Gallery of 12-tone just intonation scales: Difference between revisions

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Just Intonation is an infinite universe. You can have a JI scale with two tones or a trillion. I ([[user:Andrew_Heathwaite|1280008569]]) have an interest in JI scales large & small. A just-intoned pentatonic can be very effective in th hands of a sensitive composer.

One approach that interests me is to map an octave-repeating 12-tone JI scale to a keyboard. Of course, there are an infinite number of possible 12-tone JI scales. This page is my attempt to collect some. Please feel free to add more or make corrections as you discover them or invent them!

* [[otones12-24|otones 12-24]] a.k.a. Mode 12 of the [[OverToneSeries|Harmonic Series]]: 1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/16, 2/1
* [[http://www.anaphoria.com/centaur.html|Centaur]], a 7-limit tuning discovered by Kraig Grady: 1/1, 21/20, 9/8, 7/6, 5/4, 4/3, 7/5, 3/2, 14/9, 5/3, 7/4, 15/8, 2/1
* a 3 & 7 scale discovered by Gene Ward Smith (does it have a name?): 1/1, 28/27, 9/8, 7/6, 9/7, 4/3, 49/36, 3/2, 14/9, 12/7, 7/4, 49/27, 2/1
** see [[http://www.youtube.com/watch?v=n7mxHWdkV04|this piano improvisation]] by Aaron Krister Johnson.
* Wendy Carlos Harmonic Scale: 1/1, 17/16, 9/8, 19/16, 5/4, 21/16, 11/8, 3/2, 13/8, 27/16, 7/4, 15/8
* La Monte Young's scale from The Well-Tuned Piano: 1/1, 567/512, 9/8, 147/128, 21/16, 1323/1024, 189/128, 3/2, 49/32, 7/4, 441/256, 63/32, 2/1
* an 11-limit tuning discovered by Lou Harrison and Bill Slye: 1/1, 28/27, 9/8, 7/6, 5/4, 4/3, 11/8, 3/2, 14/9, 5/3, 7/4, 11/6, 2/1
** see David B. Doty's [[http://www.dbdoty.com/SteelSuiteIntro.html|Steel Suite]].
* [[Rodan]], a 13-limit tuning discovered by Andrew Heathwaite: 1/1, 33/32, 9/8, 39/32, 5/4, 21/16, 11/8, 3/2, 13/8, 27/16, 7/4, 15/8, 2/1
* [[http://electro-music.com/forum/topic-14631.html|11's chromatic scale]], a 11-limit tuning discovered by Carlo Serafini: 1/1, 11/10, 9/8, 7/6, 5/4, 11/8, 10/7, 3/2, 8/5, 5/3, 7/4, 20/11, 2/1

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<html><head><title>Gallery of 12-tone Just Intonation Scales</title></head><body>Just Intonation is an infinite universe. You can have a JI scale with two tones or a trillion. I (<!-- ws:start:WikiTextUserlinkRule:00:[[user:Andrew_Heathwaite|1280008569]] --><span class="membersnap">- <a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;"><img src="http://www.wikispaces.com/user/pic/Andrew_Heathwaite-lg.jpg" width="16" height="16" alt="Andrew_Heathwaite" class="userPicture" /></a> <a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;">Andrew_Heathwaite</a> <small>Jul 24, 2010</small></span><!-- ws:end:WikiTextUserlinkRule:00 -->) have an interest in JI scales large &amp; small. A just-intoned pentatonic can be very effective in th hands of a sensitive composer.<br />
<br />
One approach that interests me is to map an octave-repeating 12-tone JI scale to a keyboard. Of course, there are an infinite number of possible 12-tone JI scales. This page is my attempt to collect some. Please feel free to add more or make corrections as you discover them or invent them!<br />
<br />
<ul><li><a class="wiki_link" href="/otones12-24">otones 12-24</a> a.k.a. Mode 12 of the <a class="wiki_link" href="/OverToneSeries">Harmonic Series</a>: 1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/16, 2/1</li><li><a class="wiki_link_ext" href="http://www.anaphoria.com/centaur.html" rel="nofollow">Centaur</a>, a 7-limit tuning discovered by Kraig Grady: 1/1, 21/20, 9/8, 7/6, 5/4, 4/3, 7/5, 3/2, 14/9, 5/3, 7/4, 15/8, 2/1</li><li>a 3 &amp; 7 scale discovered by Gene Ward Smith (does it have a name?): 1/1, 28/27, 9/8, 7/6, 9/7, 4/3, 49/36, 3/2, 14/9, 12/7, 7/4, 49/27, 2/1<ul><li>see <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=n7mxHWdkV04" rel="nofollow">this piano improvisation</a> by Aaron Krister Johnson.</li></ul></li><li>Wendy Carlos Harmonic Scale: 1/1, 17/16, 9/8, 19/16, 5/4, 21/16, 11/8, 3/2, 13/8, 27/16, 7/4, 15/8</li><li>La Monte Young's scale from The Well-Tuned Piano: 1/1, 567/512, 9/8, 147/128, 21/16, 1323/1024, 189/128, 3/2, 49/32, 7/4, 441/256, 63/32, 2/1</li><li>an 11-limit tuning discovered by Lou Harrison and Bill Slye: 1/1, 28/27, 9/8, 7/6, 5/4, 4/3, 11/8, 3/2, 14/9, 5/3, 7/4, 11/6, 2/1<ul><li>see David B. Doty's <a class="wiki_link_ext" href="http://www.dbdoty.com/SteelSuiteIntro.html" rel="nofollow">Steel Suite</a>.</li></ul></li><li><a class="wiki_link" href="/Rodan">Rodan</a>, a 13-limit tuning discovered by Andrew Heathwaite: 1/1, 33/32, 9/8, 39/32, 5/4, 21/16, 11/8, 3/2, 13/8, 27/16, 7/4, 15/8, 2/1</li><li><a class="wiki_link_ext" href="http://electro-music.com/forum/topic-14631.html" rel="nofollow">11's chromatic scale</a>, a 11-limit tuning discovered by Carlo Serafini: 1/1, 11/10, 9/8, 7/6, 5/4, 11/8, 10/7, 3/2, 8/5, 5/3, 7/4, 20/11, 2/1</li></ul></body></html>

