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>2011-03-~~26 17~~:22:44 UTC</tt>.<br>

: This revision was by author [[User:lobawad|lobawad]] and made on <tt>2011-04-13 04:24:00 UTC</tt>.<br>

: The original revision id was <tt>~~214249270~~</tt>.<br>

: The original revision id was <tt>219787948</tt>.<br>

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

Since (5/4)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess ~~5/4-~~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.

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

Line 21:

Line 20:

EDOs: 9, 10, 19, 86

==11-limit==

Commas: 45/44, 49/48, 56/55

Line 29:

Line 28:

EDOs: 9, 10, 19

==13-limit==

Commas: 45/44, 49/48, 56/55, 78/77

Line 37:

Line 36:

EDOs: 9, 10, 19

=Negric=

Commas: 33/32, 49/48, 77/75

Line 46:

Line 45:

Badness: 0.0306

==13-limit==

Commas: 33/32, 49/48, 65/64, 91/90

Line 55:

Line 54:

Badness: 0.0202

=Wizard=

Commas: 225/224, 118098/117649

Line 65:

Line 64:

Badness: 0.0408

==11-limit==

Commas: 225/224, 385/384, 4000/3993

Line 74:

Line 73:

Badness: 0.0185

==Lizard==

Commas: 225/224, 351/350, 364/363, 385/384

Line 83:

Line 82:

Badness: 0.0218

===17-limit===

Commas: 221/220, 273/272, 289/288, 351/350, 375/374

Line 92:

Line 91:

Badness: 0.0145

===19-limit===

Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342

Line 101:

Line 100:

Badness: 0.0157

==Gizzard==

Commas: 225/224, 385/384, 325/324, 1573/1568

Line 110:

Line 109:

Badness: 0.0203

===17-limit===

Commas: 225/224, 289/288, 325/324, 375/374, 385/384

Line 128:

Line 127:

Badness: 0.0148

=Tritonic=

Commas: 225/224, 50421/50000

Line 137:

Line 136:

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

==11-limit==

Commas: 225/224, 385/384, 27783/27500

Line 145:

Line 144:

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

=Septimin=

Commas: 225/224, 84035/82944

Line 154:

Line 153:

EDOs: 9, 32, 41, 91, 132

==11-limit==

Commas: 225/224, 385/384, 2401/2376

Line 162:

Line 161:

EDOs: 9, 32, 41, 91

==13-limit==

Commas: 105/104, 144/143, 196/195, 245/242

Line 170:

Line 169:

EDOs: 9, 41, 91

=Slender=

Commas: 225/225, 589824/588245

Line 180:

Line 179:

Badness: 0.0569

==11-limit==

Commas: 225/224, 385/384, 1331/1323

Line 189:

Line 188:

Badness: 25.342

==13-limit==

Commas: 225/224, 275/273, 385/384, 1331/1323

Line 198:

Line 197:

Badness: 25.913

=Triton=

Commas: 225/224, 1029/1000

Line 207:

Line 206:

EDOs: 19, 135, 289

=Marvo=

Commas: 225/224, 78125000/78121827

Line 216:

Line 215:

EDOs: 65, 72

==11-limit==

Commas: 225/224, 243/242, 4000/3993

Line 225:

Line 224:

<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"><html><head><title>Marvel temperaments</title></head><body><a href="#Negri">Negri</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 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 />

<br />

Since (5/4)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess ~~5/4-~~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 />

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 />

<br />

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

Line 240:

Line 238:

<br />

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

Commas: 45/44, 49/48, 56/55<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 126.474<br />

Line 248:

Line 246:

<br />

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

Commas: 45/44, 49/48, 56/55, 78/77<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 126.431<br />

Line 256:

Line 254:

<br />

<h1 id="toc3"><a name="Negric"></a>Negric</h1>

Commas: 33/32, 49/48, 77/75<br />

<br />

POTE generator: ~15/14 = 127.039<br />

Line 265:

Line 263:

<br />

<h2 id="toc4"><a name="Negric-13-limit"></a>13-limit</h2>

Commas: 33/32, 49/48, 65/64, 91/90<br />

<br />

POTE generator: ~15/14 = 127.039<br />

Line 274:

Line 272:

<br />

<h1 id="toc5"><a name="Wizard"></a>Wizard</h1>

Commas: 225/224, 118098/117649<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.256<br />

Line 284:

Line 282:

<br />

<h2 id="toc6"><a name="Wizard-11-limit"></a>11-limit</h2>

Commas: 225/224, 385/384, 4000/3993<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.232<br />

Line 293:

