Kleismic family: 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>2012-06-~~04 16~~:32:02 UTC</tt>.<br>

: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-07-10 20:24:13 UTC</tt>.<br>

: The original revision id was <tt>~~342569596~~</tt>.<br>

: The original revision id was <tt>352115606</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]]

The [[5-limit]] parent comma for the **kleismic family** is 15625/15552, the kleisma. Its monzo is |-6 -5 6>, and flipping that yields <<6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This highly accurate 5-limit temperament is commonly called **Hanson**, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].

The [[5-limit]] parent comma for the **kleismic family** is 15625/15552, the kleisma. Its monzo is |-6 -5 6>, and flipping that yields <<6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called **Hanson**, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].

[[POTE tuning|POTE generator]]: 317.007

Line 19:

Line 18:

[[http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3|In Hanson11]] by [[Chris Vaisvil]]

=Seven limit children=

The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.

=Keemun=

[[Comma|Commas]]: 49/48, 126/125

Line 32:

Line 31:

[[Badness]]: 0.0274

==11-limit==

[[Comma]]s: 49/48, 56/55, 100/99

Line 41:

Line 40:

[[Badness]]: 0.0274

==13-limit==

[[Comma]]s: 49/48, 56/55, 78/77, 100/99

Line 50:

Line 49:

[[Badness]]: 0.0297

===Keema===

Commas: 49/48, 56/55, 91/90, 100/99

Line 59:

Line 58:

Badness: 0.0227

===Kumbaya===

Commas: 40/39, 49/48, 56/55, 66/65

Line 68:

Line 67:

Badness: 0.0316

==Qeema==

Commas: 45/44, 49/48, 126/125

Line 77:

Line 76:

Badness: 0.0401

===13-limit===

Commas: 45/44, 49/48, 78/77, 126/125

Line 86:

Line 85:

Badness: 0.0294

==Darjeeling==

Commas: 49/48, 55/54, 77/75

Line 95:

Line 94:

Badness: 0.0276

===13-limit Darjeeling===

Commas: 49/48, 55/54, 66/65, 77/75

Line 104:

Line 103:

Badness: 0.02144

=Catalan=

Commas: 64/63, 15625/15552

Line 114:

Line 113:

Badness: 0.0949

=Catakleismic=

[[Comma|Commas]]: 225/224, 4375/4374

Line 124:

Line 123:

[[Badness]]: 0.0215

==11-limit==

[[Comma|Commas]]: 225/224, 385/384, 4375/4374

Line 133:

Line 132:

[[Badness]]: 0.0218

==13-limit==

[[Comma|Commas]]: 169/168, 225/224, 325/324, 540/539

Line 142:

Line 141:

[[Badness]]: 0.0169

=Cataclysmic=

Commas: 99/98, 176/175, 2200/2187

Line 151:

Line 150:

Badness: 0.0400

==13-limit==

Commas: 99/98, 169/168, 176/175, 275/273

POTE generator: ~6/5 = 317.036

Map: [<1 0 1 -3 -5 0|, <0 6 5 22 32 14|]

Line 160:

Line 159:

Badness: 0.0226

=Catalytic=

Commas: 225/224, 441/440, 4375/4374

Line 169:

Line 168:

Badness: 0.0304

==13-limit==

Commas: 169/168 225/224 325/324 1716/1715

Line 178:

Line 177:

Badness: 0.0223

=Countercata=

[[Comma|Commas]]: 15625/15552, 5120/5103

Line 188:

Line 187:

[[Badness]]: 0.0521

==11-limit==

[[Comma]]s: 385/384, 2200/2187, 3388/3375

Line 197:

Line 196:

[[Badness]]: 0.0398

==13-limit==

[[Comma]]s: 325/324, 352/351, 385/384, 625/624

Line 206:

Line 205:

[[Badness]]: 0.0202

=Metakleismic=

[[Comma]]s: 15625/15552, 179200/177147

Line 216:

Line 215:

[[Badness]]: 0.1635

==11-limit==

[[Comma]]s: 896/891, 2200/2187, 14700/14641

Line 225:

Line 224:

[[Badness]]: 0.0486

==13-limit==

[[Comma]]s: 325/324, 352/351, 364/363, 625/624

Line 234:

Line 233:

[[Badness]]: 0.0244

=Hemikleismic=

Commas: 4000/3969, 6144/6125

Line 243:

Line 242:

Badness: 0.0521

==11-limit==

Commas: 121/120, 176/175, 4000/3969

Line 252:

Line 251:

Badness: 0.0380

==13-limit==

Commas: 121/120, 176/175, 275/273, 325/324

Line 261:

Line 260:

Badness: 0.0260

=Clyde=

[[Comma|Commas]]: 245/243, 3136/3125

Line 277:

Line 276:

Badness: 0.0473

==11-limit==

Commas: 245/243, 3136/3125, 385/384

Line 286:

Line 285:

Badness: 0.0474

==13-limit==

Commas: 196/195, 245/243, 385/384, 625/624

Line 295:

Line 294:

Badness: 0.0268

=Bikleismic=

Commas: 225/224, 243/242, 4375/4356

POTE generator: ~6/5 = 316.721

Map: [<2 0 2 -6 -1|, <0 6 5 22 15|]

EDOs: 72, 106, 178, 250, 322c, 394c, 466bc, 538bc, 610bc

Badness: 0.0293

==13-limit==

Commas: 169/168, 225/224, 243/242, 325/324

POTE generator: ~6/5 = 316.726

Map: [<2 0 2 -6 -1 0|, <0 6 5 22 15 14|]

EDOs: 72, 106, 322cff, 394cff, 466bcff, 538bcfff

Badness: 0.0218

=Tritikleismic=

[[Comma]]s: 15625/15552, 1029/1024

Line 323:

Line 322:

[[Badness]]: 0.0563

==11-limit==

[[Comma]]s: 385/384, 441/440, 4000/3993

Line 332:

