Middle-Eastern music

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author hstraub and made on 2013-05-17 03:18:59 UTC.

The original revision id was 432292286.

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:

Along with the [[Indian]] tradition, the music of the Middle and Near East (Arabic, Turkish, and Persian) is one of the important microtonal <span class="wiki_link_ext">music</span> traditions.

A central concept is "maqam" (pl. maqamat), which corresponds somewhat (but not exactly) to the Western "mode". An introduction to maqam theory can be found on [[http://www.maqamworld.com/|http://www.maqamworld.com]]. The Arabic maqam and Turkish makam systems differ to some degree from the related Persian system of dastgah.

The use of microtones in these systems can be extremely subtle, as is demonstrated in a [[http://shumays.libsyn.com/index.php?post_id=177745|podcast]] by Arabic violin player Sami Abu Shumays: by his count, there could be 12 different notes within a half step.

[[toc|flat]]
----

=Maqamat in equal temperaments= 

There have been various endeavors, also in recent history, to establish a common tuning standard. A few of these are described in a [[http://www.ozanyarman.com/files/34%27ten_79%27a.pdf|paper by Ozan Yarman]]. However, none of these have been really successful (at least not as successful as 12edo in Western music). Given the subtleties sketched in the above mentioned podacst, this task is certainly nontrivial, if not finally impossible.

Depending on the accurateness that is wanted, we can distinguish different levels

==Level 1== 
An absolute minimal rule set a tuning system for maqams has to fulfill could be summarized as follows:
* There have to be minor and major seconds, minor and major thirds, pure fourths and the octaver complements of all these. Preferably organized in a pythagorean structure.
* Additionally, at least one type of neutral second and neutral third is necessary.

The smallest EDOs that fulfill these conditions are [[17edo]] and [[24edo]], which are indeed both used for maqam music. Especially 24edo has found a certain dissemination.

The [[maqamic]] tempreament reflects this concept in the framework of [[regular temperaments]].

==Level 2== 
Systems that just fulfill level 1 are still generally considered bad compromises. An additional quite basic requirement for a more accurate maqam system is the availability of two kinds of neutral seconds, a smaller one for the Bayati tetrachord and a larger one for the Rast tetrachord. Moreover, the major second whould preferably be a "major" wholetone, while the minor second should be a "small" semitone - as a consequence, the wholetone is to be divided into a smaller semitone (limma) and a larger one (apotome) - minor seconds will be available in two varieties, too.

Important EDOs that meet these requirements are [[53edo]] and [[72edo]]. Both of these have found a certain dissemination in middle-eastern music.

For turkish musik, Ozan Yarman also proposes [[34edo]] and [[41edo]] as acceptable compromises. These have the property that the larger neutral second has a character close to a minor wholetone, and, playing the Rast maqam with it, the third note is less a neutral third than a 5/4-style major third. This matches the turkish variant of Rast which indeed has such a third - the arabic variant, however, is lower. 41edo and 34edo can thus be considered suited for turkish music but less so for arabic music.

And here we see another nemesis of the tentatives to establish a common tuning standard: there is not one middle-eastern system but many. There are not just differences between arabic and turkish systems bt also regional differences within the respective cultures...

==Level 3== 
Even [[53edo]] and [[72edo]] do not cover all details. For these. there are some other, still larger subdivisions that have been investigated.

A system that meets the tuning needs to a satisfactory degree is proposed in [[@http://www.ozanyarman.com/files/doctorate_thesis.pdf|Ozan Yarman's dissertation]] (also summarized in the mentioned [[@http://www.ozanyarman.com/files/34ten79a.pdf|paper]] ): a 79-tone [[MOSScales|MOS]] subset of [[159edo]]. A short description (quoting a post to the tuning list) is also [[79MOS 159edo|here]].

[[Tsaharuk]], as proposed by [[Jacques Dudon]], can be realized in [[77edo]], [[94edo]], [[111edo]], [[128edo]], [[145edo]], [[171edo]], [[359edo]].

The mentioned [[Maqamat in maqamic temperament|maqamic temperament]] can be realized in any equal temperament that supports 2.3.5.11 maqamic, including 17c (the important non-patent val for [[17edo]]), [[24edo]], [[31edo]], and [[55edo]].

