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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | en = 27edt |
| : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-02-23 07:47:13 UTC</tt>.<br>
| | | de = 27-EDT |
| : The original revision id was <tt>204273694</tt>.<br>
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| : The revision comment was: <tt></tt><br>
| | {{Infobox ET}} |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | {{ED intro}} |
| <h4>Original Wikitext content:</h4>
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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;white-space: pre-wrap ! important" class="old-revision-html">||~ Details || last edit by <span style="outline: medium none;">[[image:http://c1.wikicdn.com/i/user_none_sm.jpg width="16" height="16" caption="hstraub" link="http://www.wikispaces.com/user/view/hstraub"]][[http://www.wikispaces.com/user/view/hstraub|hstraub]]</span> [[page/diff/12edt/16763978|Feb 12, 2008 3:49 am]] - [[page/history/12edt|1 revision]] || [[image:http://c1.wikicdn.com/i/w/W_close.gif caption="hide details"]] ||
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| ||~ Markierungen || [[12edt#|bearbeiten]]
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| Speichern[[12edt#|Abbrechen]] ||
| | == Theory == |
| | 27edt corresponds 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]]. In fact, the [[prime edo]]s that approximate the 3-limit well often correspond to composite edts: e.g. [[19edo]] → [[30edt]], [[29edo]] → [[46edt]] and [[31edo]] → [[49edt]]. |
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| | Compared to 17edo, 27edt approximates the [[prime interval|primes]] [[7/1|7]], [[11/1|11]], and [[13/1|13]] better; it approximates prime [[5/1|5]] equally poorly, but maps it to 40 steps rather than 39 in the [[patent val]], corresponding to the 17c [[val]], often considered the better mapping as it equates [[5/4]] and [[6/5]] to major and minor thirds rather than to a neutral third, and 5 has the same sharp tendency as 7 and 11. |
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| =[[#Division of the tritave (3/1) into 12 equal parts]]Division of the tritave (3/1) into 27 equal parts=
| | From a purely tritave-based perspective, it [[support]]s the [[minalzidar]] temperament, but otherwise it can be used as a retuning of 17edo with closer-to-just harmonic properties in the no-fives 2.3.7.11.13 subgroup. |
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| Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 cents, which is nearly identical to one step of 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.
| | === Harmonics === |
| | {{Harmonics in equal|27|3|1|intervals=integer|columns=11}} |
| | {{Harmonics in equal|27|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 27edt (continued)}} |
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| 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]].</pre></div> | | === Subsets and supersets === |
| <h4>Original HTML content:</h4>
| | Since 27 factors into primes as 3<sup>3</sup>, 27edt contains [[3edt]] and [[9edt]] as subset edts. |
| <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>27edt</title></head><body>
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| | === Miscellany === |
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| | 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 {{w|Klingon}} music since the tradtional Klingon number system is also based on 3. The rather harsh harmonic character of 27edt would suit very well, too<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_86909.html Yahoo! Tuning Group | ''the evil 27 equal temp scale from outer space'']</ref><ref>[https://web.archive.org/web/20100624113458/https://www.klingon.org/smboard/index.php?topic=1810.0 Klingon Imperial Forums | ''klingon music theory'']</ref>. |
| <th>Details<br />
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| <td>last edit by <span style="outline: medium none;"><!-- ws:start:WikiTextRemoteImageRule:20:&lt;a href=&quot;http://www.wikispaces.com/user/view/hstraub&quot; rel=&quot;nofollow&quot;&gt;&lt;img src=&quot;http://c1.wikicdn.com/i/user_none_sm.jpg&quot; alt=&quot;hstraub&quot; title=&quot;hstraub&quot; style=&quot;height: 16px; width: 16px;&quot; /&gt;&lt;/a&gt; --><table class="captionBox"><tr><td class="captionedImage"><a href="http://www.wikispaces.com/user/view/hstraub" rel="nofollow"><img src="http://c1.wikicdn.com/i/user_none_sm.jpg" alt="hstraub" title="hstraub" style="height: 16px; width: 16px;" /></a></td></tr><tr><td class="imageCaption">hstraub</td></tr></table><!-- ws:end:WikiTextRemoteImageRule:20 --><a class="wiki_link_ext" href="http://www.wikispaces.com/user/view/hstraub" rel="nofollow">hstraub</a></span> <a class="wiki_link" href="http://page.wikispaces.com/-/diff/12edt/16763978">Feb 12, 2008 3:49 am</a> - [[page/history/12edt|1 revision]]<br />
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| <td><!-- ws:start:WikiTextRemoteImageRule:21:&lt;img src=&quot;http://c1.wikicdn.com/i/w/W_close.gif&quot; alt=&quot;hide details&quot; title=&quot;hide details&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="http://c1.wikicdn.com/i/w/W_close.gif" alt="hide details" title="hide details" /></td></tr><tr><td class="imageCaption">hide details</td></tr></table><!-- ws:end:WikiTextRemoteImageRule:21 --><br />
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| <th>Markierungen<br />
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| <td>[[12edt#|bearbeiten]]<br />
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| Speichern[[12edt#|Abbrechen]]<br />
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| | This being said, such a proposal is rather short-sighted from a general cultural perspective, since any kind of living creature would most likely gravitate towards some form of [[low-complexity JI]], and while 27edt will gain appreciation in base-3 cultures at some point, it may not be the first temperament they discover. That would be like aliens assuming dominant tuning in human music is [[100ed10]] (or 1000ed10 or variation thereof) just because we count in base 10. |
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| <!-- 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:2:&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:2 -->Division of the tritave (3/1) into 27 equal parts</h1>
| | == Intervals == |
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| | {{Interval table}} |
| Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 cents, which is nearly identical to one step of 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 prime number.<br />
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| | == See also == |
| 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>.</body></html></pre></div>
| | * [[10edf]] – relative edf |
| | * [[17edo]] – relative edo |
| | * [[44ed6]] – relative ed6 |
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| | == Notes == |