Line 331:

[[Badness]]: 0.0193

==13-limit==

[[Comma]]s: 325/324, 364/363, 441/440, 625/624

Line 341:

Line 340:

[[Badness]]: 0.0157

=Quadritikleismic=

[[Comma]]s: 15625/15552, 2401/2400

Line 351:

Line 350:

[[Badness]]: 0.0392

==11-limit==

Commas: 385/384, 1375/1372, 6250/6237

Line 360:

Line 359:

[[Badness]]: 0.0234

==13-limit==

Commas: 325/324, 385/384, 625/624, 1573/1568

Line 369:

Line 368:

[[Badness]]: 0.0187

=Kleiboh=

Commas: 1728/1715, 3125/3087

POTE generator: ~25/21 = 294.303

Line 379:

Line 378:

Badness: 0.0765

==11-limit==

Commas: 176/175, 540/539, 3125/3087

Line 388:

Line 387:

Badness: 0.0528

==13-limit==

Commas: 176/175, 275/273, 325/324, 540/539

POTE generator: ~13/11 = 294.187

Line 397:

Line 396:

Badness: 0.0311

=Novemkleismic=

Commas: 15625/15552, 40353607/40310784

Line 407:

Line 406:

Badness: 0.1934

==11-limit==

Commas: 1375/1372, 4000/3993, 15625/15552

Line 416:

Line 415:

Badness: 0.05172

==13-limit==

Commas: 325/324, 625/624, 1375/1372, 4000/3993

Line 425:

Line 424:

Badness: 0.0391

=Sqrtphi=

Commas: 15625/15552, 16875/16807

Line 436:

Line 435:

Badness: 0.0704

==11-limit==

Commas: 540/539, 1375/1372, 4375/4356

Line 445:

Line 444:

Badness: 0.0255

==13-limit==

Commas: 325/324, 364/363, 625/624, 1375/1372

Line 454:

Line 453:

Badness: 0.0200

==17-limit==

Commas: 325/324, 364/363, 375/374, 540/539, 595/594

Line 463:

Line 462:

Badness: 0.0130

==19-limit==

Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594

Line 472:

Line 471:

Badness: 0.0147

==Scales==

[[sqrtphi17]]

[[sqrtphi23]]

[[sqrtphi49]]

==Music==

[[http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3|Prelude for Piano in Square root of Phi Tuning]] by [[Chris Vaisvil]]

[[http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3|A Fight for Phi]] by Vito Sicurella</pre></div>

Line 533:

Line 532:

<div style="margin-left: 2em;"><a href="#Sqrtphi-Music">Music</a></div>

</div>

~~<br />~~

The <a class="wiki_link" href="/5-limit">5-limit</a> parent comma for the <strong>kleismic family</strong> is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This highly accurate 5-limit temperament is commonly called <strong>Hanson</strong>, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a> and <a class="wiki_link" href="/140edo">140edo</a>.<br />

The <a class="wiki_link" href="/5-limit">5-limit</a> parent comma for the <strong>kleismic family</strong> is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called <strong>Hanson</strong>, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a> and <a class="wiki_link" href="/140edo">140edo</a>.<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.007<br />

Line 546:

Line 544:

<br />

<h1 id="toc0"><a name="Seven limit children"></a>Seven limit children</h1>

The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.<br />

<br />

<h1 id="toc1"><a name="Keemun"></a>Keemun</h1>

<a class="wiki_link" href="/Comma">Commas</a>: 49/48, 126/125<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 316.473<br />

Line 559:

Line 557:

<br />

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

<a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 56/55, 100/99<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 317.576<br />

Line 568:

Line 566:

<br />

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

<a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 56/55, 78/77, 100/99<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 316.611<br />

Line 577:

Line 575:

<br />

<h3 id="toc4"><a name="Keemun-13-limit-Keema"></a>Keema</h3>

Commas: 49/48, 56/55, 91/90, 100/99<br />

<br />

POTE generator: ~6/5 = 317.423<br />

Line 586:

Line 584:

<br />

<h3 id="toc5"><a name="Keemun-13-limit-Kumbaya"></a>Kumbaya</h3>

Commas: 40/39, 49/48, 56/55, 66/65<br />

<br />

POTE generator: ~6/5 = 318.595<br />

Line 595:

Line 593:

<br />

<h2 id="toc6"><a name="Keemun-Qeema"></a>Qeema</h2>

Commas: 45/44, 49/48, 126/125<br />

<br />

POTE generator: ~6/5 = 314.730<br />

Line 604:

Line 602:

<br />

<h3 id="toc7"><a name="Keemun-Qeema-13-limit"></a>13-limit</h3>

Commas: 45/44, 49/48, 78/77, 126/125<br />

<br />

POTE generator: ~6/5 = 315.044<br />

Line 613:

Line 611:

<br />

<h2 id="toc8"><a name="Keemun-Darjeeling"></a>Darjeeling</h2>

Commas: 49/48, 55/54, 77/75<br />

<br />

POTE generator: ~6/5 = 317.656<br />

Line 622:

Line 620:

<br />

<h3 id="toc9"><a name="Keemun-Darjeeling-13-limit Darjeeling"></a>13-limit Darjeeling</h3>

Commas: 49/48, 55/54, 66/65, 77/75<br />

<br />

POTE generator: ~6/5 = 317.298<br />

Line 631:

Line 629:

<br />

<h1 id="toc10"><a name="Catalan"></a>Catalan</h1>

Commas: 64/63, 15625/15552<br />

<br />

POTE generator: ~6/5 = 318.267<br />

Line 641:

Line 639:

<br />

<h1 id="toc11"><a name="Catakleismic"></a>Catakleismic</h1>

<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 4375/4374<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.732<br />

Line 651:

Line 649:

<br />

<h2 id="toc12"><a name="Catakleismic-11-limit"></a>11-limit</h2>

<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 385/384, 4375/4374<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.719<br />

