Marvel temperaments: Difference between revisions

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:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2011-06-~~20 20~~:36:01 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-22 17:25:47 UTC</tt>.<br>

: The original revision id was <tt>~~237843849~~</tt>.<br>

: The original revision id was <tt>238258159</tt>.<br>

: The revision comment was: <tt></tt><br>

: The revision comment was: <tt>some edo links added</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">[[toc|flat]]

This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.

This page discusses some of the temperaments tempering out [[225_224|225/224]], the [[marvel comma]] or [[septimal kleisma]]. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.

Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.

=Negri=

~~Commas~~: 49/48, 225/224

[[Comma]]s: 49/48, 225/224

[[POTE tuning|POTE temperament]]: 125.608

Map: [<1 2 2 3|, <0 -4 3 -2|]

[[Map]]: [<1 2 2 3|, <0 -4 3 -2|]

Wedgie: <<4 -3 2 -14 -8 13||

[[Wedgie]]: <<4 -3 2 -14 -8 13||

EDOs: 9, 10, 19, 86

EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]]

==11-limit==

Line 28:

Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|]

EDOs: 9, 10, 19

Badness: 0.0262

[[Badness]]: 0.0262

==13-limit==

Line 44:

Map: [<1 2 2 3 2|, <0 -4 3 -2 14|]

EDOs: 9, 10, 19, 29, 48, 77

EDOs: 9, 10, 19, [[29edo|29]], [[48edo|48]], [[77edo|77]]

Badness: 0.0387

Line 62:

Map: [<1 2 2 3 3|, <0 -4 3 -2 4|]

EDOs: 9, 19, 85

EDOs: 9, 19, [[85edo|85]]

Badness: 0.0306

Line 81:

Map: [<2 1 5 2|, <0 6 -1 10|]

Wedgie: <<12 -2 20 -31 -2 52||

EDOs: 22, 50, 72, 382, 454

EDOs: [[22edo|22]], [[50edo|50]], [[72edo|72]], [[382edo|382]], [[454edo|454]]

Badness: 0.0408

Line 90:

Map: [<2 1 5 2 8|, <0 6 -1 10 -3|]

EDOs: 22, 50, 72, 166, 310

EDOs: 22, 50, 72, [[166edo|166]], [[310edo|310]]

Badness: 0.0185

Line 117:

Map: [<2 1 5 2 8 11 6 2|, <0 6 -1 10 -3 -10 6 18|]

EDOs: 22, 50, 72, 194, 460

EDOs: 22, 50, 72, [[194edo|194]], [[460edo|460]]

Badness: 0.0157

Line 126:

Map: [<2 1 5 2 8 -2|, <0 6 -1 10 -3 26|]

EDOs: 22, 28, 50, 72, 94, 166

EDOs: 22, [[28edo|28]], 50, 72, [[94edo|94]], 166

Badness: 0.0203

Line 135:

Map: [<2 1 5 2 8 -2 6|, <0 6 -1 10 -3 26 6|]

EDOs: 22, 72, 94, 166, 238

EDOs: 22, 72, 94, 166, [[238edo|238]]

Badness: 0.0136

Line 154:

Map: [<1 4 -3 -3|, <0 -5 11 12|]

Wedgie: <<5 -11 -12 -29 -33 3||

EDOs: 29, 31, 60, 91, 122, 213

EDOs: [[29edo|29]], [[31edo|31]], [[60edo|60]], [[91edo|91]], [[122edo|122]], [[213edo|213]]

==11-limit==

Line 162:

Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|]

EDOs: 29, 31, 60, 91, 122, 153

EDOs: 29, 31, 60, 91, 122, [[153edo|153]]

=Septimin=

Line 171:

Map: [<1 4 1 5|, <0 -11 6 -10|]

Wedgie: <<11 -6 10 -35 -15 40||

EDOs: 9, 32, 41, 91, 132

EDOs: 9, [[32edo|32]], 41, 91, [[132edo|132]]

==11-limit==

Line 245:

<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>Marvel temperaments</title></head><body><a href="#Negri">Negri</a> | <a href="#Negril">Negril</a> | <a href="#Negric">Negric</a> | <a href="#Wizard">Wizard</a> | <a href="#Tritonic">Tritonic</a> | <a href="#Septimin">Septimin</a> | <a href="#Slender">Slender</a> | <a href="#Triton">Triton</a> | <a href="#Marvo">Marvo</a>

