Magic: Difference between revisions

Revision as of 11:44, 26 December 2012

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2012-12-26 11:44:27 UTC.

The original revision id was 394649608.

The revision comment was: Reverted to Nov 3, 2012 11:49 am: I don't know what the hell Cameron thinks he is doing

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

**Magic** is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the [[magic comma]] 3125/3072 is tempered out, making it a member of the [[Magic family]]. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as [[Magic family#Muggles|muggles]], but there's basically no reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.)

EDOs that contain good magic scales include [[19edo]], [[22edo]], [[41edo]] and [[104edo]].

Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24.
* [[3L 4s]]: LsLsLss where L = 6/5
* [[3L 7s]]: LssLssLsss where L = 7/6
* [[3L 10s]]: LsssLsssLssss where L = 9/8
* [[3L 13s]]: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related [[Magic family#Magic-Telepathy|telepathy]] temperament). In 22edo they are identical.

==Interval chain== 
|| 0. || 380.352 || 760.704 || 1141.056 || 321.408 || 701.76 || 1082.112 || 262.464 || 642.816 || 1023.168 || 203.52 || 583.872 || 964.224 || 144.576 ||
|| 1/1 || 5/4 || 14/9 || 48/25~125/64 || 6/5 || 3/2 || 15/8 || 7/6 || (16/11) || 9/5 || 9/8 || 7/5 || 7/4 || (12/11) ||

The generator chain val for 13-limit magic is <0 5 1 12 -8 18|, so that five generators give an approximate 3, twelve 14, minus eight 11/64, and eighteen 52.

=Spectrum of Magic Tunings by Eigenmonzos= 
||~ Eigenmonzo ||~ Major Third ||
|| 6/5 || 378.910 ||
|| 10/9 || 379.733 ||
|| 7/5 || 380.228 ||
|| 4/3 || 380.391 (5, 7 and 9 limit minimax) ||
|| 11/9 || 380.700 (11 limit minimax) ||
|| 8/7 || 380.735 ||
|| 12/11 || 380.818 ||
|| 14/11 || 380.875 ||
|| 7/6 || 380.982 ||
|| 11/8 || 381.085 ||
|| 11/10 || 381.666 ||
|| 9/7 || 382.458 ||
|| 5/4 || 386.314 ||

=[[Chords of magic]]= 

=Music=
[[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3|Chromatic piece in magic 16]]
[[magic16]]
[[http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3|A Piece in Paulsmagic]]
[[paulsmagic]]
[[@http://www.chrisvaisvil.com/|Chris Vaisvil]] 

[[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Thinking_CBobro.mp3|Magical Thinking]]
//A brief example of using "magic temperament" http://xenharmonic.wikispaces.com/Magic+family 
to equate the intervals 36/35 and 25/24 into one "semitone" step, specifically to distinguish between seventh chords using 7:4 and 9:5, i.e. harmonic 4:5:6:7 chords and traditional "dominant" chords tuned with a 6:5 above the 3:2. For analog organ and faded chrysanthemum-Cameron Bobro//

[[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Daydream_CBobro.mp3|Magical Daydream]]
//A brief demonstration of the near-Just musical temperament which flattens the pure major third of 5:4 by a few cents, such that 5 major thirds does not exceed 3:1 (a pure fifth + 1 octave), but meets it precisely. In a purely tuned system, the thirds would exceed 3:1 by what is known as the small diesis, (a ratio 3125/3072, about thirty cents). This temperament, then, brings (almost) pure thirds and pure fifths together. Cameron Bobro//

[[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3|Evening Horizon]]
//The earliest implementation (by happy accident, it seems) of this temperament was, to my knowledge, by Paul von Janko over a century ago. More recently, an online tuning community has elaborated many precise variations, calling the temperament "magic".. This piece is a demonstration of the array of pitches created by using 22 generators (the slightly tempered 5:4) within the octave, an approach which creates a "moment of symmetry", with all pitches separated by the same two intervals. This has many curious repercussions, creating some musical possibilities and restricting others. Cameron Bobro//

Original HTML content:

