Gallery of 12-tone just intonation scales: Difference between revisions
Wikispaces>genewardsmith **Imported revision 201420402 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 201420948 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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>2011-02-13 20: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-13 20:51:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>201420948</tt>.<br> | ||
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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<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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* [[bihexany]] Hole around [0, 1/2, 1/2, 1/2] | * [[bihexany]] Hole around [0, 1/2, 1/2, 1/2] | ||
* [[prism]] Carl Lumma scale | * [[prism]] Carl Lumma scale | ||
* [[pris]] | * [[pris]] optimized (15/14)^3 (16/15)^4 (21/20)^3 (25/24)^2 scale | ||
* [[glumma]] a <12 19 27 34|-epimorphic rectangular scale | * [[glumma]] a <12 19 27 34|-epimorphic rectangular scale | ||
* [[rectoo]] Hahn reduced circle of fifths via <12 19 27 34| | * [[rectoo]] Hahn reduced circle of fifths via <12 19 27 34| | ||
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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 /> | 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 /> | ||
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<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 &amp; 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> | <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 &amp; 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 &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="/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>: &quot;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).&quot;</li></ul></body></html></pre></div> | ||