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:<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2012-02-10 16:18:27 UTC</tt>.<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2012-02-19 10:20:02 UTC</tt>.<br>

: The original revision id was <tt>~~300647670~~</tt>.<br>

: The original revision id was <tt>303113340</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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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 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated.

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. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. The 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the [[septimal kleisma]], 225/224.

=Intervals=

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

<br />

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 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated.<br />

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. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. The 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a>, 225/224.<br />

<br />

<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 16:18:27 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2012-02-19 10:20:02 UTC</tt>.<br>
-: The original revision id was <tt>300647670</tt>.<br>
+: The original revision id was <tt>303113340</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 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated.
+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. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. The 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the [[septimal kleisma]], 225/224.
 =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 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated.&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. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. The 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt;, 225/224.&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;