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

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Just Intonation is an infinite universe. A justly-intoned pentatonic can be very effective in the hands of a sensitive composer, and in this electronic age that same composer on another day can use a scale with hundreds of notes.

One approach to making just intonation not only practical but easy is to map an [[Period scale|octave-repeating]] 12-tone JI scale to a standard keyboard. This page collects some of these scales, and a [[Gallery of 12-note tempered scales|companion page]] does the same with tempered scales.

* [[otones12-24|otones 12-24]] a.k.a. Mode 12 of the [[OverToneSeries|Harmonic Series]]
* [[genovese_12]] Denny Genovese's superposition of harmonics 8-16 and subharmonics 6-12
* [[centaur]], a 7-limit tuning [[http://www.anaphoria.com/centaur.html|discovered by Kraig Grady]]
* [[nofives]] a 3 & 7 scale discovered by Gene Ward Smith
** see [[http://www.youtube.com/watch?v=n7mxHWdkV04|this piano improvisation]] by Aaron Krister Johnson.
* [[duohex]] a scale with two hexanies
* [[dwarf12_7]] the 7-limit 12-note dwarf
* [[dwarf12_11]] the 11-limit 12-note dwarf
* [[breedball3]] the third breed ball around 49/40-7/4
* [[12highschool1]] first 12-note highschool scale
* [[12highschool2]] second 12-note highschool scale
* [[hahn12]] Hahn-reduced 12 note scale
* [[hexy]] maximized 9-limit harmony containing a hexany
* [[bihexany]] Hole around [0, 1/2, 1/2, 1/2]
* [[prism]] Carl Lumma scale
* [[pris]] optimized (15/14)^3 (16/15)^4 (21/20)^3 (25/24)^2 scale
* [[glumma]] a <12 19 27 34|-epimorphic rectangular scale
* [[rectoo]] Hahn reduced circle of fifths via <12 19 27 34|
* [[blue-ji]] John O'Sullivan and Carl Lumma
* [[wilson_class]] Erv Wilson's class
* [[stelhex]] Stellated two out of 1 3 5 7 hexany
* [[stelhex2]] Stellated two out of 1 3 5 9 hexany 
* [[stexhex5]] Stellated two out of 1 3 7 9 hexany, stellation is degenerate  
* [[max scales]] 31 dyads 26 triads 6 tetrads 2 pentads
* [[cv scales]] [[Periodic scale|epimorphic scales]] with three major and two minor tetrads
* [[carlos_harm]] Wendy Carlos Harmonic Scale
* [[young-lm_piano]] La Monte Young's scale from The Well-Tuned Piano
* [[steel]] an 11-limit tuning discovered by Lou Harrison and Bill Slye
** see David B. Doty's [[http://www.dbdoty.com/SteelSuiteIntro.html|Steel Suite]].
* [[serafini-11]] Serafini's [[http://electro-music.com/forum/topic-14631.html|11's chromatic scale]], an 11-limit tuning discovered by [[Carlo Serafini]]