<html><head><title>Magic</title></head><body><strong>Magic</strong> is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the <a class="wiki_link" href="/magic%20comma">magic comma</a> 3125/3072 is tempered out, making it a member of the <a class="wiki_link" href="/Magic%20family">Magic family</a>. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as <a class="wiki_link" href="/Magic%20family#Muggles">muggles</a>, but there's basically no reason to use it unless you're using <a class="wiki_link" href="/19edo">19edo</a>, in which case it's identical to magic anyway.)<br />
<br />
EDOs that contain good magic scales include <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/41edo">41edo</a> and <a class="wiki_link" href="/104edo">104edo</a>.<br />
<br />
Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24.<br />
<ul><li><a class="wiki_link" href="/3L%204s">3L 4s</a>: LsLsLss where L = 6/5</li><li><a class="wiki_link" href="/3L%207s">3L 7s</a>: LssLssLsss where L = 7/6</li><li><a class="wiki_link" href="/3L%2010s">3L 10s</a>: LsssLsssLssss where L = 9/8</li><li><a class="wiki_link" href="/3L%2013s">3L 13s</a>: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related <a class="wiki_link" href="/Magic%20family#Magic-Telepathy">telepathy</a> temperament). In 22edo they are identical.</li></ul><br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Interval chain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Interval chain</h2>
 

<table class="wiki_table">
    <tr>
        <td>0.<br />
</td>
        <td>380.352<br />
</td>
        <td>760.704<br />
</td>
        <td>1141.056<br />
</td>
        <td>321.408<br />
</td>
        <td>701.76<br />
</td>
        <td>1082.112<br />
</td>
        <td>262.464<br />
</td>
        <td>642.816<br />
</td>
        <td>1023.168<br />
</td>
        <td>203.52<br />
</td>
        <td>583.872<br />
</td>
        <td>964.224<br />
</td>
        <td>144.576<br />
</td>
    </tr>
    <tr>
        <td>1/1<br />
</td>
        <td>5/4<br />
</td>
        <td>14/9<br />
</td>
        <td>48/25~125/64<br />
</td>
        <td>6/5<br />
</td>
        <td>3/2<br />
</td>
        <td>15/8<br />
</td>
        <td>7/6<br />
</td>
        <td>(16/11)<br />
</td>
        <td>9/5<br />
</td>
        <td>9/8<br />
</td>
        <td>7/5<br />
</td>
        <td>7/4<br />
</td>
        <td>(12/11)<br />
</td>
    </tr>
</table>

<br />
The generator chain val for 13-limit magic is &lt;0 5 1 12 -8 18|, so that five generators give an approximate 3, twelve 14, minus eight 11/64, and eighteen 52.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Spectrum of Magic Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:2 -->Spectrum of Magic Tunings by Eigenmonzos</h1>
 

<table class="wiki_table">
    <tr>
        <th>Eigenmonzo<br />
</th>
        <th>Major Third<br />
</th>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>378.910<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>379.733<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>380.228<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>380.391 (5, 7 and 9 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>380.700 (11 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>380.735<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>380.818<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>380.875<br />
</td>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>380.982<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>381.085<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>381.666<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>382.458<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>386.314<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Chords of magic"></a><!-- ws:end:WikiTextHeadingRule:4 --><a class="wiki_link" href="/Chords%20of%20magic">Chords of magic</a></h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h1>
<a class="wiki_link_ext" href="http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3" rel="nofollow">Chromatic piece in magic 16</a><br />
<a class="wiki_link" href="/magic16">magic16</a><br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3" rel="nofollow">A Piece in Paulsmagic</a><br />
<a class="wiki_link" href="/paulsmagic">paulsmagic</a><br />
<a class="wiki_link_ext" href="http://www.chrisvaisvil.com/" rel="nofollow" target="_blank">Chris Vaisvil</a> <br />
<br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Thinking_CBobro.mp3" rel="nofollow">Magical Thinking</a><br />
<em>A brief example of using &quot;magic temperament&quot; <!-- ws:start:WikiTextUrlRule:269:http://xenharmonic.wikispaces.com/Magic+family --><a href="http://xenharmonic.wikispaces.com/Magic+family">http://xenharmonic.wikispaces.com/Magic+family</a><!-- ws:end:WikiTextUrlRule:269 --> <br />
to equate the intervals 36/35 and 25/24 into one &quot;semitone&quot; step, specifically to distinguish between seventh chords using 7:4 and 9:5, i.e. harmonic 4:5:6:7 chords and traditional &quot;dominant&quot; chords tuned with a 6:5 above the 3:2. For analog organ and faded chrysanthemum-Cameron Bobro</em><br />
<br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Daydream_CBobro.mp3" rel="nofollow">Magical Daydream</a><br />
<em>A brief demonstration of the near-Just musical temperament which flattens the pure major third of 5:4 by a few cents, such that 5 major thirds does not exceed 3:1 (a pure fifth + 1 octave), but meets it precisely. In a purely tuned system, the thirds would exceed 3:1 by what is known as the small diesis, (a ratio 3125/3072, about thirty cents). This temperament, then, brings (almost) pure thirds and pure fifths together. Cameron Bobro</em><br />
<br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow">Evening Horizon</a><br />
<em>The earliest implementation (by happy accident, it seems) of this temperament was, to my knowledge, by Paul von Janko over a century ago. More recently, an online tuning community has elaborated many precise variations, calling the temperament &quot;magic&quot;.. This piece is a demonstration of the array of pitches created by using 22 generators (the slightly tempered 5:4) within the octave, an approach which creates a &quot;moment of symmetry&quot;, with all pitches separated by the same two intervals. This has many curious repercussions, creating some musical possibilities and restricting others. Cameron Bobro</em></body></html>

