30edt: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 588431640 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 596310862 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-21 00:26:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>596310862</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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Because 19edo has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat. | Because 19edo has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat. | ||
=== === | === === | ||
===<span style="font-size: 1.4em;">Intervals of 30edt</span>=== | |||
|| Degrees || Cents || Approximate Ratios || Sigma scale name || | |||
|| 0 || 0 || <span style="color: #660000;">[[1_1|1/1]]</span> || C || | |||
|| 1 || 63.3985 || 28/27, 27/26 || C#/Dbb || | |||
|| 2 || 126.797 || [[14_13|14/13]], [[15_14|15/14]], [[16_15|16/15]], 29/27 || Cx/Db || | |||
|| 3 || 190.1955 || 10/9~9/8 || D || | |||
|| 4 || 253.594 || [[15_13|15/13]] || D#/Ebb || | |||
|| 5 || 316.9925 || 6/5 || Dx/Eb || | |||
|| 6 || 380.391 || <span style="color: #660000;">[[5_4|5/4]]</span> || E || | |||
|| 7 || 443.7895 || 9/7 || E#/Fb || | |||
|| 8 || 507.188 || [[4_3|4/3]] || F || | |||
|| 9 || 570.5865 || 7/5 || F#/Gbb || | |||
|| 10 || 633.985 || [[13_9|13/9]] || Fx/Gb || | |||
|| 11 || 697.3835 || 3/2 || G || | |||
|| 12 || 760.782 || <span style="color: #660000;">[[14_9|14/9]]</span> || G#/Hbb || | |||
|| 13 || 824.1805 || 8/5 || Gx/Hb || | |||
|| 14 || 887.579 || [[5_3|5/3]] || H || | |||
|| 15 || 950.9775 || 19/11 || H#/Jbb || | |||
|| 16 || 1014.376 || [[9_5|9/5]] || Hx/Jb || | |||
|| 17 || 1077.7745 || 13/7 || J || | |||
|| 18 || 1141.173 || <span style="color: #660000;">[[27_14|27/14]]</span> || J#/Kb || | |||
|| 19 || 1204.5715 || 2/1 || K || | |||
|| 20 || 1267.970 || [[27_13|27/13]] || K#/Lbb || | |||
|| 21 || 1331.3685 || 28/13 || Kx/Lb || | |||
|| 22 || 1394.767 || [[9_4|9/4]] ([[9_8|9/8]] plus an octave) || L || | |||
|| 23 || 1458.1655 || 7/3 || L#/Abb || | |||
|| 24 || 1521.564 || [[12_5|12/5]] (<span style="color: #660000;">[[6_5|6/5]]</span> plus an octave) || Lx/Ab || | |||
|| 25 || 1584.9625 || 5/2 || A || | |||
|| 26 || 1648.361 || [[13_5|13/5]] ([[13_10|13/10]] plus an octave) || A#/Bb || | |||
|| 27 || 1711.7595 || 8/3 || B || | |||
|| 28 || 1775.158 || [[14_5|14/5]] ([[7_5|7/5]] plus an octave) || B#/Cbb || | |||
|| 29 || 1838.5565 || 26/9 || Bx/Cb || | |||
|| 30 || 1901.955 || [[3_1|3/1]] || C || | |||
30edt contains all [[19edo]] intervals within 3/1, all temepered progressively sharper. The accumulation of the .241 cent sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615 cents flatter than that in 6edo. | |||
30edt also contains all the MOS contained in 15edt, being the double of this equal division. Being even, 30edt introduces | |||
MOS with an even number of periods per tritave such as a 6L 6s similar to Hexe Dodecatonic. This MOS has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an unfair Sigma scale of 8L 3s and the major scale is LLsLLLsLLsL. The sharp 9/7 of 7 degrees, in addition to generating a Lambda MOS will generate a 4L 9s unfair Superlambda MOS which does not border on being atonal as the 17edt rendition does. | |||
---- | ---- | ||
===**Compositions in 30edt**=== | ===**Compositions in 30edt**=== | ||
| Line 19: | Line 58: | ||
Because 19edo has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.<br /> | Because 19edo has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.<br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h3> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h3> | ||
<hr /> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x--Intervals of 30edt"></a><!-- ws:end:WikiTextHeadingRule:2 --><span style="font-size: 1.4em;">Intervals of 30edt</span></h3> | ||
<!-- ws:start:WikiTextHeadingRule: | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>Degrees<br /> | |||
</td> | |||
<td>Cents<br /> | |||
</td> | |||
<td>Approximate Ratios<br /> | |||
</td> | |||
<td>Sigma scale name<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> | |||
<td>C<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>63.3985<br /> | |||
</td> | |||
<td>28/27, 27/26<br /> | |||
</td> | |||
<td>C#/Dbb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<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> | |||
<td>Cx/Db<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>190.1955<br /> | |||
</td> | |||
<td>10/9~9/8<br /> | |||
</td> | |||
<td>D<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>253.594<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/15_13">15/13</a><br /> | |||
</td> | |||
<td>D#/Ebb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5<br /> | |||
</td> | |||
<td>316.9925<br /> | |||
</td> | |||
<td>6/5<br /> | |||
</td> | |||
<td>Dx/Eb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<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> | |||
<td>E<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>443.7895<br /> | |||
</td> | |||
<td>9/7<br /> | |||
</td> | |||
<td>E#/Fb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8<br /> | |||
</td> | |||
<td>507.188<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/4_3">4/3</a><br /> | |||
</td> | |||
<td>F<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9<br /> | |||
</td> | |||
<td>570.5865<br /> | |||
</td> | |||
<td>7/5<br /> | |||
</td> | |||
<td>F#/Gbb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10<br /> | |||
