Archytas clan: Difference between revisions

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<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>2012-05-~~02 15~~:01:08 UTC</tt>.<br>

: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-05-16 13:46:08 UTC</tt>.<br>

: The original revision id was <tt>~~328850770~~</tt>.<br>

: The original revision id was <tt>336046186</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]]

The //archytas clan// tempers out the [[http://en.wikipedia.org/wiki/Septimal_comma|Archytas comma]], 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of [[22edo]]. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under [[diaschismic family]], dominant under [[meantone family]], augene under [[augmented family]] and porcupine under [[porcupine family]]. The rest are considered below.

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Badness: 0.0256

==11-limit==

Commas: 28/27, 49/48, 55/54

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Badness: 0.0246

==13-limit==

Commas: 28/27, 40/39, 49/48, 55/54

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Badness: 0.0205

==Farrier==

Commas: 28/27, 49/48, 77/75

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Badness: 0.0292

==Ferrum==

Commas: 28/27, 35/33, 49/48

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Badness: 0.0328

===13-limit===

Commas: 55/54, 64/63, 65/63, 364/363

POTE generator: ~3/2 = 708.703

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Badness: 0.3585

==7-limit==

Commas: 64/63, 686/675

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Music: [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3|Beatles Improv]] by Herman Miller

==11-limit==

Commas: 64/63, 100/99, 686/675

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Badness: 0.0456

==13-limit==

Commas: 64/63, 91/90, 100/99, 169/168

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Badness: 0.0302

==Ringo==

Commas: 56/55, 64/63, 540/539

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Badness: 0.0329

===13-limit===

Commas: 56/55, 64/63, 78/77, 91/90

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Badness: 0.0566

==11-limit==

Commas: 45/44, 64/63, 99/98

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Commas: 64/63, 3125/3087

[[POTE tuning|POTE generator]]: 98.153

[[POTE tuning|POTE generator]]: ~16/15 = 98.153

Map: [<1 2 2 2|, <0 -5 4 10|]

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Badness: 0.0623

==11-limit==

Commas: 64/63, 100/99, 1375/1372

POTE generator: ~16/15 = 98.019

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Badness: 0.0408

==13-limit==

Commas: 64/63 100/99 196/195 275/273

POTE generator: ~16/15 = 97.910

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Badness: 0.0309

=Fervor=

Comma: 67108864/61509375

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Badness: 0.8526

==7-limit==

Commas: 64/63, 9604/9375

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Badness: 0.1085

==11-limit==

Commas: 56/55, 64/63, 1350/1331

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Badness: 0.0521

==13-limit==

Commas: 56/55, 64/63, 78/77, 507/500

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Badness: 0.0322

==Quasisoup==

Commas: 55/54, 64/63, 2430/2401

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Badness: 0.0835

=Progress=

Comma: 32768/30375

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Badness: 0.2461

==7-limit==

Commas: 64/63, 392/375

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Badness: 0.0664

==11-limit==

Commas: 56/55, 64/63, 77/75

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Badness: 0.0310

==13-limit==

Commas: 56/55, 64/63, 66/65, 77/75

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Badness: 0.0262

==Progressive==

Commas: 26/25, 56/55, 64/63, 77/75

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Map: [<1 0 5 6 4 9|, <0 3 -5 -6 -1 -10|]

EDOs: 15f, 17c, 32c, 49c

Badness: 0.0327

Badness: 0.0327</pre></div>

</pre></div>

<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>Archytas clan</title></head><body><a href="#Mother">Mother</a> | <a href="#Blacksmith">Blacksmith</a> | <a href="#Superpyth">Superpyth</a> | <a href="#Beatles">Beatles</a> | <a href="#Schism">Schism</a> | <a href="#Passion">Passion</a> | <a href="#Fervor">Fervor</a> | <a href="#Quasisuper">Quasisuper</a> | <a href="#Progress">Progress</a>