@@ 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:lobawad|lobawad]] and made on <tt>2012-12-26 10:06:31 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-12-26 11:44:27 UTC</tt>.<br>
-: The original revision id was <tt>394642110</tt>.<br>
+: The original revision id was <tt>394649608</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>Reverted to Nov 3, 2012 11:49 am: I don't know what the hell Cameron thinks he is doing</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>
-<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">**Magic** is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the [[magic comma]] &lt;span class="skype_pnh_print_container_1356533824"&gt;3125/3072&lt;/span&gt;&lt;span class="skype_pnh_container"&gt;&lt;span class="skype_pnh_mark"&gt; begin_of_the_skype_highlighting&lt;/span&gt; &lt;span class="skype_pnh_highlighting_inactive_common"&gt;&lt;span class="skype_pnh_textarea_span"&gt;[[image:chrome-extension://lifbcibllhkdhoafpjfnlhfpfgnpldfl/numbers_button_skype_logo.png]]&lt;span class="skype_pnh_free_text_span"&gt;FREE &lt;/span&gt;&lt;span class="skype_pnh_text_span"&gt;3125/3072&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="skype_pnh_mark"&gt;end_of_the_skype_highlighting&lt;/span&gt;&lt;/span&gt; is tempered out, making it a member of the [[Magic family]]. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as [[Magic family#Muggles|muggles]], but there's basically no reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.)
+<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">**Magic** is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the [[magic comma]] 3125/3072 is tempered out, making it a member of the [[Magic family]]. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as [[Magic family#Muggles|muggles]], but there's basically no reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.)
 EDOs that contain good magic scales include [[19edo]], [[22edo]], [[41edo]] and [[104edo]].
@@ Line 40: / Line 40: @@
 =[[Chords of magic]]=
 =Music=
-//[[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3|Chromatic piece in magic 16]]//
+[[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3|Chromatic piece in magic 16]]
 [[magic16]]
-//[[http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3|A Piece in Paulsmagic]]//
+[[http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3|A Piece in Paulsmagic]]
 [[paulsmagic]]
 [[@http://www.chrisvaisvil.com/|Chris Vaisvil]]
-//[[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Daydream_CBobro.mp3|Magical Daydream]]//
+[[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Thinking_CBobro.mp3|Magical Thinking]]
-//A brief demonstration of the near-Just musical temperament which flattens the pure major third of 5:4 by a few cents, such that 5 major thirds does not exceed 3:1 (a pure fifth + 1 octave), but meets it precisely. In a purely tuned system, the thirds would exceed 3:1 by what is known as the small diesis, (a ratio &lt;span class="skype_pnh_print_container_1356533824"&gt;3125/3072&lt;/span&gt;&lt;span class="skype_pnh_container"&gt;&lt;span class="skype_pnh_mark"&gt; begin_of_the_skype_highlighting&lt;/span&gt; &lt;span class="skype_pnh_highlighting_inactive_common"&gt;&lt;span class="skype_pnh_textarea_span"&gt;[[image:chrome-extension://lifbcibllhkdhoafpjfnlhfpfgnpldfl/numbers_button_skype_logo.png]]&lt;span class="skype_pnh_free_text_span"&gt;FREE &lt;/span&gt;&lt;span class="skype_pnh_text_span"&gt;3125/3072&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="skype_pnh_mark"&gt;end_of_the_skype_highlighting&lt;/span&gt;&lt;/span&gt;, about thirty cents). This temperament, then, brings (almost) pure thirds and pure fifths together. Cameron Bobro//
+//A brief example of using "magic temperament" http://xenharmonic.wikispaces.com/Magic+family
+to equate the intervals 36/35 and 25/24 into one "semitone" step, specifically to distinguish between seventh chords using 7:4 and 9:5, i.e. harmonic 4:5:6:7 chords and traditional "dominant" chords tuned with a 6:5 above the 3:2. For analog organ and faded chrysanthemum-Cameron Bobro//
-//[[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3|Evening Horizon]]//
+[[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Daydream_CBobro.mp3|Magical Daydream]]