Line 660:

Line 658:

<br />

<h2 id="toc13"><a name="Catakleismic-13-limit"></a>13-limit</h2>

<a class="wiki_link" href="/Comma">Commas</a>: 169/168, 225/224, 325/324, 540/539<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.738<br />

Line 669:

Line 667:

<br />

<h1 id="toc14"><a name="Cataclysmic"></a>Cataclysmic</h1>

Commas: 99/98, 176/175, 2200/2187<br />

<br />

POTE generator: ~6/5 = 317.042<br />

Line 678:

Line 676:

<br />

<h2 id="toc15"><a name="Cataclysmic-13-limit"></a>13-limit</h2>

Commas: 99/98, 169/168, 176/175, 275/273<br />

<br />

POTE generator: ~6/5 = 317.036<br />

<br />

Map: [&lt;1 0 1 -3 -5 0|, &lt;0 6 5 22 32 14|]<br />

Line 687:

Line 685:

<br />

<h1 id="toc16"><a name="Catalytic"></a>Catalytic</h1>

Commas: 225/224, 441/440, 4375/4374<br />

<br />

POTE generator: ~6/5 = 316.653<br />

Line 696:

Line 694:

<br />

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

Commas: 169/168 225/224 325/324 1716/1715<br />

<br />

POTE generator: ~6/5 = 316.639<br />

Line 705:

Line 703:

<br />

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

<a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 5120/5103<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.121<br />

Line 715:

Line 713:

<br />

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

<a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 2200/2187, 3388/3375<br />

<br />

POTE generator: ~6/5 = 317.162<br />

Line 724:

Line 722:

<br />

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

<a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 352/351, 385/384, 625/624<br />

<br />

POTE generator: ~6/5 = 317.162<br />

Line 733:

Line 731:

<br />

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

<a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 179200/177147<br />

<br />

POTE generator: ~6/5 = 317.314<br />

Line 743:

Line 741:

<br />

<h2 id="toc22"><a name="Metakleismic-11-limit"></a>11-limit</h2>

<a class="wiki_link" href="/Comma">Comma</a>s: 896/891, 2200/2187, 14700/14641<br />

<br />

POTE generator: ~6/5 = 317.311<br />

Line 752:

Line 750:

<br />

<h2 id="toc23"><a name="Metakleismic-13-limit"></a>13-limit</h2>

<a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 352/351, 364/363, 625/624<br />

<br />

POTE generator: ~6/5 = 317.311<br />

Line 761:

Line 759:

<br />

<h1 id="toc24"><a name="Hemikleismic"></a>Hemikleismic</h1>

Commas: 4000/3969, 6144/6125<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 158.649<br />

Line 770:

Line 768:

<br />

<h2 id="toc25"><a name="Hemikleismic-11-limit"></a>11-limit</h2>

Commas: 121/120, 176/175, 4000/3969<br />

<br />

POTE generator: ~11/10 = 158.677<br />

Line 779:

Line 777:

<br />

<h2 id="toc26"><a name="Hemikleismic-13-limit"></a>13-limit</h2>

Commas: 121/120, 176/175, 275/273, 325/324<br />

<br />

POTE generator: ~11/10 = 158.655<br />

Line 788:

Line 786:

<br />

<h1 id="toc27"><a name="Clyde"></a>Clyde</h1>

<a class="wiki_link" href="/Comma">Commas</a>: 245/243, 3136/3125<br />

<br />

7 and 9 limit minimax<br />

Line 804:

Line 802:

<br />

<h2 id="toc28"><a name="Clyde-11-limit"></a>11-limit</h2>

Commas: 245/243, 3136/3125, 385/384<br />

<br />

POTE generator: ~9/7 = 441.355<br />

Line 813:

Line 811:

<br />

<h2 id="toc29"><a name="Clyde-13-limit"></a>13-limit</h2>

Commas: 196/195, 245/243, 385/384, 625/624<br />

<br />

POTE generator: ~9/7 = 441.363<br />

Line 822:

Line 820:

<br />

<h1 id="toc30"><a name="Bikleismic"></a>Bikleismic</h1>

Commas: 225/224, 243/242, 4375/4356<br />

<br />

POTE generator: ~6/5 = 316.721<br />

<br />

Map: [&lt;2 0 2 -6 -1|, &lt;0 6 5 22 15|]<br />

EDOs: 72, 106, 178, 250, 322c, 394c, 466bc, 538bc, 610bc<br />

Badness: 0.0293<br />

<br />

<h2 id="toc31"><a name="Bikleismic-13-limit"></a>13-limit</h2>

Commas: 169/168, 225/224, 243/242, 325/324<br />

<br />

POTE generator: ~6/5 = 316.726<br />

<br />

Map: [&lt;2 0 2 -6 -1 0|, &lt;0 6 5 22 15 14|]<br />

EDOs: 72, 106, 322cff, 394cff, 466bcff, 538bcfff<br />

Badness: 0.0218<br />

<br />

<h1 id="toc32"><a name="Tritikleismic"></a>Tritikleismic</h1>

<a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 1029/1024<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.872<br />

Line 850:

Line 848:

<br />

<h2 id="toc33"><a name="Tritikleismic-11-limit"></a>11-limit</h2>

<a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 441/440, 4000/3993<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.881<br />

Line 859:

Line 857:

<br />

<h2 id="toc34"><a name="Tritikleismic-13-limit"></a>13-limit</h2>

<a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 364/363, 441/440, 625/624<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.959<br />

Line 868:

Line 866:

<br />

<h1 id="toc35"><a name="Quadritikleismic"></a>Quadritikleismic</h1>

<a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 2401/2400<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.9999<br />

Line 878:

Line 876:

<br />

<h2 id="toc36"><a name="Quadritikleismic-11-limit"></a>11-limit</h2>

Commas: 385/384, 1375/1372, 6250/6237<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.925<br />

Line 887:

Line 885:

<br />

<h2 id="toc37"><a name="Quadritikleismic-13-limit"></a>13-limit</h2>

Commas: 325/324, 385/384, 625/624, 1573/1568<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.989<br />

Line 896:

Line 894:

<br />

<h1 id="toc38"><a name="Kleiboh"></a>Kleiboh</h1>

Commas: 1728/1715, 3125/3087 <br />

Commas: 1728/1715, 3125/3087<br />

<br />

POTE generator: ~25/21 = 294.303<br />

Line 906:

Line 904:

<br />

<h2 id="toc39"><a name="Kleiboh-11-limit"></a>11-limit</h2>

Commas: 176/175, 540/539, 3125/3087<br />

<br />

POTE generator: ~25/21 = 294.181<br />

Line 915:

Line 913:

<br />

<h2 id="toc40"><a name="Kleiboh-13-limit"></a>13-limit</h2>

Commas: 176/175, 275/273, 325/324, 540/539 <br />

Commas: 176/175, 275/273, 325/324, 540/539<br />

<br />

POTE generator: ~13/11 = 294.187<br />

Line 924:

Line 922:

<br />

<h1 id="toc41"><a name="Novemkleismic"></a>Novemkleismic</h1>

Commas: 15625/15552, 40353607/40310784<br />

<br />

POTE generator: ~6/5 = 317.005<br />

Line 934:

Line 932:

<br />

<h2 id="toc42"><a name="Novemkleismic-11-limit"></a>11-limit</h2>

Commas: 1375/1372, 4000/3993, 15625/15552<br />

<br />

POTE generator: ~6/5 = 317.010<br />

Line 943:

Line 941:

<br />

<h2 id="toc43"><a name="Novemkleismic-13-limit"></a>13-limit</h2>

Commas: 325/324, 625/624, 1375/1372, 4000/3993<br />

<br />

POTE generator: ~6/5 = 317.086<br />

Line 952:

Line 950:

<br />

<h1 id="toc44"><a name="Sqrtphi"></a>Sqrtphi</h1>

Commas: 15625/15552, 16875/16807<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~125/98 = 416.603 cents<br />

Line 963:

Line 961:

<br />

<h2 id="toc45"><a name="Sqrtphi-11-limit"></a>11-limit</h2>

Commas: 540/539, 1375/1372, 4375/4356<br />

<br />

POTE generator: ~14/11 = 416.604<br />

Line 972:

Line 970:

<br />

<h2 id="toc46"><a name="Sqrtphi-13-limit"></a>13-limit</h2>

Commas: 325/324, 364/363, 625/624, 1375/1372<br />

<br />

POTE generator: ~14/11 = 416.585<br />

Line 981:

Line 979:

<br />

<h2 id="toc47"><a name="Sqrtphi-17-limit"></a>17-limit</h2>

Commas: 325/324, 364/363, 375/374, 540/539, 595/594<br />

<br />

POTE generator: ~14/11 = 416.585<br />

Line 990:

Line 988:

<br />

<h2 id="toc48"><a name="Sqrtphi-19-limit"></a>19-limit</h2>

Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594<br />

<br />

POTE generator: ~14/11 = 416.580<br />

Line 999:

Line 997:

<br />

<h2 id="toc49"><a name="Sqrtphi-Scales"></a>Scales</h2>

<a class="wiki_link" href="/sqrtphi17">sqrtphi17</a><br />

<a class="wiki_link" href="/sqrtphi23">sqrtphi23</a><br />

<a class="wiki_link" href="/sqrtphi49">sqrtphi49</a><br />

<br />

<h2 id="toc50"><a name="Sqrtphi-Music"></a>Music</h2>

<a class="wiki_link_ext" href="http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3" rel="nofollow">Prelude for Piano in Square root of Phi Tuning</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />

<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3" rel="nofollow">A Fight for Phi</a> by Vito Sicurella</body></html></pre></div>

