Tour of regular temperaments: 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:genewardsmith|genewardsmith]] and made on <tt>2010-05-~~30 14~~:38:27 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-06-01 04:38:20 UTC</tt>.<br>

: The original revision id was <tt>~~145876003~~</tt>.<br>

: The original revision id was <tt>146166319</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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===[[Magic family]]===

The magic family tempers out 3125/3072, known as the magic comma or small diesis, has a generator which is a flattened major third. It's optimal, in a sense, for 9-limit harmony with a tuning close to 41-EDO. It's more accurate than meantone and simpler than schismatic. It works with 19 and 22 note scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1. It's a little tricky to work with because 3/2 fifths are a relatively complex interval and it doesn't naturally work with scales of around 7 notes to the octave.

The magic family tempers out 3125/3072, known as the magic comma or small diesis, has a generator which is a flattened major third.

===Miracle[[#miracle]]===

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<br />

<h3 id="toc4"><a name="x-Meantone family-Magic family"></a><a class="wiki_link" href="/Magic%20family">Magic family</a></h3>

The magic family tempers out 3125/3072, known as the magic comma or small diesis, has a generator which is a flattened major third. It's optimal, in a sense, for 9-limit harmony with a tuning close to 41-EDO. It's more accurate than meantone and simpler than schismatic. It works with 19 and 22 note scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1. It's a little tricky to work with because 3/2 fifths are a relatively complex interval and it doesn't naturally work with scales of around 7 notes to the octave.<br />

The magic family tempers out 3125/3072, known as the magic comma or small diesis, has a generator which is a flattened major third. <br />

<br />

<h3 id="toc5"><a name="x-Meantone family-Miracle"></a>Miracle<a name="miracle"></a></h3>

@@ 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>2010-05-30 14:38:27 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-06-01 04:38:20 UTC</tt>.<br>
-: The original revision id was <tt>145876003</tt>.<br>
+: The original revision id was <tt>146166319</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 23: / Line 23: @@
 ===[[Magic family]]===
-The magic family tempers out 3125/3072, known as the magic comma or small diesis, has a generator which is a flattened major third. It's optimal, in a sense, for 9-limit harmony with a tuning close to 41-EDO. It's more accurate than meantone and simpler than schismatic. It works with 19 and 22 note scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1. It's a little tricky to work with because 3/2 fifths are a relatively complex interval and it doesn't naturally work with scales of around 7 notes to the octave.
+The magic family tempers out 3125/3072, known as the magic comma or small diesis, has a generator which is a flattened major third.
 ===Miracle[[#miracle]]===
@@ Line 76: / Line 76: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Meantone family-Magic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;a class="wiki_link" href="/Magic%20family"&gt;Magic family&lt;/a&gt;&lt;/h3&gt;
-  The magic family tempers out 3125/3072, known as the magic comma or small diesis, has a generator which is a flattened major third. It's optimal, in a sense, for 9-limit harmony with a tuning close to 41-EDO. It's more accurate than meantone and simpler than schismatic. It works with 19 and 22 note scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1. It's a little tricky to work with because 3/2 fifths are a relatively complex interval and it doesn't naturally work with scales of around 7 notes to the octave.&lt;br /&gt;
+  The magic family tempers out 3125/3072, known as the magic comma or small diesis, has a generator which is a flattened major third. &lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-Meantone family-Miracle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Miracle&lt;!-- ws:start:WikiTextAnchorRule:31:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@miracle&amp;quot; title=&amp;quot;Anchor: miracle&amp;quot;/&amp;gt; --&gt;&lt;a name="miracle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:31 --&gt;&lt;/h3&gt;