<br />

This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.<br />

This page discusses some of the temperaments tempering out <a class="wiki_link" href="/225_224">225/224</a>, the <a class="wiki_link" href="/marvel%20comma">marvel comma</a> or <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a>. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.<br />

<br />

Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.<br />

<br />

<h1 id="toc0"><a name="Negri"></a>Negri</h1>

~~Commas~~: 49/48, 225/224<br />

<a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 225/224<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 125.608<br />

<br />

Map: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]<br />

Wedgie: &lt;&lt;4 -3 2 -14 -8 13||<br />

<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;4 -3 2 -14 -8 13||<br />

EDOs: 9, 10, 19, 86<br />

EDOs: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/86edo">86</a><br />

<br />

<h2 id="toc1"><a name="Negri-11-limit"></a>11-limit</h2>

Line 265:

Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]<br />

EDOs: 9, 10, 19<br />

Badness: 0.0262<br />

<a class="wiki_link" href="/Badness">Badness</a>: 0.0262<br />

<br />

<h2 id="toc2"><a name="Negri-13-limit"></a>13-limit</h2>

Line 281:

<br />

Map: [&lt;1 2 2 3 2|, &lt;0 -4 3 -2 14|] <br />

EDOs: 9, 10, 19, 29, 48, 77<br />

EDOs: 9, 10, 19, <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/48edo">48</a>, <a class="wiki_link" href="/77edo">77</a><br />

Badness: 0.0387<br />

<br />

Line 299:

<br />

Map: [&lt;1 2 2 3 3|, &lt;0 -4 3 -2 4|]<br />

EDOs: 9, 19, 85<br />

EDOs: 9, 19, <a class="wiki_link" href="/85edo">85</a><br />

Badness: 0.0306<br />

<br />

Line 318:

Map: [&lt;2 1 5 2|, &lt;0 6 -1 10|]<br />

Wedgie: &lt;&lt;12 -2 20 -31 -2 52||<br />

EDOs: 22, 50, 72, 382, 454<br />

EDOs: <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/50edo">50</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/382edo">382</a>, <a class="wiki_link" href="/454edo">454</a><br />

Badness: 0.0408<br />

<br />

Line 327:

<br />

Map: [&lt;2 1 5 2 8|, &lt;0 6 -1 10 -3|]<br />

EDOs: 22, 50, 72, 166, 310<br />

EDOs: 22, 50, 72, <a class="wiki_link" href="/166edo">166</a>, <a class="wiki_link" href="/310edo">310</a><br />

Badness: 0.0185<br />

<br />

Line 354:

<br />

Map: [&lt;2 1 5 2 8 11 6 2|, &lt;0 6 -1 10 -3 -10 6 18|]<br />

EDOs: 22, 50, 72, 194, 460<br />

EDOs: 22, 50, 72, <a class="wiki_link" href="/194edo">194</a>, <a class="wiki_link" href="/460edo">460</a><br />

Badness: 0.0157<br />

<br />

Line 363:

<br />

Map: [&lt;2 1 5 2 8 -2|, &lt;0 6 -1 10 -3 26|]<br />

EDOs: 22, 28, 50, 72, 94, 166<br />

EDOs: 22, <a class="wiki_link" href="/28edo">28</a>, 50, 72, <a class="wiki_link" href="/94edo">94</a>, 166<br />

Badness: 0.0203<br />

<br />

Line 372:

<br />

Map: [&lt;2 1 5 2 8 -2 6|, &lt;0 6 -1 10 -3 26 6|]<br />

EDOs: 22, 72, 94, 166, 238<br />

EDOs: 22, 72, 94, 166, <a class="wiki_link" href="/238edo">238</a><br />

Badness: 0.0136<br />

<br />

Line 391:

Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]<br />

Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||<br />

EDOs: 29, 31, 60, 91, 122, 213<br />

EDOs: <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/60edo">60</a>, <a class="wiki_link" href="/91edo">91</a>, <a class="wiki_link" href="/122edo">122</a>, <a class="wiki_link" href="/213edo">213</a><br />

