33ed4

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Revision as of 18:48, 9 January 2015 by Wikispaces>jauernig (**Imported revision 536806944 - Original comment: **)
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This revision was by author jauernig and made on 2015-01-09 18:48:39 UTC.
The original revision id was 536806944.
The revision comment was:

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Original Wikitext content:

**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|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).

**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

Original HTML content:

<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 />
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 />
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 />
<strong>Music</strong><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>
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