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>2011-07-19 02:53:57 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-19 03:00:07 UTC</tt>.

: The original revision id was <tt>~~241896240~~</tt>.

: The original revision id was <tt>241896704</tt>.

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

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If you're a classically-trained musician and you'd like to start with some EDOs that have some relationship to common-practice tonal music, starting with reasonably-low EDOs that give a good approximation to 3/2 (the perfect 5th) can be rewarding. These include 17, 19, 22, 29, 31, 39, 41, 43, 46, 50 and 53. All of these can be notated with some variant on the [[Nominal-Accidental Chains#A-G circle-of-fifths notation|A-G "circle of fifths" notation]], while other EDOs, including 24, 34, 36, 38, 44 or 51 involve more than one such circle.

Some EDOs, such as 26, 27, 32, 33 or 37 have fifths which are reasonably good but quite audibly not just. Other EDOs, such as 11, 13, 14, 15, 16, 18, 21, 23 or 25, are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.

Some EDOs, such as 26, 27, 32, 33 or 37 have fifths which are reasonably good but quite audibly not just. Other EDOs, such as 11, 13, 14, 15, 16, 18, 20, 21, 23 or 25, are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.

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 no 7-edo intervals are redundant with those of smaller EDOs. See [[prime numbers#prime numbers in EDOs|prime numbers in EDOs]] for more details.

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If you're a classically-trained musician and you'd like to start with some EDOs that have some relationship to common-practice tonal music, starting with reasonably-low EDOs that give a good approximation to 3/2 (the perfect 5th) can be rewarding. These include 17, 19, 22, 29, 31, 39, 41, 43, 46, 50 and 53. All of these can be notated with some variant on the <a class="wiki_link" href="/Nominal-Accidental%20Chains#A-G circle-of-fifths notation">A-G &quot;circle of fifths&quot; notation</a>, while other EDOs, including 24, 34, 36, 38, 44 or 51 involve more than one such circle.

Some EDOs, such as 26, 27, 32, 33 or 37 have fifths which are reasonably good but quite audibly not just. Other EDOs, such as 11, 13, 14, 15, 16, 18, 21, 23 or 25, are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.

Some EDOs, such as 26, 27, 32, 33 or 37 have fifths which are reasonably good but quite audibly not just. Other EDOs, such as 11, 13, 14, 15, 16, 18, 20, 21, 23 or 25, are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.

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 no 7-edo intervals are redundant with those of smaller EDOs. See <a class="wiki_link" href="/prime%20numbers#prime numbers in EDOs">prime numbers in EDOs</a> for more details.

@@ 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>2011-07-19 02:53:57 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-19 03:00:07 UTC</tt>.<br>
-: The original revision id was <tt>241896240</tt>.<br>
+: The original revision id was <tt>241896704</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: @@
 If you're a classically-trained musician and you'd like to start with some EDOs that have some relationship to common-practice tonal music, starting with reasonably-low EDOs that give a good approximation to 3/2 (the perfect 5th) can be rewarding. These include 17, 19, 22, 29, 31, 39, 41, 43, 46, 50 and 53. All of these can be notated with some variant on the [[Nominal-Accidental Chains#A-G circle-of-fifths notation|A-G "circle of fifths" notation]], while other EDOs, including 24, 34, 36, 38, 44 or 51 involve more than one such circle.
-Some EDOs, such as 26, 27, 32, 33 or 37 have fifths which are reasonably good but quite audibly not just. Other EDOs, such as 11, 13, 14, 15, 16, 18, 21, 23 or 25, are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.
+Some EDOs, such as 26, 27, 32, 33 or 37 have fifths which are reasonably good but quite audibly not just. Other EDOs, such as 11, 13, 14, 15, 16, 18, 20, 21, 23 or 25, are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.
 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 no 7-edo intervals are redundant with those of smaller EDOs. See [[prime numbers#prime numbers in EDOs|prime numbers in EDOs]] for more details.
@@ Line 102: / Line 102: @@
 If you're a classically-trained musician and you'd like to start with some EDOs that have some relationship to common-practice tonal music, starting with reasonably-low EDOs that give a good approximation to 3/2 (the perfect 5th) can be rewarding. These include 17, 19, 22, 29, 31, 39, 41, 43, 46, 50 and 53. All of these can be notated with some variant on the &lt;a class="wiki_link" href="/Nominal-Accidental%20Chains#A-G circle-of-fifths notation"&gt;A-G &amp;quot;circle of fifths&amp;quot; notation&lt;/a&gt;, while other EDOs, including 24, 34, 36, 38, 44 or 51 involve more than one such circle. &lt;br /&gt;
 &lt;br /&gt;
-Some EDOs, such as 26, 27, 32, 33 or 37 have fifths which are reasonably good but quite audibly not just. Other EDOs, such as 11, 13, 14, 15, 16, 18, 21, 23 or 25, are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.&lt;br /&gt;
+Some EDOs, such as 26, 27, 32, 33 or 37 have fifths which are reasonably good but quite audibly not just. Other EDOs, such as 11, 13, 14, 15, 16, 18, 20, 21, 23 or 25, are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.&lt;br /&gt;
 &lt;br /&gt;
 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. 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. See &lt;a class="wiki_link" href="/prime%20numbers#prime numbers in EDOs"&gt;prime numbers in EDOs&lt;/a&gt; for more details.&lt;br /&gt;