16edo: Difference between revisions

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<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>2010-04-12 05:33:00 UTC</tt>.<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2010-04-12 05:36:09 UTC</tt>.<br>

: The original revision id was <tt>~~133664031~~</tt>.<br>

: The original revision id was <tt>133664275</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>

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==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 ~~25cent~~ difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic ~~intervals~~. 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 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.) 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 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 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.) 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.

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).

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<h2 id="toc1"><a name="x16 tone equal temperament-Theory"></a>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 ~~25cent~~ difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic ~~intervals~~. 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 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.) 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.<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 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.) 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.<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 />

@@ 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>2010-04-12 05:33:00 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2010-04-12 05:36:09 UTC</tt>.<br>
-: The original revision id was <tt>133664031</tt>.<br>
+: The original revision id was <tt>133664275</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 10: / Line 10: @@
 ==Theory==
 -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 25cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic intervals. 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 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.) 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 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 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.) 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.
 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).
@@ Line 69: / Line 71: @@
 &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 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.&lt;br /&gt;
-The 25cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic intervals. 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 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.) 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.&lt;br /&gt;
+The 25 cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic genera.&lt;br /&gt;
+&lt;br /&gt;
+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 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.) 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.&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 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;