25edo: Difference between revisions

Revision as of 16:08, 13 March 2011

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This revision was by author Osmiorisbendi and made on 2011-03-13 16:08:18 UTC.

The original revision id was 210043894.

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Original Wikitext content:

=<span style="color: #006b2e;">25 tone equal temperament</span>= 

25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of [[5EDO]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7.

25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a [2, 5, 7] [[Just intonation subgroups|subgroup]] tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is [[50EDO]].

If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO.

Some example of a keyboard in 25-EDO

[[image:mm25.PNG]]

==Intervals== 

|| Degrees of 25-EDO || Cents value ||
|| 0 || 0 ||
|| 1 || 48 ||
|| 2 || 96 ||
|| 3 || 144 ||
|| 4 || 192 ||
|| 5 || 240 ||
|| 6 || 288 ||
|| 7 || 336 ||
|| 8 || 384 ||
|| 9 || 432 ||
|| 10 || 480 ||
|| 11 || 528 ||
|| 12 || 576 ||
|| 13 || 624 ||
|| 14 || 672 ||
|| 15 || 720 ||
|| 16 || 768 ||
|| 17 || 816 ||
|| 18 || 864 ||
|| 19 || 912 ||
|| 20 || 960 ||
|| 21 || 1008 ||
|| 22 || 1056 ||
|| 23 || 1104 ||
|| 24 || 1152 ||

Original HTML content:

<html><head><title>25edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x25 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #006b2e;">25 tone equal temperament</span></h1>
 <br />
25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of <a class="wiki_link" href="/5EDO">5EDO</a> as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7.<br />
<br />
25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a [2, 5, 7] <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is <a class="wiki_link" href="/50EDO">50EDO</a>.<br />
<br />
If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO.<br />
<br />
Some example of a keyboard in 25-EDO<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:162:&lt;img src=&quot;/file/view/mm25.PNG/179204243/mm25.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/mm25.PNG/179204243/mm25.PNG" alt="mm25.PNG" title="mm25.PNG" /><!-- ws:end:WikiTextLocalImageRule:162 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x25 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
 <br />


<table class="wiki_table">
    <tr>
        <td>Degrees of 25-EDO<br />
</td>
        <td>Cents value<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>48<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>96<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>144<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>192<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>240<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>288<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>336<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>384<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>432<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>480<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>528<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>576<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>624<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>672<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>720<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>768<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>816<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>864<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>912<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>960<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>1008<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>1056<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>1104<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>1152<br />
</td>
    </tr>
</table>

</body></html>

25edo: Difference between revisions

Revision as of 16:08, 13 March 2011

IMPORTED REVISION FROM WIKISPACES

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