=Unequal temperaments for maqamat= 

In equal temperaments, as seen above, there is always a tradeoff between the diverging requirements of high pitch accuracy and a manageable pitch count. One possible way out of this dilemma is use of unequal temperaments. These allow for playing of multiple maqamat with comparatively few notes, with, on the other hand, restrictions in the possibilities to modulate.

A paper by [[Erv Wilson]], describing a variety of layouts of mideast tunings on generalized keyboards, can be found here: [[http://anaphoria.com/RAST.PDF]].

[[Ozan Yarman]] has developed a number of such temperaments, e.g. Yarman24 (24 notes), [[http://launch.groups.yahoo.com/group/tuning/message/78631|Yarman29]] (29 notes) and [[http://www.ozanyarman.com/yarman36.html|Yarman36]] (36 notes).
All these and more are available in the [[http://www.huygens-fokker.org/scala/downloads.html|scala file archive]].

A lot of research in this field has been done by [[Julien Jalaleddine Weiss]]. See [[tuning systems for qanun|tuning systems for the qanun]] , or [[http://stefanpohlit.com/dissertation.engl..htm|Stefan Pohlit's dissertation]].

[[Tsaharuk]] is a 77 notes per octave linear or planar temperament proposed by [[Jacques Dudon]] based on Julien Jalaleddine Weiss qanun tunings.

Unequal temperaments for maqamat were also developed by [[Margo Schulter]] , e.g. [[http://launch.groups.yahoo.com/group/JustIntonation/message/1005|Bamm]] (20 or 24 notes) and [[http://launch.groups.yahoo.com/group/tuning/message/100839|Turquoise17]] (17 notes).

See also;
[[Turkish maqam music temperaments]]
[[Maqamat in maqamic temperament]]

=External links= 

===Arabic=== 
[[http://www.maqamworld.com|Arabic Maqam World]] (Johnny Farraj, Sami Abu Shumays //et al//)
[[http://www.classicalarabicmusic.com/scales.htm|Classical Arabic Music]]
[[http://www.oud.eclipse.co.uk|The Oud]] (David Parfitt, discusses both Arabic and Turkish //maqâm// theory)
[[http://www.alsiadi.com|ALSIADI.com]] (focuses on Halabi/Aleppo traditional music; describes //maq////â////m////â////t// in terms of 53-tone Pythagorean tuning)
[[http://foredofico.org/CERMAA/|CERMAA]] (academic research for arabic and related music, namely various articles by [[Amine Beyhom]])

===Turkish=== 
[[http://www.hinesmusic.com/What_Are_Makams.html|Tetrachords and Makams of Turkey]] - another theory site
[[http://www.turkishmusicportal.org]] - listening
[[http://www.turkishmusic.org/index.html|http://www.turkishmusic.org]] - listening
http://www.turkishmusic.org/index18.html - listening

===Persian=== 
[[http://240edo.googlepages.com/persianmusic]] - a list of links related to Persian music, maintained by [[Shaahin Mohajeri]]

<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 734px; width: 1px;"> [[http://x31eq.com/cgi-bin/rt.cgi?ets=7&limit=2_3_5_11&key=7_11_16_24|7]], [[http://x31eq.com/cgi-bin/rt.cgi?ets=24&limit=2_3_5_11&key=24_38_56_83|24]], [[http://x31eq.com/cgi-bin/rt.cgi?ets=31&limit=2_3_5_11&key=31_49_72_107|31]], [[http://x31eq.com/cgi-bin/rt.cgi?ets=14&limit=2_3_5_11&key=14_22_32_48|14c]], [[http://x31eq.com/cgi-bin/rt.cgi?ets=17&limit=2_3_5_11&key=17_27_40_59|17c]], [[http://x31eq.com/cgi-bin/rt.cgi?ets=38&limit=2_3_5_11&key=38_60_88_131|38]], [[http://x31eq.com/cgi-bin/rt.cgi?ets=10&limit=2_3_5_11&key=10_16_24_35|10c]], [[http://x31eq.com/cgi-bin/rt.cgi?ets=21&limit=2_3_5_11&key=21_33_48_72|21ce]], [[http://x31eq.com/cgi-bin/rt.cgi?ets=45&limit=2_3_5_11&key=45_71_104_155|45e]], [[http://x31eq.com/cgi-bin/rt.cgi?ets=55&limit=2_3_5_11&key=55_87_128_190|55]]</span>

Original HTML content:

