15edt
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author Kosmorsky and made on 2011-08-21 14:21:35 UTC.
- The original revision id was 247416427.
- The revision comment was:
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Original Wikitext content:
=<span style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; line-height: normal;">15 Equal Divisions of the Tritave</span>= || Degrees || Cents || Approximate Ratios || || 0 || 0 || <span style="color: #660000;">[[1_1|1/1]]</span> || || 1 || 126.797 || [[14_13|14/13]], [[15_14|15/14]], [[16_15|16/15]], 29/27 || || 2 || 253.594 || 15/13 || || 3 || 380.391 || <span style="color: #660000;">[[5_4|5/4]]</span> || || 4 || 507.188 || [[4_3|4/3]] || || 5 || 633.985 || [[13_9|13/9]] || || 6 || 760.782 || <span style="color: #660000;">[[14_9|14/9]]</span> || || 7 || 887.579 || [[5_3|5/3]] || || 8 || 1014.376 || [[9_5|9/5]], 17/9 || || 9 || 1141.173 || <span style="color: #660000;">[[27_14|27/14]]</span> || || 10 || 1267.970 || 27/13 || || 11 || 1394.767 || 9/4 ([[9_8|9/8]] plus an octave) || || 12 || 1521.564 || 12/5 (<span style="color: #660000;">[[6_5|6/5]]</span> plus an octave) || || 13 || 1648.361 || 13/5 ([[13_10|13/10]] plus an octave) || || 14 || 1775.158 || 14/5 ([[7_5|7/5]] plus an octave) || || 15 || 1901.955 || 3/1 || 15edt contains 4 intervals from [[5edt]] and 2 intervals from [[3edt]], meaning that it contains 6 redundant intervals and 8 new intervals. The new intervals introduced include good approximations to 15/14, 15/13, 4/3, 5/3 and their tritave inverses. This allows for new chord possibilities such as 1:3:4:5:9:12:13:14:15:16... 15edt also contains a 5L5s MOS similar to Blackwood Decatonic, which I call Ebony. This MOS has a period of 1/5 of the tritave and the generator is a single step. The major scale is sLsLsLsLsL, and the minor scale is LsLsLsLsLs. 15edt approximates the 5th and 13th harmonics (and 29th) very well. Taking these as consonances one obtains an 3L+3s MOS "augmented scale", in which three 13/9 intervals close to a tritave, and a 5th harmonic is stacked on each of these.
Original HTML content:
<html><head><title>15edt</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x15 Equal Divisions of the Tritave"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; line-height: normal;">15 Equal Divisions of the Tritave</span></h1>
<br />
<table class="wiki_table">
<tr>
<td>Degrees<br />
</td>
<td>Cents<br />
</td>
<td>Approximate Ratios<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
<td><span style="color: #660000;"><a class="wiki_link" href="/1_1">1/1</a></span><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>126.797<br />
</td>
<td><a class="wiki_link" href="/14_13">14/13</a>, <a class="wiki_link" href="/15_14">15/14</a>, <a class="wiki_link" href="/16_15">16/15</a>, 29/27<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>253.594<br />
</td>
<td>15/13<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>380.391<br />
</td>
<td><span style="color: #660000;"><a class="wiki_link" href="/5_4">5/4</a></span><br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>507.188<br />
</td>
<td><a class="wiki_link" href="/4_3">4/3</a><br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>633.985<br />
</td>
<td><a class="wiki_link" href="/13_9">13/9</a><br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>760.782<br />
</td>
<td><span style="color: #660000;"><a class="wiki_link" href="/14_9">14/9</a></span><br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>887.579<br />
</td>
<td><a class="wiki_link" href="/5_3">5/3</a><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>1014.376<br />
</td>
<td><a class="wiki_link" href="/9_5">9/5</a>, 17/9<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>1141.173<br />
</td>
<td><span style="color: #660000;"><a class="wiki_link" href="/27_14">27/14</a></span><br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>1267.970<br />
</td>
<td>27/13<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>1394.767<br />
</td>
<td>9/4 (<a class="wiki_link" href="/9_8">9/8</a> plus an octave)<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>1521.564<br />
</td>
<td>12/5 (<span style="color: #660000;"><a class="wiki_link" href="/6_5">6/5</a></span> plus an octave)<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>1648.361<br />
</td>
<td>13/5 (<a class="wiki_link" href="/13_10">13/10</a> plus an octave)<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>1775.158<br />
</td>
<td>14/5 (<a class="wiki_link" href="/7_5">7/5</a> plus an octave)<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>1901.955<br />
</td>
<td>3/1<br />
</td>
</tr>
</table>
<br />
15edt contains 4 intervals from <a class="wiki_link" href="/5edt">5edt</a> and 2 intervals from <a class="wiki_link" href="/3edt">3edt</a>, meaning that it contains 6 redundant intervals and 8 new intervals. The new intervals introduced include good approximations to 15/14, 15/13, 4/3, 5/3 and their tritave inverses. This allows for new chord possibilities such as 1:3:4:5:9:12:13:14:15:16...<br />
<br />
15edt also contains a 5L5s MOS similar to Blackwood Decatonic, which I call Ebony. This MOS has a period of 1/5 of the tritave and the generator is a single step. The major scale is sLsLsLsLsL, and the minor scale is LsLsLsLsLs.<br />
<br />
15edt approximates the 5th and 13th harmonics (and 29th) very well. Taking these as consonances one obtains an 3L+3s MOS "augmented scale", in which three 13/9 intervals close to a tritave, and a 5th harmonic is stacked on each of these.</body></html>