41edo: Difference between revisions

Wikispaces>jdfreivald
**Imported revision 395842882 - Original comment: **
Wikispaces>Gedankenwelt
**Imported revision 440469648 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2013-01-04 12:39:56 UTC</tt>.<br>
: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2013-07-04 11:39:07 UTC</tt>.<br>
: The original revision id was <tt>395842882</tt>.<br>
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[[toc|flat]]
[[toc|flat]]
=Introduction=  
=Introduction=  
The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 [[cent]]s, an [[interval]] close in size to [[64_63|64/63]], the [[Septimal comma|septimal comma]]. 41-ET can be seen as a tuning of the //[[Schismatic family#Garibaldi|Garibaldi temperament]]// &lt;ref&gt;[[http://x31eq.com/schismic.htm|"Schismic Temperaments"]] at x31eq.com the websize of [[Graham Breed]]&lt;/ref&gt; , &lt;ref&gt;[[http://x31eq.com/decimal_lattice.htm|"Lattices with Decimal Notation"]] at x31eq.com&lt;/ref&gt; , &lt;ref&gt;[[http://en.wikipedia.org/wiki/Schismatic_temperament|Schismatic temperament]]&lt;/ref&gt; the //[[Magic family|Magic temperament]]// &lt;ref&gt;[[http://en.wikipedia.org/wiki/Magic_temperament|Magic temperament]]&lt;/ref&gt; and the superkleismic (41&amp;26) temperament. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] after 31; it is not, however, a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13_10|13/10]] is 14 cents sharp. Various 13-limit [[magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.
The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 [[cent]]s, an [[interval]] close in size to [[64_63|64/63]], the [[Septimal comma|septimal comma]]. 41-ET can be seen as a tuning of the //[[Schismatic family#Garibaldi|Garibaldi temperament]]// &lt;ref&gt;[[http://x31eq.com/schismic.htm|"Schismic Temperaments"]] at x31eq.com the website of [[Graham Breed]]&lt;/ref&gt; , &lt;ref&gt;[[http://x31eq.com/decimal_lattice.htm|"Lattices with Decimal Notation"]] at x31eq.com&lt;/ref&gt; , &lt;ref&gt;[[http://en.wikipedia.org/wiki/Schismatic_temperament|Schismatic temperament]]&lt;/ref&gt; the //[[Magic family|Magic temperament]]// &lt;ref&gt;[[http://en.wikipedia.org/wiki/Magic_temperament|Magic temperament]]&lt;/ref&gt; and the superkleismic (41&amp;26) temperament. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] after 31; it is not, however, a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13_10|13/10]] is 14 cents sharp. Various 13-limit [[magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.


41-ET forms the foundation of the [[http://www.h-pi.com/theory/huntsystem1.html|H-System]], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [[http://www.h-pi.com/theory/huntsystem2.html|average JND]] from the 41-ET circle in [[205edo]].
41-ET forms the foundation of the [[http://www.h-pi.com/theory/huntsystem1.html|H-System]], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [[http://www.h-pi.com/theory/huntsystem2.html|average JND]] from the 41-ET circle in [[205edo]].
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|| 0 || 0.00 || [[1_1|1/1]] || do ||  ||  ||
|| 0 || 0.00 || [[1_1|1/1]] || do ||  ||  ||
|| 1 || 29.27 || [[81_80|81/80]] || di ||  ||  ||
|| 1 || 29.27 || [[81_80|81/80]] || di ||  ||  ||
|| 2 || 58.54 || [[25_24|25/24]], [[28_27|28/27]], [[33_32|33/32]] || ro ||   ||  ||
|| 2 || 58.54 || [[25_24|25/24]], [[28_27|28/27]], [[33_32|33/32]] || ro || [[Gamelismic clan#Miracle-Hemimiracle|Hemimiracle]] ||  ||