~~<br />~~

The <em>archytas clan</em> tempers out the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow">Archytas comma</a>, 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of <a class="wiki_link" href="/22edo">22edo</a>. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under <a class="wiki_link" href="/diaschismic%20family">diaschismic family</a>, dominant under <a class="wiki_link" href="/meantone%20family">meantone family</a>, augene under <a class="wiki_link" href="/augmented%20family">augmented family</a> and porcupine under <a class="wiki_link" href="/porcupine%20family">porcupine family</a>. The rest are considered below.<br />

The <em>archytas clan</em> tempers out the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow">Archytas comma</a>, 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of <a class="wiki_link" href="/22edo">22edo</a>. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under <a class="wiki_link" href="/diaschismic%20family">diaschismic family</a>, dominant under <a class="wiki_link" href="/meantone%20family">meantone family</a>, augene under <a class="wiki_link" href="/augmented%20family">augmented family</a> and porcupine under <a class="wiki_link" href="/porcupine%20family">porcupine family</a>. The rest are considered below.<br />

<br />

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

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<br />

<h2 id="toc2"><a name="Blacksmith-11-limit"></a>11-limit</h2>

Commas: 28/27, 49/48, 55/54<br />

<br />

POTE generator: ~5/4 = 394.948<br />

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<br />

<h2 id="toc3"><a name="Blacksmith-13-limit"></a>13-limit</h2>

Commas: 28/27, 40/39, 49/48, 55/54<br />

<br />

POTE generator: ~5/4 = 391.0367<br />

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<br />

<h2 id="toc4"><a name="Blacksmith-Farrier"></a>Farrier</h2>

Commas: 28/27, 49/48, 77/75<br />

<br />

POTE generator: ~5/4 = 398.070<br />

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<br />

<h2 id="toc5"><a name="Blacksmith-Ferrum"></a>Ferrum</h2>

Commas: 28/27, 35/33, 49/48<br />

<br />

POTE generator: ~5/4 = 374.763<br />

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<br />

<h3 id="toc10"><a name="Superpyth-Suprapyth-13-limit"></a>13-limit</h3>

Commas: 55/54, 64/63, 65/63, 364/363 <br />

Commas: 55/54, 64/63, 65/63, 364/363<br />

<br />

POTE generator: ~3/2 = 708.703<br />

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<br />

<h2 id="toc12"><a name="Beatles-7-limit"></a>7-limit</h2>

Commas: 64/63, 686/675<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~49/40 = 355.904<br />

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<br />

<h2 id="toc13"><a name="Beatles-11-limit"></a>11-limit</h2>

Commas: 64/63, 100/99, 686/675<br />

<br />

POTE generator: ~49/40 = 356.140<br />

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<br />

<h2 id="toc14"><a name="Beatles-13-limit"></a>13-limit</h2>

Commas: 64/63, 91/90, 100/99, 169/168<br />

<br />

POTE generator: ~16/13 = 356.229<br />

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<br />

<h2 id="toc15"><a name="Beatles-Ringo"></a>Ringo</h2>

Commas: 56/55, 64/63, 540/539<br />

<br />

POTE generator: ~11/9 = 355.419<br />

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<br />

<h3 id="toc16"><a name="Beatles-Ringo-13-limit"></a>13-limit</h3>

Commas: 56/55, 64/63, 78/77, 91/90<br />

<br />

POTE generator: ~11/9 = 355.456<br />

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<br />

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

Commas: 45/44, 64/63, 99/98<br />

<br />

POTE generator ~3/2 = 702.136<br />

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Commas: 64/63, 3125/3087<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 98.153<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~16/15 = 98.153<br />

