21edo: 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>2011-07-22 21:08:47 UTC</tt>.<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2011-07-22 21:13:40 UTC</tt>.<br>

: The original revision id was <tt>~~242487747~~</tt>.<br>

: The original revision id was <tt>242488071</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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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=21 equal divisions of the octave=

Twenty one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome~~, and the medium magic diesis~~. The system can be treated as three intertwining 7-edo or "equi-heptatonic" scales, or as seven 3-edo ''augmented'' triads. Some other cool things about 21-edo: it has an 11-limit minor third/wide sixth, 7-limit neutral third and sixth, a 7/4 harmonic seventh or grave ~~minor~~ seventh ~~1280/729 approximation (whichever you please)~~. The ~~harmonic occurs~~ at 968.826 cents ~~while the~~ 21-tone ~~7/4 approximation is 971.4286 cents, or~~ 2.6 cents ~~off~~.

Twenty one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome. The system can be treated as three intertwining 7-edo or "equi-heptatonic" scales, or as seven 3-edo ''augmented'' triads. Some other cool things about 21-edo: it has an 11-limit minor third/wide sixth, 7-limit neutral third and sixth, a 7/4 harmonic seventh and grave seventh. The 7/4 at 968.826 cents is only off in 21-tone by 2.6 cents.

Twenty-one has a period of 1/3 of the octave ~~as opposed to 1/4 found in diminished families like 12-tet~~ and 16-tet. Some sources claim that cultures in North and South Africa ( Zambezi / Angola / Chopi, etc), as well as ancient traditional Chinese music used 7-edo (or slight alterations within the pitch sets).

Twenty-one has a period of 1/3 of the octave and boasts a neat scale dubbed "Whitewood".

0. 1/1 C

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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>21edo</title></head><body><h1 id="toc0"><a name="x21 equal divisions of the octave"></a>21 equal divisions of the octave</h1>

<br />

Twenty one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome~~, and the medium magic diesis~~. The system can be treated as three intertwining 7-edo or &quot;equi-heptatonic&quot; scales, or as seven 3-edo ''augmented'' triads. Some other cool things about 21-edo: it has an 11-limit minor third/wide sixth, 7-limit neutral third and sixth, a 7/4 harmonic seventh or grave ~~minor~~ seventh ~~1280/729 approximation (whichever you please)~~. The ~~harmonic occurs~~ at 968.826 cents ~~while the~~ 21-tone ~~7/4 approximation is 971.4286 cents, or~~ 2.6 cents ~~off~~.<br />

Twenty one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome. The system can be treated as three intertwining 7-edo or &quot;equi-heptatonic&quot; scales, or as seven 3-edo ''augmented'' triads. Some other cool things about 21-edo: it has an 11-limit minor third/wide sixth, 7-limit neutral third and sixth, a 7/4 harmonic seventh and grave seventh. The 7/4 at 968.826 cents is only off in 21-tone by 2.6 cents.<br />

<br />

Twenty-one has a period of 1/3 of the octave ~~as opposed to 1/4 found in diminished families like 12-tet~~ and 16-tet. Some sources claim that cultures in North and South Africa ( Zambezi / Angola / Chopi, etc), as well as ancient traditional Chinese music used 7-edo (or slight alterations within the pitch sets).<br />

Twenty-one has a period of 1/3 of the octave and boasts a neat scale dubbed &quot;Whitewood&quot;.<br />

<br />

0. 1/1 C<br />

@@ 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>2011-07-22 21:08:47 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-07-22 21:13:40 UTC</tt>.<br>
-: The original revision id was <tt>242487747</tt>.<br>
+: The original revision id was <tt>242488071</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 8: / Line 8: @@
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=21 equal divisions of the octave=
-Twenty one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome, and the medium magic diesis. The system can be treated as three intertwining 7-edo or "equi-heptatonic" scales, or as seven 3-edo ''augmented'' triads. Some other cool things about 21-edo: it has an 11-limit minor third/wide sixth, 7-limit neutral third and sixth, a 7/4 harmonic seventh or grave minor seventh 1280/729 approximation (whichever you please). The harmonic occurs at 968.826 cents while the 21-tone 7/4 approximation is 971.4286 cents, or 2.6 cents off.
+Twenty one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome. The system can be treated as three intertwining 7-edo or "equi-heptatonic" scales, or as seven 3-edo ''augmented'' triads. Some other cool things about 21-edo: it has an 11-limit minor third/wide sixth, 7-limit neutral third and sixth, a 7/4 harmonic seventh and grave seventh. The 7/4 at 968.826 cents is only off in 21-tone by 2.6 cents.
-Twenty-one has a period of 1/3 of the octave as opposed to 1/4 found in diminished families like 12-tet and 16-tet. Some sources claim that cultures in North and South Africa ( Zambezi / Angola / Chopi, etc), as well as ancient traditional Chinese music used 7-edo (or slight alterations within the pitch sets).
+Twenty-one has a period of 1/3 of the octave and boasts a neat scale dubbed "Whitewood".
 . 1/1 C
@@ Line 75: / Line 75: @@
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;21edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x21 equal divisions of the octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;21 equal divisions of the octave&lt;/h1&gt;
   &lt;br /&gt;
-Twenty one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome, and the medium magic diesis. The system can be treated as three intertwining 7-edo or &amp;quot;equi-heptatonic&amp;quot; scales, or as seven 3-edo ''augmented'' triads. Some other cool things about 21-edo: it has an 11-limit minor third/wide sixth, 7-limit neutral third and sixth, a 7/4 harmonic seventh or grave minor seventh 1280/729 approximation (whichever you please). The harmonic occurs at 968.826 cents while the 21-tone 7/4 approximation is 971.4286 cents, or 2.6 cents off.&lt;br /&gt;
+Twenty one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome. The system can be treated as three intertwining 7-edo or &amp;quot;equi-heptatonic&amp;quot; scales, or as seven 3-edo ''augmented'' triads. Some other cool things about 21-edo: it has an 11-limit minor third/wide sixth, 7-limit neutral third and sixth, a 7/4 harmonic seventh and grave seventh. The 7/4 at 968.826 cents is only off in 21-tone by 2.6 cents.&lt;br /&gt;
 &lt;br /&gt;
-Twenty-one has a period of 1/3 of the octave as opposed to 1/4 found in diminished families like 12-tet and 16-tet. Some sources claim that cultures in North and South Africa ( Zambezi / Angola / Chopi, etc), as well as ancient traditional Chinese music used 7-edo (or slight alterations within the pitch sets).&lt;br /&gt;
+Twenty-one has a period of 1/3 of the octave and boasts a neat scale dubbed &amp;quot;Whitewood&amp;quot;.&lt;br /&gt;
 &lt;br /&gt;
 . 1/1 C&lt;br /&gt;