* [[biggulp]] Big Gulp tuning
** listen to Chris Vaisvil's improv [[http://tinyurl.com/4omx9af|here]].
* [[harrisonm_rev]] Michael Harrison's [[http://www.michaelharrison.com/harmonic-tunings.html|Revelation Tuning]]
* [[sonbirkezsorted]] Sonbirkez Huzzam scale
* [[mohajira-to-slendro]] Dudon's "From Mohajira to Aeolian and Slendros"
* [[sevish]] Sean "Sevish" Archibald's "Trapped in a Cycle" scale
* [[malcolm2]] Alexander Malcolm's 1721 scale
* [[Secor5_23TX]] George Secor's synchronous 5/23-comma temperament extraordinaire
* [[bicycle]] George Secor's (also Wilson's and Heathwaite's) 13-limit harmonic bicycle
* [[harrison_cinna]] Lou Harrison, "Incidental Music for Corneille's Cinna"

Original HTML content:

<html><head><title>Gallery of 12-tone Just Intonation Scales</title></head><body>Just Intonation is an infinite universe. A justly-intoned pentatonic can be very effective in the hands of a sensitive composer, and in this electronic age that same composer on another day can use a scale with hundreds of notes.<br />
<br />
One approach to making just intonation not only practical but easy is to map an <a class="wiki_link" href="/Period%20scale">octave-repeating</a> 12-tone JI scale to a standard keyboard. This page collects some of these scales, and a <a class="wiki_link" href="/Gallery%20of%2012-note%20tempered%20scales">companion page</a> does the same with tempered scales.<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></li><li><a class="wiki_link" href="/genovese_12">genovese_12</a> Denny Genovese's superposition of harmonics 8-16 and subharmonics 6-12</li><li><a class="wiki_link" href="/centaur">centaur</a>, a 7-limit tuning <a class="wiki_link_ext" href="http://www.anaphoria.com/centaur.html" rel="nofollow">discovered by Kraig Grady</a></li><li><a class="wiki_link" href="/nofives">nofives</a> a 3 &amp; 7 scale discovered by Gene Ward Smith<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><a class="wiki_link" href="/duohex">duohex</a> a scale with two hexanies</li><li><a class="wiki_link" href="/dwarf12_7">dwarf12_7</a> the 7-limit 12-note dwarf</li><li><a class="wiki_link" href="/dwarf12_11">dwarf12_11</a> the 11-limit 12-note dwarf</li><li><a class="wiki_link" href="/breedball3">breedball3</a> the third breed ball around 49/40-7/4</li><li><a class="wiki_link" href="/12highschool1">12highschool1</a> first 12-note highschool scale</li><li><a class="wiki_link" href="/12highschool2">12highschool2</a> second 12-note highschool scale</li><li><a class="wiki_link" href="/hahn12">hahn12</a> Hahn-reduced 12 note scale</li><li><a class="wiki_link" href="/hexy">hexy</a> maximized 9-limit harmony containing a hexany</li><li><a class="wiki_link" href="/bihexany">bihexany</a> Hole around [0, 1/2, 1/2, 1/2]</li><li><a class="wiki_link" href="/prism">prism</a> Carl Lumma scale</li><li><a class="wiki_link" href="/pris">pris</a> optimized (15/14)^3 (16/15)^4 (21/20)^3 (25/24)^2 scale</li><li><a class="wiki_link" href="/glumma">glumma</a> a &lt;12 19 27 34|-epimorphic rectangular scale</li><li><a class="wiki_link" href="/rectoo">rectoo</a> Hahn reduced circle of fifths via &lt;12 19 27 34|</li><li><a class="wiki_link" href="/blue-ji">blue-ji</a> John O'Sullivan and Carl Lumma</li><li><a class="wiki_link" href="/wilson_class">wilson_class</a> Erv Wilson's class</li><li><a class="wiki_link" href="/stelhex">stelhex</a> Stellated two out of 1 3 5 7 hexany</li><li><a class="wiki_link" href="/stelhex2">stelhex2</a> Stellated two out of 1 3 5 9 hexany</li><li><a class="wiki_link" href="/stexhex5">stexhex5</a> Stellated two out of 1 3 7 9 hexany, stellation is degenerate</li><li><a class="wiki_link" href="/max%20scales">max scales</a> 31 dyads 26 triads 6 tetrads 2 pentads</li><li><a class="wiki_link" href="/cv%20scales">cv scales</a> <a class="wiki_link" href="/Periodic%20scale">epimorphic scales</a> with three major and two minor tetrads</li><li><a class="wiki_link" href="/carlos_harm">carlos_harm</a> Wendy Carlos Harmonic Scale</li><li><a class="wiki_link" href="/young-lm_piano">young-lm_piano</a> La Monte Young's scale from The Well-Tuned Piano</li><li><a class="wiki_link" href="/steel">steel</a> an 11-limit tuning discovered by Lou Harrison and Bill Slye<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="/serafini-11">serafini-11</a> Serafini's <a class="wiki_link_ext" href="http://electro-music.com/forum/topic-14631.html" rel="nofollow">11's chromatic scale</a>, an 11-limit tuning discovered by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a></li><li><a class="wiki_link" href="/biggulp">biggulp</a> Big Gulp tuning<ul><li>listen to Chris Vaisvil's improv <a class="wiki_link_ext" href="http://tinyurl.com/4omx9af" rel="nofollow">here</a>.