53edo: 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:

: This revision was by author [[User:guest|guest]] and made on <tt>2012-02-10 09:55:58 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2012-02-10 13:39:18 UTC</tt>.

: The original revision id was <tt>~~300487176~~</tt>.

: The original revision id was <tt>300586856</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.

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One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.

The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO can be considered an extended Pythagorean tuning using the notes: 0, 4, 9, 13, 18, 22, 26/27, 31, 35, 40, 44, 49, 53. The thirds are close to just as well, and therefore 5-limit tuning can closely be approximated using the notes: 0, __5__, 9, __14__, __17__, 22, 26/27, 31, __36__, __39__, 44, __48__, 53.

The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO can be considered an extended Pythagorean tuning using the notes: 0, 4, 9, 13, 18, 22, 26/27, 31, 35, 40, 44, 49, 53. The thirds are close to just as well, and therefore 5-limit tuning can closely be approximated using the notes: 0, __5__, 9, __14__, __17__, 22, 26/27, 31, __36__, __39__, 44, __48__, 53. Because 1 degree is very close to both the [[Syntonic Comma|Syntonic]] and [[Pythagorean comma|Pythagorean commas]], 53EDO is very flexible and wolf intervals can be avoided simply by using the note above or below rather than retuning the note e.g. in the 5-limit scale mentioned above, 14 to 44 is a wolf fifth, but 45 can be used instead of

=Intervals=

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One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.

The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO can be considered an extended Pythagorean tuning using the notes: 0, 4, 9, 13, 18, 22, 26/27, 31, 35, 40, 44, 49, 53. The thirds are close to just as well, and therefore 5-limit tuning can closely be approximated using the notes: 0, 5, 9, 14, 17, 22, 26/27, 31, 36, 39, 44, 48, 53.

The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO can be considered an extended Pythagorean tuning using the notes: 0, 4, 9, 13, 18, 22, 26/27, 31, 35, 40, 44, 49, 53. The thirds are close to just as well, and therefore 5-limit tuning can closely be approximated using the notes: 0, 5, 9, 14, 17, 22, 26/27, 31, 36, 39, 44, 48, 53. Because 1 degree is very close to both the <a class="wiki_link" href="/Syntonic%20Comma">Syntonic</a> and <a class="wiki_link" href="/Pythagorean%20comma">Pythagorean commas</a>, 53EDO is very flexible and wolf intervals can be avoided simply by using the note above or below rather than retuning the note e.g. in the 5-limit scale mentioned above, 14 to 44 is a wolf fifth, but 45 can be used instead of

<h1 id="toc2"><a name="Intervals"></a>Intervals</h1>

@@ 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>2012-02-10 09:55:58 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2012-02-10 13:39:18 UTC</tt>.<br>
-: The original revision id was <tt>300487176</tt>.<br>
+: The original revision id was <tt>300586856</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 26: / Line 26: @@
 One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.
-The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO can be considered an extended Pythagorean tuning using the notes: 0, 4, 9, 13, 18, 22, 26/27, 31, 35, 40, 44, 49, 53. The thirds are close to just as well, and therefore 5-limit tuning can closely be approximated using the notes: 0, __5__, 9, __14__, __17__, 22, 26/27, 31, __36__, __39__, 44, __48__, 53.
+The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO can be considered an extended Pythagorean tuning using the notes: 0, 4, 9, 13, 18, 22, 26/27, 31, 35, 40, 44, 49, 53. The thirds are close to just as well, and therefore 5-limit tuning can closely be approximated using the notes: 0, __5__, 9, __14__, __17__, 22, 26/27, 31, __36__, __39__, 44, __48__, 53. Because 1 degree is very close to both the [[Syntonic Comma|Syntonic]] and [[Pythagorean comma|Pythagorean commas]], 53EDO is very flexible and wolf intervals can be avoided simply by using the note above or below rather than retuning the note e.g. in the 5-limit scale mentioned above, 14 to 44 is a wolf fifth, but 45 can be used instead of
 =Intervals=
@@ Line 167: / Line 167: @@
 One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.&lt;br /&gt;
 &lt;br /&gt;
-The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO can be considered an extended Pythagorean tuning using the notes: 0, 4, 9, 13, 18, 22, 26/27, 31, 35, 40, 44, 49, 53. The thirds are close to just as well, and therefore 5-limit tuning can closely be approximated using the notes: 0, &lt;u&gt;5&lt;/u&gt;, 9, &lt;u&gt;14&lt;/u&gt;, &lt;u&gt;17&lt;/u&gt;, 22, 26/27, 31, &lt;u&gt;36&lt;/u&gt;, &lt;u&gt;39&lt;/u&gt;, 44, &lt;u&gt;48&lt;/u&gt;, 53.&lt;br /&gt;
+The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO can be considered an extended Pythagorean tuning using the notes: 0, 4, 9, 13, 18, 22, 26/27, 31, 35, 40, 44, 49, 53. The thirds are close to just as well, and therefore 5-limit tuning can closely be approximated using the notes: 0, &lt;u&gt;5&lt;/u&gt;, 9, &lt;u&gt;14&lt;/u&gt;, &lt;u&gt;17&lt;/u&gt;, 22, 26/27, 31, &lt;u&gt;36&lt;/u&gt;, &lt;u&gt;39&lt;/u&gt;, 44, &lt;u&gt;48&lt;/u&gt;, 53. Because 1 degree is very close to both the &lt;a class="wiki_link" href="/Syntonic%20Comma"&gt;Syntonic&lt;/a&gt; and &lt;a class="wiki_link" href="/Pythagorean%20comma"&gt;Pythagorean commas&lt;/a&gt;, 53EDO is very flexible and wolf intervals can be avoided simply by using the note above or below rather than retuning the note e.g. in the 5-limit scale mentioned above, 14 to 44 is a wolf fifth, but 45 can be used instead of&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals&lt;/h1&gt;