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:~~Kosmorsky~~|~~Kosmorsky~~]] and made on <tt>2012-03-~~25 18~~:04:38 UTC</tt>.<br>

: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-06-02 09:30:55 UTC</tt>.<br>

: The original revision id was <tt>~~314427540~~</tt>.<br>

: The original revision id was <tt>342024146</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>

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

25EDO divides the [[octave]] in 25 equal steps of exact size 48 [[cent]]s 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 ([[5_4|5/4]]) and 7 ([[7_4|7/4]]?).

25EDO divides the [[octave]] in 25 equal steps of exact size 48 [[cent]]s 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 ([[5_4|5/4]]) and 7 ([[7_4|7/4]]?). It also tunes sixix temperament with a sharp fifth.

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_7|8/7]]s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a [[128_125|128/125]] [[diesis]] and two [[septimal tritones]] of [[7_5|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]]. And alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for [[mavila]] temperament.

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=Music=

[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Rapoport/StudyInFives.mp3|Study in Fives]] by [[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29|Paul Rapoport]]

[[media type="file" key="25edochorale.mid"]]Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded "The <span class="il">25edo</span> canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.")

[[media type="file" key="25edochorale.mid" width="300" height="50"]]Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded "The <span class="il">25edo</span> canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.")

[[media type="file" key="25 edo prelude largo.mid"]]Peter Kosmorsky (2011, Blackwood)

[[media type="file" key="25 edo prelude largo.mid" width="300" height="50"]]Peter Kosmorsky (2011, Blackwood)

=Intervals=

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<h1 id="toc0"><a name="x25 tone equal temperament"></a><span style="color: #006b2e;">25 tone equal temperament</span></h1>

<br />

25EDO divides the <a class="wiki_link" href="/octave">octave</a> in 25 equal steps of exact size 48 <a class="wiki_link" href="/cent">cent</a>s each. It is a good way to tune the <a class="wiki_link" href="/Blackwood%20temperament">Blackwood temperament</a>, 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 (<a class="wiki_link" href="/5_4">5/4</a>) and 7 (<a class="wiki_link" href="/7_4">7/4</a>?).<br />

25EDO divides the <a class="wiki_link" href="/octave">octave</a> in 25 equal steps of exact size 48 <a class="wiki_link" href="/cent">cent</a>s each. It is a good way to tune the <a class="wiki_link" href="/Blackwood%20temperament">Blackwood temperament</a>, 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 (<a class="wiki_link" href="/5_4">5/4</a>) and 7 (<a class="wiki_link" href="/7_4">7/4</a>?). It also tunes sixix temperament with a sharp fifth.<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 <a class="wiki_link" href="/8_7">8/7</a>s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a <a class="wiki_link" href="/128_125">128/125</a> <a class="wiki_link" href="/diesis">diesis</a> and two <a class="wiki_link" href="/septimal%20tritones">septimal tritones</a> of <a class="wiki_link" href="/7_5">7/5</a> 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>. And alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for <a class="wiki_link" href="/mavila">mavila</a> temperament.<br />

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<h1 id="toc1"><a name="Music"></a>Music</h1>

<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Rapoport/StudyInFives.mp3" rel="nofollow">Study in Fives</a> by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29" rel="nofollow">Paul Rapoport</a><br />

<embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25edochorale.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed>Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded &quot;The <span class="il">25edo</span> canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.&quot;)<br />

<embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25edochorale.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed>Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded &quot;The <span class="il">25edo</span> canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.&quot;)<br />

<embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25+edo+prelude+largo.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed>Peter Kosmorsky (2011, Blackwood)<br />

<embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25+edo+prelude+largo.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed>Peter Kosmorsky (2011, Blackwood)<br />

