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 thought of as a Diminished Temperament for it's 1/4 octave period. Also as a Slendro temperament with a supermajor second generator (250cents), or as a Pelog or Mavila temperament generated by (fifths greater than 600 and less than 686 cents). The tuning could be popular for it's easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones. The 25 cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic genera. It can be It can be treated as 4 interwoven diminished seventh arpeggios, or as 2 interwoven 8-edo scales (narrow 11-limit whole tones which when stacked produce traditional 300 cent 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. There are two minor seventh intervals. harmonic seventh at step 13, a 7/4 ratio approximation, off by 3.5879 cents, followed by an undecimal 11/6 ratio or neutral seventh. The septimal intervals are the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , septimal semi-augmented fifth (54/35), and the septimal harmonic seventh (7/4). The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4 tone undecimal neutral seventh (11/6) 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 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 and a strange familiarity - the diminished. Hence, why 16-tone is a truly Xenharmonic system. In 16-edo Diatonic scales played are dissonant because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth. The septimal semi diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales like the "Anti-Diatonic" Mavila (which reverses step sizes of diatonic), Diminished, Happy, Rice, Grumpy, Mosh, and Decatonic can be more interesting and suitable. 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 equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Diminished Temperament for it's 1/4 octave period. Also as a Slendro temperament with a supermajor second generator (250cents), or as a Pelog or Mavila temperament generated by (fifths greater than 600 and less than 686 cents). The tuning could be popular for it's easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones.<br /> The 25 cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic genera.<br /> <br /> It can be It can be treated as 4 interwoven diminished seventh arpeggios, or as 2 interwoven 8-edo scales (narrow 11-limit whole tones which when stacked produce traditional 300 cent 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. There are two minor seventh intervals. harmonic seventh at step 13, a 7/4 ratio approximation, off by 3.5879 cents, followed by an undecimal 11/6 ratio or neutral seventh. The septimal intervals are the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , septimal semi-augmented<br /> fifth (54/35), and the septimal harmonic seventh (7/4).<br /> The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4 tone undecimal neutral seventh (11/6)<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 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 and a strange familiarity - the diminished. Hence, why 16-tone is a truly Xenharmonic system.<br /> In 16-edo Diatonic scales played are dissonant because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth. The septimal semi diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales like the "Anti-Diatonic" Mavila (which reverses step sizes of diatonic), Diminished, Happy, Rice, Grumpy, Mosh, and Decatonic can be more interesting and suitable.<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>