|| 3 || 87.80 || [[21_20|21/20]], [[22_21|22/21]] || rih || 88cET (approx) / [[octacot]] ||  ||
|| 3 || 87.80 || [[21_20|21/20]], [[22_21|22/21]] || rih || 88cET (approx) / [[octacot]] ||  ||
|| 4 || 117.07 || [[16_15|16/15]], [[15_14|15/14]] || ra || [[Miracle]] ||  ||
|| 4 || 117.07 || [[16_15|16/15]], [[15_14|15/14]] || ra || [[Miracle]] ||  ||
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|| 8 || 234.15 || [[8_7|8/7]] || ri || [[Rodan]]/[[guiron]] || 11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1 ||
|| 8 || 234.15 || [[8_7|8/7]] || ri || [[Rodan]]/[[guiron]] || 11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1 ||
|| 9 || 263.41 || [[7_6|7/6]], [[32_25|32/25]] || ma || [[Septimin]] || 9-tone MOS: 5 4 5 5 4 5 4 5 4 ||
|| 9 || 263.41 || [[7_6|7/6]], [[32_25|32/25]] || ma || [[Septimin]] || 9-tone MOS: 5 4 5 5 4 5 4 5 4 ||
|| 10 || 292.68 || [[32_27|32/27]] || meh ||   ||  ||
|| 10 || 292.68 || [[32_27|32/27]] || meh || [[Keemic temperaments#Quasitemp|Quasitemp]] ||  ||
|| 11 || 321.95 || [[6_5|6/5]] || me || [[Superkleismic]] || 11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3 ||
|| 11 || 321.95 || [[6_5|6/5]] || me || [[Superkleismic]] || 11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3 ||
|| 12 || 351.22 || [[11_9|11/9]],[[27_22|27/22]] || mu || [[Hemififths]]/[[karadeniz]] || 10-tone MOS: 5 2 5 5 2 5 5 5 2 5 ||
|| 12 || 351.22 || [[11_9|11/9]],[[27_22|27/22]] || mu || [[Hemififths]]/[[karadeniz]] || 10-tone MOS: 5 2 5 5 2 5 5 5 2 5 ||
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|| 14 || 409.76 || [[14_11|14/11]], [[81_64|81/64]] || maa || [[Hocus]] ||  ||
|| 14 || 409.76 || [[14_11|14/11]], [[81_64|81/64]] || maa || [[Hocus]] ||  ||
|| 15 || 439.02 || [[9_7|9/7]] || mo ||  || 11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4 ||
|| 15 || 439.02 || [[9_7|9/7]] || mo ||  || 11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4 ||
|| 16 || 468.29 || [[21_16|21/16]] || fe ||   ||  ||
|| 16 || 468.29 || [[21_16|21/16]] || fe || [[Keemic temperaments#Barbad|Barbad]] ||  ||
|| 17 || 497.56 || [[4_3|4/3]] || fa || [[Schismatic]] ([[helmholtz]], [[Garibaldi temperament|garibaldi]], [[cassandra]]) ||  ||
|| 17 || 497.56 || [[4_3|4/3]] || fa || [[Schismatic]] ([[helmholtz]], [[Garibaldi temperament|garibaldi]], [[cassandra]]) ||  ||
|| 18 || 526.83 || [[15_11|15/11]], [[27_20|27/20]] || fih ||   || 9-tone MOS: 5 5 3 5 5 5 5 3 5 ||
|| 18 || 526.83 || [[15_11|15/11]], [[27_20|27/20]] || fih || [[Magic family#Trismegistus|Trismegistus]] || 9-tone MOS: 5 5 3 5 5 5 5 3 5 ||
|| 19 || 556.10 || [[11_8|11/8]] || fu ||  ||  ||
|| 19 || 556.10 || [[11_8|11/8]] || fu ||  ||  ||
|| 20 || 585.37 || [[7_5|7/5]] || fi || [[Pluto]] ||  ||
|| 20 || 585.37 || [[7_5|7/5]] || fi || [[Pluto]] ||  ||
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=Music=  
=Music=  
[[http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro|EveningHorizon]] ////[[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3|play]]//// by Cameron Bobro
[[http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro|EveningHorizon]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3|play]] by Cameron Bobro


=Links=  
=Links=  
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* [[Magic22 as srutis#magic22assrutis]] describes a possible use of 41edo for [[indian]] music.
* [[Magic22 as srutis#magic22assrutis]] describes a possible use of 41edo for [[indian]] music.