</li></ul></li><li><a class="wiki_link" href="/harrisonm_rev">harrisonm_rev</a> Michael Harrison's <a class="wiki_link_ext" href="http://www.michaelharrison.com/harmonic-tunings.html" rel="nofollow">Revelation Tuning</a></li><li><a class="wiki_link" href="/sonbirkezsorted">sonbirkezsorted</a> Sonbirkez Huzzam scale</li><li><a class="wiki_link" href="/mohajira-to-slendro">mohajira-to-slendro</a> Dudon's &quot;From Mohajira to Aeolian and Slendros&quot;</li><li><a class="wiki_link" href="/sevish">sevish</a> Sean &quot;Sevish&quot; Archibald's &quot;Trapped in a Cycle&quot; scale</li><li><a class="wiki_link" href="/malcolm2">malcolm2</a> Alexander Malcolm's 1721 scale</li><li><a class="wiki_link" href="/Secor5_23TX">Secor5_23TX</a> George Secor's synchronous 5/23-comma temperament extraordinaire</li><li><a class="wiki_link" href="/bicycle">bicycle</a> George Secor's (also Wilson's and Heathwaite's) 13-limit harmonic bicycle</li><li><a class="wiki_link" href="/harrison_cinna">harrison_cinna</a> Lou Harrison, &quot;Incidental Music for Corneille's Cinna&quot;</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:genewardsmith|genewardsmith]] and made on <tt>2011-03-02 13:12:35 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-02 13:32:00 UTC</tt>.<br>
-: The original revision id was <tt>206550414</tt>.<br>
+: The original revision id was <tt>206562978</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">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 &amp; small. A just-intoned pentatonic can be very effective in th hands of a sensitive composer.
+<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">Just Intonation is an infinite universe. A justly-intoned pentatonic can be very effective in the hands of a sensitive composer, and in this electronic age that same composer on another day can use a scale with hundreds of notes.
-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!
+One approach to making just intonation not only practical but easy is to map an [[Period scale|octave-repeating]] 12-tone JI scale to a standard keyboard. This page collects some of these scales, and a [[Gallery of 12-note tempered scales|companion page]] does the same with tempered scales.
 * [[otones12-24|otones 12-24]] a.k.a. Mode 12 of the [[OverToneSeries|Harmonic Series]]
@@ Line 51: / Line 51: @@
 * [[harrison_cinna]] Lou Harrison, "Incidental Music for Corneille's Cinna"</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;
+<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. A justly-intoned pentatonic can be very effective in the hands of a sensitive composer, and in this electronic age that same composer on another day can use a scale with hundreds of notes.&lt;br /&gt;
 &lt;br /&gt;
-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;
+One approach to making just intonation not only practical but easy is to map an &lt;a class="wiki_link" href="/Period%20scale"&gt;octave-repeating&lt;/a&gt; 12-tone JI scale to a standard keyboard. This page collects some of these scales, and a &lt;a class="wiki_link" href="/Gallery%20of%2012-note%20tempered%20scales"&gt;companion page&lt;/a&gt; does the same with tempered scales.&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;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/genovese_12"&gt;genovese_12&lt;/a&gt; Denny Genovese's superposition of harmonics 8-16 and subharmonics 6-12&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/centaur"&gt;centaur&lt;/a&gt;, a 7-limit tuning &lt;a class="wiki_link_ext" href="http://www.anaphoria.com/centaur.html" rel="nofollow"&gt;discovered by Kraig Grady&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/nofives"&gt;nofives&lt;/a&gt; a 3 &amp;amp; 7 scale discovered by Gene Ward Smith&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;&lt;a class="wiki_link" href="/duohex"&gt;duohex&lt;/a&gt; a scale with two hexanies&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/dwarf12_7"&gt;dwarf12_7&lt;/a&gt; the 7-limit 12-note dwarf&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/dwarf12_11"&gt;dwarf12_11&lt;/a&gt; the 11-limit 12-note