<br />

Map: [&lt;1 2 2 2|, &lt;0 -5 4 10|]<br />

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<br />

<h2 id="toc20"><a name="Passion-11-limit"></a>11-limit</h2>

Commas: 64/63, 100/99, 1375/1372 <br />

Commas: 64/63, 100/99, 1375/1372<br />

<br />

POTE generator: ~16/15 = 98.019<br />

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<br />

<h2 id="toc21"><a name="Passion-13-limit"></a>13-limit</h2>

Commas: 64/63 100/99 196/195 275/273 <br />

Commas: 64/63 100/99 196/195 275/273<br />

<br />

POTE generator: ~16/15 = 97.910<br />

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<br />

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

Comma: 67108864/61509375<br />

<br />

POTE generator: ~64/45 = 577.705<br />

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<br />

<h2 id="toc23"><a name="Fervor-7-limit"></a>7-limit</h2>

Commas: 64/63, 9604/9375<br />

<br />

POTE generator: ~7/5 = 577.777<br />

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<br />

<h2 id="toc24"><a name="Fervor-11-limit"></a>11-limit</h2>

Commas: 56/55, 64/63, 1350/1331<br />

<br />

POTE generator: ~7/5 = 577.850<br />

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<br />

<h2 id="toc25"><a name="Fervor-13-limit"></a>13-limit</h2>

Commas: 56/55, 64/63, 78/77, 507/500<br />

<br />

POTE generator: ~7/5 = 578.060<br />

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<br />

<h2 id="toc28"><a name="Quasisuper-Quasisoup"></a>Quasisoup</h2>

Commas: 55/54, 64/63, 2430/2401<br />

<br />

POTE generator: ~3/2 = 709.021<br />

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<br />

<h1 id="toc29"><a name="Progress"></a>Progress</h1>

Comma: 32768/30375<br />

<br />

POTE generator: ~64/45 = 561.264<br />

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<br />

<h2 id="toc30"><a name="Progress-7-limit"></a>7-limit</h2>

Commas: 64/63, 392/375<br />

<br />

POTE generator: ~7/5 = 562.122<br />

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<br />

<h2 id="toc31"><a name="Progress-11-limit"></a>11-limit</h2>

Commas: 56/55, 64/63, 77/75<br />

<br />

POTE generator: ~7/5 = 562.085<br />

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<br />

<h2 id="toc32"><a name="Progress-13-limit"></a>13-limit</h2>

Commas: 56/55, 64/63, 66/65, 77/75<br />

<br />

POTE generator: ~7/5 = 562.365<br />

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<br />

<h2 id="toc33"><a name="Progress-Progressive"></a>Progressive</h2>

Commas: 26/25, 56/55, 64/63, 77/75<br />

<br />

POTE generator: ~7/5 = 563.239<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>2012-05-02 15:01:08 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-05-16 13:46:08 UTC</tt>.<br>
-: The original revision id was <tt>328850770</tt>.<br>
+: The original revision id was <tt>336046186</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]]
 The //archytas clan// tempers out the [[http://en.wikipedia.org/wiki/Septimal_comma|Archytas comma]], 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of [[22edo]]. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under [[diaschismic family]], dominant under [[meantone family]], augene under [[augmented family]] and porcupine under [[porcupine family]]. The rest are considered below.
@@ Line 30: / Line 29: @@
 Badness: 0.0256
 ==11-limit==
 Commas: 28/27, 49/48, 55/54
@@ Line 39: / Line 38: @@
 Badness: 0.0246
 ==13-limit==
 Commas: 28/27, 40/39, 49/48, 55/54
@@ Line 48: / Line 47: @@
 Badness: 0.0205
 ==Farrier==
 Commas: 28/27, 49/48, 77/75
@@ Line 57: / Line 56: @@
 Badness: 0.0292
 ==Ferrum==
 Commas: 28/27, 35/33, 49/48
@@ Line 109: / Line 108: @@
 Badness: 0.0328
 ===13-limit===
 Commas: 55/54, 64/63, 65/63, 364/363
 POTE generator: ~3/2 = 708.703
@@ Line 127: / Line 126: @@
 Badness: 0.3585
 ==7-limit==
 Commas: 64/63, 686/675
@@ Line 139: / Line 138: @@
 Music: [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3|Beatles Improv]] by Herman Miller
 ==11-limit==