@@ 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>2012-06-04 16:32:02 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-07-10 20:24:13 UTC</tt>.<br>
-: The original revision id was <tt>342569596</tt>.<br>
+: The original revision id was <tt>352115606</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]]
+The [[5-limit]] parent comma for the **kleismic family** is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This highly accurate 5-limit temperament is commonly called **Hanson**, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].
-The [[5-limit]] parent comma for the **kleismic family** is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called **Hanson**, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].
 [[POTE tuning|POTE generator]]: 317.007
@@ Line 19: / Line 18: @@
 [[http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3|In Hanson11]] by [[Chris Vaisvil]]
 =Seven limit children=
 The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.
 =Keemun=
 [[Comma|Commas]]: 49/48, 126/125
@@ Line 32: / Line 31: @@
 [[Badness]]: 0.0274
 ==11-limit==
 [[Comma]]s: 49/48, 56/55, 100/99
@@ Line 41: / Line 40: @@
 [[Badness]]: 0.0274
 ==13-limit==
 [[Comma]]s: 49/48, 56/55, 78/77, 100/99
@@ Line 50: / Line 49: @@
 [[Badness]]: 0.0297
 ===Keema===
 Commas: 49/48, 56/55, 91/90, 100/99
@@ Line 59: / Line 58: @@
 Badness: 0.0227
 ===Kumbaya===
 Commas: 40/39, 49/48, 56/55, 66/65
@@ Line 68: / Line 67: @@
 Badness: 0.0316
 ==Qeema==
 Commas: 45/44, 49/48, 126/125
@@ Line 77: / Line 76: @@
 Badness: 0.0401
 ===13-limit===
 Commas: 45/44, 49/48, 78/77, 126/125
@@ Line 86: / Line 85: @@
 Badness: 0.0294
 ==Darjeeling==
 Commas: 49/48, 55/54, 77/75
@@ Line 95: / Line 94: @@
 Badness: 0.0276
 ===13-limit Darjeeling===
 Commas: 49/48, 55/54, 66/65, 77/75
@@ Line 104: / Line 103: @@
 Badness: 0.02144
 =Catalan=
 Commas: 64/63, 15625/15552
@@ Line 114: / Line 113: @@
 Badness: 0.0949
 =Catakleismic=
 [[Comma|Commas]]: 225/224, 4375/4374
@@ Line 124: / Line 123: @@
 [[Badness]]: 0.0215
 ==11-limit==
 [[Comma|Commas]]: 225/224, 385/384, 4375/4374
@@ Line 133: / Line 132: @@
 [[Badness]]: 0.0218
 ==13-limit==
 [[Comma|Commas]]: 169/168, 225/224, 325/324, 540/539
@@ Line 142: / Line 141: @@
 [[Badness]]: 0.0169
 =Cataclysmic=
 Commas: 99/98, 176/175, 2200/2187
@@ Line 151: / Line 150: @@
 Badness: 0.0400
 ==13-limit==
 Commas: 99/98, 169/168, 176/175, 275/273
-POTE generator: ~6/5 =  317.036
+POTE generator: ~6/5 = 317.036
 Map: [&lt;1 0 1 -3 -5 0|, &lt;0 6 5 22 32 14|]
@@ Line 160: / Line 159: @@
 Badness: 0.0226
 =Catalytic=
 Commas: 225/224, 441/440, 4375/4374
@@ Line 169: / Line 168: @@
 Badness: 0.0304
 ==13-limit==
 Commas: 169/168 225/224 325/324 1716/1715
@@ Line 178: / Line 177: @@
 Badness: 0.0223
 =Countercata=
 [[Comma|Commas]]: 15625/15552, 5120/5103
@@ Line 188: / Line 187: @@
 [[Badness]]: 0.0521
 ==11-limit==
 [[Comma]]s: 385/384, 2200/2187, 3388/3375
@@ Line 197: / Line 196: @@
 [[Badness]]: 0.0398
 ==13-limit==
 [[Comma]]s: 325/324, 352/351, 385/384, 625/624
@@ Line 206: / Line 205: @@
 [[Badness]]: 0.0202
 =Metakleismic=
 [[Comma]]s: 15625/15552, 179200/177147
@@ Line 216: / Line 215: @@
 [[Badness]]: 0.1635
 ==11-limit==
 [[Comma]]s: 896/891, 2200/2187, 14700/14641
@@ Line 225: / Line 224: @@
 [[Badness]]: 0.0486
 ==13-limit==
 [[Comma]]s: 325/324, 352/351, 364/363, 625/624
@@ Line 234: / Line 233: @@
 [[Badness]]: 0.0244
 =Hemikleismic=
 Commas: 4000/3969, 6144/6125
@@ Line 243: / Line 242: @@
 Badness: 0.0521
 ==11-limit==
 Commas: 121/120, 176/175, 4000/3969
@@ Line 252: / Line 251: @@
 Badness: 0.0380
 ==13-limit==
 Commas: 121/120, 176/175, 275/273, 325/324
@@ Line 261: / Line 260: @@
 Badness: 0.0260
 =Clyde=
 [[Comma|Commas]]: 245/243, 3136/3125
@@ Line 277: / Line 276: @@
 Badness: 0.0473
 ==11-limit==
 Commas: 245/243, 3136/3125, 385/384
@@ Line 286: / Line 285: @@
 Badness: 0.0474
 ==13-limit==
 Commas: 196/195, 245/243, 385/384, 625/624
@@ Line 295: / Line 294: @@
 Badness: 0.0268
 =Bikleismic=
 Commas: 225/224, 243/242, 4375/4356
 POTE generator: ~6/5 = 316.721
-Map: [&lt;2 0 2 -6 -1|,  &lt;0 6 5 22 15|]
+Map: [&lt;2 0 2 -6 -1|, &lt;0 6 5 22 15|]
 EDOs: 72, 106, 178, 250, 322c, 394c, 466bc, 538bc, 610bc
 Badness: 0.0293
 ==13-limit==
 Commas: 169/168, 225/224, 243/242, 325/324
 POTE generator: ~6/5 = 316.726
-Map: [&lt;2 0 2 -6 -1 0|,  &lt;0 6 5 22 15 14|]
+Map: [&lt;2 0 2 -6 -1 0|, &lt;0 6 5 22 15 14|]
 EDOs: 72, 106, 322cff, 394cff, 466bcff, 538bcfff
 Badness: 0.0218
 =Tritikleismic=
 [[Comma]]s: 15625/15552, 1029/1024
@@ Line 323: / Line 322: @@
 [[Badness]]: 0.0563
 ==11-limit==
 [[Comma]]s: 385/384, 441/440, 4000/3993
@@ Line 332: / Line 331: @@
 [[Badness]]: 0.0193
 ==13-limit==
 [[Comma]]s: 325/324, 364/363, 441/440, 625/624
@@ Line 341: / Line 340: @@
 [[Badness]]: 0.0157
 =Quadritikleismic=
 [[Comma]]s: 15625/15552, 2401/2400
@@ Line 351: / Line 350: @@
 [[Badness]]: 0.0392
 ==11-limit==
 Commas: 385/384, 1375/1372, 6250/6237
@@ Line 360: / Line 359: @@
 [[Badness]]: 0.0234
 ==13-limit==
 Commas: 325/324, 385/384, 625/624, 1573/1568
@@ Line 369: / Line 368: @@
 [[Badness]]: 0.0187
 =Kleiboh=
 Commas: 1728/1715, 3125/3087
 POTE generator: ~25/21 = 294.303
@@ Line 379: / Line 378: @@
 Badness: 0.0765
 ==11-limit==
 Commas: 176/175, 540/539, 3125/3087
@@ Line 388: / Line 387: @@
 Badness: 0.0528
 ==13-limit==
 Commas: 176/175, 275/273, 325/324, 540/539
 POTE generator: ~13/11 = 294.187
@@ Line 397: / Line 396: @@
 Badness: 0.0311
 =Novemkleismic=
 Commas: 15625/15552, 40353607/40310784
@@ Line 407: / Line 406: @@
 Badness: 0.1934
 ==11-limit==
 Commas: 1375/1372, 4000/3993, 15625/15552
@@ Line 416: / Line 415: @@
 Badness: 0.05172
 ==13-limit==
 Commas: 325/324, 625/624, 1375/1372, 4000/3993
@@ Line 425: / Line 424: @@
 Badness: 0.0391
 =Sqrtphi=
 Commas: 15625/15552, 16875/16807
@@ Line 436: / Line 435: @@
 Badness: 0.0704
 ==11-limit==
 Commas: 540/539, 1375/1372, 4375/4356
@@ Line 445: / Line 444: @@
 Badness: 0.0255
 ==13-limit==
 Commas: 325/324, 364/363, 625/624, 1375/1372
@@ Line 454: / Line 453: @@
 Badness: 0.0200
 ==17-limit==
 Commas: 325/324, 364/363, 375/374, 540/539, 595/594
@@ Line 463: / Line 462: @@
 Badness: 0.0130
 ==19-limit==
 Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594
@@ Line 472: / Line 471: @@
 Badness: 0.0147
 ==Scales==
 [[sqrtphi17]]
 [[sqrtphi23]]
 [[sqrtphi49]]
 ==Music==
 [[http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3|Prelude for Piano in Square root of Phi Tuning]] by [[Chris Vaisvil]]
 [[http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3|A Fight for Phi]] by Vito Sicurella</pre></div>
@@ Line 533: / Line 532: @@
