EDO: 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:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2011-07-04 00:27:22 UTC</tt>.

: This revision was by author [[User:lobawad|lobawad]] and made on <tt>2011-07-04 16:55:40 UTC</tt>.

: The original revision id was <tt>~~239883411~~</tt>.

: The original revision id was <tt>239955517</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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You will quickly find that the //factorization// of the total number of notes in each EDO has consequences for its structure and the way it relates to other EDOs.

For example, 6 = 2 x 3, so 6-edo contains all of the intervals in both 2-edo and 3-edo. On the other hand, 7 is a prime number, so ~~all of~~ 7-edo intervals are ~~un-~~redundant with smaller EDOs.

For example, 6 = 2 x 3, so 6-edo contains all of the intervals in both 2-edo and 3-edo. On the other hand, 7 is a prime number, so no 7-edo intervals are redundant with those of smaller EDOs.

The [[MOSScales|Moments of Symmetry]] paradigm is a fascinating way of thinking about building sub-scales of EDOs and relating them to non-EDO scales.

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|| [[205edo]] || [[206edo]] || || [[208edo]] || || || || [[212edo]] || || || || ||

|| || || || || || || || [[224edo]] || [[225edo]] || || || ||

|| || || || [[232edo]] || || || || || || || || [[240edo]] ||

|| || || || || || [[246edo]] || || || || || || ||

|| [[253edo]] || || || || || || || || || || || ||

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You will quickly find that the factorization of the total number of notes in each EDO has consequences for its structure and the way it relates to other EDOs.

For example, 6 = 2 x 3, so 6-edo contains all of the intervals in both 2-edo and 3-edo. On the other hand, 7 is a prime number, so ~~all of~~ 7-edo intervals are ~~un-~~redundant with smaller EDOs.

For example, 6 = 2 x 3, so 6-edo contains all of the intervals in both 2-edo and 3-edo. On the other hand, 7 is a prime number, so no 7-edo intervals are redundant with those of smaller EDOs.

The <a class="wiki_link" href="/MOSScales">Moments of Symmetry</a> paradigm is a fascinating way of thinking about building sub-scales of EDOs and relating them to non-EDO scales.

@@ 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:genewardsmith|genewardsmith]] and made on <tt>2011-07-04 00:27:22 UTC</tt>.<br>
+: This revision was by author [[User:lobawad|lobawad]] and made on <tt>2011-07-04 16:55:40 UTC</tt>.<br>
-: The original revision id was <tt>239883411</tt>.<br>
+: The original revision id was <tt>239955517</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 18: / Line 18: @@
 You will quickly find that the //factorization// of the total number of notes in each EDO has consequences for its structure and the way it relates to other EDOs.
-For example, 6 = 2 x 3, so 6-edo contains all of the intervals in both 2-edo and 3-edo. On the other hand, 7 is a prime number, so all of 7-edo intervals are un-redundant with smaller EDOs.
+For example, 6 = 2 x 3, so 6-edo contains all of the intervals in both 2-edo and 3-edo. On the other hand, 7 is a prime number, so no 7-edo intervals are redundant with those of smaller EDOs.
 The [[MOSScales|Moments of Symmetry]] paradigm is a fascinating way of thinking about building sub-scales of EDOs and relating them to non-EDO scales.
@@ Line 49: / Line 49: @@
 || [[205edo]] || [[206edo]] ||   || [[208edo]] ||   ||   ||   || [[212edo]] ||   ||   ||   ||   ||
 ||   ||   ||   ||   ||   ||   ||   || [[224edo]] || [[225edo]] ||   ||   ||   ||
-||   ||   ||   || [[232edo]] ||  ||  ||   ||   ||   ||   ||   || [[240edo]] ||
+||   ||   ||   || [[232edo]] ||   ||   ||   ||   ||   ||   ||   || [[240edo]] ||
 ||   ||   ||   ||   ||   || [[246edo]] ||   ||   ||   ||   ||   ||   ||
 || [[253edo]] ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
@@ Line 72: / Line 72: @@
 You will quickly find that the &lt;em&gt;factorization&lt;/em&gt; of the total number of notes in each EDO has consequences for its structure and the way it relates to other EDOs.&lt;br /&gt;
 &lt;br /&gt;
-For example, 6 = 2 x 3, so 6-edo contains all of the intervals in both 2-edo and 3-edo. On the other hand, 7 is a prime number, so all of 7-edo intervals are un-redundant with smaller EDOs.&lt;br /&gt;
+For example, 6 = 2 x 3, so 6-edo contains all of the intervals in both 2-edo and 3-edo. On the other hand, 7 is a prime number, so no 7-edo intervals are redundant with those of smaller EDOs.&lt;br /&gt;
 &lt;br /&gt;
 The &lt;a class="wiki_link" href="/MOSScales"&gt;Moments of Symmetry&lt;/a&gt; paradigm is a fascinating way of thinking about building sub-scales of EDOs and relating them to non-EDO scales.&lt;br /&gt;