48edo: 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:xenwolf|xenwolf]] and made on <tt>2011-03-~~30 02~~:58:42 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-07-01 12:34:45 UTC</tt>.<br>

: The original revision id was <tt>~~215347780~~</tt>.<br>

: The original revision id was <tt>239667443</tt>.<br>

: The revision comment was: <tt>~~some links added~~</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>

<h4>Original Wikitext content:</h4>

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=Basics=

The //48 equal division// divides the [[octave]] into 48 1/8th tones of precisely 25 [[cent]]s each. Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the [[5-limit]], but tempers out [[2401_2400|2401/2400]] in the 7-limit, making it a tuning for [[Meantone family|squares temperament]]. In the [[11-limit]] we can add [[99_98|99/98]] and [[121_120|121/120]] to the list, and in the [[13-limit]], [[66_65|66/65]]. While [[31edo]] can also do 13-limit squares, 48 might be preferred for some purposes.

The //48 equal division// divides the [[octave]] into 48 1/8th tones of precisely 25 [[cent]]s each. Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the [[5-limit]], but [[tempering out|tempers out]] [[2401_2400|2401/2400]] in the [[7-limit]], making it a tuning for [[Meantone family|squares temperament]]. In the [[11-limit]] we can add [[99_98|99/98]] and [[121_120|121/120]] to the list, and in the [[13-limit]], [[66_65|66/65]]. While [[31edo]] can also do 13-limit squares, 48 might be preferred for some purposes.

=Temperaments=

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<br />

<h1 id="toc0"><a name="Basics"></a>Basics</h1>

The <em>48 equal division</em> divides the <a class="wiki_link" href="/octave">octave</a> into 48 1/8th tones of precisely 25 <a class="wiki_link" href="/cent">cent</a>s each. Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the <a class="wiki_link" href="/5-limit">5-limit</a>, but tempers out <a class="wiki_link" href="/2401_2400">2401/2400</a> in the 7-limit, making it a tuning for <a class="wiki_link" href="/Meantone%20family">squares temperament</a>. In the <a class="wiki_link" href="/11-limit">11-limit</a> we can add <a class="wiki_link" href="/99_98">99/98</a> and <a class="wiki_link" href="/121_120">121/120</a> to the list, and in the <a class="wiki_link" href="/13-limit">13-limit</a>, <a class="wiki_link" href="/66_65">66/65</a>. While <a class="wiki_link" href="/31edo">31edo</a> can also do 13-limit squares, 48 might be preferred for some purposes.<br />

The <em>48 equal division</em> divides the <a class="wiki_link" href="/octave">octave</a> into 48 1/8th tones of precisely 25 <a class="wiki_link" href="/cent">cent</a>s each. Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the <a class="wiki_link" href="/5-limit">5-limit</a>, but <a class="wiki_link" href="/tempering%20out">tempers out</a> <a class="wiki_link" href="/2401_2400">2401/2400</a> in the <a class="wiki_link" href="/7-limit">7-limit</a>, making it a tuning for <a class="wiki_link" href="/Meantone%20family">squares temperament</a>. In the <a class="wiki_link" href="/11-limit">11-limit</a> we can add <a class="wiki_link" href="/99_98">99/98</a> and <a class="wiki_link" href="/121_120">121/120</a> to the list, and in the <a class="wiki_link" href="/13-limit">13-limit</a>, <a class="wiki_link" href="/66_65">66/65</a>. While <a class="wiki_link" href="/31edo">31edo</a> can also do 13-limit squares, 48 might be preferred for some purposes.<br />

<br />

<h1 id="toc1"><a name="Temperaments"></a>Temperaments</h1>

@@ 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:xenwolf|xenwolf]] and made on <tt>2011-03-30 02:58:42 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-07-01 12:34:45 UTC</tt>.<br>
-: The original revision id was <tt>215347780</tt>.<br>
+: The original revision id was <tt>239667443</tt>.<br>
-: The revision comment was: <tt>some links added</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>
 <h4>Original Wikitext content:</h4>
@@ Line 10: / Line 10: @@
 =Basics=
-The //48 equal division// divides the [[octave]] into 48 1/8th tones of precisely 25 [[cent]]s each. Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the [[5-limit]], but tempers out [[2401_2400|2401/2400]] in the 7-limit, making it a tuning for [[Meantone family|squares temperament]]. In the [[11-limit]] we can add [[99_98|99/98]] and [[121_120|121/120]] to the list, and in the [[13-limit]], [[66_65|66/65]]. While [[31edo]] can also do 13-limit squares, 48 might be preferred for some purposes.
+The //48 equal division// divides the [[octave]] into 48 1/8th tones of precisely 25 [[cent]]s each. Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the [[5-limit]], but [[tempering out|tempers out]] [[2401_2400|2401/2400]] in the [[7-limit]], making it a tuning for [[Meantone family|squares temperament]]. In the [[11-limit]] we can add [[99_98|99/98]] and [[121_120|121/120]] to the list, and in the [[13-limit]], [[66_65|66/65]]. While [[31edo]] can also do 13-limit squares, 48 might be preferred for some purposes.
 =Temperaments=
@@ Line 27: / Line 27: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Basics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Basics&lt;/h1&gt;
-The &lt;em&gt;48 equal division&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 48 1/8th tones of precisely 25 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, but tempers out &lt;a class="wiki_link" href="/2401_2400"&gt;2401/2400&lt;/a&gt; in the 7-limit, making it a tuning for &lt;a class="wiki_link" href="/Meantone%20family"&gt;squares temperament&lt;/a&gt;. In the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; we can add &lt;a class="wiki_link" href="/99_98"&gt;99/98&lt;/a&gt; and &lt;a class="wiki_link" href="/121_120"&gt;121/120&lt;/a&gt; to the list, and in the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;, &lt;a class="wiki_link" href="/66_65"&gt;66/65&lt;/a&gt;. While &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; can also do 13-limit squares, 48 might be preferred for some purposes.&lt;br /&gt;
+The &lt;em&gt;48 equal division&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 48 1/8th tones of precisely 25 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, but &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; &lt;a class="wiki_link" href="/2401_2400"&gt;2401/2400&lt;/a&gt; in the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, making it a tuning for &lt;a class="wiki_link" href="/Meantone%20family"&gt;squares temperament&lt;/a&gt;. In the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; we can add &lt;a class="wiki_link" href="/99_98"&gt;99/98&lt;/a&gt; and &lt;a class="wiki_link" href="/121_120"&gt;121/120&lt;/a&gt; to the list, and in the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;, &lt;a class="wiki_link" href="/66_65"&gt;66/65&lt;/a&gt;. While &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; can also do 13-limit squares, 48 might be preferred for some purposes.&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="Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Temperaments&lt;/h1&gt;