Line 291:

<br />

<h2 id="toc7"><a name="Wizard-Lizard"></a>Lizard</h2>

Commas: 225/224, 351/350, 364/363, 385/384<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.389<br />

Line 302:

Line 300:

<br />

<h3 id="toc8"><a name="Wizard-Lizard-17-limit"></a>17-limit</h3>

Commas: 221/220, 273/272, 289/288, 351/350, 375/374<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.381<br />

Line 311:

Line 309:

<br />

<h3 id="toc9"><a name="Wizard-Lizard-19-limit"></a>19-limit</h3>

Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~5/4 = 383.477<br />

Line 320:

Line 318:

<br />

<h2 id="toc10"><a name="Wizard-Gizzard"></a>Gizzard</h2>

Commas: 225/224, 385/384, 325/324, 1573/1568<br />

<br />

POTE generator: ~5/4 = 383.170<br />

Line 329:

Line 327:

<br />

<h3 id="toc11"><a name="Wizard-Gizzard-17-limit"></a>17-limit</h3>

Commas: 225/224, 289/288, 325/324, 375/374, 385/384<br />

<br />

POTE generator: ~5/4 = 383.175<br />

Line 347:

Line 345:

<br />

<h1 id="toc13"><a name="Tritonic"></a>Tritonic</h1>

Commas: 225/224, 50421/50000<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 580.286<br />

Line 356:

Line 354:

<br />

<h2 id="toc14"><a name="Tritonic-11-limit"></a>11-limit</h2>

Commas: 225/224, 385/384, 27783/27500<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 580.389<br />

Line 364:

Line 362:

<br />

<h1 id="toc15"><a name="Septimin"></a>Septimin</h1>

Commas: 225/224, 84035/82944<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.632<br />

Line 373:

Line 371:

<br />

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

Commas: 225/224, 385/384, 2401/2376<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.634<br />

Line 381:

Line 379:

<br />

<h2 id="toc17"><a name="Septimin-13-limit"></a>13-limit</h2>

Commas: 105/104, 144/143, 196/195, 245/242<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.700<br />

Line 389:

Line 387:

<br />

<h1 id="toc18"><a name="Slender"></a>Slender</h1>

Commas: 225/225, 589824/588245<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~49/48 = 38.413<br />

Line 399:

Line 397:

<br />

<h2 id="toc19"><a name="Slender-11-limit"></a>11-limit</h2>

Commas: 225/224, 385/384, 1331/1323<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~49/48 = 38.387<br />

Line 408:

Line 406:

<br />

<h2 id="toc20"><a name="Slender-13-limit"></a>13-limit</h2>

Commas: 225/224, 275/273, 385/384, 1331/1323<br />

<br />

POTE generator: ~49/48 = 38.314<br />

Line 417:

Line 415:

<br />

<h1 id="toc21"><a name="Triton"></a>Triton</h1>

Commas: 225/224, 1029/1000<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 568.865<br />

Line 426:

Line 424:

<br />

<h1 id="toc22"><a name="Marvo"></a>Marvo</h1>

Commas: 225/224, 78125000/78121827<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: (~27/20) 516.694<br />

Line 435:

Line 433:

<br />

<h2 id="toc23"><a name="Marvo-11-limit"></a>11-limit</h2>

Commas: 225/224, 243/242, 4000/3993<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 516.699<br />

