25edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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

: This revision was by author [[User:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2010-05-~~25 03~~:48:26 UTC</tt>.<br>

: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2010-11-13 15:42:35 UTC</tt>.<br>

: The original revision id was <tt>~~144461681~~</tt>.<br>

: The original revision id was <tt>179204617</tt>.<br>

: The revision comment was: <tt></tt><br>

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

<h4>Original Wikitext content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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.

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=25 tone equal temperament=

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.</pre></div>

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]]</pre></div>

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>25edo</title></head><body>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 />

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>25edo</title></head><body><h1 id="toc0"><a name="x25 tone equal temperament"></a>25 tone equal temperament</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.</body></html></pre></div>

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 />

<img src="/file/view/mm25.PNG/179204243/mm25.PNG" alt="mm25.PNG" title="mm25.PNG" /></body></html></pre></div>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-25 03:48:26 UTC</tt>.<br>
+: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2010-11-13 15:42:35 UTC</tt>.<br>
-: The original revision id was <tt>144461681</tt>.<br>
+: The original revision id was <tt>179204617</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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.
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=25 tone equal temperament=
+EDO 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.
 EDO 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.</pre></div>
+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]]</pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;25edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;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 &lt;a class="wiki_link" href="/5EDO"&gt;5EDO&lt;/a&gt; as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7.&lt;br /&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;25edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x25 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;25 tone equal temperament&lt;/h1&gt;
+ &lt;br /&gt;
+EDO 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 &lt;a class="wiki_link" href="/5EDO"&gt;5EDO&lt;/a&gt; as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7.&lt;br /&gt;
 &lt;br /&gt;
 EDO 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] &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup&lt;/a&gt; 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 &lt;a class="wiki_link" href="/50EDO"&gt;50EDO&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO.&lt;/body&gt;&lt;/html&gt;</pre></div>
+If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO.&lt;br /&gt;
+&lt;br /&gt;
+Some example of a keyboard in 25-EDO&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:2:&amp;lt;img src=&amp;quot;/file/view/mm25.PNG/179204243/mm25.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/mm25.PNG/179204243/mm25.PNG" alt="mm25.PNG" title="mm25.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>