<html><head><title>Arabic, Turkish, Persian</title></head><body>Along with the <a class="wiki_link" href="/Indian">Indian</a> tradition, the music of the Middle and Near East (Arabic, Turkish, and Persian) is one of the important microtonal <span class="wiki_link_ext">music</span> traditions.<br />
<br />
A central concept is &quot;maqam&quot; (pl. maqamat), which corresponds somewhat (but not exactly) to the Western &quot;mode&quot;. An introduction to maqam theory can be found on <a class="wiki_link_ext" href="http://www.maqamworld.com/" rel="nofollow">http://www.maqamworld.com</a>. The Arabic maqam and Turkish makam systems differ to some degree from the related Persian system of dastgah.<br />
<br />
The use of microtones in these systems can be extremely subtle, as is demonstrated in a <a class="wiki_link_ext" href="http://shumays.libsyn.com/index.php?post_id=177745" rel="nofollow">podcast</a> by Arabic violin player Sami Abu Shumays: by his count, there could be 12 different notes within a half step.<br />
<br />
<!-- ws:start:WikiTextTocRule:18:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><a href="#Maqamat in equal temperaments">Maqamat in equal temperaments</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Unequal temperaments for maqamat">Unequal temperaments for maqamat</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#External links">External links</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: -->
<!-- ws:end:WikiTextTocRule:28 --><hr />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Maqamat in equal temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->Maqamat in equal temperaments</h1>
 <br />
There have been various endeavors, also in recent history, to establish a common tuning standard. A few of these are described in a <a class="wiki_link_ext" href="http://www.ozanyarman.com/files/34%27ten_79%27a.pdf" rel="nofollow">paper by Ozan Yarman</a>. However, none of these have been really successful (at least not as successful as 12edo in Western music). Given the subtleties sketched in the above mentioned podacst, this task is certainly nontrivial, if not finally impossible.<br />
<br />
Depending on the accurateness that is wanted, we can distinguish different levels<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Maqamat in equal temperaments-Level 1"></a><!-- ws:end:WikiTextHeadingRule:2 -->Level 1</h2>
 An absolute minimal rule set a tuning system for maqams has to fulfill could be summarized as follows:<br />
<ul><li>There have to be minor and major seconds, minor and major thirds, pure fourths and the octaver complements of all these. Preferably organized in a pythagorean structure.</li><li>Additionally, at least one type of neutral second and neutral third is necessary.</li></ul><br />
The smallest EDOs that fulfill these conditions are <a class="wiki_link" href="/17edo">17edo</a> and <a class="wiki_link" href="/24edo">24edo</a>, which are indeed both used for maqam music. Especially 24edo has found a certain dissemination.<br />
<br />
The <a class="wiki_link" href="/maqamic">maqamic</a> tempreament reflects this concept in the framework of <a class="wiki_link" href="/regular%20temperaments">regular temperaments</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Maqamat in equal temperaments-Level 2"></a><!-- ws:end:WikiTextHeadingRule:4 -->Level 2</h2>
 Systems that just fulfill level 1 are still generally considered bad compromises. An additional quite basic requirement for a more accurate maqam system is the availability of two kinds of neutral seconds, a smaller one for the Bayati tetrachord and a larger one for the Rast tetrachord. Moreover, the major second whould preferably be a &quot;major&quot; wholetone, while the minor second should be a &quot;small&quot; semitone - as a consequence, the wholetone is to be divided into a smaller semitone (limma) and a larger one (apotome) - minor seconds will be available in two varieties, too.<br />
<br />
Important EDOs that meet these requirements are <a class="wiki_link" href="/53edo">53edo</a> and <a class="wiki_link" href="/72edo">72edo</a>. Both of these have found a certain dissemination in middle-eastern music.<br />
<br />
