16edo
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=16 tone equal temperament= ==Theory== 16-tone is a tuning which has been less popular but can be very rewarding. 16-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. The 25cent difference in the steps can sound to a trained ear like phantom Pythagorean commas / enharmonic genera. 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.) The harmonic seventh, 7/4, approximation is off by 3.5879 cents. One neat xenharmonic aspect of 16-tone is how the 11-limit whole tone scale using the neutral second, interlocks with the diminished scale, similar to how the augmented scale and whole tone relationship in 12-tone (the whole tone divides the major third in 12, in 16-it's the minor third). In 16-tone, because of the 25 cent difference in the steps from 100 in 12-tone, a western "twelve tone ear" hears dissonance with more complexity and less familiarity than even 24-tone, yet within a more manageable number of tones. Hence, why 16-tone is a truly Xenharmonic system. 0. 1/1 C 1. 75.000 cents C# Dbb 2. 150.000 cents Cx Db 3. 225.000 cents D 4. 300.000 cents D# Ebb 5. 375.000 cents Dx Eb 6. 450.000 cents E Fb 7. 525.000 cents F 8. 600.000 cents F# Gbb 9. 675.000 cents Fx Gb 10. 750.000 cents G Abb 11. 825.000 cents G# Ab 12. 900.000 cents A 13. 975.000 cents A# Bbb 14. 1050.000 cents Ax Bb 15. 1125.000 cents B Cb 16. 2/1 C 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 is a tuning which has been less popular but can be very rewarding. 16-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. The 25cent difference in the steps can sound to a trained ear like phantom Pythagorean commas / enharmonic genera. 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.) The harmonic seventh, 7/4, approximation is off by 3.5879 cents.<br /> <br /> One neat xenharmonic aspect of 16-tone is how the 11-limit whole tone scale using the neutral second, interlocks with the diminished scale, similar to how the augmented scale and whole tone relationship in 12-tone (the whole tone divides the major third in 12, in 16-it's the minor third).<br /> <br /> In 16-tone, because of the 25 cent difference in the steps from 100 in 12-tone, a western "twelve tone ear" hears dissonance with more complexity and less familiarity than even 24-tone, yet within a more manageable number of tones. Hence, why 16-tone is a truly Xenharmonic system.<br /> <br /> 0. 1/1 C<br /> 1. 75.000 cents C# Dbb<br /> 2. 150.000 cents Cx Db<br /> 3. 225.000 cents D<br /> 4. 300.000 cents D# Ebb<br /> 5. 375.000 cents Dx Eb<br /> 6. 450.000 cents E Fb<br /> 7. 525.000 cents F<br /> 8. 600.000 cents F# Gbb<br /> 9. 675.000 cents Fx Gb<br /> 10. 750.000 cents G Abb<br /> 11. 825.000 cents G# Ab<br /> 12. 900.000 cents A<br /> 13. 975.000 cents A# Bbb<br /> 14. 1050.000 cents Ax Bb<br /> 15. 1125.000 cents B Cb<br /> 16. 2/1 C<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>