37edo: Difference between revisions

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:~~hstraub~~|~~hstraub~~]] and made on <tt>2011-06-~~22 07~~:17:58 UTC</tt>.<br>

: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2011-07-30 01:53:35 UTC</tt>.<br>

: The original revision id was <tt>~~238143999~~</tt>.<br>

: The original revision id was <tt>243481051</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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26\37 = 843.2 cents

This means 37 is quite accurate on the 2.5.7.11 subgroup, where it shares the same tuning as 111et. In fact, on the larger [[k*N subgroups|3*37 subgroup]] 2.27.5.7.11.51.57 subgroup not only shares the same tuning as 19-limit 111et, it tempers out the same commas.

This means 37 is quite accurate on the 2.5.7.11.13 subgroup, where it shares the same tuning as 111et. In fact, on the larger [[k*N subgroups|3*37 subgroup]] 2.27.5.7.11.51.57 subgroup not only shares the same tuning as 19-limit 111et, it tempers out the same commas.

=The Two Fifths=

Line 36:

"minor third" = 8\37 = 259.5 cents

"major third" = 14\37 = 454.1 cents

If the minor third of 259.5 cents is mapped to 7/6, this superpythagorean scale can be thought of as a variety of [[The Biosphere|Biome]] temperament.

37edo has great potential as a xenharmonic system, which high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions.

Line 99:

Line 100:

26\37 = 843.2 cents<br />

<br />

This means 37 is quite accurate on the 2.5.7.11 subgroup, where it shares the same tuning as 111et. In fact, on the larger <a class="wiki_link" href="/k%2AN%20subgroups">3*37 subgroup</a> 2.27.5.7.11.51.57 subgroup not only shares the same tuning as 19-limit 111et, it tempers out the same commas.<br />

This means 37 is quite accurate on the 2.5.7.11.13 subgroup, where it shares the same tuning as 111et. In fact, on the larger <a class="wiki_link" href="/k%2AN%20subgroups">3*37 subgroup</a> 2.27.5.7.11.51.57 subgroup not only shares the same tuning as 19-limit 111et, it tempers out the same commas.<br />

<br />

<h1 id="toc1"><a name="The Two Fifths"></a>The Two Fifths</h1>

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Line 117:

&quot;minor third&quot; = 8\37 = 259.5 cents<br />

&quot;major third&quot; = 14\37 = 454.1 cents<br />

If the minor third of 259.5 cents is mapped to 7/6, this superpythagorean scale can be thought of as a variety of <a class="wiki_link" href="/The%20Biosphere">Biome</a> temperament.<br />

<br />

37edo has great potential as a xenharmonic system, which high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions.<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:hstraub|hstraub]] and made on <tt>2011-06-22 07:17:58 UTC</tt>.<br>
+: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2011-07-30 01:53:35 UTC</tt>.<br>
-: The original revision id was <tt>238143999</tt>.<br>
+: The original revision id was <tt>243481051</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 19: / Line 19: @@
 \37 = 843.2 cents
-This means 37 is quite accurate on the 2.5.7.11 subgroup, where it shares the same tuning as 111et. In fact, on the larger [[k*N subgroups|3*37 subgroup]] 2.27.5.7.11.51.57 subgroup not only shares the same tuning as 19-limit 111et, it tempers out the same commas.
+This means 37 is quite accurate on the 2.5.7.11.13 subgroup, where it shares the same tuning as 111et. In fact, on the larger [[k*N subgroups|3*37 subgroup]] 2.27.5.7.11.51.57 subgroup not only shares the same tuning as 19-limit 111et, it tempers out the same commas.
 =The Two Fifths=
@@ Line 36: / Line 36: @@
 "minor third" = 8\37 = 259.5 cents
 "major third" = 14\37 = 454.1 cents
+If the minor third of 259.5 cents is mapped to 7/6, this superpythagorean scale can be thought of as a variety of [[The Biosphere|Biome]] temperament.
 edo has great potential as a xenharmonic system, which high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions.
@@ Line 99: / Line 100: @@
 \37 = 843.2 cents&lt;br /&gt;
 &lt;br /&gt;
-This means 37 is quite accurate on the 2.5.7.11 subgroup, where it shares the same tuning as 111et. In fact, on the larger &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;3*37 subgroup&lt;/a&gt; 2.27.5.7.11.51.57 subgroup not only shares the same tuning as 19-limit 111et, it tempers out the same commas.&lt;br /&gt;
+This means 37 is quite accurate on the 2.5.7.11.13 subgroup, where it shares the same tuning as 111et. In fact, on the larger &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;3*37 subgroup&lt;/a&gt; 2.27.5.7.11.51.57 subgroup not only shares the same tuning as 19-limit 111et, it tempers out the same commas.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="The Two Fifths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;The Two Fifths&lt;/h1&gt;
@@ Line 116: / Line 117: @@
 &amp;quot;minor third&amp;quot; = 8\37 = 259.5 cents&lt;br /&gt;
 &amp;quot;major third&amp;quot; = 14\37 = 454.1 cents&lt;br /&gt;
+If the minor third of 259.5 cents is mapped to 7/6, this superpythagorean scale can be thought of as a variety of &lt;a class="wiki_link" href="/The%20Biosphere"&gt;Biome&lt;/a&gt; temperament.&lt;br /&gt;
 &lt;br /&gt;
 edo has great potential as a xenharmonic system, which high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions.&lt;br /&gt;