Xenharmonic Wiki

33ed4

Revision as of 19:09, 9 January 2015 by Wikispaces>jauernig (**Imported revision 536807520 - Original comment: **)

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author jauernig and made on 2015-01-09 19:09:03 UTC.
The original revision id was 536807520.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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 ||~ in 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 />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h3>
 

<table class="wiki_table">
    <tr>
        <th>degree<br />
</th>
        <th>in cents<br />
</th>
        <th>nearest JI<br />
interval<br />
</th>
        <th>in cents<br />
</th>
        <th>difference<br />
in cents<br />
</th>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">72,7<br />
</td>
        <td style="text-align: right;">24/23<br />
</td>
        <td style="text-align: right;">73,7<br />
</td>
        <td style="text-align: right;">-1,0<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">2<br />
</td>
        <td style="text-align: right;">145,5<br />
</td>
        <td style="text-align: right;">25/23<br />
</td>
        <td style="text-align: right;">144,4<br />
</td>
        <td style="text-align: right;">1,1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">3<br />
</td>
        <td style="text-align: right;">218,2<br />
</td>
        <td style="text-align: right;">17/15<br />
</td>
        <td style="text-align: right;">216,6<br />
</td>
        <td style="text-align: right;">1,6<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">4<br />
</td>
        <td style="text-align: right;">290,9<br />
</td>
        <td style="text-align: right;">13/11<br />
</td>
        <td style="text-align: right;">289,2<br />
</td>
        <td style="text-align: right;">1,7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">5<br />
</td>
        <td style="text-align: right;">363,6<br />
</td>
        <td style="text-align: right;">16/13<br />
</td>
        <td style="text-align: right;">359,5<br />
</td>
        <td style="text-align: right;">4,1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;"><strong>6</strong><br />
</td>
        <td style="text-align: right;"><strong>436,4</strong><br />
</td>
        <td style="text-align: right;"><strong>9/7</strong><br />
</td>
        <td style="text-align: right;"><strong>435,1</strong><br />
</td>
        <td style="text-align: right;"><strong>1,3</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">7<br />
</td>
        <td style="text-align: right;">509,1<br />
</td>
        <td style="text-align: right;">51/38<br />
</td>
        <td style="text-align: right;">509,4<br />
</td>
        <td style="text-align: right;">-0,3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;"><strong>8</strong><br />
</td>
        <td style="text-align: right;"><strong>581,8</strong><br />
</td>
        <td style="text-align: right;"><strong>7/5</strong><br />
</td>
        <td style="text-align: right;"><strong>582,5</strong><br />
</td>
        <td style="text-align: right;"><strong>-0,7</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">9<br />
</td>
        <td style="text-align: right;">654,5<br />
</td>
        <td style="text-align: right;">19/13<br />
</td>
        <td style="text-align: right;">657,0<br />
</td>
        <td style="text-align: right;">-2,5<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">10<br />
</td>
        <td style="text-align: right;">727,3<br />
</td>
        <td style="text-align: right;">35/23<br />
</td>
        <td style="text-align: right;">726,9<br />
</td>
        <td style="text-align: right;">0,4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">11<br />
</td>
        <td style="text-align: right;">800,0<br />
</td>
        <td style="text-align: right;">27/17<br />
</td>
        <td style="text-align: right;">800,9<br />
</td>
        <td style="text-align: right;">-0,9<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">12<br />
</td>
        <td style="text-align: right;">872,7<br />
</td>
        <td style="text-align: right;">53/32<br />
</td>
        <td style="text-align: right;">873,5<br />
</td>
        <td style="text-align: right;">-0,8<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">13<br />
</td>
        <td style="text-align: right;">945,5<br />
</td>
        <td style="text-align: right;">19/11<br />
</td>
        <td style="text-align: right;">946,2<br />
</td>
        <td style="text-align: right;">-0,7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;"><strong>14</strong><br />
</td>
        <td style="text-align: right;"><strong>1018,2</strong><br />
</td>
        <td style="text-align: right;"><strong>9/5</strong><br />
</td>
        <td style="text-align: right;"><strong>1017,6</strong><br />
</td>
        <td style="text-align: right;"><strong>0,6</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">15<br />
</td>
        <td style="text-align: right;">1090,9<br />
</td>
        <td style="text-align: right;">15/8<br />
</td>
        <td style="text-align: right;">1088,3<br />
</td>
        <td style="text-align: right;">2,6<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">16<br />
</td>
        <td style="text-align: right;">1163,6<br />
</td>
        <td style="text-align: right;">45/23<br />
</td>
        <td style="text-align: right;">1161,9<br />
</td>
        <td style="text-align: right;">1,7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">17<br />