<br />

<h2 id="toc16"><a name="Tritonic-11-limit"></a>11-limit</h2>

Line 399:

<br />

Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]<br />

EDOs: 29, 31, 60, 91, 122, 153<br />

EDOs: 29, 31, 60, 91, 122, <a class="wiki_link" href="/153edo">153</a><br />

<br />

<h1 id="toc17"><a name="Septimin"></a>Septimin</h1>

Line 408:

Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]<br />

Wedgie: &lt;&lt;11 -6 10 -35 -15 40||<br />

EDOs: 9, 32, 41, 91, 132<br />

EDOs: 9, <a class="wiki_link" href="/32edo">32</a>, 41, 91, <a class="wiki_link" href="/132edo">132</a><br />

<br />

<h2 id="toc18"><a name="Septimin-11-limit"></a>11-limit</h2>

@@ 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:genewardsmith|genewardsmith]] and made on <tt>2011-06-20 20:36:01 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-22 17:25:47 UTC</tt>.<br>
-: The original revision id was <tt>237843849</tt>.<br>
+: The original revision id was <tt>238258159</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>some edo links added</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">[[toc|flat]]
-This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.
+This page discusses some of the temperaments tempering out [[225_224|225/224]], the [[marvel comma]] or [[septimal kleisma]]. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.
 Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.
 =Negri=
-Commas: 49/48, 225/224
+[[Comma]]s: 49/48, 225/224
 [[POTE tuning|POTE temperament]]: 125.608
-Map: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]
+[[Map]]: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]
-Wedgie: &lt;&lt;4 -3 2 -14 -8 13||
+[[Wedgie]]: &lt;&lt;4 -3 2 -14 -8 13||
-EDOs: 9, 10, 19, 86
+EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]]
 ==11-limit==
@@ Line 28: / Line 28: @@
 Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]
 EDOs: 9, 10, 19
-Badness: 0.0262
+[[Badness]]: 0.0262
 ==13-limit==
@@ Line 44: / Line 44: @@
 Map: [&lt;1 2 2 3 2|, &lt;0 -4 3 -2 14|]
-EDOs: 9, 10, 19, 29, 48, 77
+EDOs: 9, 10, 19, [[29edo|29]], [[48edo|48]], [[77edo|77]]
 Badness: 0.0387
@@ Line 62: / Line 62: @@
 Map: [&lt;1 2 2 3 3|, &lt;0 -4 3 -2 4|]
-EDOs: 9, 19, 85
+EDOs: 9, 19, [[85edo|85]]
 Badness: 0.0306
@@ Line 81: / Line 81: @@
 Map: [&lt;2 1 5 2|, &lt;0 6 -1 10|]
 Wedgie: &lt;&lt;12 -2 20 -31 -2 52||
-EDOs: 22, 50, 72, 382, 454
+EDOs: [[22edo|22]], [[50edo|50]], [[72edo|72]], [[382edo|382]], [[454edo|454]]
 Badness: 0.0408
@@ Line 90: / Line 90: @@
 Map: [&lt;2 1 5 2 8|, &lt;0 6 -1 10 -3|]
-EDOs: 22, 50, 72, 166, 310
+EDOs: 22, 50, 72, [[166edo|166]], [[310edo|310]]
 Badness: 0.0185
@@ Line 117: / Line 117: @@
 Map: [&lt;2 1 5 2 8 11 6 2|, &lt;0 6 -1 10 -3 -10 6 18|]
-EDOs: 22, 50, 72, 194, 460
+EDOs: 22, 50, 72, [[194edo|194]], [[460edo|460]]
 Badness: 0.0157
@@ Line 126: / Line 126: @@
 Map: [&lt;2 1 5 2 8 -2|, &lt;0 6 -1 10 -3 26|]
-EDOs: 22, 28, 50, 72, 94, 166
+EDOs: 22, [[28edo|28]], 50, 72, [[94edo|94]], 166
 Badness: 0.0203
@@ Line 135: / Line 135: @@
 Map: [&lt;2 1 5 2 8 -2 6|, &lt;0 6 -1 10 -3 26 6|]
-EDOs: 22, 72, 94, 166, 238
+EDOs: 22, 72, 94, 166, [[238edo|238]]
 Badness: 0.0136
@@ Line 154: / Line 154: @@
 Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]
 Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||
-EDOs: 29, 31, 60, 91, 122, 213
