16edo: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~Andrew_Heathwaite~~|~~Andrew_Heathwaite~~]] and made on <tt>2010-08-~~07 13~~:48:39 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2010-08-16 02:04:52 UTC</tt>.

: The original revision id was <tt>~~155549041~~</tt>.

: The original revision id was <tt>156694117</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 9:

----

16-edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most ~~just~~ musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step.

16-edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most low-integer musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step.

[[user:Andrew_Heathwaite|1281203319]] adds: If we take the 300-cent minor third as an approximation of the harmonic 19th (19/16, approximately 297.5 cents), that adds another overtone which can combine with the approximation of the harmonic seventh to form a 16:19:28 triad. The interval between the 28th & 19th overtones, 28:19, measures approximately 671.3 cents, which is 3.7 cents away from 16edo's "narrow fifth".

Line 87:

<hr />

16-edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most ~~just~~ musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step.

16-edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most low-integer musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step.

- <a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;"><img src="http://www.wikispaces.com/user/pic/Andrew_Heathwaite-lg.jpg" width="16" height="16" alt="Andrew_Heathwaite" class="userPicture" /></a> <a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;">Andrew_Heathwaite</a> Aug 7, 2010 adds: If we take the 300-cent minor third as an approximation of the harmonic 19th (19/16, approximately 297.5 cents), that adds another overtone which can combine with the approximation of the harmonic seventh to form a 16:19:28 triad. The interval between the 28th &amp; 19th overtones, 28:19, measures approximately 671.3 cents, which is 3.7 cents away from 16edo's &quot;narrow fifth&quot;.

@@ 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-08-07 13:48:39 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2010-08-16 02:04:52 UTC</tt>.<br>
-: The original revision id was <tt>155549041</tt>.<br>
+: The original revision id was <tt>156694117</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: @@
 ----
--edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most just musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step.
+-edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most low-integer musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step.
 [[user:Andrew_Heathwaite|1281203319]] adds: If we take the 300-cent minor third as an approximation of the harmonic 19th (19/16, approximately 297.5 cents), that adds another overtone which can combine with the approximation of the harmonic seventh to form a 16:19:28 triad. The interval between the 28th &amp; 19th overtones, 28:19, measures approximately 671.3 cents, which is 3.7 cents away from 16edo's "narrow fifth".
@@ Line 87: / Line 87: @@
 &lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;hr /&gt;
 &lt;br /&gt;
--edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most just musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step.&lt;br /&gt;
+-edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most low-integer musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextUserlinkRule:00:[[user:Andrew_Heathwaite|1281203319]] --&gt;&lt;span class="membersnap"&gt;- &lt;a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;"&gt;&lt;img src="http://www.wikispaces.com/user/pic/Andrew_Heathwaite-lg.jpg" width="16" height="16" alt="Andrew_Heathwaite" class="userPicture" /&gt;&lt;/a&gt; &lt;a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;"&gt;Andrew_Heathwaite&lt;/a&gt; &lt;small&gt;Aug 7, 2010&lt;/small&gt;&lt;/span&gt;&lt;!-- ws:end:WikiTextUserlinkRule:00 --&gt; adds: If we take the 300-cent minor third as an approximation of the harmonic 19th (19/16, approximately 297.5 cents), that adds another overtone which can combine with the approximation of the harmonic seventh to form a 16:19:28 triad. The interval between the 28th &amp;amp; 19th overtones, 28:19, measures approximately 671.3 cents, which is 3.7 cents away from 16edo's &amp;quot;narrow fifth&amp;quot;.&lt;br /&gt;