Gallery of 12-tone just intonation scales
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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 * [[nofives]] a 3 & 7 scale discovered by Gene Ward Smith: 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. * [[duohex]] a scale with two hexanies: 15/14 9/8 6/5 5/4 9/7 10/7 3/2 45/28 12/7 9/5 15/8 2 * [[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 * [[wilson_helix]] Wilson's Helix Song * 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 * Michael Harrison's [[http://www.michaelharrison.com/harmonic-tunings.html|Revelation Tuning]]: "The twelve pitches are tuned to the following twelve harmonics or “overtones” of the fundamental note F. For white keys: F=1, C=3, G=9, D=27, A=81, E=243, and B=729 (all of which are multiples of the prime number 3); and for black keys: E-flat=7, B-flat=21, F#=63, C#=189, and G#=567 (all of which are multiples of the primes 3 and 7)."
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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 & 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 class="wiki_link" href="/nofives">nofives</a> a 3 & 7 scale discovered by Gene Ward Smith: 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><a class="wiki_link" href="/duohex">duohex</a> a scale with two hexanies: 15/14 9/8 6/5 5/4 9/7 10/7 3/2 45/28 12/7 9/5 15/8 2</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 <12 19 27 34|-epimorphic rectangular scale</li><li><a class="wiki_link" href="/rectoo">rectoo</a> Hahn reduced circle of fifths via <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="/wilson_helix">wilson_helix</a> Wilson's Helix Song</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 <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>: 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 <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a>: 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><li>Michael Harrison's <a class="wiki_link_ext" href="http://www.michaelharrison.com/harmonic-tunings.html" rel="nofollow">Revelation Tuning</a>: "The twelve pitches are tuned to the following twelve harmonics or “overtones” of the fundamental note F. For white keys: F=1, C=3, G=9, D=27, A=81, E=243, and B=729 (all of which are multiples of the prime number 3); and for black keys: E-flat=7, B-flat=21, F#=63, C#=189, and G#=567 (all of which are multiples of the primes 3 and 7)."</li></ul></body></html>