* see also [[Magic family]]
* see also [[Magic family]]
* Sword, Ron.[[@http://www.ronsword.com| "Tetracontamonophonic Scales for Guitar"]]</pre></div>
* Sword, Ron. [[@http://www.ronsword.com|"Tetracontamonophonic Scales for Guitar"]]</pre></div>
<h4>Original HTML content:</h4>
<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;41edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="color: #004d25; font-family: 'Times New Roman',Times,serif; font-size: 20px;"&gt;&lt;strong&gt;41 Tone Equal Temperament&lt;/strong&gt;&lt;/span&gt;&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;41edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="color: #004d25; font-family: 'Times New Roman',Times,serif; font-size: 20px;"&gt;&lt;strong&gt;41 Tone Equal Temperament&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextTocRule:27:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;a href="#Introduction"&gt;Introduction&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#Temperaments"&gt;Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt; | &lt;a href="#Harmonic Scale"&gt;Harmonic Scale&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt; | &lt;a href="#Nonoctave Temperaments"&gt;Nonoctave Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt; | &lt;a href="#Links"&gt;Links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;
&lt;!-- ws:start:WikiTextTocRule:27:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;a href="#Introduction"&gt;Introduction&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#Temperaments"&gt;Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt; | &lt;a href="#Harmonic Scale"&gt;Harmonic Scale&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt; | &lt;a href="#Nonoctave Temperaments"&gt;Nonoctave Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt; | &lt;a href="#Links"&gt;Links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;
&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Introduction"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Introduction&lt;/h1&gt;
&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Introduction"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Introduction&lt;/h1&gt;
  The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, an &lt;a class="wiki_link" href="/interval"&gt;interval&lt;/a&gt; close in size to &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, the &lt;a class="wiki_link" href="/Septimal%20comma"&gt;septimal comma&lt;/a&gt;. 41-ET can be seen as a tuning of the &lt;em&gt;&lt;a class="wiki_link" href="/Schismatic%20family#Garibaldi"&gt;Garibaldi temperament&lt;/a&gt;&lt;/em&gt; &lt;!-- ws:start:WikiTextRefRule:2:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://x31eq.com/schismic.htm&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;amp;quot;Schismic Temperaments&amp;amp;quot;&amp;lt;/a&amp;gt; at x31eq.com the websize of &amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Graham%20Breed&amp;quot;&amp;gt;Graham Breed&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-1" class="reference"&gt;&lt;a href="#cite_note-1"&gt;[1]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:2 --&gt; , &lt;!-- ws:start:WikiTextRefRule:4:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://x31eq.com/decimal_lattice.htm&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;amp;quot;Lattices with Decimal Notation&amp;amp;quot;&amp;lt;/a&amp;gt; at x31eq.com&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-2" class="reference"&gt;&lt;a href="#cite_note-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:4 --&gt; , &lt;!-- ws:start:WikiTextRefRule:6:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://en.wikipedia.org/wiki/Schismatic_temperament&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;Schismatic temperament&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-3" class="reference"&gt;&lt;a href="#cite_note-3"&gt;[3]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:6 --&gt; the &lt;em&gt;&lt;a class="wiki_link" href="/Magic%20family"&gt;Magic temperament&lt;/a&gt;&lt;/em&gt; &lt;!-- ws:start:WikiTextRefRule:8:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://en.wikipedia.org/wiki/Magic_temperament&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;Magic temperament&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-4" class="reference"&gt;&lt;a href="#cite_note-4"&gt;[4]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:8 --&gt; and the superkleismic (41&amp;amp;26) temperament. It is the second smallest equal temperament (after &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;) whose perfect fifth is closer to just intonation than that of &lt;a class="wiki_link" href="/12edo"&gt;12-ET&lt;/a&gt;, and is the seventh &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt; after 31; it is not, however, a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta gap edo&lt;/a&gt;. This has to do with the fact that it can deal with the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; fairly well, and the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; perhaps close enough for government work, though its &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt; is 14 cents sharp. Various 13-limit &lt;a class="wiki_link" href="/magic%20extensions"&gt;magic extensions&lt;/a&gt; are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.&lt;br /&gt;
  The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, an &lt;a class="wiki_link" href="/interval"&gt;interval&lt;/a&gt; close in size to &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, the &lt;a class="wiki_link" href="/Septimal%20comma"&gt;septimal comma&lt;/a&gt;. 41-ET can be seen as a tuning of the &lt;em&gt;&lt;a class="wiki_link" href="/Schismatic%20family#Garibaldi"&gt;Garibaldi temperament&lt;/a&gt;&lt;/em&gt; &lt;!-- ws:start:WikiTextRefRule:2:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://x31eq.com/schismic.htm&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;amp;quot;Schismic Temperaments&amp;amp;quot;&amp;lt;/a&amp;gt; at x31eq.com the website of &amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Graham%20Breed&amp;quot;&amp;gt;Graham Breed&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-1" class="reference"&gt;&lt;a href="#cite_note-1"&gt;[1]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:2 --&gt; , &lt;!