 Commas: 64/63, 100/99, 686/675
@@ Line 148: / Line 147: @@
 Badness: 0.0456
 ==13-limit==
 Commas: 64/63, 91/90, 100/99, 169/168
@@ Line 157: / Line 156: @@
 Badness: 0.0302
 ==Ringo==
 Commas: 56/55, 64/63, 540/539
@@ Line 166: / Line 165: @@
 Badness: 0.0329
 ===13-limit===
 Commas: 56/55, 64/63, 78/77, 91/90
@@ Line 185: / Line 184: @@
 Badness: 0.0566
 ==11-limit==
 Commas: 45/44, 64/63, 99/98
@@ Line 197: / Line 196: @@
 Commas: 64/63, 3125/3087
-[[POTE tuning|POTE generator]]: 98.153
+[[POTE tuning|POTE generator]]: ~16/15 = 98.153
 Map: [&lt;1 2 2 2|, &lt;0 -5 4 10|]
@@ Line 205: / Line 204: @@
 Badness: 0.0623
 ==11-limit==
 Commas: 64/63, 100/99, 1375/1372
 POTE generator: ~16/15 = 98.019
@@ Line 214: / Line 213: @@
 Badness: 0.0408
 ==13-limit==
 Commas: 64/63 100/99 196/195 275/273
 POTE generator: ~16/15 = 97.910
@@ Line 223: / Line 222: @@
 Badness: 0.0309
 =Fervor=
 Comma: 67108864/61509375
@@ Line 232: / Line 231: @@
 Badness: 0.8526
 ==7-limit==
 Commas: 64/63, 9604/9375
@@ Line 242: / Line 241: @@
 Badness: 0.1085
 ==11-limit==
 Commas: 56/55, 64/63, 1350/1331
@@ Line 251: / Line 250: @@
 Badness: 0.0521
 ==13-limit==
 Commas: 56/55, 64/63, 78/77, 507/500
@@ Line 281: / Line 280: @@
 Badness: 0.0322
 ==Quasisoup==
 Commas: 55/54, 64/63, 2430/2401
@@ Line 290: / Line 289: @@
 Badness: 0.0835
 =Progress=
 Comma: 32768/30375
@@ Line 299: / Line 298: @@
 Badness: 0.2461
 ==7-limit==
 Commas: 64/63, 392/375
@@ Line 309: / Line 308: @@
 Badness: 0.0664
 ==11-limit==
 Commas: 56/55, 64/63, 77/75
@@ Line 318: / Line 317: @@
 Badness: 0.0310
 ==13-limit==
 Commas: 56/55, 64/63, 66/65, 77/75
@@ Line 327: / Line 326: @@
 Badness: 0.0262
 ==Progressive==
 Commas: 26/25, 56/55, 64/63, 77/75
@@ Line 334: / Line 333: @@
 Map: [&lt;1 0 5 6 4 9|, &lt;0 3 -5 -6 -1 -10|]
 EDOs: 15f, 17c, 32c, 49c
-Badness: 0.0327
+Badness: 0.0327</pre></div>
-</pre></div>
 <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;Archytas clan&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:68:&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:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;a href="#Mother"&gt;Mother&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt; | &lt;a href="#Blacksmith"&gt;Blacksmith&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;!-- 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="#Superpyth"&gt;Superpyth&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&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;!-- ws:start:WikiTextTocRule:80: --&gt; | &lt;a href="#Beatles"&gt;Beatles&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt; | &lt;a href="#Schism"&gt;Schism&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt; | &lt;a href="#Passion"&gt;Passion&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt; | &lt;a href="#Fervor"&gt;Fervor&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt; | &lt;a href="#Quasisuper"&gt;Quasisuper&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt; | &lt;a href="#Progress"&gt;Progress&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt;&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:103 --&gt;The &lt;em&gt;archytas clan&lt;/em&gt; tempers out the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow"&gt;Archytas comma&lt;/a&gt;, 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under &lt;a class="wiki_link" href="/diaschismic%20family"&gt;diaschismic family&lt;/a&gt;, dominant under &lt;a class="wiki_link" href="/meantone%20family"&gt;meantone family&lt;/a&gt;, augene under &lt;a class="wiki_link" href="/augmented%20family"&gt;augmented family&lt;/a&gt; and porcupine under &lt;a class="wiki_link" href="/porcupine%20family"&gt;porcupine family&lt;/a&gt;. The rest are considered below.&lt;br /&gt;