dwarf&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/breedball3"&gt;breedball3&lt;/a&gt; the third breed ball around 49/40-7/4&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/12highschool1"&gt;12highschool1&lt;/a&gt; first 12-note highschool scale&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/12highschool2"&gt;12highschool2&lt;/a&gt; second 12-note highschool scale&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/hahn12"&gt;hahn12&lt;/a&gt; Hahn-reduced 12 note scale&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/hexy"&gt;hexy&lt;/a&gt; maximized 9-limit harmony containing a hexany&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/bihexany"&gt;bihexany&lt;/a&gt; Hole around [0, 1/2, 1/2, 1/2]&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/prism"&gt;prism&lt;/a&gt; Carl Lumma scale&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/pris"&gt;pris&lt;/a&gt; optimized (15/14)^3 (16/15)^4 (21/20)^3 (25/24)^2 scale&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/glumma"&gt;glumma&lt;/a&gt; a &amp;lt;12 19 27 34|-epimorphic rectangular scale&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/rectoo"&gt;rectoo&lt;/a&gt; Hahn reduced circle of fifths via &amp;lt;12 19 27 34|&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/blue-ji"&gt;blue-ji&lt;/a&gt; John O'Sullivan and Carl Lumma&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/wilson_class"&gt;wilson_class&lt;/a&gt; Erv Wilson's class&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/stelhex"&gt;stelhex&lt;/a&gt; Stellated two out of 1 3 5 7 hexany&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/stelhex2"&gt;stelhex2&lt;/a&gt; Stellated two out of 1 3 5 9 hexany&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/stexhex5"&gt;stexhex5&lt;/a&gt; Stellated two out of 1 3 7 9 hexany, stellation is degenerate&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/max%20scales"&gt;max scales&lt;/a&gt; 31 dyads 26 triads 6 tetrads 2 pentads&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/cv%20scales"&gt;cv scales&lt;/a&gt; &lt;a class="wiki_link" href="/Periodic%20scale"&gt;epimorphic scales&lt;/a&gt; with three major and two minor tetrads&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/carlos_harm"&gt;carlos_harm&lt;/a&gt; Wendy Carlos Harmonic Scale&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/young-lm_piano"&gt;young-lm_piano&lt;/a&gt; La Monte Young's scale from The Well-Tuned Piano&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/steel"&gt;steel&lt;/a&gt; an 11-limit tuning discovered by Lou Harrison and Bill Slye&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="/serafini-11"&gt;serafini-11&lt;/a&gt; Serafini's &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;, an 11-limit tuning discovered by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/biggulp"&gt;biggulp&lt;/a&gt; Big Gulp tuning&lt;ul&gt;&lt;li&gt;listen to Chris Vaisvil's improv &lt;a class="wiki_link_ext" href="http://tinyurl.com/4omx9af" rel="nofollow"&gt;here&lt;/a&gt;.&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/harrisonm_rev"&gt;harrisonm_rev&lt;/a&gt; Michael Harrison's &lt;a class="wiki_link_ext" href="http://www.michaelharrison.com/harmonic-tunings.html" rel="nofollow"&gt;Revelation Tuning&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/sonbirkezsorted"&gt;sonbirkezsorted&lt;/a&gt; Sonbirkez Huzzam scale&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/mohajira-to-slendro"&gt;mohajira-to-slendro&lt;/a&gt; Dudon's &amp;quot;From Mohajira to Aeolian and Slendros&amp;quot;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/sevish"&gt;sevish&lt;/a&gt; Sean &amp;quot;Sevish&amp;quot; Archibald's &amp;quot;Trapped in a Cycle&amp;quot; scale&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/malcolm2"&gt;malcolm2&lt;/a&gt; Alexander Malcolm's 1721 scale&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Secor5_23TX"&gt;Secor5_23TX&lt;/a&gt; George Secor's synchronous 5/23-comma temperament extraordinaire&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/bicycle"&gt;bicycle&lt;/a&gt; George Secor's (also Wilson's and Heathwaite's) 13-limit harmonic bicycle&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/harrison_cinna"&gt;harrison_cinna&lt;/a&gt; Lou Harrison, &amp;quot;Incidental Music for Corneille's Cinna&amp;quot;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

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