27edt
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:<h1> --><h1 id="toc0"><a name="Division of the tritave (3/1) into 27 equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 --><!-- ws:start:WikiTextAnchorRule:4:<img src="/i/anchor.gif" class="WikiAnchor" alt="Anchor" id="wikitext@@anchor@@Division of the tritave (3/1) into 12 equal parts" title="Anchor: Division of the tritave (3/1) into 12 equal parts"/> --><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:<h2> --><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>