+//A brief demonstration of the near-Just musical temperament which flattens the pure major third of 5:4 by a few cents, such that 5 major thirds does not exceed 3:1 (a pure fifth + 1 octave), but meets it precisely. In a purely tuned system, the thirds would exceed 3:1 by what is known as the small diesis, (a ratio 3125/3072, about thirty cents). This temperament, then, brings (almost) pure thirds and pure fifths together. Cameron Bobro//
+[[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3|Evening Horizon]]
 //The earliest implementation (by happy accident, it seems) of this temperament was, to my knowledge, by Paul von Janko over a century ago. More recently, an online tuning community has elaborated many precise variations, calling the temperament "magic".. This piece is a demonstration of the array of pitches created by using 22 generators (the slightly tempered 5:4) within the octave, an approach which creates a "moment of symmetry", with all pitches separated by the same two intervals. This has many curious repercussions, creating some musical possibilities and restricting others. Cameron Bobro//</pre></div>
 <h4>Original HTML content:</h4>
-<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;Magic&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;Magic&lt;/strong&gt; is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the &lt;a class="wiki_link" href="/magic%20comma"&gt;magic comma&lt;/a&gt; &lt;span class="skype_pnh_print_container_1356533824"&gt;3125/3072&lt;/span&gt;&lt;span class="skype_pnh_container"&gt;&lt;span class="skype_pnh_mark"&gt; begin_of_the_skype_highlighting&lt;/span&gt; &lt;span class="skype_pnh_highlighting_inactive_common"&gt;&lt;span class="skype_pnh_textarea_span"&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:166:&amp;lt;img src=&amp;quot;chrome-extension://lifbcibllhkdhoafpjfnlhfpfgnpldfl/numbers_button_skype_logo.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="chrome-extension://lifbcibllhkdhoafpjfnlhfpfgnpldfl/numbers_button_skype_logo.png" alt="external image numbers_button_skype_logo.png" title="external image numbers_button_skype_logo.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:166 --&gt;&lt;span class="skype_pnh_free_text_span"&gt;FREE &lt;/span&gt;&lt;span class="skype_pnh_text_span"&gt;3125/3072&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="skype_pnh_mark"&gt;end_of_the_skype_highlighting&lt;/span&gt;&lt;/span&gt; is tempered out, making it a member of the &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic family&lt;/a&gt;. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as &lt;a class="wiki_link" href="/Magic%20family#Muggles"&gt;muggles&lt;/a&gt;, but there's basically no reason to use it unless you're using &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, in which case it's identical to magic anyway.)&lt;br /&gt;
+<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;Magic&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;Magic&lt;/strong&gt; is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the &lt;a class="wiki_link" href="/magic%20comma"&gt;magic comma&lt;/a&gt; 3125/3072 is tempered out, making it a member of the &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic family&lt;/a&gt;. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as &lt;a class="wiki_link" href="/Magic%20family#Muggles"&gt;muggles&lt;/a&gt;, but there's basically no reason to use it unless you're using &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, in which case it's identical to magic anyway.)&lt;br /&gt;
 &lt;br /&gt;
 EDOs that contain good magic scales include &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt; and &lt;a class="wiki_link" href="/104edo"&gt;104edo&lt;/a&gt;.&lt;br /&gt;
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 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Music&lt;/h1&gt;
- &lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3" rel="nofollow"&gt;Chromatic piece in magic 16&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3" rel="nofollow"&gt;Chromatic piece in magic 16&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="/magic16"&gt;magic16&lt;/a&gt;&lt;br /&gt;
