|
|
| (28 intermediate revisions by 9 users not shown) |
| Line 1: |
Line 1: |
| <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}} It corresponds to 6.8380[[edo]]. |
| : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2017-12-23 15:11:35 UTC</tt>.<br>
| |
| : The original revision id was <tt>624205195</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>
| |
| <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">=Equal division of the perfect fifth (3/2) into 4 equal parts=
| |
|
| |
|
| **4edf** divides the [[Perfect fifth]] into 4 [[equal]] intervals, each 175.489 [[cent]]s in size.
| | == Theory == |
| This division is said to be used in traditional scales of [[Georgian|Georgia]]. See the [[http://launch.groups.yahoo.com/group/tuning/message/100326|discussion on the Yahoo tuning list]].
| | 4edf is related to the [[tetracot]] temperament, which [[tempering out|tempers out]] [[20000/19683]] in the 5-limit. |
|
| |
|
| ==Intervals== | | === Harmonics === |
| ||~ degree ||~ cents value ||~ octave-reduced cents value || | | {{Harmonics in equal|4|3|2}} |
| || 0 || 0 || ||
| |
| || 1 || 175.489 || ||
| |
| || 2 || 350.978 || ||
| |
| || 3 || 526.466 || ||
| |
| || 4 || 701.955 || ||
| |
| || 5 || 877.444 || ||
| |
| || 6 || 1052.933 || ||
| |
| ||~ second octave ||~ ||~ ||
| |
| || 7 || 1228.421 || 28.421 ||
| |
| || 8 || 1403.910 || 203.910 ||
| |
| || 9 || 1579.399 || 379.399 ||
| |
| || 10 || 1754.888 || 554.888 ||
| |
| || 11 || 1930.376 || 730.376 ||
| |
| || 12 || 2105.865 || 905.865 ||
| |
| || 13 || 2281.354 || 1081.354 ||
| |
| ||~ third octave ||~ ||~ ||
| |
| || 14 || 2456.843 || 56.843 ||
| |
|
| |
|
| ==Compositions== | | == Intervals == |
| [[http://www.seraph.it/dep/det/repetitions1.mp3|Repetitions 1]] [[http://www.youtube.com/watch?v=XEklMo0tIW0|Repetitions 1 video]] by [[Carlo Serafini]]</pre></div>
| |
| <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>4edf</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Equal division of the perfect fifth (3/2) into 4 equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 -->Equal division of the perfect fifth (3/2) into 4 equal parts</h1>
| |
| <br />
| |
| <strong>4edf</strong> divides the <a class="wiki_link" href="/Perfect%20fifth">Perfect fifth</a> into 4 <a class="wiki_link" href="/equal">equal</a> intervals, each 175.489 <a class="wiki_link" href="/cent">cent</a>s in size.<br />
| |
| This division is said to be used in traditional scales of <a class="wiki_link" href="/Georgian">Georgia</a>. See the <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100326" rel="nofollow">discussion on the Yahoo tuning list</a>.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Equal division of the perfect fifth (3/2) into 4 equal parts-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable center-1 right-2 center-3" |
| <tr>
| | |- |
| <th>degree<br />
| | ! # |
| </th>
| | ! Cents |
| <th>cents value<br />
| | ! Tetratonic<br>Notation |
| </th>
| | |- |
| <th>octave-reduced cents value<br />
| | | 0 |
| </th>
| | | 0.0 |
| </tr>
| | | C |
| <tr>
| | |- |
| <td>0<br />
| | | 1 |
| </td>
| | | 175.5 |
| <td>0<br />
| | | D |
| </td>
| | |- |
| <td><br />
| | | 2 |
| </td>
| | | 351.0 |
| </tr>
| | | E |
| <tr>
| | |- |
| <td>1<br />
| | | 3 |
| </td>
| | | 526.5 |
| <td>175.489<br />
| | | F |
| </td>
| | |- |
| <td><br />
| | | 4 |
| </td>
| | | 702.0 |
| </tr>
| | | C |
| <tr>
| | |- |
| <td>2<br />
| | | 5 |
| </td>
| | | 877.4 |
| <td>350.978<br />
| | | D |
| </td>
| | |- |
| <td><br />
| | | 6 |
| </td>
| | | 1052.9 |
| </tr>
| | | E |
| <tr>
| | |- |
| <td>3<br />
| | | 7 |
| </td>
| | | 1228.4 |
| <td>526.466<br />
| | | F |
| </td>
| | |- |
| <td><br />
| | | 8 |
| </td>
| | | 1403.9 |
| </tr>
| | | C |
| <tr>
| | |- |
| <td>4<br />
| | | 9 |
| </td>
| | | 1579.4 |
| <td>701.955<br />
| | | D |
| </td>
| | |- |
| <td><br />
| | | 10 |
| </td>
| | | 1754.9 |
| </tr>
| | | E |
| <tr>
| | |- |
| <td>5<br />
| | | 11 |
| </td>
| | | 1930.4 |
| <td>877.444<br />
| | | F |
| </td>
| | |- |
| <td><br />
| | | 12 |
| </td>
| | | 2105.9 |
| </tr>
| | | C |
| <tr>
| | |- |
| <td>6<br />
| | | 13 |
| </td>
| | | 2281.4 |
| <td>1052.933<br />
| | | D |
| </td>
| | |- |
| <td><br />
| | | 14 |
| </td>
| | | 2456.8 |
| </tr>
| | | E |
| <tr>
| | |} |
| <th>second octave<br />
| |
| </th>
| |
| <th><br />
| |
| </th>
| |
| <th><br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>1228.421<br />
| |
| </td>
| |
| <td>28.421<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td>1403.910<br />
| |
| </td>
| |
| <td>203.910<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9<br />
| |
| </td>
| |
| <td>1579.399<br />
| |
| </td>
| |
| <td>379.399<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10<br />
| |
| </td>
| |
| <td>1754.888<br />
| |
| </td>
| |
| <td>554.888<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11<br />
| |
| </td>
| |
| <td>1930.376<br />
| |
| </td>
| |
| <td>730.376<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td>2105.865<br />
| |
| </td>
| |
| <td>905.865<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td>2281.354<br />
| |
| </td>
| |
| <td>1081.354<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th>third octave<br />
| |
| </th>
| |
| <th><br />
| |
| </th>
| |
| <th><br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>14<br />
| |
| </td>
| |
| <td>2456.843<br />
| |
| </td>
| |
| <td>56.843<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | == Music == |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Equal division of the perfect fifth (3/2) into 4 equal parts-Compositions"></a><!-- ws:end:WikiTextHeadingRule:4 -->Compositions</h2>
| | ; [[Carlo Serafini]] |
| <a class="wiki_link_ext" href="http://www.seraph.it/dep/det/repetitions1.mp3" rel="nofollow">Repetitions 1</a> <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=XEklMo0tIW0" rel="nofollow">Repetitions 1 video</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a></body></html></pre></div>
| | * ''Repetitions 1'' – [http://www.seraph.it/dep/det/repetitions1.mp3 play] | [https://www.youtube.com/watch?v=XEklMo0tIW0 YouTube] |
| | |
| | [[Category:Listen]] |