 &lt;!-- ws:end:WikiTextTocRule:152 --&gt;&lt;!-- ws:start:WikiTextTocRule:153: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Sqrtphi-Music"&gt;Music&lt;/a&gt;&lt;/div&gt;
 &lt;!-- ws:end:WikiTextTocRule:153 --&gt;&lt;!-- ws:start:WikiTextTocRule:154: --&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:154 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:154 --&gt;The &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; parent comma for the &lt;strong&gt;kleismic family&lt;/strong&gt; is 15625/15552, the kleisma. Its monzo is |-6 -5 6&amp;gt;, and flipping that yields &amp;lt;&amp;lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This highly accurate 5-limit temperament is commonly called &lt;strong&gt;Hanson&lt;/strong&gt;, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87edo&lt;/a&gt; and &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt;.&lt;br /&gt;
-The &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; parent comma for the &lt;strong&gt;kleismic family&lt;/strong&gt; is 15625/15552, the kleisma. Its monzo is |-6 -5 6&amp;gt;, and flipping that yields &amp;lt;&amp;lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called &lt;strong&gt;Hanson&lt;/strong&gt;, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87edo&lt;/a&gt; and &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 317.007&lt;br /&gt;
@@ Line 546: / Line 544: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h1&gt;
-The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.&lt;br /&gt;
+ The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Keemun"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Keemun&lt;/h1&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 49/48, 126/125&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 49/48, 126/125&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~6/5 = 316.473&lt;br /&gt;
@@ Line 559: / Line 557: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Keemun-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 56/55, 100/99&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 56/55, 100/99&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~6/5 = 317.576&lt;br /&gt;
@@ Line 568: / Line 566: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Keemun-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 56/55, 78/77, 100/99&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 56/55, 78/77, 100/99&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~6/5 = 316.611&lt;br /&gt;
@@ Line 577: / Line 575: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Keemun-13-limit-Keema"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Keema&lt;/h3&gt;
-Commas: 49/48, 56/55, 91/90, 100/99&lt;br /&gt;
+ Commas: 49/48, 56/55, 91/90, 100/99&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.423&lt;br /&gt;
@@ Line 586: / Line 584: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Keemun-13-limit-Kumbaya"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Kumbaya&lt;/h3&gt;
-Commas: 40/39, 49/48, 56/55, 66/65&lt;br /&gt;
+ Commas: 40/39, 49/48, 56/55, 66/65&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 318.595&lt;br /&gt;
@@ Line 595: / Line 593: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Keemun-Qeema"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Qeema&lt;/h2&gt;
-Commas: 45/44, 49/48, 126/125&lt;br /&gt;
+ Commas: 45/44, 49/48, 126/125&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 314.730&lt;br /&gt;
@@ Line 604: / Line 602: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Keemun-Qeema-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h3&gt;
-Commas: 45/44, 49/48, 78/77, 126/125&lt;br /&gt;
+ Commas: 45/44, 49/48, 78/77, 126/125&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 315.044&lt;br /&gt;
@@ Line 613: / Line 611: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Keemun-Darjeeling"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Darjeeling&lt;/h2&gt;
-Commas: 49/48, 55/54, 77/75&lt;br /&gt;
+ Commas: 49/48, 55/54, 77/75&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.656&lt;br /&gt;
@@ Line 622: / Line 620: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Keemun-Darjeeling-13-limit Darjeeling"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;13-limit Darjeeling&lt;/h3&gt;
-Commas: 49/48, 55/54, 66/65, 77/75&lt;br /&gt;
+ Commas: 49/48, 55/54, 66/65, 77/75&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.298&lt;br /&gt;
@@ Line 631: / Line 629: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Catalan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Catalan&lt;/h1&gt;
-Commas: 64/63, 15625/15552&lt;br /&gt;
+ Commas: 64/63, 15625/15552&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 318.267&lt;br /&gt;
@@ Line 641: / Line 639: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Catakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Catakleismic&lt;/h1&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 4375/4374&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.732&lt;br /&gt;
@@ Line 651: / Line 649: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Catakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;11-limit&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 385/384, 4375/4374&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 385/384, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.719&lt;br /&gt;
@@ Line 660: / Line 658: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Catakleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;13-limit&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 169/168, 225/224, 325/324, 540/539&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 169/168, 225/224, 325/324, 540/539&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.738&lt;br /&gt;
@@ Line 669: / Line 667: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Cataclysmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Cataclysmic&lt;/h1&gt;
-Commas: 99/98, 176/175, 2200/2187&lt;br /&gt;
+ Commas: 99/98, 176/175, 2200/2187&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.042&lt;br /&gt;
@@ Line 678: / Line 676: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Cataclysmic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;13-limit&lt;/h2&gt;
-Commas: 99/98, 169/168, 176/175, 275/273&lt;br /&gt;
+ Commas: 99/98, 169/168, 176/175, 275/273&lt;br /&gt;
 &lt;br /&gt;
-POTE generator: ~6/5 =  317.036&lt;br /&gt;
+POTE generator: ~6/5 = 317.036&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1 -3 -5 0|, &amp;lt;0 6 5 22 32 14|]&lt;br /&gt;
@@ Line 687: / Line 685: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Catalytic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Catalytic&lt;/h1&gt;