-&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3" rel="nofollow"&gt;A Piece in Paulsmagic&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3" rel="nofollow"&gt;A Piece in Paulsmagic&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="/paulsmagic"&gt;paulsmagic&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://www.chrisvaisvil.com/" rel="nofollow" target="_blank"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://www.chrisvaisvil.com/" rel="nofollow" target="_blank"&gt;Chris Vaisvil&lt;/a&gt; &lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Thinking_CBobro.mp3" rel="nofollow"&gt;Magical Thinking&lt;/a&gt;&lt;br /&gt;
+&lt;em&gt;A brief example of using &amp;quot;magic temperament&amp;quot; &lt;!-- ws:start:WikiTextUrlRule:269:http://xenharmonic.wikispaces.com/Magic+family --&gt;&lt;a href="http://xenharmonic.wikispaces.com/Magic+family"&gt;http://xenharmonic.wikispaces.com/Magic+family&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:269 --&gt; &lt;br /&gt;
+to equate the intervals 36/35 and 25/24 into one &amp;quot;semitone&amp;quot; step, specifically to distinguish between seventh chords using 7:4 and 9:5, i.e. harmonic 4:5:6:7 chords and traditional &amp;quot;dominant&amp;quot; chords tuned with a 6:5 above the 3:2. For analog organ and faded chrysanthemum-Cameron Bobro&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Daydream_CBobro.mp3" rel="nofollow"&gt;Magical Daydream&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Daydream_CBobro.mp3" rel="nofollow"&gt;Magical Daydream&lt;/a&gt;&lt;br /&gt;
-&lt;em&gt;A brief demonstration of the near-Just musical temperament which flattens the pure major third of 5:4 by a few cents, such that 5 major thirds does not exceed 3:1 (a pure fifth + 1 octave), but meets it precisely. In a purely tuned system, the thirds would exceed 3:1 by what is known as the small diesis, (a ratio &lt;span class="skype_pnh_print_container_1356533824"&gt;3125/3072&lt;/span&gt;&lt;span class="skype_pnh_container"&gt;&lt;span class="skype_pnh_mark"&gt; begin_of_the_skype_highlighting&lt;/span&gt; &lt;span class="skype_pnh_highlighting_inactive_common"&gt;&lt;span class="skype_pnh_textarea_span"&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:167:&amp;lt;img src=&amp;quot;chrome-extension://lifbcibllhkdhoafpjfnlhfpfgnpldfl/numbers_button_skype_logo.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="chrome-extension://lifbcibllhkdhoafpjfnlhfpfgnpldfl/numbers_button_skype_logo.png" alt="external image numbers_button_skype_logo.png" title="external image numbers_button_skype_logo.png" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:167 --&gt;&lt;span class="skype_pnh_free_text_span"&gt;FREE &lt;/span&gt;&lt;span class="skype_pnh_text_span"&gt;3125/3072&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="skype_pnh_mark"&gt;end_of_the_skype_highlighting&lt;/span&gt;&lt;/span&gt;, about thirty cents). This temperament, then, brings (almost) pure thirds and pure fifths together. Cameron Bobro&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;A brief demonstration of the near-Just musical temperament which flattens the pure major third of 5:4 by a few cents, such that 5 major thirds does not exceed 3:1 (a pure fifth + 1 octave), but meets it precisely. In a purely tuned system, the thirds would exceed 3:1 by what is known as the small diesis, (a ratio 3125/3072, about thirty cents). This temperament, then, brings (almost) pure thirds and pure fifths together. Cameron Bobro&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow"&gt;Evening Horizon&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow"&gt;Evening Horizon&lt;/a&gt;&lt;br /&gt;
 &lt;em&gt;The earliest implementation (by happy accident, it seems) of this temperament was, to my knowledge, by Paul von Janko over a century ago. More recently, an online tuning community has elaborated many precise variations, calling the temperament &amp;quot;magic&amp;quot;.. This piece is a demonstration of the array of pitches created by using 22 generators (the slightly tempered 5:4) within the octave, an approach which creates a &amp;quot;moment of symmetry&amp;quot;, with all pitches separated by the same two intervals. This has many curious repercussions, creating some musical possibilities and restricting others. Cameron Bobro&lt;/em&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

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