33ed4: Difference between revisions
Wikispaces>jauernig **Imported revision 536805560 - Original comment: ** |
Wikispaces>jauernig **Imported revision 536806944 - 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:jauernig|jauernig]] and made on <tt>2015-01-09 18: | : This revision was by author [[User:jauernig|jauernig]] and made on <tt>2015-01-09 18:48:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>536806944</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> | ||
<h4>Original Wikitext content:</h4> | <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">33ed4 is the Equal Divisions of the Double Octave into 33 narrow chromatic semitones each of 72.727 [[xenharmonic/cent|cent]]s. It takes out every second step of 33edo and falls between 16edo and 17edo. So even degree 16 or degree 17 can play the role of the octave, depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of equivocal tuning. | <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">**33ed4** is the [[ED4|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[xenharmonic/cent|cent]]s. It takes out every second step of [[33edo]] and falls between [[16edo]] and [[17edo]]. So even degree 16 or degree 17 can play the role of the [[octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of equivocal tuning. | ||
It has a 9/5 which is 0.6 cents sharp, a 7/5 which is 0.7 cents flat, and a 9/7 which is 1.3 cents sharp. Therefore it is closely related to 13edt, the Bohlen-Pierce scale, although it has no pure 3/1, which is 11.1 cents flat. | It has a [[9_5|9/5]] which is 0.6 cents sharp, a [[7_5|7/5]] which is 0.7 cents flat, and a [[9_7|9/7]] which is 1.3 cents sharp. Therefore it is closely related to [[13edt]], the [[Bohlen-Pierce]] scale, although it has no pure [[3_1|3/1]], which is 11.1 cents flat. | ||
Furthermore it has some 11-limit, 13-limit, 17-limit and even 23-limit which are very close (most of them under or nearby 1 cent). | Furthermore it has some [[11-limit]], [[13-limit]], [[17-limit]] and even [[23-limit]] which are very close (most of them under or nearby 1 cent). | ||
Intervals | **Intervals** | ||
|| degree || cents || nearest JI | |||
interval || in cents || difference | |||
in cents || | |||
|| 1 || 72,7 || 24/23 || 73,7 || -1,0 || | |||
|| 2 || 145,5 || 25/23 || 144,4 || 1,1 || | |||
|| 3 || 218,2 || 17/15 || 216,6 || 1,6 || | |||
|| 4 || 290,9 || 13/11 || 289,2 || 1,7 || | |||
|| 5 || 363,6 || 16/13 || 359,5 || 4,1 || | |||
|| 6 || 436,4 || **9/7** || 435,1 || 1,3 || | |||
|| 7 || 509,1 || 51/38 || 509,4 || -0,3 || | |||
|| 8 || 581,8 || **7/5** || 582,5 || -0,7 || | |||
|| 9 || 654,5 || 19/13 || 657,0 || -2,5 || | |||
|| 10 || 727,3 || 35/23 || 726,9 || 0,4 || | |||
|| 11 || 800,0 || 27/17 || 800,9 || -0,9 || | |||
|| 12 || 872,7 || 53/32 || 873,5 || -0,8 || | |||
|| 13 || 945,5 || 19/11 || 946,2 || -0,7 || | |||
|| 14 || 1018,2 || **9/5** || 1017,6 || 0,6 || | |||
|| 15 || 1090,9 || 15/8 || 1088,3 || 2,6 || | |||
|| 16 || 1163,6 || 45/23 || 1161,9 || 1,7 || | |||
|| 17 || 1236,4 || 49/24 || 1235,7 || 0,7 || | |||
|| 18 || 1309,1 || 32/15 || 1311,7 || -2,6 || | |||
|| 19 || 1381,8 || 20/9 || 1382,4 || -0,6 || | |||
|| 20 || 1454,5 || 44/19 || 1453,8 || 0,7 || | |||
|| 21 || 1527,3 || 29/12 || 1527,6 || -0,3 || | |||
|| 22 || 1600,0 || 68/27 || 1599,1 || 0,9 || | |||
|| 23 || 1672,7 || 21/8 || 1670,8 || 1,9 || | |||
|| 24 || 1745,5 || 52/19 || 1743,0 || 2,5 || | |||
|| 25 || 1818,2 || **20/7** || 1817,5 || 0,7 || | |||
|| 26 || 1890,9 || 116/39 || 1887,1 || 3,8 || | |||
|| 27 || 1963,6 || 28/9 || 1964,9 || -1,3 || | |||
|| 28 || 2036,4 || 13/4 || 2040,5 || -4,1 || | |||
|| 29 || 2109,1 || 44/13 || 2110,8 || -1,7 || | |||
|| 30 || 2181,8 || 60/17 || 2183,3 || -1,5 || | |||
|| 31 || 2254,5 || 114/31 || 2254,4 || 0,1 || | |||
|| 32 || 2327,3 || 23/6 || 2326,3 || 1,0 || | |||
|| 33 || 2400,0 || 4/1 || 2400,0 || 0,0 || | |||
**Music** | |||
[[http://soundcloud.com/ahornberg/sets/equivocal-tuning-33ed4|Equivocal Tuning]] by Ahornberg</pre></div> | |||
