 12 equal parts"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:4 --&gt;Division of the tritave (3/1) into 27 equal parts&lt;/h1&gt;
   &lt;br /&gt;
-Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, which is nearly identical to one step of &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt; (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a &lt;a class="wiki_link" href="/prime%20number"&gt;prime number&lt;/a&gt;.&lt;br /&gt;
+Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, corresponding to 17.035 edo, which is nearly identical to one step of &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt; (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a &lt;a class="wiki_link" href="/prime%20number"&gt;prime number&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). See, e.g., &lt;a class="wiki_link_ext" href="http://launch.dir.groups.yahoo.com/group/tuning/message/86909" rel="nofollow"&gt;http://launch.dir.groups.yahoo.com/group/tuning/message/86909&lt;/a&gt; and &lt;a class="wiki_link_ext" href="http://www.klingon.org/smboard/index.php?topic=1810.0" rel="nofollow"&gt;http://www.klingon.org/smboard/index.php?topic=1810.0&lt;/a&gt;.&lt;br /&gt;

27edt: Difference between revisions

Revision as of 16:25, 6 September 2011

IMPORTED REVISION FROM WIKISPACES

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