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

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-16 19:10:47 UTC</tt>.<br>

: The original revision id was <tt>202550724</tt>.<br>

&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" 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_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;&lt;a class="wiki_link" href="/nofives"&gt;nofives&lt;/a&gt; a 3 &amp;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&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: 15/14 9/8 6/5 5/4 9/7 10/7 3/2 45/28 12/7 9/5 15/8 2&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="/wilson_helix"&gt;wilson_helix&lt;/a&gt; Wilson's Helix Song&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/stelhex"&gt;stelhex&lt;/a&gt;&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;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 &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;: 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 &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt;: 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;li&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;: &amp;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).&amp;quot;&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="/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>