<h4>Original HTML content:</h4> | <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>33ed4</title></head><body>33ed4 is the Equal Divisions of the Double Octave into 33 narrow chromatic semitones each of 72.727 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s. It takes out every second step of 33edo and falls between 16edo and 17edo. So even degree 16 or degree 17 can play the role of the octave, depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of equivocal tuning.<br /> | <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>33ed4</title></head><body><strong>33ed4</strong> is the <a class="wiki_link" href="/ED4">Equal Divisions of the Double Octave</a> into 33 narrow chromatic semitones each of 72.727 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s. It takes out every second step of <a class="wiki_link" href="/33edo">33edo</a> and falls between <a class="wiki_link" href="/16edo">16edo</a> and <a class="wiki_link" href="/17edo">17edo</a>. So even degree 16 or degree 17 can play the role of the <a class="wiki_link" href="/octave">octave</a>, depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of equivocal tuning.<br /> | ||
<br /> | <br /> | ||
It has a 9/5 which is 0.6 cents sharp, a 7/5 which is 0.7 cents flat, and a 9/7 which is 1.3 cents sharp. Therefore it is closely related to 13edt, the Bohlen-Pierce scale, although it has no pure 3/1, which is 11.1 cents flat.<br /> | It has a <a class="wiki_link" href="/9_5">9/5</a> which is 0.6 cents sharp, a <a class="wiki_link" href="/7_5">7/5</a> which is 0.7 cents flat, and a <a class="wiki_link" href="/9_7">9/7</a> which is 1.3 cents sharp. Therefore it is closely related to <a class="wiki_link" href="/13edt">13edt</a>, the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, although it has no pure <a class="wiki_link" href="/3_1">3/1</a>, which is 11.1 cents flat.<br /> | ||
<br /> | <br /> | ||
Furthermore it has some 11-limit, 13-limit, 17-limit and even 23-limit which are very close (most of them under or nearby 1 cent).<br /> | Furthermore it has some <a class="wiki_link" href="/11-limit">11-limit</a>, <a class="wiki_link" href="/13-limit">13-limit</a>, <a class="wiki_link" href="/17-limit">17-limit</a> and even <a class="wiki_link" href="/23-limit">23-limit</a> which are very close (most of them under or nearby 1 cent).<br /> | ||
<br /> | |||
<strong>Intervals</strong><br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>degree<br /> | |||
</td> | |||
<td>cents<br /> | |||
</td> | |||
<td>nearest JI<br /> | |||
interval<br /> | |||
</td> | |||
<td>in cents<br /> | |||
</td> | |||
<td>difference<br /> | |||
in cents<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>72,7<br /> | |||
</td> | |||
<td>24/23<br /> | |||
</td> | |||
<td>73,7<br /> | |||
</td> | |||
<td>-1,0<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>145,5<br /> | |||
</td> | |||
<td>25/23<br /> | |||
</td> | |||
<td>144,4<br /> | |||
</td> | |||
<td>1,1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>218,2<br /> | |||
</td> | |||
<td>17/15<br /> | |||
</td> | |||
<td>216,6<br /> | |||
</td> | |||
<td>1,6<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>290,9<br /> | |||
</td> | |||
<td>13/11<br /> | |||
</td> | |||
<td>289,2<br /> | |||
</td> | |||
<td>1,7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5<br /> | |||
</td> | |||
<td>363,6<br /> | |||
</td> | |||
<td>16/13<br /> | |||
</td> | |||
<td>359,5<br /> | |||
</td> | |||
<td>4,1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<br /> | |||
</td> | |||
<td>436,4<br /> | |||
</td> | |||
<td><strong>9/7</strong><br /> | |||
</td> | |||
<td>435,1<br /> | |||
</td> | |||
<td>1,3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>509,1<br /> | |||
</td> | |||
<td>51/38<br /> | |||
</td> | |||
<td>509,4<br /> | |||
</td> | |||
<td>-0,3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8<br /> | |||
</td> | |||
<td>581,8<br /> | |||
</td> | |||
<td><strong>7/5</strong><br /> | |||
</td> | |||
<td>582,5<br /> | |||
</td> | |||
<td>-0,7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9<br /> | |||
</td> | |||
<td>654,5<br /> | |||
</td> | |||
<td>19/13<br /> | |||
</td> | |||
<td>657,0<br /> | |||
</td> | |||
<td>-2,5<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10<br /> | |||
</td> | |||
<td>727,3<br /> | |||
</td> | |||
<td>35/23<br /> | |||
</td> | |||
<td>726,9<br /> | |||
</td> | |||
<td>0,4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11<br /> | |||
</td> | |||
<td>800,0<br /> | |||
</td> | |||
<td>27/17<br /> | |||
</td> | |||
<td>800,9<br /> | |||
</td> | |||
<td>-0,9<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12<br /> | |||
</td> | |||
<td>872,7<br /> | |||
</td> | |||
<td>53/32<br /> | |||
</td> | |||