-Commas: 225/224, 441/440, 4375/4374&lt;br /&gt;
+ Commas: 225/224, 441/440, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 316.653&lt;br /&gt;
@@ Line 696: / Line 694: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Catalytic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;13-limit&lt;/h2&gt;
-Commas: 169/168 225/224 325/324 1716/1715&lt;br /&gt;
+ Commas: 169/168 225/224 325/324 1716/1715&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 316.639&lt;br /&gt;
@@ Line 705: / Line 703: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Countercata"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Countercata&lt;/h1&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 15625/15552, 5120/5103&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 15625/15552, 5120/5103&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 317.121&lt;br /&gt;
@@ Line 715: / Line 713: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Countercata-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 385/384, 2200/2187, 3388/3375&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 385/384, 2200/2187, 3388/3375&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.162&lt;br /&gt;
@@ Line 724: / Line 722: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Countercata-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;13-limit&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 325/324, 352/351, 385/384, 625/624&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 325/324, 352/351, 385/384, 625/624&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.162&lt;br /&gt;
@@ Line 733: / Line 731: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Metakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Metakleismic&lt;/h1&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 15625/15552, 179200/177147&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 15625/15552, 179200/177147&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.314&lt;br /&gt;
@@ Line 743: / Line 741: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Metakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;11-limit&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 896/891, 2200/2187, 14700/14641&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 896/891, 2200/2187, 14700/14641&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.311&lt;br /&gt;
@@ Line 752: / Line 750: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Metakleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;13-limit&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 325/324, 352/351, 364/363, 625/624&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 325/324, 352/351, 364/363, 625/624&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.311&lt;br /&gt;
@@ Line 761: / Line 759: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Hemikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Hemikleismic&lt;/h1&gt;
-Commas: 4000/3969, 6144/6125&lt;br /&gt;
+ Commas: 4000/3969, 6144/6125&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 158.649&lt;br /&gt;
@@ Line 770: / Line 768: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Hemikleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;11-limit&lt;/h2&gt;
-Commas: 121/120, 176/175, 4000/3969&lt;br /&gt;
+ Commas: 121/120, 176/175, 4000/3969&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~11/10 = 158.677&lt;br /&gt;
@@ Line 779: / Line 777: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Hemikleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;13-limit&lt;/h2&gt;
-Commas: 121/120, 176/175, 275/273, 325/324&lt;br /&gt;
+ Commas: 121/120, 176/175, 275/273, 325/324&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~11/10 = 158.655&lt;br /&gt;
@@ Line 788: / Line 786: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Clyde"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Clyde&lt;/h1&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 245/243, 3136/3125&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 245/243, 3136/3125&lt;br /&gt;
 &lt;br /&gt;
 and 9 limit minimax&lt;br /&gt;
@@ Line 804: / Line 802: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Clyde-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;11-limit&lt;/h2&gt;
-Commas: 245/243, 3136/3125, 385/384&lt;br /&gt;
+ Commas: 245/243, 3136/3125, 385/384&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~9/7 = 441.355&lt;br /&gt;
@@ Line 813: / Line 811: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Clyde-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;13-limit&lt;/h2&gt;
-Commas: 196/195, 245/243, 385/384, 625/624&lt;br /&gt;
+ Commas: 196/195, 245/243, 385/384, 625/624&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~9/7 = 441.363&lt;br /&gt;
@@ Line 822: / Line 820: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc30"&gt;&lt;a name="Bikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;Bikleismic&lt;/h1&gt;
-Commas: 225/224, 243/242, 4375/4356&lt;br /&gt;
+ Commas: 225/224, 243/242, 4375/4356&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 316.721&lt;br /&gt;
 &lt;br /&gt;
-Map: [&amp;lt;2 0 2 -6 -1|,  &amp;lt;0 6 5 22 15|]&lt;br /&gt;
+Map: [&amp;lt;2 0 2 -6 -1|, &amp;lt;0 6 5 22 15|]&lt;br /&gt;
 EDOs: 72, 106, 178, 250, 322c, 394c, 466bc, 538bc, 610bc&lt;br /&gt;
 Badness: 0.0293&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Bikleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;13-limit&lt;/h2&gt;
-Commas: 169/168, 225/224, 243/242, 325/324&lt;br /&gt;
+ Commas: 169/168, 225/224, 243/242, 325/324&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 316.726&lt;br /&gt;
 &lt;br /&gt;
-Map: [&amp;lt;2 0 2 -6 -1 0|,  &amp;lt;0 6 5 22 15 14|]&lt;br /&gt;
+Map: [&amp;lt;2 0 2 -6 -1 0|, &amp;lt;0 6 5 22 15 14|]&lt;br /&gt;
 EDOs: 72, 106, 322cff, 394cff, 466bcff, 538bcfff&lt;br /&gt;
 Badness: 0.0218&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc32"&gt;&lt;a name="Tritikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;Tritikleismic&lt;/h1&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 15625/15552, 1029/1024&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 15625/15552, 1029/1024&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.872&lt;br /&gt;
@@ Line 850: / Line 848: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Tritikleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;11-limit&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 385/384, 441/440, 4000/3993&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 385/384, 441/440, 4000/3993&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.881&lt;br /&gt;
