Gallery of 12-tone just intonation scales

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author genewardsmith and made on 2011-03-04 19:32:45 UTC.

The original revision id was 207494568.

The revision comment was:

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

Original Wikitext content:

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 in an octave.

One approach to making just intonation not only practical but easy is to map an [[Periodic scale|octave-repeating]] 12-tone JI scale to a standard keyboard. This page collects some of these scales, and a [[Gallery of 12-tone Tempered Scales|companion page]] does the same for 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.
* [[omaha]] A 2.3.11 subgroup scale
* [[portsmouth]] A 2.3.7.11 subgroup scale
* [[unimajor]] A 2.3.11/7 subgroup scale
* [[canton]] A 2.3.11/7.13/7 subgroup scale
* [[locomotive]] A 2.9.11.13 subgroup scale
* [[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]
* [[hahn_7]] Paul Hahn's scale with 32 consonant 7-limit dyads. TL '99
* [[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
** [[http://alonetone.com/vaisvil/tracks/sweeneys-agony-remix-by-johnny-pumphandle.mp3|Sweeney's Agony]]
* [[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]].
* [[ptolex]] John Lyle Smith's extended septimal Ptolemy
* [[http://www.notonlymusic.com/board/download/file.php?id=1993|Te Deum Laudamus]]
* [[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"
* [[oljare]] Mats Öljare, scale for "Tampere" (2001)

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 in an octave.<br />
<br />
One approach to making just intonation not only practical but easy is to map an <a class="wiki_link" href="/Periodic%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-tone%20Tempered%20Scales">companion page</a> does the same for 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="/omaha">omaha</a> A 2.3.11 subgroup scale</li><li><a class="wiki_link" href="/portsmouth">portsmouth</a> A 2.3.7.11 subgroup scale</li><li><a class="wiki_link" href="/unimajor">unimajor</a> A 2.3.11/7 subgroup scale</li><li><a class="wiki_link" href="/canton">canton</a> A 2.3.11/7.13/7 subgroup scale</li><li><a class="wiki_link" href="/locomotive">locomotive</a> A 2.9.11.13 subgroup scale</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="/hahn_7">hahn_7</a> Paul Hahn's scale with 32 consonant 7-limit dyads. TL '99</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<ul><li><a class="wiki_link_ext" href="http://alonetone.com/vaisvil/tracks/sweeneys-agony-remix-by-johnny-pumphandle.mp3" rel="nofollow">Sweeney's Agony</a></li></ul></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="/ptolex">ptolex</a> John Lyle Smith's extended septimal Ptolemy</li><li><a class="wiki_link_ext" href="http://www.notonlymusic.com/board/download/file.php?id=1993" rel="nofollow">Te Deum Laudamus</a></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><li><a class="wiki_link" href="/oljare">oljare</a> Mats Öljare, scale for &quot;Tampere&quot; (2001)</li></ul></body></html>