For turkish musik, Ozan Yarman also proposes <a class="wiki_link" href="/34edo">34edo</a> and <a class="wiki_link" href="/41edo">41edo</a> as acceptable compromises. These have the property that the larger neutral second has a character close to a minor wholetone, and, playing the Rast maqam with it, the third note is less a neutral third than a 5/4-style major third. This matches the turkish variant of Rast which indeed has such a third - the arabic variant, however, is lower. 41edo and 34edo can thus be considered suited for turkish music but less so for arabic music.<br />
<br />
And here we see another nemesis of the tentatives to establish a common tuning standard: there is not one middle-eastern system but many. There are not just differences between arabic and turkish systems bt also regional differences within the respective cultures...<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Maqamat in equal temperaments-Level 3"></a><!-- ws:end:WikiTextHeadingRule:6 -->Level 3</h2>
 Even <a class="wiki_link" href="/53edo">53edo</a> and <a class="wiki_link" href="/72edo">72edo</a> do not cover all details. For these. there are some other, still larger subdivisions that have been investigated.<br />
<br />
A system that meets the tuning needs to a satisfactory degree is proposed in <a class="wiki_link_ext" href="http://www.ozanyarman.com/files/doctorate_thesis.pdf" rel="nofollow" target="_blank">Ozan Yarman's dissertation</a> (also summarized in the mentioned <a class="wiki_link_ext" href="http://www.ozanyarman.com/files/34ten79a.pdf" rel="nofollow" target="_blank">paper</a> ): a 79-tone <a class="wiki_link" href="/MOSScales">MOS</a> subset of <a class="wiki_link" href="/159edo">159edo</a>. A short description (quoting a post to the tuning list) is also <a class="wiki_link" href="/79MOS%20159edo">here</a>.<br />
<br />
<a class="wiki_link" href="/Tsaharuk">Tsaharuk</a>, as proposed by <a class="wiki_link" href="/Jacques%20Dudon">Jacques Dudon</a>, can be realized in <a class="wiki_link" href="/77edo">77edo</a>, <a class="wiki_link" href="/94edo">94edo</a>, <a class="wiki_link" href="/111edo">111edo</a>, <a class="wiki_link" href="/128edo">128edo</a>, <a class="wiki_link" href="/145edo">145edo</a>, <a class="wiki_link" href="/171edo">171edo</a>, <a class="wiki_link" href="/359edo">359edo</a>.<br />
<br />
The mentioned <a class="wiki_link" href="/Maqamat%20in%20maqamic%20temperament">maqamic temperament</a> can be realized in any equal temperament that supports 2.3.5.11 maqamic, including 17c (the important non-patent val for <a class="wiki_link" href="/17edo">17edo</a>), <a class="wiki_link" href="/24edo">24edo</a>, <a class="wiki_link" href="/31edo">31edo</a>, and <a class="wiki_link" href="/55edo">55edo</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Unequal temperaments for maqamat"></a><!-- ws:end:WikiTextHeadingRule:8 -->Unequal temperaments for maqamat</h1>
 <br />
In equal temperaments, as seen above, there is always a tradeoff between the diverging requirements of high pitch accuracy and a manageable pitch count. One possible way out of this dilemma is use of unequal temperaments. These allow for playing of multiple maqamat with comparatively few notes, with, on the other hand, restrictions in the possibilities to modulate.<br />
<br />
A paper by <a class="wiki_link" href="/Erv%20Wilson">Erv Wilson</a>, describing a variety of layouts of mideast tunings on generalized keyboards, can be found here: <a class="wiki_link_ext" href="http://anaphoria.com/RAST.PDF" rel="nofollow">http://anaphoria.com/RAST.PDF</a>.<br />
<br />
<a class="wiki_link" href="/Ozan%20Yarman">Ozan Yarman</a> has developed a number of such temperaments, e.g. Yarman24 (24 notes), <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/78631" rel="nofollow">Yarman29</a> (29 notes) and <a class="wiki_link_ext" href="http://www.ozanyarman.com/yarman36.html" rel="nofollow">Yarman36</a> (36 notes).<br />
All these and more are available in the <a class="wiki_link_ext" href="http://www.huygens-fokker.org/scala/downloads.html" rel="nofollow">scala file archive</a>.<br />
<br />
A lot of research in this field has been done by <a class="wiki_link" href="/Julien%20Jalaleddine%20Weiss">Julien Jalaleddine Weiss</a>. See <a class="wiki_link" href="/tuning%20systems%20for%20qanun">tuning systems for the qanun</a> , or <a class="wiki_link_ext" href="http://stefanpohlit.com/dissertation.engl..htm" rel="nofollow">Stefan Pohlit's dissertation</a>.<br />
<br />