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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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-07-24 17:57:07 UTC</tt>.<br>
+: This revision was by author [[User:seraph57|seraph57]] and made on <tt>2010-07-24 18:13:00 UTC</tt>.<br>
-: The original revision id was <tt>153889313</tt>.<br>
+: The original revision id was <tt>153890433</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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 * an 11-limit tuning discovered by Lou Harrison and Bill Slye: 1/1, 28/27, 9/8, 7/6, 5/4, 4/3, 11/8, 3/2, 14/9, 5/3, 7/4, 11/6, 2/1
 ** see David B. Doty's [[http://www.dbdoty.com/SteelSuiteIntro.html|Steel Suite]].
-* [[Rodan]], a 13-limit tuning discovered by Andrew Heathwaite: 1/1, 33/32, 9/8, 39/32, 5/4, 21/16, 11/8, 3/2, 13/8, 27/16, 7/4, 15/8, 2/1</pre></div>
+* [[Rodan]], a 13-limit tuning discovered by Andrew Heathwaite: 1/1, 33/32, 9/8, 39/32, 5/4, 21/16, 11/8, 3/2, 13/8, 27/16, 7/4, 15/8, 2/1
+* [[http://electro-music.com/forum/topic-14631.html|11's chromatic scale]], a 11-limit tuning discovered by Carlo Serafini: 1/1, 11/10, 9/8, 7/6, 5/4, 11/8, 10/7, 3/2, 8/5, 5/3, 7/4, 20/11, 2/1</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;Gallery of 12-tone Just Intonation Scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Just Intonation is an infinite universe. You can have a JI scale with two tones or a trillion. I (&lt;!-- ws:start:WikiTextUserlinkRule:00:[[user:Andrew_Heathwaite|1280008569]] --&gt;&lt;span class="membersnap"&gt;- &lt;a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;"&gt;&lt;img src="http://www.wikispaces.com/user/pic/Andrew_Heathwaite-lg.jpg" width="16" height="16" alt="Andrew_Heathwaite" class="userPicture" /&gt;&lt;/a&gt; &lt;a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;"&gt;Andrew_Heathwaite&lt;/a&gt; &lt;small&gt;Jul 24, 2010&lt;/small&gt;&lt;/span&gt;&lt;!-- ws:end:WikiTextUserlinkRule:00 --&gt;) have an interest in JI scales large &amp;amp; small. A just-intoned pentatonic can be very effective in th hands of a sensitive composer.&lt;br /&gt;
@@ Line 24: / Line 25: @@
 One approach that interests me is to map an octave-repeating 12-tone JI scale to a keyboard. Of course, there are an infinite number of possible 12-tone JI scales. This page is my attempt to collect some. Please feel free to add more or make corrections as you discover them or invent them!&lt;br /&gt;
 &lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/otones12-24"&gt;otones 12-24&lt;/a&gt; a.k.a. Mode 12 of the &lt;a class="wiki_link" href="/OverToneSeries"&gt;Harmonic Series&lt;/a&gt;: 1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/16, 2/1&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.anaphoria.com/centaur.html" rel="nofollow"&gt;Centaur&lt;/a&gt;, a 7-limit tuning discovered by Kraig Grady: 1/1, 21/20, 9/8, 7/6, 5/4, 4/3, 7/5, 3/2, 14/9, 5/3, 7/4, 15/8, 2/1&lt;/li&gt;&lt;li&gt;a 3 &amp;amp; 7 scale discovered by Gene Ward Smith (does it have a name?): 1/1, 28/27, 9/8, 7/6, 9/7, 4/3, 49/36, 3/2, 14/9, 12/7, 7/4, 49/27, 2/1&lt;ul&gt;&lt;li&gt;see &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=n7mxHWdkV04" rel="nofollow"&gt;this piano improvisation&lt;/a&gt; by Aaron Krister Johnson.