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 15:57:19 UTC</tt>.<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2012-02-10 16:03:45 UTC</tt>.<br>

: The original revision id was <tt>~~300641834~~</tt>.<br>

: The original revision id was <tt>300643644</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 thirds are close to just as well, and therefore 5-limit tuning can closely be approximated e.g. ~~by using 14- and 17- degree intervals which are very close to 5/4 and 6/5 respectively~~ instead of 13- and 18- ~~degrees~~ which are extremely close to the Pythagorean minor(32/27) and major(81/64) thirds. 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 the note in the scale rather than retuning the note in the scale.

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 e.g. instead of 13- and 18- degree intervals which are extremely close to the Pythagorean minor(32/27) and major(81/64) thirds respectively, the 14- and 17- degree intervals which are very close to 5/4 and 6/5, respectively, can be used. Some feel that the 5/4 and 6/5 intervals are more "consonant" or "harmonic" because they involve simpler numbers, but others feel that the Pythagorean intervals are more "consonant" or "harmonic" because the numbers in the ratios only have prime factors of 2 and 3 (not 5, which is "less consonant" according to that view). (see [[432hz]]) 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 the note in the scale rather than retuning the note in the scale.

=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 thirds are close to just as well, and therefore 5-limit tuning can closely be approximated e.g. ~~by using~~ 14- and 17- degree intervals which are very close to 5/4 and 6/5 respectively ~~instead of 13-~~ and ~~18- degrees which~~ are ~~extremely close to~~ the Pythagorean ~~minor~~(~~32/27~~) ~~and major~~(81/64) ~~thirds.~~ 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 the note in the scale rather than retuning the note in the scale.<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 thirds are close to just as well, and therefore 5-limit tuning can closely be approximated e.g. instead of 13- and 18- degree intervals which are extremely close to the Pythagorean minor(32/27) and major(81/64) thirds respectively, the 14- and 17- degree intervals which are very close to 5/4 and 6/5, respectively, can be used. Some feel that the 5/4 and 6/5 intervals are more &quot;consonant&quot; or &quot;harmonic&quot; because they involve simpler numbers, but others feel that the Pythagorean intervals are more &quot;consonant&quot; or &quot;harmonic&quot; because the numbers in the ratios only have prime factors of 2 and 3 (not 5, which is &quot;less consonant&quot; according to that view). (see <a class="wiki_link" href="/432hz">432hz</a>) 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 the note in the scale rather than retuning the note in the scale.<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 15:57:19 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2012-02-10 16:03:45 UTC</tt>.<br>
-: The original revision id was <tt>300641834</tt>.<br>
+: The original revision id was <tt>300643644</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 e.g. by using 14- and 17- degree intervals which are very close to 5/4 and 6/5 respectively instead of 13- and 18- degrees which are extremely close to the Pythagorean minor(32/27) and major(81/64) thirds. 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 the note in the scale rather than retuning the note in the scale.
+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 e.g. instead of 13- and 18- degree intervals which are extremely close to the Pythagorean minor(32/27) and major(81/64) thirds respectively, the 14- and 17- degree intervals which are very close to 5/4 and 6/5, respectively, can be used. Some feel that the 5/4 and 6/5 intervals are more "consonant" or "harmonic" because they involve simpler numbers, but others feel that the Pythagorean intervals are more "consonant" or "harmonic" because the numbers in the ratios only have prime factors of 2 and 3 (not 5, which is "less consonant" according to that view). (see [[432hz]]) 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 the note in the scale rather than retuning the note in the scale.
 =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 e.g. by using 14- and 17- degree intervals which are very close to 5/4 and 6/5 respectively instead of 13- and 18- degrees which are extremely close to the Pythagorean minor(32/27) and major(81/64) thirds. 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 the note in the scale rather than retuning the note in the scale.&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 e.g. instead of 13- and 18- degree intervals which are extremely close to the Pythagorean minor(32/27) and major(81/64) thirds respectively, the 14- and 17- degree intervals which are very close to 5/4 and 6/5, respectively, can be used. Some feel that the 5/4 and 6/5 intervals are more &amp;quot;consonant&amp;quot; or &amp;quot;harmonic&amp;quot; because they involve simpler numbers, but others feel that the Pythagorean intervals are more &amp;quot;consonant&amp;quot; or &amp;quot;harmonic&amp;quot; because the numbers in the ratios only have prime factors of 2 and 3 (not 5, which is &amp;quot;less consonant&amp;quot; according to that view). (see &lt;a class="wiki_link" href="/432hz"&gt;432hz&lt;/a&gt;) 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 the note in the scale rather than retuning the note in the scale.&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;