@@ 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>2011-03-26 17:22:44 UTC</tt>.<br>
+: This revision was by author [[User:lobawad|lobawad]] and made on <tt>2011-04-13 04:24:00 UTC</tt>.<br>
-: The original revision id was <tt>214249270</tt>.<br>
+: The original revision id was <tt>219787948</tt>.<br>
 : The revision comment was: <tt></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.
-Since (5/4)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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.
+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
@@ Line 21: / Line 20: @@
 EDOs: 9, 10, 19, 86
 ==11-limit==
 Commas: 45/44, 49/48, 56/55
@@ Line 29: / Line 28: @@
 EDOs: 9, 10, 19
 ==13-limit==
 Commas: 45/44, 49/48, 56/55, 78/77
@@ Line 37: / Line 36: @@
 EDOs: 9, 10, 19
 =Negric=
 Commas: 33/32, 49/48, 77/75
@@ Line 46: / Line 45: @@
 Badness: 0.0306
 ==13-limit==
 Commas: 33/32, 49/48, 65/64, 91/90
@@ Line 55: / Line 54: @@
 Badness: 0.0202
 =Wizard=
 Commas: 225/224, 118098/117649
@@ Line 65: / Line 64: @@
 Badness: 0.0408
 ==11-limit==
 Commas: 225/224, 385/384, 4000/3993
@@ Line 74: / Line 73: @@
 Badness: 0.0185
 ==Lizard==
 Commas: 225/224, 351/350, 364/363, 385/384
@@ Line 83: / Line 82: @@
 Badness: 0.0218
 ===17-limit===
 Commas: 221/220, 273/272, 289/288, 351/350, 375/374
@@ Line 92: / Line 91: @@
 Badness: 0.0145
 ===19-limit===
 Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
@@ Line 101: / Line 100: @@
 Badness: 0.0157
 ==Gizzard==
 Commas: 225/224, 385/384, 325/324, 1573/1568
@@ Line 110: / Line 109: @@
 Badness: 0.0203
 ===17-limit===
 Commas: 225/224, 289/288, 325/324, 375/374, 385/384
@@ Line 128: / Line 127: @@
 Badness: 0.0148
 =Tritonic=
 Commas: 225/224, 50421/50000
@@ Line 137: / Line 136: @@
 EDOs: 29, 31, 60, 91, 122, 213
 ==11-limit==
 Commas: 225/224, 385/384, 27783/27500
@@ Line 145: / Line 144: @@
 EDOs: 29, 31, 60, 91, 122, 153
 =Septimin=
 Commas: 225/224, 84035/82944
@@ Line 154: / Line 153: @@
 EDOs: 9, 32, 41, 91, 132
 ==11-limit==
 Commas: 225/224, 385/384, 2401/2376
@@ Line 162: / Line 161: @@
 EDOs: 9, 32, 41, 91
 ==13-limit==
 Commas: 105/104, 144/143, 196/195, 245/242
@@ Line 170: / Line 169: @@
 EDOs: 9, 41, 91
 =Slender=
 Commas: 225/225, 589824/588245
@@ Line 180: / Line 179: @@
 Badness: 0.0569
 ==11-limit==
 Commas: 225/224, 385/384, 1331/1323
@@ Line 189: / Line 188: @@
 Badness: 25.342
 ==13-limit==
 Commas: 225/224, 275/273, 385/384, 1331/1323
@@ Line 198: / Line 197: @@
 Badness: 25.913
 =Triton=
 Commas: 225/224, 1029/1000
@@ Line 207: / Line 206: @@
 EDOs: 19, 135, 289
 =Marvo=
 Commas: 225/224, 78125000/78121827
@@ Line 216: / Line 215: @@
 EDOs: 65, 72
 ==11-limit==
 Commas: 225/224, 243/242, 4000/3993
@@ Line 225: / Line 224: @@
 <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;Marvel temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:48:&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:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;a href="#Negri"&gt;Negri&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt; | &lt;a href="#Negric"&gt;Negric&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt; | &lt;a href="#Wizard"&gt;Wizard&lt;/a&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;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&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;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Tritonic"&gt;Tritonic&lt;/a&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;a href="#Septimin"&gt;Septimin&lt;/a&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;a href="#Slender"&gt;Slender&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&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="#Triton"&gt;Triton&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt; | &lt;a href="#Marvo"&gt;Marvo&lt;/a&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;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:73 --&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 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;
 &lt;br /&gt;
-Since (5/4)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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;
+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;
+ Commas: 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;
@@ Line 240: / Line 238: @@
 &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;
-Commas: 45/44, 49/48, 56/55&lt;br /&gt;
+ Commas: 45/44, 49/48, 56/55&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 126.474&lt;br /&gt;
@@ Line 248: / Line 246: @@
 &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;
-Commas: 45/44, 49/48, 56/55, 78/77&lt;br /&gt;
+ Commas: 45/44, 49/48, 56/55, 78/77&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 126.431&lt;br /&gt;
@@ Line 256: / Line 254: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Negric"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Negric&lt;/h1&gt;
-Commas: 33/32, 49/48, 77/75&lt;br /&gt;
+ Commas: 33/32, 49/48, 77/75&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~15/14 = 127.039&lt;br /&gt;
@@ Line 265: / Line 263: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Negric-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
-Commas: 33/32, 49/48, 65/64, 91/90&lt;br /&gt;
+ Commas: 33/32, 49/48, 65/64, 91/90&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~15/14 = 127.039&lt;br /&gt;
@@ Line 274: / Line 272: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Wizard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Wizard&lt;/h1&gt;
-Commas: 225/224, 118098/117649&lt;br /&gt;