</td>
        <td style="text-align: right;">1236,4<br />
</td>
        <td style="text-align: right;">49/24<br />
</td>
        <td style="text-align: right;">1235,7<br />
</td>
        <td style="text-align: right;">0,7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">18<br />
</td>
        <td style="text-align: right;">1309,1<br />
</td>
        <td style="text-align: right;">32/15<br />
</td>
        <td style="text-align: right;">1311,7<br />
</td>
        <td style="text-align: right;">-2,6<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;"><strong>19</strong><br />
</td>
        <td style="text-align: right;"><strong>1381,8</strong><br />
</td>
        <td style="text-align: right;"><strong>20/9</strong><br />
</td>
        <td style="text-align: right;"><strong>1382,4</strong><br />
</td>
        <td style="text-align: right;"><strong>-0,6</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">20<br />
</td>
        <td style="text-align: right;">1454,5<br />
</td>
        <td style="text-align: right;">44/19<br />
</td>
        <td style="text-align: right;">1453,8<br />
</td>
        <td style="text-align: right;">0,7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">21<br />
</td>
        <td style="text-align: right;">1527,3<br />
</td>
        <td style="text-align: right;">29/12<br />
</td>
        <td style="text-align: right;">1527,6<br />
</td>
        <td style="text-align: right;">-0,3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">22<br />
</td>
        <td style="text-align: right;">1600,0<br />
</td>
        <td style="text-align: right;">68/27<br />
</td>
        <td style="text-align: right;">1599,1<br />
</td>
        <td style="text-align: right;">0,9<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">23<br />
</td>
        <td style="text-align: right;">1672,7<br />
</td>
        <td style="text-align: right;">21/8<br />
</td>
        <td style="text-align: right;">1670,8<br />
</td>
        <td style="text-align: right;">1,9<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">24<br />
</td>
        <td style="text-align: right;">1745,5<br />
</td>
        <td style="text-align: right;">52/19<br />
</td>
        <td style="text-align: right;">1743,0<br />
</td>
        <td style="text-align: right;">2,5<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;"><strong>25</strong><br />
</td>
        <td style="text-align: right;"><strong>1818,2</strong><br />
</td>
        <td style="text-align: right;"><strong>20/7</strong><br />
</td>
        <td style="text-align: right;"><strong>1817,5</strong><br />
</td>
        <td style="text-align: right;"><strong>0,7</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">26<br />
</td>
        <td style="text-align: right;">1890,9<br />
</td>
        <td style="text-align: right;">116/39<br />
</td>
        <td style="text-align: right;">1887,1<br />
</td>
        <td style="text-align: right;">3,8<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;"><strong>27</strong><br />
</td>
        <td style="text-align: right;"><strong>1963,6</strong><br />
</td>
        <td style="text-align: right;"><strong>28/9</strong><br />
</td>
        <td style="text-align: right;">1964,9<br />
</td>
        <td style="text-align: right;"><strong>-1,3</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">28<br />
</td>
        <td style="text-align: right;">2036,4<br />
</td>
        <td style="text-align: right;">13/4<br />
</td>
        <td style="text-align: right;">2040,5<br />
</td>
        <td style="text-align: right;">-4,1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">29<br />
</td>
        <td style="text-align: right;">2109,1<br />
</td>
        <td style="text-align: right;">44/13<br />
</td>
        <td style="text-align: right;">2110,8<br />
</td>
        <td style="text-align: right;">-1,7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">30<br />
</td>
        <td style="text-align: right;">2181,8<br />
</td>
        <td style="text-align: right;">60/17<br />
</td>
        <td style="text-align: right;">2183,3<br />
</td>
        <td style="text-align: right;">-1,5<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">31<br />
</td>
        <td style="text-align: right;">2254,5<br />
</td>
        <td style="text-align: right;">114/31<br />
</td>
        <td style="text-align: right;">2254,4<br />
</td>
        <td style="text-align: right;">0,1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">32<br />
</td>
        <td style="text-align: right;">2327,3<br />
</td>
        <td style="text-align: right;">23/6<br />
</td>
        <td style="text-align: right;">2326,3<br />
</td>
        <td style="text-align: right;">1,0<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;"><strong>33</strong><br />
</td>
        <td style="text-align: right;"><strong>2400,0</strong><br />
</td>
        <td style="text-align: right;"><strong>4/1</strong><br />
</td>
        <td style="text-align: right;"><strong>2400,0</strong><br />
</td>
        <td style="text-align: right;"><strong>0,0</strong><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x--Music"></a><!-- ws:end:WikiTextHeadingRule:2 -->Music</h3>
 <a class="wiki_link_ext" href="http://soundcloud.com/ahornberg/sets/equivocal-tuning-33ed4" rel="nofollow">Equivocal Tuning</a> by Ahornberg</body></html>
Retrieved from "https://en.xen.wiki/index.php?title=33ed4&oldid=8112"