-The &lt;em&gt;archytas clan&lt;/em&gt; tempers out the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow"&gt;Archytas comma&lt;/a&gt;, 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under &lt;a class="wiki_link" href="/diaschismic%20family"&gt;diaschismic family&lt;/a&gt;, dominant under &lt;a class="wiki_link" href="/meantone%20family"&gt;meantone family&lt;/a&gt;, augene under &lt;a class="wiki_link" href="/augmented%20family"&gt;augmented family&lt;/a&gt; and porcupine under &lt;a class="wiki_link" href="/porcupine%20family"&gt;porcupine family&lt;/a&gt;. The rest are considered below.&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="Mother"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Mother&lt;/h1&gt;
@@ Line 362: / Line 359: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Blacksmith-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
-Commas: 28/27, 49/48, 55/54&lt;br /&gt;
+ Commas: 28/27, 49/48, 55/54&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 394.948&lt;br /&gt;
@@ Line 371: / Line 368: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Blacksmith-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
-Commas: 28/27, 40/39, 49/48, 55/54&lt;br /&gt;
+ Commas: 28/27, 40/39, 49/48, 55/54&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 391.0367&lt;br /&gt;
@@ Line 380: / Line 377: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Blacksmith-Farrier"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Farrier&lt;/h2&gt;
-Commas: 28/27, 49/48, 77/75&lt;br /&gt;
+ Commas: 28/27, 49/48, 77/75&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 398.070&lt;br /&gt;
@@ Line 389: / Line 386: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Blacksmith-Ferrum"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Ferrum&lt;/h2&gt;
-Commas: 28/27, 35/33, 49/48&lt;br /&gt;
+ Commas: 28/27, 35/33, 49/48&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5/4 = 374.763&lt;br /&gt;
@@ Line 441: / Line 438: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Superpyth-Suprapyth-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h3&gt;
-Commas: 55/54, 64/63, 65/63, 364/363 &lt;br /&gt;
+ Commas: 55/54, 64/63, 65/63, 364/363&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~3/2 = 708.703&lt;br /&gt;
@@ Line 459: / Line 456: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Beatles-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;7-limit&lt;/h2&gt;
-Commas: 64/63, 686/675&lt;br /&gt;
+ Commas: 64/63, 686/675&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~49/40 = 355.904&lt;br /&gt;
@@ Line 471: / Line 468: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Beatles-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;11-limit&lt;/h2&gt;
-Commas: 64/63, 100/99, 686/675&lt;br /&gt;
+ Commas: 64/63, 100/99, 686/675&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~49/40 = 356.140&lt;br /&gt;
@@ Line 480: / Line 477: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Beatles-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;13-limit&lt;/h2&gt;
-Commas: 64/63, 91/90, 100/99, 169/168&lt;br /&gt;
+ Commas: 64/63, 91/90, 100/99, 169/168&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~16/13 = 356.229&lt;br /&gt;
@@ Line 489: / Line 486: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Beatles-Ringo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Ringo&lt;/h2&gt;
-Commas: 56/55, 64/63, 540/539&lt;br /&gt;
+ Commas: 56/55, 64/63, 540/539&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~11/9 = 355.419&lt;br /&gt;
@@ Line 498: / Line 495: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Beatles-Ringo-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;13-limit&lt;/h3&gt;
-Commas: 56/55, 64/63, 78/77, 91/90&lt;br /&gt;
+ Commas: 56/55, 64/63, 78/77, 91/90&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~11/9 = 355.456&lt;br /&gt;
@@ Line 517: / Line 514: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Schism-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;11-limit&lt;/h2&gt;
-Commas: 45/44, 64/63, 99/98&lt;br /&gt;
+ Commas: 45/44, 64/63, 99/98&lt;br /&gt;
 &lt;br /&gt;
 POTE generator ~3/2 = 702.136&lt;br /&gt;
@@ Line 528: / Line 525: @@
   Commas: 64/63, 3125/3087&lt;br /&gt;