<br />

<h1 id="toc2"><a name="Intervals"></a>Intervals</h1>

@@ Line 1: / Line 1: @@
 <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:Kosmorsky|Kosmorsky]] and made on <tt>2012-03-25 18:04:38 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-06-02 09:30:55 UTC</tt>.<br>
-: The original revision id was <tt>314427540</tt>.<br>
+: The original revision id was <tt>342024146</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>
@@ Line 9: / Line 9: @@
 =&lt;span style="color: #006b2e;"&gt;25 tone equal temperament&lt;/span&gt;=
-EDO divides the [[octave]] in 25 equal steps of exact size 48 [[cent]]s 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 ([[5_4|5/4]]) and 7 ([[7_4|7/4]]?).
+EDO divides the [[octave]] in 25 equal steps of exact size 48 [[cent]]s 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 ([[5_4|5/4]]) and 7 ([[7_4|7/4]]?). It also tunes sixix temperament with a sharp fifth.
 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_7|8/7]]s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a [[128_125|128/125]] [[diesis]] and two [[septimal tritones]] of [[7_5|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]]. And alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for [[mavila]] temperament.
@@ Line 17: / Line 17: @@
 =Music=
 [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Rapoport/StudyInFives.mp3|Study in Fives]] by [[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29|Paul Rapoport]]
-[[media type="file" key="25edochorale.mid"]]Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded "The &lt;span class="il"&gt;25edo&lt;/span&gt; canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.")
+[[media type="file" key="25edochorale.mid" width="300" height="50"]]Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded "The &lt;span class="il"&gt;25edo&lt;/span&gt; canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.")
-[[media type="file" key="25 edo prelude largo.mid"]]Peter Kosmorsky (2011, Blackwood)
+[[media type="file" key="25 edo prelude largo.mid" width="300" height="50"]]Peter Kosmorsky (2011, Blackwood)
 =Intervals=
@@ Line 83: / Line 83: @@
 &lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:2:&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:2 --&gt;&lt;span style="color: #006b2e;"&gt;25 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
-EDO divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; in 25 equal steps of exact size 48 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. It is a good way to tune the &lt;a class="wiki_link" href="/Blackwood%20temperament"&gt;Blackwood temperament&lt;/a&gt;, 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 (&lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;) and 7 (&lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;?).&lt;br /&gt;
+EDO divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; in 25 equal steps of exact size 48 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. It is a good way to tune the &lt;a class="wiki_link" href="/Blackwood%20temperament"&gt;Blackwood temperament&lt;/a&gt;, 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 (&lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;) and 7 (&lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;?). It also tunes sixix temperament with a sharp fifth.&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 &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a &lt;a class="wiki_link" href="/128_125"&gt;128/125&lt;/a&gt; &lt;a class="wiki_link" href="/diesis"&gt;diesis&lt;/a&gt; and two &lt;a class="wiki_link" href="/septimal%20tritones"&gt;septimal tritones&lt;/a&gt; of &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt; 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;. And alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for &lt;a class="wiki_link" href="/mavila"&gt;mavila&lt;/a&gt; temperament.&lt;br /&gt;
@@ Line 91: / Line 91: @@
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Music&lt;/h1&gt;
   &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Rapoport/StudyInFives.mp3" rel="nofollow"&gt;Study in Fives&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29" rel="nofollow"&gt;Paul Rapoport&lt;/a&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/25edochorale.mid?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;25edochorale.mid&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25edochorale.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded &amp;quot;The &lt;span class="il"&gt;25edo&lt;/span&gt; canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.&amp;quot;)&lt;br /&gt;
+&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/25edochorale.mid?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;25edochorale.mid&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25edochorale.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded &amp;quot;The &lt;span class="il"&gt;25edo&lt;/span&gt; canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.&amp;quot;)&lt;br /&gt;
-&lt;!-- ws:start:WikiTextMediaRule:1:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/25%20edo%20prelude%20largo.mid?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;25 edo prelude largo.mid&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25+edo+prelude+largo.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:1 --&gt;Peter Kosmorsky (2011, Blackwood)&lt;br /&gt;
+&lt;!-- ws:start:WikiTextMediaRule:1:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/25%20edo%20prelude%20largo.mid?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;25 edo prelude largo.mid&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25+edo+prelude+largo.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:1 --&gt;Peter Kosmorsky (2011, Blackwood)&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Intervals&lt;/h1&gt;