16edo
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=16 tone equal temperament= ==Theory== 16-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be treated as 4 interwoven diminished seven arpeggios, or as 2 interwoven 8-edo scales (narrow 11-limit whole tones which when stacked produce minor third intervals). 16-tone has the same stacked minor thirds diminished seventh scale/chord available in 12, and It is often cited that the most consonant chords involve the tritone. (However with the correct timbre, one can suggest consonance with any tuning.) 1 octave into 8 equal parts = 2 2 2 2 2 2 2 2 = 3/4 tone Neutral Second Progression 2 octaves into 8 equal parts = 4 4 4 4 4 4 4 4 = Classic Minor Third Progression 3 octaves into 8 equal parts = 6 6 6 6 6 6 6 6 = 9/4tone or Septimal semi-dim Fourth Progression 4 octaves into 8 equal parts = 8 8 8 8 8 8 8 8 = Tritone Progression 5 octaves into 8 equal parts = 10 10 10 10 10 10 10 10 = Septimal semi-aug Fifth Progression 6 octaves into 8 equal parts = 12 12 12 12 12 12 12 12 = Classic Sixth Progression 7 octaves into 8 equal parts = 14 14 14 14 14 14 14 14 = 21/4 tone or Neutral Seventh Progression 8 octaves into 8 equal parts = 16 16 16 16 16 16 16 16 = Octave Progression 9 octaves into 8 equal parts = 18 18 18 18 18 18 18 18 = Ninth Progression [[http://www.armodue.com/ricerche.htm|Armodue]]: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions - translation, anyone? [[image:http://ronsword.com/images/ESG_sm.jpg width="120" height="161"]] Sword, Ronald. "Hexadecaphonic Scales for Guitar." IAAA Press, UK-USA. First Ed: Feb, 2010. (superfourth tuning). Sword, Ronald. "Esadekaphonic Scales for Guitar." IAAA Press, UK-USA. First Ed: April, 2009. (semi-diminished fourth tuning) ==Compositions== [[http://www.io.com/%7Ehmiller/midi/16tet.mid|Etude in 16-tone equal tuning]] by Herman Miller [[http://www.jeanpierrepoulin.com/mp3/Armodue78.mp3|Armodue78]] by [[@http://www.jeanpierrepoulin.com/|Jean-Pierre Poulin]] [[@http://ronsword.com/sounds/16chordscale_improv.mp3|Chord-scale Improvisation in 16-tet]] by Ron Sword [[@http://www.ronsword.com/sounds/ron_sword_16_improv.mp3|Chromatic 16-tet Improvisation]] by Ron Sword [[@http://www.ronswohttp://www.ronsword.com/sounds/Ron%20Sword%20-%2016-tone%20acoustic%20improvisation.mp3|16-tet Acoustic Improvisation]] by Ron Sword [[@http://www.ronsword.com/sounds/ronsword_miracle528_part3.mp3|16-tet Miracle Drone]] by Ron Sword
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<html><head><title>16edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x16 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->16 tone equal temperament</h1> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x16 tone equal temperament-Theory"></a><!-- ws:end:WikiTextHeadingRule:2 -->Theory</h2> 16-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be treated as 4 interwoven diminished seven arpeggios, or as 2 interwoven 8-edo scales (narrow 11-limit whole tones which when stacked produce minor third intervals). 16-tone has the same stacked minor thirds diminished seventh scale/chord available in 12, and It is often cited that the most consonant chords involve the tritone. (However with the correct timbre, one can suggest consonance with any tuning.)<br /> <br /> <br /> <br /> 1 octave into 8 equal parts = 2 2 2 2 2 2 2 2 = 3/4 tone Neutral Second Progression<br /> 2 octaves into 8 equal parts = 4 4 4 4 4 4 4 4 = Classic Minor Third Progression<br /> 3 octaves into 8 equal parts = 6 6 6 6 6 6 6 6 = 9/4tone or Septimal semi-dim Fourth Progression<br /> 4 octaves into 8 equal parts = 8 8 8 8 8 8 8 8 = Tritone Progression<br /> 5 octaves into 8 equal parts = 10 10 10 10 10 10 10 10 = Septimal semi-aug Fifth Progression<br /> 6 octaves into 8 equal parts = 12 12 12 12 12 12 12 12 = Classic Sixth Progression<br /> 7 octaves into 8 equal parts = 14 14 14 14 14 14 14 14 = 21/4 tone or Neutral Seventh Progression<br /> 8 octaves into 8 equal parts = 16 16 16 16 16 16 16 16 = Octave Progression<br /> 9 octaves into 8 equal parts = 18 18 18 18 18 18 18 18 = Ninth Progression<br /> <br /> <br /> <br /> <br /> <br /> <a class="wiki_link_ext" href="http://www.armodue.com/ricerche.htm" rel="nofollow">Armodue</a>: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions - translation, anyone?<br /> <br /> <!-- ws:start:WikiTextRemoteImageRule:6:<img src="http://ronsword.com/images/ESG_sm.jpg" alt="" title="" style="height: 161px; width: 120px;" /> --><img src="http://ronsword.com/images/ESG_sm.jpg" alt="external image ESG_sm.jpg" title="external image ESG_sm.jpg" style="height: 161px; width: 120px;" /><!-- ws:end:WikiTextRemoteImageRule:6 --><br /> Sword, Ronald. "Hexadecaphonic Scales for Guitar." IAAA Press, UK-USA. First Ed: Feb, 2010. (superfourth tuning).<br /> Sword, Ronald. "Esadekaphonic Scales for Guitar." IAAA Press, UK-USA. First Ed: April, 2009. (semi-diminished fourth tuning)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x16 tone equal temperament-Compositions"></a><!-- ws:end:WikiTextHeadingRule:4 -->Compositions</h2> <br /> <a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/16tet.mid" rel="nofollow">Etude in 16-tone equal tuning</a> by Herman Miller<br /> <a class="wiki_link_ext" href="http://www.jeanpierrepoulin.com/mp3/Armodue78.mp3" rel="nofollow">Armodue78</a> by <a class="wiki_link_ext" href="http://www.jeanpierrepoulin.com/" rel="nofollow" target="_blank">Jean-Pierre Poulin</a><br /> <br /> <a class="wiki_link_ext" href="http://ronsword.com/sounds/16chordscale_improv.mp3" rel="nofollow" target="_blank">Chord-scale Improvisation in 16-tet</a> by Ron Sword<br /> <a class="wiki_link_ext" href="http://www.ronsword.com/sounds/ron_sword_16_improv.mp3" rel="nofollow" target="_blank">Chromatic 16-tet Improvisation</a> by Ron Sword<br /> <a class="wiki_link_ext" href="http://www.ronswohttp://www.ronsword.com/sounds/Ron%20Sword%20-%2016-tone%20acoustic%20improvisation.mp3" rel="nofollow" target="_blank">16-tet Acoustic Improvisation</a> by Ron Sword<br /> <a class="wiki_link_ext" href="http://www.ronsword.com/sounds/ronsword_miracle528_part3.mp3" rel="nofollow" target="_blank">16-tet Miracle Drone</a> by Ron Sword</body></html>