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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2011-08-16 13:20:15 UTC</tt>.<br>
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| : The original revision id was <tt>246265831</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <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">=5 Equal Divisions of the Tritave=
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| || Degrees || Cents || Approximate Ratios ||
| | == Theory == |
| || 0 || 0 || [[1_1|1/1]] ||
| | 5edt has steps too large to be used melodically, though it has some notable harmonic properties shared by other 5''n''-edts (such as [[10edt]], [[15edt]], etc.). It has a surprisingly accurate [[5/4]] major third (only 5.92{{cent}} flat), five of them making a tritave. (This phenomenon cannot be seen in single-digit [[edo]]s, and it is not until [[19edo]] that an approximation of 5/4 to within 10{{c}} can be seen.) 5edt therefore tempers out [[3125/3072]], the magic comma. Two of these major thirds give a septimal minor sixth, meaning that it also tempers out the marvel comma [[225/224]]. |
| || 1 || 380.391 || [[5_4|5/4]] ||
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| || 2 || 760.782 || [[14_9|14/9]] ||
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| || 3 || 1141.173 || [[27_14|27/14]] ||
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| || 4 || 1521.564 || 12/5 (tritave-inversion of [[6_5|6/5]]) ||
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| || 5 || 1901.955 || 3/1 ||
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| <span style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; line-height: normal;">5edt isn't very useful melodically, though it has many notable harmonic properties shared by other 5n-edts (EDTs with 5 as a prime factor). It has a surprisingly accurate major third, five of them making a tritave. It therefore tempers out 3125/3072, the magic comma. Two of these major thirds give a septimal minor sixth, meaning that it also tempers out the 7-limit comma 225/224.</span>
| | 5edt is the first edt to encompass elements of [[5-limit]] harmony. The available chords are 4:5:12 and 5:12:15; being inversions of each other, they essentially act as "major" and "minor" chords. This is similar to [[6edt]], which contains the same chords but with the major thirds transposed an octave higher, and vice versa. Also available is the chord 9:14:27, which can express the single [[7-limit]] consonance found in 5edt. |
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| 5edt is the lowest equal division of the tritave to encompass 5-limit harmony. The available chords are 4:5:12 and 5:12:15; essentially major and minor chords. This is similar to [[6edt]], which contains the same chords but with the major thirds transposed an octave higher, and vice versa.
| | === Harmonics === |
| | {{Harmonics in equal|5|3|1|columns=15}} |
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| | === Subsets and supersets === |
| | 5edt is the 3rd [[prime equal division|prime edt]], after [[3edt]] and before [[7edt]]. |
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| ==Other 5n-edts:== | | == Intervals == |
| [[10edt]] | | {| class="wikitable right-all left-4" |
| [[15edt]] | | |- |
| [[20edt]] | | ! # |
| [[25edt]] | | ! Cents |
| [[30edt]] | | ! Hekts |
| ...</pre></div>
| | ! Approximate ratios |
| <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>5edt</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5 Equal Divisions of the Tritave"></a><!-- ws:end:WikiTextHeadingRule:0 -->5 Equal Divisions of the Tritave</h1>
| | | 0 |
| <br />
| | | 0 |
| | | 0 |
| | | [[1/1]] |
| | |- |
| | | 1 |
| | | 380 |
| | | 260 |
| | | [[5/4]] |
| | |- |
| | | 2 |
| | | 761 |
| | | 520 |
| | | [[14/9]] |
| | |- |
| | | 3 |
| | | 1141 |
| | | 780 |
| | | [[27/14]] |
| | |- |
| | | 4 |
| | | 1522 |
| | | 1040 |
| | | [[12/5]] |
| | |- |
| | | 5 |
| | | 1902 |
| | | 1300 |
| | | [[3/1]] |
| | |} |
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| | | [[Category:Todo:add sound example]] |
| <table class="wiki_table">
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| <tr>
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| <td>Degrees<br />
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| </td>
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| <td>Cents<br />
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| </td>
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| <td>Approximate Ratios<br />
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| </td>
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| </tr>
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| <tr>
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| <td>0<br />
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| </td>
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| <td>0<br />
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| </td>
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| <td><a class="wiki_link" href="/1_1">1/1</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>1<br />
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| </td>
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| <td>380.391<br />
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| </td>
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| <td><a class="wiki_link" href="/5_4">5/4</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>2<br />
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| </td>
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| <td>760.782<br />
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| </td>
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| <td><a class="wiki_link" href="/14_9">14/9</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>3<br />
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| </td>
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| <td>1141.173<br />
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| </td>
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| <td><a class="wiki_link" href="/27_14">27/14</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>4<br />
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| </td>
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| <td>1521.564<br />
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| </td>
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| <td>12/5 (tritave-inversion of <a class="wiki_link" href="/6_5">6/5</a>)<br />
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| </td>
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| </tr>
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| <tr>
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| <td>5<br />
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| </td>
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| <td>1901.955<br />
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| </td>
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| <td>3/1<br />
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| </td>
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| </tr>
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| </table>
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| <br />
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| <span style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; line-height: normal;">5edt isn't very useful melodically, though it has many notable harmonic properties shared by other 5n-edts (EDTs with 5 as a prime factor). It has a surprisingly accurate major third, five of them making a tritave. It therefore tempers out 3125/3072, the magic comma. Two of these major thirds give a septimal minor sixth, meaning that it also tempers out the 7-limit comma 225/224.</span><br />
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| <br />
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| 5edt is the lowest equal division of the tritave to encompass 5-limit harmony. The available chords are 4:5:12 and 5:12:15; essentially major and minor chords. This is similar to <a class="wiki_link" href="/6edt">6edt</a>, which contains the same chords but with the major thirds transposed an octave higher, and vice versa.<br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x5 Equal Divisions of the Tritave-Other 5n-edts:"></a><!-- ws:end:WikiTextHeadingRule:2 -->Other 5n-edts:</h2>
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| <a class="wiki_link" href="/10edt">10edt</a><br />
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| <a class="wiki_link" href="/15edt">15edt</a><br />
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| <a class="wiki_link" href="/20edt">20edt</a><br />
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| <a class="wiki_link" href="/25edt">25edt</a><br />
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| <a class="wiki_link" href="/30edt">30edt</a><br />
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| ...</body></html></pre></div>
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