46edo: 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:~~Andrew_Heathwaite~~|~~Andrew_Heathwaite~~]] and made on <tt>2011-03-~~04 17~~:54:32 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-03-28 03:00:28 UTC</tt>.<br>

: The original revision id was <tt>~~207480856~~</tt>.<br>

: The original revision id was <tt>214556250</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">=<span style="color: #300094; font-size: 111%;">46 tone equal temperament</span>=

The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the octave into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 ~~cents~~, an interval close in size to 66/65, the interval from 13/11 to 6/5.

The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the [[octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[cent]]s, an interval close in size to [[66_65|66/65]], the interval from [[13_11|13/11]] to [[6_5|6/5]].

46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. Rank two temperaments it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The 11-limit [[Target tunings|minimax]] tuning for [[Starling family|valentine temperament]], (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the 13-limit, though others award that distinction to [[41edo]].

46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. [[Rank two temperaments]] it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The [[11-limit]] [[Target tunings|minimax]] tuning for [[Starling family|valentine temperament]], (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the [[13-limit]], though others award that distinction to [[41edo]].

The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the just fifth and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.

The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the [[just fifth]] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.

46edo can be treated as two [[23edo]]'s separated by an interval of 26.09 cents.

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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>46edo</title></head><body><h1 id="toc0"><a name="x46 tone equal temperament"></a><span style="color: #300094; font-size: 111%;">46 tone equal temperament</span></h1>

<br />

The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the octave into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 ~~cents~~, an interval close in size to 66/65, the interval from 13/11 to 6/5.<br />

The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 <a class="wiki_link" href="/cent">cent</a>s, an interval close in size to <a class="wiki_link" href="/66_65">66/65</a>, the interval from <a class="wiki_link" href="/13_11">13/11</a> to <a class="wiki_link" href="/6_5">6/5</a>.<br />

<br />

46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. Rank two temperaments it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The 11-limit <a class="wiki_link" href="/Target%20tunings">minimax</a> tuning for <a class="wiki_link" href="/Starling%20family">valentine temperament</a>, (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the 13-limit, though others award that distinction to <a class="wiki_link" href="/41edo">41edo</a>.<br />

46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. <a class="wiki_link" href="/Rank%20two%20temperaments">Rank two temperaments</a> it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The <a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/Target%20tunings">minimax</a> tuning for <a class="wiki_link" href="/Starling%20family">valentine temperament</a>, (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the <a class="wiki_link" href="/13-limit">13-limit</a>, though others award that distinction to <a class="wiki_link" href="/41edo">41edo</a>.<br />

<br />

The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the just fifth and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.<br />

The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the <a class="wiki_link" href="/just%20fifth">just fifth</a> and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.<br />

<br />

46edo can be treated as two <a class="wiki_link" href="/23edo">23edo</a>'s separated by an interval of 26.09 cents.<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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-03-04 17:54:32 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-03-28 03:00:28 UTC</tt>.<br>
-: The original revision id was <tt>207480856</tt>.<br>
+: The original revision id was <tt>214556250</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">=&lt;span style="color: #300094; font-size: 111%;"&gt;46 tone equal temperament&lt;/span&gt;=
-The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the octave into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 cents, an interval close in size to 66/65, the interval from 13/11 to 6/5.
+The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the [[octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[cent]]s, an interval close in size to [[66_65|66/65]], the interval from [[13_11|13/11]] to [[6_5|6/5]].
-et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. Rank two temperaments it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The 11-limit [[Target tunings|minimax]] tuning for [[Starling family|valentine temperament]], (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the 13-limit, though others award that distinction to [[41edo]].
+et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. [[Rank two temperaments]] it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The [[11-limit]] [[Target tunings|minimax]] tuning for [[Starling family|valentine temperament]], (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the [[13-limit]], though others award that distinction to [[41edo]].
-The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the just fifth and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.
+The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the [[just fifth]] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.
 edo can be treated as two [[23edo]]'s separated by an interval of 26.09 cents.
@@ Line 85: / Line 85: @@
 <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;46edo&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="x46 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #300094; font-size: 111%;"&gt;46 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
-The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the octave into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 cents, an interval close in size to 66/65, the interval from 13/11 to 6/5.&lt;br /&gt;
+The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, an interval close in size to &lt;a class="wiki_link" href="/66_65"&gt;66/65&lt;/a&gt;, the interval from &lt;a class="wiki_link" href="/13_11"&gt;13/11&lt;/a&gt; to &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. Rank two temperaments it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The 11-limit &lt;a class="wiki_link" href="/Target%20tunings"&gt;minimax&lt;/a&gt; tuning for &lt;a class="wiki_link" href="/Starling%20family"&gt;valentine temperament&lt;/a&gt;, (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the 13-limit, though others award that distinction to &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;.&lt;br /&gt;
+et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. &lt;a class="wiki_link" href="/Rank%20two%20temperaments"&gt;Rank two temperaments&lt;/a&gt; it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Target%20tunings"&gt;minimax&lt;/a&gt; tuning for &lt;a class="wiki_link" href="/Starling%20family"&gt;valentine temperament&lt;/a&gt;, (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;, though others award that distinction to &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the just fifth and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.&lt;br /&gt;
+The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the &lt;a class="wiki_link" href="/just%20fifth"&gt;just fifth&lt;/a&gt; and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.&lt;br /&gt;
 &lt;br /&gt;
 edo can be treated as two &lt;a class="wiki_link" href="/23edo"&gt;23edo&lt;/a&gt;'s separated by an interval of 26.09 cents.&lt;br /&gt;