Magic
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author x31eq and made on 2014-08-17 09:31:25 UTC.
- The original revision id was 518738930.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
<span style="display: block; text-align: right;">Other languages: [[xenharmonie/Magische Temperaturen#x-7-Limit-magisch|Deutsch]]</span> **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]]= =[[Magic Tetrachords]]= =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://micro.soonlabel.com/41edo/20130910_magic%5b19%5dor_41_the_magic_of_belief.mp3|The Magic of Belief]]// Magic[19] in 41et tuning [[@http://www.chrisvaisvil.com/|Chris Vaisvil]] //[[https://soundcloud.com/jdfreivald/little-magical-object|Little Magical Object]]// [[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/little-magical-object.mp3|play]] Magic[19] in 41et tuning by [[Jake Freivald]] //[[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// //[[http://x31eq.com/music/dingsheng.mp3|Golden Age]] disco involving magic comma pumps.// //[[http://x31eq.com/music/dingshi.mp3|Extravagant Food]] a single magic comma pump in under 60 seconds in 60-equal.// //[[http://x31eq.com/music/jitter.ogg|Gene's Jitterbug]] 9-limit harmony, may not require magic.//
Original HTML content:
<html><head><title>Magic</title></head><body><span style="display: block; text-align: right;">Other languages: <a class="wiki_link" href="http://xenharmonie.wikispaces.com/Magische%20Temperaturen#x-7-Limit-magisch">Deutsch</a></span><br />
<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:<h2> --><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 <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:<h1> --><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:<h1> --><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>
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Magic Tetrachords"></a><!-- ws:end:WikiTextHeadingRule:6 --><a class="wiki_link" href="/Magic%20Tetrachords">Magic Tetrachords</a></h1>
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:8 -->Music</h1>
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3" rel="nofollow">Chromatic piece in magic 16</a></em><br />
<a class="wiki_link" href="/magic16">magic16</a><br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3" rel="nofollow">A Piece in Paulsmagic</a></em><br />
<a class="wiki_link" href="/paulsmagic">paulsmagic</a><br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/41edo/20130910_magic%5b19%5dor_41_the_magic_of_belief.mp3" rel="nofollow">The Magic of Belief</a></em> Magic[19] in 41et tuning<br />
<a class="wiki_link_ext" href="http://www.chrisvaisvil.com/" rel="nofollow" target="_blank">Chris Vaisvil</a><br />
<em><a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/little-magical-object" rel="nofollow">Little Magical Object</a></em> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/little-magical-object.mp3" rel="nofollow">play</a> Magic[19] in 41et tuning by <a class="wiki_link" href="/Jake%20Freivald">Jake Freivald</a><br />
<br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Daydream_CBobro.mp3" rel="nofollow">Magical Daydream</a></em><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 />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow">Evening Horizon</a></em><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 "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</em><br />
<br />
<em><a class="wiki_link_ext" href="http://x31eq.com/music/dingsheng.mp3" rel="nofollow">Golden Age</a> disco involving magic comma pumps.</em><br />
<em><a class="wiki_link_ext" href="http://x31eq.com/music/dingshi.mp3" rel="nofollow">Extravagant Food</a> a single magic comma pump in under 60 seconds in 60-equal.</em><br />
<em><a class="wiki_link_ext" href="http://x31eq.com/music/jitter.ogg" rel="nofollow">Gene's Jitterbug</a> 9-limit harmony, may not require magic.</em></body></html>