16edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:guest|guest]] and made on <tt>2010-02-~~20 02~~:12:52 UTC</tt>.<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2010-04-12 03:01:40 UTC</tt>.<br>

: The original revision id was <tt>~~121706035~~</tt>.<br>

: The original revision id was <tt>133651837</tt>.<br>

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==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 trapped within the 12-tone minor third. 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.

16-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Slendro temperament with a supermajor second generator (250cents), or as a Pelog or Mavila temperament. The 25cent difference in the steps can sound to a trained ear like phantom Pythagorean commas / enharmonic genera trapped within the 12-tone minor third. 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).

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<br />

<h2 id="toc1"><a name="x16 tone equal temperament-Theory"></a>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 trapped within the 12-tone minor third. 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 />

16-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Slendro temperament with a supermajor second generator (250cents), or as a Pelog or Mavila temperament. The 25cent difference in the steps can sound to a trained ear like phantom Pythagorean commas / enharmonic genera trapped within the 12-tone minor third. 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 />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:guest|guest]] and made on <tt>2010-02-20 02:12:52 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2010-04-12 03:01:40 UTC</tt>.<br>
-: The original revision id was <tt>121706035</tt>.<br>
+: The original revision id was <tt>133651837</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 9: / Line 9: @@
 ==Theory==
--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 trapped within the 12-tone minor third. 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.
+-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Slendro temperament with a supermajor second generator (250cents), or as a Pelog or Mavila temperament. The 25cent difference in the steps can sound to a trained ear like phantom Pythagorean commas / enharmonic genera trapped within the 12-tone minor third. 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).
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   &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x16 tone equal temperament-Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Theory&lt;/h2&gt;
--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 trapped within the 12-tone minor third. 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.&lt;br /&gt;
+-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Slendro temperament with a supermajor second generator (250cents), or as a Pelog or Mavila temperament. The 25cent difference in the steps can sound to a trained ear like phantom Pythagorean commas / enharmonic genera trapped within the 12-tone minor third. 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.&lt;br /&gt;
 &lt;br /&gt;
 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).&lt;br /&gt;