25edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2011-04-02 17:52:08 UTC.
- The original revision id was 216499096.
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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. In fact, on the subgroup 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for wide range of harmony. 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:<h1> --><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. In fact, on the subgroup 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for wide range of harmony.<br />
<br />
Some example of a keyboard in 25-EDO<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:162:<img src="/file/view/mm25.PNG/179204243/mm25.PNG" alt="" title="" /> --><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:<h2> --><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>