<a class="wiki_link" href="/Tsaharuk">Tsaharuk</a> is a 77 notes per octave linear or planar temperament proposed by <a class="wiki_link" href="/Jacques%20Dudon">Jacques Dudon</a> based on Julien Jalaleddine Weiss qanun tunings.<br />
<br />
Unequal temperaments for maqamat were also developed by <a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a> , e.g. <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/JustIntonation/message/1005" rel="nofollow">Bamm</a> (20 or 24 notes) and <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100839" rel="nofollow">Turquoise17</a> (17 notes).<br />
<br />
See also;<br />
<a class="wiki_link" href="/Turkish%20maqam%20music%20temperaments">Turkish maqam music temperaments</a><br />
<a class="wiki_link" href="/Maqamat%20in%20maqamic%20temperament">Maqamat in maqamic temperament</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:10 -->External links</h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="External links--Arabic"></a><!-- ws:end:WikiTextHeadingRule:12 -->Arabic</h3>
 <a class="wiki_link_ext" href="http://www.maqamworld.com" rel="nofollow">Arabic Maqam World</a> (Johnny Farraj, Sami Abu Shumays <em>et al</em>)<br />
<a class="wiki_link_ext" href="http://www.classicalarabicmusic.com/scales.htm" rel="nofollow">Classical Arabic Music</a><br />
<a class="wiki_link_ext" href="http://www.oud.eclipse.co.uk" rel="nofollow">The Oud</a> (David Parfitt, discusses both Arabic and Turkish <em>maqâm</em> theory)<br />
<a class="wiki_link_ext" href="http://www.alsiadi.com" rel="nofollow">ALSIADI.com</a> (focuses on Halabi/Aleppo traditional music; describes <em>maq</em><em>â</em><em>m</em><em>â</em><em>t</em> in terms of 53-tone Pythagorean tuning)<br />
<a class="wiki_link_ext" href="http://foredofico.org/CERMAA/" rel="nofollow">CERMAA</a> (academic research for arabic and related music, namely various articles by <a class="wiki_link" href="/Amine%20Beyhom">Amine Beyhom</a>)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="External links--Turkish"></a><!-- ws:end:WikiTextHeadingRule:14 -->Turkish</h3>
 <a class="wiki_link_ext" href="http://www.hinesmusic.com/What_Are_Makams.html" rel="nofollow">Tetrachords and Makams of Turkey</a> - another theory site<br />
<a class="wiki_link_ext" href="http://www.turkishmusicportal.org" rel="nofollow">http://www.turkishmusicportal.org</a> - listening<br />
<a class="wiki_link_ext" href="http://www.turkishmusic.org/index.html" rel="nofollow">http://www.turkishmusic.org</a> - listening<br />
<!-- ws:start:WikiTextUrlRule:176:http://www.turkishmusic.org/index18.html --><a class="wiki_link_ext" href="http://www.turkishmusic.org/index18.html" rel="nofollow">http://www.turkishmusic.org/index18.html</a><!-- ws:end:WikiTextUrlRule:176 --> - listening<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="External links--Persian"></a><!-- ws:end:WikiTextHeadingRule:16 -->Persian</h3>
 <a class="wiki_link_ext" href="http://240edo.googlepages.com/persianmusic" rel="nofollow">http://240edo.googlepages.com/persianmusic</a> - a list of links related to Persian music, maintained by <a class="wiki_link" href="/Shaahin%20Mohajeri">Shaahin Mohajeri</a><br />
<br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 734px; width: 1px;"> <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=7&amp;limit=2_3_5_11&amp;key=7_11_16_24" rel="nofollow">7</a>, <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=24&amp;limit=2_3_5_11&amp;key=24_38_56_83" rel="nofollow">24</a>, <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=31&amp;limit=2_3_5_11&amp;key=31_49_72_107" rel="nofollow">31</a>, <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=14&amp;limit=2_3_5_11&amp;key=14_22_32_48" rel="nofollow">14c</a>, <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=17&amp;limit=2_3_5_11&amp;key=17_27_40_59" rel="nofollow">17c</a>, <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=38&amp;limit=2_3_5_11&amp;key=38_60_88_131" rel="nofollow">38</a>, <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=10&amp;limit=2_3_5_11&amp;key=10_16_24_35" rel="nofollow">10c</a>, <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=21&amp;limit=2_3_5_11&amp;key=21_33_48_72" rel="nofollow">21ce</a>, <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=45&amp;limit=2_3_5_11&amp;key=45_71_104_155" rel="nofollow">45e</a>, <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=55&amp;limit=2_3_5_11&amp;key=55_87_128_190" rel="nofollow">55</a></span></body></html>