+ Commas: 225/224, 118098/117649&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.256&lt;br /&gt;
@@ Line 284: / Line 282: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Wizard-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11-limit&lt;/h2&gt;
-Commas: 225/224, 385/384, 4000/3993&lt;br /&gt;
+ Commas: 225/224, 385/384, 4000/3993&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.232&lt;br /&gt;
@@ Line 293: / Line 291: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Wizard-Lizard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Lizard&lt;/h2&gt;
-Commas: 225/224, 351/350, 364/363, 385/384&lt;br /&gt;
+ Commas: 225/224, 351/350, 364/363, 385/384&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.389&lt;br /&gt;
@@ Line 302: / Line 300: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Wizard-Lizard-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;17-limit&lt;/h3&gt;
-Commas: 221/220, 273/272, 289/288, 351/350, 375/374&lt;br /&gt;
+ Commas: 221/220, 273/272, 289/288, 351/350, 375/374&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.381&lt;br /&gt;
@@ Line 311: / Line 309: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Wizard-Lizard-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;19-limit&lt;/h3&gt;
-Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342&lt;br /&gt;
+ Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~5/4 = 383.477&lt;br /&gt;
@@ Line 320: / Line 318: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Wizard-Gizzard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Gizzard&lt;/h2&gt;
-Commas: 225/224, 385/384, 325/324, 1573/1568&lt;br /&gt;
+ Commas: 225/224, 385/384, 325/324, 1573/1568&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 383.170&lt;br /&gt;
@@ Line 329: / Line 327: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="Wizard-Gizzard-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;17-limit&lt;/h3&gt;
-Commas: 225/224, 289/288, 325/324, 375/374, 385/384&lt;br /&gt;
+ Commas: 225/224, 289/288, 325/324, 375/374, 385/384&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 383.175&lt;br /&gt;
@@ Line 347: / Line 345: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Tritonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Tritonic&lt;/h1&gt;
-Commas: 225/224, 50421/50000&lt;br /&gt;
+ Commas: 225/224, 50421/50000&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 580.286&lt;br /&gt;
@@ Line 356: / Line 354: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Tritonic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11-limit&lt;/h2&gt;
-Commas: 225/224, 385/384, 27783/27500&lt;br /&gt;
+ Commas: 225/224, 385/384, 27783/27500&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 580.389&lt;br /&gt;
@@ Line 364: / Line 362: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Septimin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Septimin&lt;/h1&gt;
-Commas: 225/224, 84035/82944&lt;br /&gt;
+ Commas: 225/224, 84035/82944&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 263.632&lt;br /&gt;
@@ Line 373: / Line 371: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Septimin-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h2&gt;
-Commas: 225/224, 385/384, 2401/2376&lt;br /&gt;
+ Commas: 225/224, 385/384, 2401/2376&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 263.634&lt;br /&gt;
@@ Line 381: / Line 379: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Septimin-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;13-limit&lt;/h2&gt;
-Commas: 105/104, 144/143, 196/195, 245/242&lt;br /&gt;
+ Commas: 105/104, 144/143, 196/195, 245/242&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 263.700&lt;br /&gt;
@@ Line 389: / Line 387: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Slender"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Slender&lt;/h1&gt;
-Commas: 225/225, 589824/588245&lt;br /&gt;
+ Commas: 225/225, 589824/588245&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~49/48 = 38.413&lt;br /&gt;
@@ Line 399: / Line 397: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Slender-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
-Commas: 225/224, 385/384, 1331/1323&lt;br /&gt;
+ Commas: 225/224, 385/384, 1331/1323&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~49/48 = 38.387&lt;br /&gt;
@@ Line 408: / Line 406: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Slender-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;13-limit&lt;/h2&gt;
-Commas: 225/224, 275/273, 385/384, 1331/1323&lt;br /&gt;
+ Commas: 225/224, 275/273, 385/384, 1331/1323&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~49/48 = 38.314&lt;br /&gt;
@@ Line 417: / Line 415: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Triton"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Triton&lt;/h1&gt;
-Commas: 225/224, 1029/1000&lt;br /&gt;
+ Commas: 225/224, 1029/1000&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 568.865&lt;br /&gt;
@@ Line 426: / Line 424: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Marvo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Marvo&lt;/h1&gt;
-Commas: 225/224, 78125000/78121827&lt;br /&gt;
+ Commas: 225/224, 78125000/78121827&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: (~27/20) 516.694&lt;br /&gt;
@@ Line 435: / Line 433: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Marvo-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;11-limit&lt;/h2&gt;
-Commas: 225/224, 243/242, 4000/3993&lt;br /&gt;
+ Commas: 225/224, 243/242, 4000/3993&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 516.699&lt;br /&gt;