-- ws:start:WikiTextRefRule:4:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://x31eq.com/decimal_lattice.htm&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;amp;quot;Lattices with Decimal Notation&amp;amp;quot;&amp;lt;/a&amp;gt; at x31eq.com&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-2" class="reference"&gt;&lt;a href="#cite_note-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:4 --&gt; , &lt;!-- ws:start:WikiTextRefRule:6:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://en.wikipedia.org/wiki/Schismatic_temperament&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;Schismatic temperament&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-3" class="reference"&gt;&lt;a href="#cite_note-3"&gt;[3]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:6 --&gt; the &lt;em&gt;&lt;a class="wiki_link" href="/Magic%20family"&gt;Magic temperament&lt;/a&gt;&lt;/em&gt; &lt;!-- ws:start:WikiTextRefRule:8:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://en.wikipedia.org/wiki/Magic_temperament&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;Magic temperament&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-4" class="reference"&gt;&lt;a href="#cite_note-4"&gt;[4]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:8 --&gt; and the superkleismic (41&amp;amp;26) temperament. It is the second smallest equal temperament (after &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;) whose perfect fifth is closer to just intonation than that of &lt;a class="wiki_link" href="/12edo"&gt;12-ET&lt;/a&gt;, and is the seventh &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt; after 31; it is not, however, a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta gap edo&lt;/a&gt;. This has to do with the fact that it can deal with the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; fairly well, and the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; perhaps close enough for government work, though its &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt; is 14 cents sharp. Various 13-limit &lt;a class="wiki_link" href="/magic%20extensions"&gt;magic extensions&lt;/a&gt; are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
41-ET forms the foundation of the &lt;a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem1.html" rel="nofollow"&gt;H-System&lt;/a&gt;, which uses the scale degrees of 41-ET as the basic &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; intervals requiring fine tuning +/- 1 &lt;a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem2.html" rel="nofollow"&gt;average JND&lt;/a&gt; from the 41-ET circle in &lt;a class="wiki_link" href="/205edo"&gt;205edo&lt;/a&gt;.&lt;br /&gt;
41-ET forms the foundation of the &lt;a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem1.html" rel="nofollow"&gt;H-System&lt;/a&gt;, which uses the scale degrees of 41-ET as the basic &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; intervals requiring fine tuning +/- 1 &lt;a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem2.html" rel="nofollow"&gt;average JND&lt;/a&gt; from the 41-ET circle in &lt;a class="wiki_link" href="/205edo"&gt;205edo&lt;/a&gt;.&lt;br /&gt;
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         &lt;td&gt;9-tone MOS: 5 5 3 5 5 5 5 3 5&lt;br /&gt;
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  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow"&gt;Wikipedia article on 41edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis"&gt;Magic22 as srutis&lt;/a&gt; describes a possible use of 41edo for &lt;a class="wiki_link" href="/indian"&gt;indian&lt;/a&gt; music.&lt;/li&gt;&lt;li&gt;see also &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic family&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Sword, Ron.&lt;a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank"&gt; &amp;quot;Tetracontamonophonic Scales for Guitar&amp;quot;&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextReferencesRule:3401: --&gt;&lt;hr class="references" /&gt;&lt;ol class="references"&gt;
  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow"&gt;Wikipedia article on 41edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis"&gt;Magic22 as srutis&lt;/a&gt; describes a possible use of 41edo for &lt;a class="wiki_link" href="/indian"&gt;indian&lt;/a&gt; music.&lt;/li&gt;&lt;li&gt;see also &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic family&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Sword, Ron. &lt;a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank"&gt;&amp;quot;Tetracontamonophonic Scales for Guitar&amp;quot;&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextReferencesRule:3405: --&gt;&lt;hr class="references" /&gt;&lt;ol class="references"&gt;
&lt;li id="cite_note-1"&gt;&lt;a href="#cite_ref-1"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://x31eq.com/schismic.htm" rel="nofollow"&gt;&amp;quot;Schismic Temperaments&amp;quot;&lt;/a&gt; at x31eq.com the websize of &lt;a class="wiki_link" href="/Graham%20Breed"&gt;Graham Breed&lt;/a&gt;&lt;/li&gt;
&lt;li id="cite_note-1"&gt;&lt;a href="#cite_ref-1"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://x31eq.com/schismic.htm" rel="nofollow"&gt;&amp;quot;Schismic Temperaments&amp;quot;&lt;/a&gt; at x31eq.com the website of &lt;a class="wiki_link" href="/Graham%20Breed"&gt;Graham Breed&lt;/a&gt;&lt;/li&gt;
&lt;li id="cite_note-2"&gt;&lt;a href="#cite_ref-2"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://x31eq.com/decimal_lattice.htm" rel="nofollow"&gt;&amp;quot;Lattices with Decimal Notation&amp;quot;&lt;/a&gt; at x31eq.com&lt;/li&gt;
&lt;li id="cite_note-2"&gt;&lt;a href="#cite_ref-2"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://x31eq.com/decimal_lattice.htm" rel="nofollow"&gt;&amp;quot;Lattices with Decimal Notation&amp;quot;&lt;/a&gt; at x31eq.com&lt;/li&gt;
&lt;li id="cite_note-3"&gt;&lt;a href="#cite_ref-3"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow"&gt;Schismatic temperament&lt;/a&gt;&lt;/li&gt;
&lt;li id="cite_note-3"&gt;&lt;a href="#cite_ref-3"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow"&gt;Schismatic temperament&lt;/a&gt;&lt;/li&gt;
&lt;li id="cite_note-4"&gt;&lt;a href="#cite_ref-4"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow"&gt;Magic temperament&lt;/a&gt;&lt;/li&gt;
&lt;li id="cite_note-4"&gt;&lt;a href="#cite_ref-4"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow"&gt;Magic temperament&lt;/a&gt;&lt;/li&gt;
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