<td>873,5<br /> | |||
</td> | |||
<td>-0,8<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13<br /> | |||
</td> | |||
<td>945,5<br /> | |||
</td> | |||
<td>19/11<br /> | |||
</td> | |||
<td>946,2<br /> | |||
</td> | |||
<td>-0,7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14<br /> | |||
</td> | |||
<td>1018,2<br /> | |||
</td> | |||
<td><strong>9/5</strong><br /> | |||
</td> | |||
<td>1017,6<br /> | |||
</td> | |||
<td>0,6<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15<br /> | |||
</td> | |||
<td>1090,9<br /> | |||
</td> | |||
<td>15/8<br /> | |||
</td> | |||
<td>1088,3<br /> | |||
</td> | |||
<td>2,6<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16<br /> | |||
</td> | |||
<td>1163,6<br /> | |||
</td> | |||
<td>45/23<br /> | |||
</td> | |||
<td>1161,9<br /> | |||
</td> | |||
<td>1,7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17<br /> | |||
</td> | |||
<td>1236,4<br /> | |||
</td> | |||
<td>49/24<br /> | |||
</td> | |||
<td>1235,7<br /> | |||
</td> | |||
<td>0,7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18<br /> | |||
</td> | |||
<td>1309,1<br /> | |||
</td> | |||
<td>32/15<br /> | |||
</td> | |||
<td>1311,7<br /> | |||
</td> | |||
<td>-2,6<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19<br /> | |||
</td> | |||
<td>1381,8<br /> | |||
</td> | |||
<td>20/9<br /> | |||
</td> | |||
<td>1382,4<br /> | |||
</td> | |||
<td>-0,6<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>20<br /> | |||
</td> | |||
<td>1454,5<br /> | |||
</td> | |||
<td>44/19<br /> | |||
</td> | |||
<td>1453,8<br /> | |||
</td> | |||
<td>0,7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>21<br /> | |||
</td> | |||
<td>1527,3<br /> | |||
</td> | |||
<td>29/12<br /> | |||
</td> | |||
<td>1527,6<br /> | |||
</td> | |||
<td>-0,3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22<br /> | |||
</td> | |||
<td>1600,0<br /> | |||
</td> | |||
<td>68/27<br /> | |||
</td> | |||
<td>1599,1<br /> | |||
</td> | |||
<td>0,9<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23<br /> | |||
</td> | |||
<td>1672,7<br /> | |||
</td> | |||
<td>21/8<br /> | |||
</td> | |||
<td>1670,8<br /> | |||
</td> | |||
<td>1,9<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>24<br /> | |||
</td> | |||
<td>1745,5<br /> | |||
</td> | |||
<td>52/19<br /> | |||
</td> | |||
<td>1743,0<br /> | |||
</td> | |||
<td>2,5<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>25<br /> | |||
</td> | |||
<td>1818,2<br /> | |||
</td> | |||
<td><strong>20/7</strong><br /> | |||
</td> | |||
<td>1817,5<br /> | |||
</td> | |||
<td>0,7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>26<br /> | |||
</td> | |||
<td>1890,9<br /> | |||
</td> | |||
<td>116/39<br /> | |||
</td> | |||
<td>1887,1<br /> | |||
</td> | |||
<td>3,8<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>27<br /> | |||
</td> | |||
<td>1963,6<br /> | |||
</td> | |||
<td>28/9<br /> | |||
</td> | |||
<td>1964,9<br /> | |||
</td> | |||
<td>-1,3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>28<br /> | |||
</td> | |||
<td>2036,4<br /> | |||
</td> | |||
<td>13/4<br /> | |||
</td> | |||
<td>2040,5<br /> | |||
</td> | |||
<td>-4,1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>29<br /> | |||
</td> | |||
<td>2109,1<br /> | |||
</td> | |||
<td>44/13<br /> | |||
</td> | |||
<td>2110,8<br /> | |||
</td> | |||
<td>-1,7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>30<br /> | |||
</td> | |||
<td>2181,8<br /> | |||
</td> | |||
<td>60/17<br /> | |||
</td> | |||
<td>2183,3<br /> | |||
</td> | |||
<td>-1,5<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>31<br /> | |||
</td> | |||
<td>2254,5<br /> | |||
</td> | |||
<td>114/31<br /> | |||
</td> | |||
<td>2254,4<br /> | |||
</td> | |||
<td>0,1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>32<br /> | |||
</td> | |||
<td>2327,3<br /> | |||
</td> | |||
<td>23/6<br /> | |||
</td> | |||
<td>2326,3<br /> | |||
</td> | |||
<td>1,0<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>33<br /> | |||
</td> | |||
<td>2400,0<br /> | |||
</td> | |||
<td>4/1<br /> | |||
</td> | |||
<td>2400,0<br /> | |||
</td> | |||
<td>0,0<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | <br /> | ||
<strong>Music</strong><br /> | |||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://soundcloud.com/ahornberg/sets/equivocal-tuning-33ed4" rel="nofollow">Equivocal Tuning</a> by Ahornberg</body></html></pre></div> | |||