</td> | |||
<td>633.985<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/13_9">13/9</a><br /> | |||
</td> | |||
<td>Fx/Gb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11<br /> | |||
</td> | |||
<td>697.3835<br /> | |||
</td> | |||
<td>3/2<br /> | |||
</td> | |||
<td>G<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12<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> | |||
<td>G#/Hbb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13<br /> | |||
</td> | |||
<td>824.1805<br /> | |||
</td> | |||
<td>8/5<br /> | |||
</td> | |||
<td>Gx/Hb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14<br /> | |||
</td> | |||
<td>887.579<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/5_3">5/3</a><br /> | |||
</td> | |||
<td>H<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15<br /> | |||
</td> | |||
<td>950.9775<br /> | |||
</td> | |||
<td>19/11<br /> | |||
</td> | |||
<td>H#/Jbb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16<br /> | |||
</td> | |||
<td>1014.376<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/9_5">9/5</a><br /> | |||
</td> | |||
<td>Hx/Jb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17<br /> | |||
</td> | |||
<td>1077.7745<br /> | |||
</td> | |||
<td>13/7<br /> | |||
</td> | |||
<td>J<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18<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> | |||
<td>J#/Kb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19<br /> | |||
</td> | |||
<td>1204.5715<br /> | |||
</td> | |||
<td>2/1<br /> | |||
</td> | |||
<td>K<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>20<br /> | |||
</td> | |||
<td>1267.970<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/27_13">27/13</a><br /> | |||
</td> | |||
<td>K#/Lbb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>21<br /> | |||
</td> | |||
<td>1331.3685<br /> | |||
</td> | |||
<td>28/13<br /> | |||
</td> | |||
<td>Kx/Lb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22<br /> | |||
</td> | |||
<td>1394.767<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/9_4">9/4</a> (<a class="wiki_link" href="/9_8">9/8</a> plus an octave)<br /> | |||
</td> | |||
<td>L<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23<br /> | |||
</td> | |||
<td>1458.1655<br /> | |||
</td> | |||
<td>7/3<br /> | |||
</td> | |||
<td>L#/Abb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>24<br /> | |||
</td> | |||
<td>1521.564<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/12_5">12/5</a> (<span style="color: #660000;"><a class="wiki_link" href="/6_5">6/5</a></span> plus an octave)<br /> | |||
</td> | |||
<td>Lx/Ab<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>25<br /> | |||
</td> | |||
<td>1584.9625<br /> | |||
</td> | |||
<td>5/2<br /> | |||
</td> | |||
<td>A<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>26<br /> | |||
</td> | |||
<td>1648.361<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/13_5">13/5</a> (<a class="wiki_link" href="/13_10">13/10</a> plus an octave)<br /> | |||
</td> | |||
<td>A#/Bb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>27<br /> | |||
</td> | |||
<td>1711.7595<br /> | |||
</td> | |||
<td>8/3<br /> | |||
</td> | |||
<td>B<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>28<br /> | |||
</td> | |||
<td>1775.158<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/14_5">14/5</a> (<a class="wiki_link" href="/7_5">7/5</a> plus an octave)<br /> | |||
</td> | |||
<td>B#/Cbb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>29<br /> | |||
</td> | |||
<td>1838.5565<br /> | |||
</td> | |||
<td>26/9<br /> | |||
</td> | |||
<td>Bx/Cb<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>30<br /> | |||
</td> | |||
<td>1901.955<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/3_1">3/1</a><br /> | |||
</td> | |||
<td>C<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
30edt contains all <a class="wiki_link" href="/19edo">19edo</a> intervals within 3/1, all temepered progressively sharper. The accumulation of the .241 cent sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615 cents flatter than that in 6edo.<br /> | |||
<br /> | |||
30edt also contains all the MOS contained in 15edt, being the double of this equal division. Being even, 30edt introduces<br /> | |||
MOS with an even number of periods per tritave such as a 6L 6s similar to Hexe Dodecatonic. This MOS has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a &quot;real&quot; 3/2, the interval of 11 degrees generates an unfair Sigma scale of 8L 3s and the major scale is LLsLLLsLLsL. The sharp 9/7 of 7 degrees, in addition to generating a Lambda MOS will generate a 4L 9s unfair Superlambda MOS which does not border on being atonal as the 17edt rendition does.<br /> | |||
<br /> | |||
<hr /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x--Compositions in 30edt"></a><!-- ws:end:WikiTextHeadingRule:4 --><strong>Compositions in 30edt</strong></h3> | |||
<br /> | <br /> | ||
<ul><li>&quot;<a class="wiki_link_ext" href="https://soundcloud.com/mason-l-green/room-full-of-steam" rel="nofollow">Room Full Of Steam</a>&quot;, Mason Green. In the key of &quot;Eb subminor&quot;.</li></ul></body></html></pre></div> | <ul><li>&quot;<a class="wiki_link_ext" href="https://soundcloud.com/mason-l-green/room-full-of-steam" rel="nofollow">Room Full Of Steam</a>&quot;, Mason Green. In the key of &quot;Eb subminor&quot;.</li></ul></body></html></pre></div> | ||