 &lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 98.153&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~16/15 = 98.153&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;1 2 2 2|, &amp;lt;0 -5 4 10|]&lt;br /&gt;
@@ Line 537: / Line 534: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Passion-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
-Commas: 64/63, 100/99, 1375/1372 &lt;br /&gt;
+ Commas: 64/63, 100/99, 1375/1372&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~16/15 = 98.019&lt;br /&gt;
@@ Line 546: / Line 543: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Passion-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;13-limit&lt;/h2&gt;
-Commas: 64/63 100/99 196/195 275/273 &lt;br /&gt;
+ Commas: 64/63 100/99 196/195 275/273&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~16/15 = 97.910&lt;br /&gt;
@@ Line 555: / Line 552: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Fervor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Fervor&lt;/h1&gt;
-Comma: 67108864/61509375&lt;br /&gt;
+ Comma: 67108864/61509375&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~64/45 = 577.705&lt;br /&gt;
@@ Line 564: / Line 561: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Fervor-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;7-limit&lt;/h2&gt;
-Commas: 64/63, 9604/9375&lt;br /&gt;
+ Commas: 64/63, 9604/9375&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~7/5 = 577.777&lt;br /&gt;
@@ Line 574: / Line 571: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Fervor-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;11-limit&lt;/h2&gt;
-Commas: 56/55, 64/63, 1350/1331&lt;br /&gt;
+ Commas: 56/55, 64/63, 1350/1331&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~7/5 = 577.850&lt;br /&gt;
@@ Line 583: / Line 580: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Fervor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;13-limit&lt;/h2&gt;
-Commas: 56/55, 64/63, 78/77, 507/500&lt;br /&gt;
+ Commas: 56/55, 64/63, 78/77, 507/500&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~7/5 = 578.060&lt;br /&gt;
@@ Line 613: / Line 610: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Quasisuper-Quasisoup"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Quasisoup&lt;/h2&gt;
-Commas: 55/54, 64/63, 2430/2401&lt;br /&gt;
+ Commas: 55/54, 64/63, 2430/2401&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~3/2 = 709.021&lt;br /&gt;
@@ Line 622: / Line 619: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc29"&gt;&lt;a name="Progress"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Progress&lt;/h1&gt;
-Comma: 32768/30375&lt;br /&gt;
+ Comma: 32768/30375&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~64/45 = 561.264&lt;br /&gt;
@@ Line 631: / Line 628: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Progress-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;7-limit&lt;/h2&gt;
-Commas: 64/63, 392/375&lt;br /&gt;
+ Commas: 64/63, 392/375&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~7/5 = 562.122&lt;br /&gt;
@@ Line 641: / Line 638: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Progress-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;11-limit&lt;/h2&gt;
-Commas: 56/55, 64/63, 77/75&lt;br /&gt;
+ Commas: 56/55, 64/63, 77/75&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~7/5 = 562.085&lt;br /&gt;
@@ Line 650: / Line 647: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc32"&gt;&lt;a name="Progress-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;13-limit&lt;/h2&gt;
-Commas: 56/55, 64/63, 66/65, 77/75&lt;br /&gt;
+ Commas: 56/55, 64/63, 66/65, 77/75&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~7/5 = 562.365&lt;br /&gt;
@@ Line 659: / Line 656: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Progress-Progressive"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;Progressive&lt;/h2&gt;
-Commas: 26/25, 56/55, 64/63, 77/75&lt;br /&gt;
+ Commas: 26/25, 56/55, 64/63, 77/75&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~7/5 = 563.239&lt;br /&gt;