35edo: Difference between revisions

Revision as of 23:11, 2 May 2012

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=<span style="color: #ff4100;">35 tone equal temperament</span>= 

35-tET or 35-[[edo|EDO]], refers to a tuning system which divides the octave into 35 steps of approximately [[cent|34.29¢]] each.

As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal edos]]: [[5edo]] and [[7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢.

35edo can represent the 2.3.5.7.11.17 [[Just intonation subgroups|subgroup]] and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators. Therefore it is a very versatile whitewood tuning.

A good beggining for start to play 35-EDO is with the Sub-diatonic scale (Pentadiatonic scale), that is a [[MOS]] of 3L2s: L s L L s; in 35-EDO is: 9 4 9 9 4

==Intervals== 
|| Degrees of 35-EDO || Cents value || Ratios in 2.3.5.7.11.17 subgroup || Ratios in 2.9.5.7.11.17 subgroup ||
|| 0 || 0 || 1/1 ||   ||
|| 1 || 34,29 ||   ||   ||
|| 2 || 68,57 ||   ||   ||
|| 3 || 102,86 || 17/16 || 17/16, 18/17 ||
|| 4 || 137,14 || 12/11 ||   ||
|| 5 || 171,43 || 11/10 || 10/9, 11/10 ||
|| 6 || 205,71 ||   || 9/8 ||
|| 7 || 240 || 8/7 || 8/7 ||
|| 8 || 274,29 || 7/6, 20/17 || 20/17 ||
|| 9 || 308,57 || 6/5 ||   ||
|| 10 || 342,86 || 17/14 || 11/9, 17/14 ||
|| 11 || 377,14 || 5/4 || 5/4 ||
|| 12 || 411,43 || 14/11 || 14/11 ||
|| 13 || 445,71 || 22/17 || 9/7, 22/17 ||
|| 14 || 480 ||   ||   ||
|| 15 || 514,29 || 4/3 ||   ||
|| 16 || 548,57 || 11/8 || 11/8 ||
|| 17 || 582,86 || 7/5, 24/17 || 7/8 ||
|| 18 || 617,14 || 10/7, 17/12 || 10/7 ||
|| 19 || 651,43 || 16/11 || 16/11 ||
|| 20 || 685,71 || 3/2 ||   ||
|| 21 || 720 ||   ||   ||
|| 22 || 754,29 || 17/11 || 14/9, 17/11 ||
|| 23 || 788,57 || 11/7 || 11/7 ||
|| 24 || 822,86 || 8/5 || 8/5 ||
|| 25 || 857,15 ||   || 18/11 ||
|| 26 || 891,43 || 5/3 ||   ||
|| 27 || 925,71 || 12/7, 17/10 || 17/10 ||
|| 28 || 960 || 7/4 || 7/4 ||
|| 29 || 994,29 ||   || 16/9 ||
|| 30 || 1028,57 || 20/11 || 20/11, 9/5 ||
|| 31 || 1062,86 || 11/6 ||   ||
|| 32 || 1097,14 || 32/17 || 32/17, 17/9 ||
|| 33 || 1131,43 ||   ||   ||
|| 34 || 1165,71 ||   ||   ||

Original HTML content:

<html><head><title>35edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x35 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ff4100;">35 tone equal temperament</span></h1>
 <br />
35-tET or 35-<a class="wiki_link" href="/edo">EDO</a>, refers to a tuning system which divides the octave into 35 steps of approximately <a class="wiki_link" href="/cent">34.29¢</a> each.<br />
<br />
As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic <a class="wiki_link" href="/macrotonal%20edos">macrotonal edos</a>: <a class="wiki_link" href="/5edo">5edo</a> and <a class="wiki_link" href="/7edo">7edo</a>. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢.<br />
<br />
35edo can represent the 2.3.5.7.11.17 <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators. Therefore it is a very versatile whitewood tuning.<br />
<br />
A good beggining for start to play 35-EDO is with the Sub-diatonic scale (Pentadiatonic scale), that is a <a class="wiki_link" href="/MOS">MOS</a> of 3L2s: L s L L s; in 35-EDO is: 9 4 9 9 4<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x35 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
 

<table class="wiki_table">
    <tr>
        <td>Degrees of 35-EDO<br />
</td>
        <td>Cents value<br />
</td>
        <td>Ratios in 2.3.5.7.11.17 subgroup<br />
</td>
        <td>Ratios in 2.9.5.7.11.17 subgroup<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
        <td>1/1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>34,29<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>68,57<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>102,86<br />
</td>
        <td>17/16<br />
</td>
        <td>17/16, 18/17<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>137,14<br />
</td>
        <td>12/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>171,43<br />
</td>
        <td>11/10<br />
</td>
        <td>10/9, 11/10<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>205,71<br />
</td>
        <td><br />
</td>
        <td>9/8<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>240<br />
</td>
        <td>8/7<br />
</td>
        <td>8/7<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>274,29<br />
</td>
        <td>7/6, 20/17<br />
</td>
        <td>20/17<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>308,57<br />
</td>
        <td>6/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>342,86<br />
</td>
        <td>17/14<br />
</td>
        <td>11/9, 17/14<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>377,14<br />
</td>
        <td>5/4<br />
</td>
        <td>5/4<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>411,43<br />
</td>
        <td>14/11<br />
</td>
        <td>14/11<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>445,71<br />
</td>
        <td>22/17<br />
</td>
        <td>9/7, 22/17<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>480<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>514,29<br />
</td>
        <td>4/3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>548,57<br />
</td>
        <td>11/8<br />
</td>
        <td>11/8<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>582,86<br />
</td>
        <td>7/5, 24/17<br />
</td>
        <td>7/8<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>617,14<br />
</td>
        <td>10/7, 17/12<br />
</td>
        <td>10/7<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>651,43<br />
</td>
        <td>16/11<br />
</td>
        <td>16/11<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>685,71<br />
</td>
        <td>3/2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>720<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>754,29<br />
</td>
        <td>17/11<br />
</td>
        <td>14/9, 17/11<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>788,57<br />
</td>
        <td>11/7<br />
</td>
        <td>11/7<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>822,86<br />
</td>
        <td>8/5<br />
</td>
        <td>8/5<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>857,15<br />
</td>
        <td><br />
</td>
        <td>18/11<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>891,43<br />
</td>
        <td>5/3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>925,71<br />
</td>
        <td>12/7, 17/10<br />
</td>
        <td>17/10<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>960<br />
</td>
        <td>7/4<br />
</td>
        <td>7/4<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>994,29<br />
</td>
        <td><br />
</td>
        <td>16/9<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>1028,57<br />
</td>
        <td>20/11<br />
</td>
        <td>20/11, 9/5<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>1062,86<br />
</td>
        <td>11/6<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>1097,14<br />
</td>
        <td>32/17<br />
</td>
        <td>32/17, 17/9<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>1131,43<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>1165,71<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>

35edo: Difference between revisions

Revision as of 23:11, 2 May 2012

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