@@ Line 859: / Line 857: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="Tritikleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;13-limit&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 325/324, 364/363, 441/440, 625/624&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 325/324, 364/363, 441/440, 625/624&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.959&lt;br /&gt;
@@ Line 868: / Line 866: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="Quadritikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Quadritikleismic&lt;/h1&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 15625/15552, 2401/2400&lt;br /&gt;
+ &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 15625/15552, 2401/2400&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.9999&lt;br /&gt;
@@ Line 878: / Line 876: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Quadritikleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;11-limit&lt;/h2&gt;
-Commas: 385/384, 1375/1372, 6250/6237&lt;br /&gt;
+ Commas: 385/384, 1375/1372, 6250/6237&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.925&lt;br /&gt;
@@ Line 887: / Line 885: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc37"&gt;&lt;a name="Quadritikleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;13-limit&lt;/h2&gt;
-Commas: 325/324, 385/384, 625/624, 1573/1568&lt;br /&gt;
+ Commas: 325/324, 385/384, 625/624, 1573/1568&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.989&lt;br /&gt;
@@ Line 896: / Line 894: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc38"&gt;&lt;a name="Kleiboh"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;Kleiboh&lt;/h1&gt;
-Commas: 1728/1715, 3125/3087 &lt;br /&gt;
+ Commas: 1728/1715, 3125/3087&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~25/21 = 294.303&lt;br /&gt;
@@ Line 906: / Line 904: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Kleiboh-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;11-limit&lt;/h2&gt;
-Commas: 176/175, 540/539, 3125/3087&lt;br /&gt;
+ Commas: 176/175, 540/539, 3125/3087&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~25/21 = 294.181&lt;br /&gt;
@@ Line 915: / Line 913: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc40"&gt;&lt;a name="Kleiboh-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;13-limit&lt;/h2&gt;
-Commas: 176/175, 275/273, 325/324, 540/539 &lt;br /&gt;
+ Commas: 176/175, 275/273, 325/324, 540/539&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~13/11 = 294.187&lt;br /&gt;
@@ Line 924: / Line 922: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc41"&gt;&lt;a name="Novemkleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;Novemkleismic&lt;/h1&gt;
-Commas: 15625/15552, 40353607/40310784&lt;br /&gt;
+ Commas: 15625/15552, 40353607/40310784&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.005&lt;br /&gt;
@@ Line 934: / Line 932: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc42"&gt;&lt;a name="Novemkleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&gt;11-limit&lt;/h2&gt;
-Commas: 1375/1372, 4000/3993, 15625/15552&lt;br /&gt;
+ Commas: 1375/1372, 4000/3993, 15625/15552&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.010&lt;br /&gt;
@@ Line 943: / Line 941: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:86:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc43"&gt;&lt;a name="Novemkleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:86 --&gt;13-limit&lt;/h2&gt;
-Commas: 325/324, 625/624, 1375/1372, 4000/3993&lt;br /&gt;
+ Commas: 325/324, 625/624, 1375/1372, 4000/3993&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.086&lt;br /&gt;
@@ Line 952: / Line 950: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc44"&gt;&lt;a name="Sqrtphi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;Sqrtphi&lt;/h1&gt;
-Commas: 15625/15552, 16875/16807&lt;br /&gt;
+ Commas: 15625/15552, 16875/16807&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~125/98 = 416.603 cents&lt;br /&gt;
@@ Line 963: / Line 961: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc45"&gt;&lt;a name="Sqrtphi-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;11-limit&lt;/h2&gt;
-Commas: 540/539, 1375/1372, 4375/4356&lt;br /&gt;
+ Commas: 540/539, 1375/1372, 4375/4356&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~14/11 = 416.604&lt;br /&gt;
@@ Line 972: / Line 970: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:92:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc46"&gt;&lt;a name="Sqrtphi-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:92 --&gt;13-limit&lt;/h2&gt;
-Commas: 325/324, 364/363, 625/624, 1375/1372&lt;br /&gt;
+ Commas: 325/324, 364/363, 625/624, 1375/1372&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~14/11 = 416.585&lt;br /&gt;
@@ Line 981: / Line 979: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc47"&gt;&lt;a name="Sqrtphi-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;17-limit&lt;/h2&gt;
-Commas: 325/324, 364/363, 375/374, 540/539, 595/594&lt;br /&gt;
+ Commas: 325/324, 364/363, 375/374, 540/539, 595/594&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~14/11 = 416.585&lt;br /&gt;
@@ Line 990: / Line 988: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc48"&gt;&lt;a name="Sqrtphi-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;19-limit&lt;/h2&gt;
-Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594&lt;br /&gt;
+ Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~14/11 = 416.580&lt;br /&gt;
@@ Line 999: / Line 997: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:98:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc49"&gt;&lt;a name="Sqrtphi-Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:98 --&gt;Scales&lt;/h2&gt;
-&lt;a class="wiki_link" href="/sqrtphi17"&gt;sqrtphi17&lt;/a&gt;&lt;br /&gt;
+ &lt;a class="wiki_link" href="/sqrtphi17"&gt;sqrtphi17&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="/sqrtphi23"&gt;sqrtphi23&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="/sqrtphi49"&gt;sqrtphi49&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc50"&gt;&lt;a name="Sqrtphi-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;Music&lt;/h2&gt;
-&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3" rel="nofollow"&gt;Prelude for Piano in Square root of Phi Tuning&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
+ &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3" rel="nofollow"&gt;Prelude for Piano in Square root of Phi Tuning&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3" rel="nofollow"&gt;A Fight for Phi&lt;/a&gt; by Vito Sicurella&lt;/body&gt;&lt;/html&gt;</pre></div>