+EDOs: [[29edo|29]], [[31edo|31]], [[60edo|60]], [[91edo|91]], [[122edo|122]], [[213edo|213]]
 ==11-limit==
@@ Line 162: / Line 162: @@
 Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]
-EDOs: 29, 31, 60, 91, 122, 153
+EDOs: 29, 31, 60, 91, 122, [[153edo|153]]
 =Septimin=
@@ Line 171: / Line 171: @@
 Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]
 Wedgie: &lt;&lt;11 -6 10 -35 -15 40||
-EDOs: 9, 32, 41, 91, 132
+EDOs: 9, [[32edo|32]], 41, 91, [[132edo|132]]
 ==11-limit==
@@ Line 245: / Line 245: @@
 <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;Marvel temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:52:&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:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;a href="#Negri"&gt;Negri&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Negril"&gt;Negril&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt; | &lt;a href="#Negric"&gt;Negric&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt; | &lt;a href="#Wizard"&gt;Wizard&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt; | &lt;a href="#Tritonic"&gt;Tritonic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt; | &lt;a href="#Septimin"&gt;Septimin&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt; | &lt;a href="#Slender"&gt;Slender&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt; | &lt;a href="#Triton"&gt;Triton&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt; | &lt;a href="#Marvo"&gt;Marvo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;
 &lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;br /&gt;
-This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.&lt;br /&gt;
+This page discusses some of the temperaments tempering out &lt;a class="wiki_link" href="/225_224"&gt;225/224&lt;/a&gt;, the &lt;a class="wiki_link" href="/marvel%20comma"&gt;marvel comma&lt;/a&gt; or &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt;. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.&lt;br /&gt;
 &lt;br /&gt;
 Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Negri"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Negri&lt;/h1&gt;
-  Commas: 49/48, 225/224&lt;br /&gt;
+  &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 225/224&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 125.608&lt;br /&gt;
 &lt;br /&gt;
-Map: [&amp;lt;1 2 2 3|, &amp;lt;0 -4 3 -2|]&lt;br /&gt;
+&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 2 2 3|, &amp;lt;0 -4 3 -2|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;4 -3 2 -14 -8 13||&lt;br /&gt;
+&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;4 -3 2 -14 -8 13||&lt;br /&gt;
-EDOs: 9, 10, 19, 86&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/86edo"&gt;86&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Negri-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
@@ Line 265: / Line 265: @@
 Map: [&amp;lt;1 2 2 3 4|, &amp;lt;0 -4 3 -2 -5|]&lt;br /&gt;
 EDOs: 9, 10, 19&lt;br /&gt;
-Badness: 0.0262&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0262&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Negri-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
@@ Line 281: / Line 281: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 2 2 3 2|, &amp;lt;0 -4 3 -2 14|] &lt;br /&gt;
-EDOs: 9, 10, 19, 29, 48, 77&lt;br /&gt;
+EDOs: 9, 10, 19, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48&lt;/a&gt;, &lt;a class="wiki_link" href="/77edo"&gt;77&lt;/a&gt;&lt;br /&gt;