&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;Wendy Carlos Harmonic Scale: 1/1, 17/16, 9/8, 19/16, 5/4, 21/16, 11/8, 3/2, 13/8, 27/16, 7/4, 15/8&lt;/li&gt;&lt;li&gt;La Monte Young's scale from The Well-Tuned Piano: 1/1, 567/512, 9/8, 147/128, 21/16, 1323/1024, 189/128, 3/2, 49/32, 7/4, 441/256, 63/32, 2/1&lt;/li&gt;&lt;li&gt;an 11-limit tuning discovered by Lou Harrison and Bill Slye: 1/1, 28/27, 9/8, 7/6, 5/4, 4/3, 11/8, 3/2, 14/9, 5/3, 7/4, 11/6, 2/1&lt;ul&gt;&lt;li&gt;see David B. Doty's &lt;a class="wiki_link_ext" href="http://www.dbdoty.com/SteelSuiteIntro.html" rel="nofollow"&gt;Steel Suite&lt;/a&gt;.&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Rodan"&gt;Rodan&lt;/a&gt;, a 13-limit tuning discovered by Andrew Heathwaite: 1/1, 33/32, 9/8, 39/32, 5/4, 21/16, 11/8, 3/2, 13/8, 27/16, 7/4, 15/8, 2/1&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/otones12-24"&gt;otones 12-24&lt;/a&gt; a.k.a. Mode 12 of the &lt;a class="wiki_link" href="/OverToneSeries"&gt;Harmonic Series&lt;/a&gt;: 1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/16, 2/1&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.anaphoria.com/centaur.html" rel="nofollow"&gt;Centaur&lt;/a&gt;, a 7-limit tuning discovered by Kraig Grady: 1/1, 21/20, 9/8, 7/6, 5/4, 4/3, 7/5, 3/2, 14/9, 5/3, 7/4, 15/8, 2/1&lt;/li&gt;&lt;li&gt;a 3 &amp;amp; 7 scale discovered by Gene Ward Smith (does it have a name?): 1/1, 28/27, 9/8, 7/6, 9/7, 4/3, 49/36, 3/2, 14/9, 12/7, 7/4, 49/27, 2/1&lt;ul&gt;&lt;li&gt;see &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=n7mxHWdkV04" rel="nofollow"&gt;this piano improvisation&lt;/a&gt; by Aaron Krister Johnson.&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;Wendy Carlos Harmonic Scale: 1/1, 17/16, 9/8, 19/16, 5/4, 21/16, 11/8, 3/2, 13/8, 27/16, 7/4, 15/8&lt;/li&gt;&lt;li&gt;La Monte Young's scale from The Well-Tuned Piano: 1/1, 567/512, 9/8, 147/128, 21/16, 1323/1024, 189/128, 3/2, 49/32, 7/4, 441/256, 63/32, 2/1&lt;/li&gt;&lt;li&gt;an 11-limit tuning discovered by Lou Harrison and Bill Slye: 1/1, 28/27, 9/8, 7/6, 5/4, 4/3, 11/8, 3/2, 14/9, 5/3, 7/4, 11/6, 2/1&lt;ul&gt;&lt;li&gt;see David B. Doty's &lt;a class="wiki_link_ext" href="http://www.dbdoty.com/SteelSuiteIntro.html" rel="nofollow"&gt;Steel Suite&lt;/a&gt;.&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Rodan"&gt;Rodan&lt;/a&gt;, a 13-limit tuning discovered by Andrew Heathwaite: 1/1, 33/32, 9/8, 39/32, 5/4, 21/16, 11/8, 3/2, 13/8, 27/16, 7/4, 15/8, 2/1&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://electro-music.com/forum/topic-14631.html" rel="nofollow"&gt;11's chromatic scale&lt;/a&gt;, a 11-limit tuning discovered by Carlo Serafini: 1/1, 11/10, 9/8, 7/6, 5/4, 11/8, 10/7, 3/2, 8/5, 5/3, 7/4, 20/11, 2/1&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Gallery of 12-tone just intonation scales: Difference between revisions

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