 Badness: 0.0387&lt;br /&gt;
 &lt;br /&gt;
@@ Line 299: / Line 299: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 2 2 3 3|, &amp;lt;0 -4 3 -2 4|]&lt;br /&gt;
-EDOs: 9, 19, 85&lt;br /&gt;
+EDOs: 9, 19, &lt;a class="wiki_link" href="/85edo"&gt;85&lt;/a&gt;&lt;br /&gt;
 Badness: 0.0306&lt;br /&gt;
 &lt;br /&gt;
@@ Line 318: / Line 318: @@
 Map: [&amp;lt;2 1 5 2|, &amp;lt;0 6 -1 10|]&lt;br /&gt;
 Wedgie: &amp;lt;&amp;lt;12 -2 20 -31 -2 52||&lt;br /&gt;
-EDOs: 22, 50, 72, 382, 454&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/382edo"&gt;382&lt;/a&gt;, &lt;a class="wiki_link" href="/454edo"&gt;454&lt;/a&gt;&lt;br /&gt;
 Badness: 0.0408&lt;br /&gt;
 &lt;br /&gt;
@@ Line 327: / Line 327: @@
 &lt;br /&gt;
 Map: [&amp;lt;2 1 5 2 8|, &amp;lt;0 6 -1 10 -3|]&lt;br /&gt;
-EDOs: 22, 50, 72, 166, 310&lt;br /&gt;
+EDOs: 22, 50, 72, &lt;a class="wiki_link" href="/166edo"&gt;166&lt;/a&gt;, &lt;a class="wiki_link" href="/310edo"&gt;310&lt;/a&gt;&lt;br /&gt;
 Badness: 0.0185&lt;br /&gt;
 &lt;br /&gt;
@@ Line 354: / Line 354: @@
 &lt;br /&gt;
 Map: [&amp;lt;2 1 5 2 8 11 6 2|, &amp;lt;0 6 -1 10 -3 -10 6 18|]&lt;br /&gt;
-EDOs: 22, 50, 72, 194, 460&lt;br /&gt;
+EDOs: 22, 50, 72, &lt;a class="wiki_link" href="/194edo"&gt;194&lt;/a&gt;, &lt;a class="wiki_link" href="/460edo"&gt;460&lt;/a&gt;&lt;br /&gt;
 Badness: 0.0157&lt;br /&gt;
 &lt;br /&gt;
@@ Line 363: / Line 363: @@
 &lt;br /&gt;
 Map: [&amp;lt;2 1 5 2 8 -2|, &amp;lt;0 6 -1 10 -3 26|]&lt;br /&gt;
-EDOs: 22, 28, 50, 72, 94, 166&lt;br /&gt;
+EDOs: 22, &lt;a class="wiki_link" href="/28edo"&gt;28&lt;/a&gt;, 50, 72, &lt;a class="wiki_link" href="/94edo"&gt;94&lt;/a&gt;, 166&lt;br /&gt;
 Badness: 0.0203&lt;br /&gt;
 &lt;br /&gt;
@@ Line 372: / Line 372: @@
 &lt;br /&gt;
 Map: [&amp;lt;2 1 5 2 8 -2 6|, &amp;lt;0 6 -1 10 -3 26 6|]&lt;br /&gt;
-EDOs: 22, 72, 94, 166, 238&lt;br /&gt;
+EDOs: 22, 72, 94, 166, &lt;a class="wiki_link" href="/238edo"&gt;238&lt;/a&gt;&lt;br /&gt;
 Badness: 0.0136&lt;br /&gt;
 &lt;br /&gt;
@@ Line 391: / Line 391: @@
 Map: [&amp;lt;1 4 -3 -3|, &amp;lt;0 -5 11 12|]&lt;br /&gt;
 Wedgie: &amp;lt;&amp;lt;5 -11 -12 -29 -33 3||&lt;br /&gt;
-EDOs: 29, 31, 60, 91, 122, 213&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/60edo"&gt;60&lt;/a&gt;, &lt;a class="wiki_link" href="/91edo"&gt;91&lt;/a&gt;, &lt;a class="wiki_link" href="/122edo"&gt;122&lt;/a&gt;, &lt;a class="wiki_link" href="/213edo"&gt;213&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Tritonic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h2&gt;
@@ Line 399: / Line 399: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 4 -3 -3 17|, &amp;lt;0 -5 11 12 -28|]&lt;br /&gt;
-EDOs: 29, 31, 60, 91, 122, 153&lt;br /&gt;
+EDOs: 29, 31, 60, 91, 122, &lt;a class="wiki_link" href="/153edo"&gt;153&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Septimin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Septimin&lt;/h1&gt;
@@ Line 408: / Line 408: @@
 Map: [&amp;lt;1 4 1 5|, &amp;lt;0 -11 6 -10|]&lt;br /&gt;
 Wedgie: &amp;lt;&amp;lt;11 -6 10 -35 -15 40||&lt;br /&gt;
-EDOs: 9, 32, 41, 91, 132&lt;br /&gt;
+EDOs: 9, &lt;a class="wiki_link" href="/32edo"&gt;32&lt;/a&gt;, 41, 91, &lt;a class="wiki_link" href="/132edo"&gt;132&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Septimin-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;11-limit&lt;/h2&gt;