Kleismic family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>2010-12-10 13:39:02 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-10 14:26:27 UTC</tt>.<br>
: The original revision id was <tt>187170975</tt>.<br>
: The original revision id was <tt>187190445</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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==Seven limit children==
==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, 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 and catakleismic both have octave period and use the minor third as a generator; catakleismic defines 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.
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===
===Keemun===
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Map: [&lt;1 0 1 2|, &lt;0 6 5 3|]
Map: [&lt;1 0 1 2|, &lt;0 6 5 3|]
EDOs: 19, 91
===Catakleismic===
[[Comma|Commas]]: 225/224, 4375/4374
[[POTE tuning|POTE generator]]: 316.732
Map: [&lt;1 0 1 -3|, &lt;0 6 5 22|]
EDOs: 53, 72, 197
===Countercata===
[[Comma|Commas]]: 15625/15552, 5120/5103
[[POTE tuning|POTE generator]]: 317.121
Map: [&lt;1 0 1 11|, &lt;0 6 5 -31|]
EDOs: 53, 140
===Hemikleismic===
Commas: 4000/3969, 6144/6125
[[POTE tuning|POTE generator]]: 158.649
Map: [&lt;1 0 1 4|, &lt;0 12 10 -9|]
EDOs: 53, 121


===Clyde===
===Clyde===
Line 35: Line 63:
Map: [&lt;1 6 6 12|, &lt;0 -12 -10 -25|]
Map: [&lt;1 6 6 12|, &lt;0 -12 -10 -25|]
[[Generator|Generators]]: 2, 9/7
[[Generator|Generators]]: 2, 9/7
[[Edo|Edos]]: [[19edo|19]], [[49edo|49]], [[68edo|68]], [[87edo|87]], [[155edo|155]]</pre></div>
[[Edo|Edos]]: [[19edo|19]], [[49edo|49]], [[68edo|68]], [[87edo|87]], [[155edo|155]]
 
===Tritikleismic===
Commas: 15625/15552, 1029/1024
 
[[POTE tuning|POTE generator]]: 316.872
 
Map: [&lt;3 0 3 10|, &lt;0 6 5 -2|]
 
EDOs: 72, 231
 
===Quadritikleismic===
Commas: 15625/15552, 2401/2400
 
[[POTE tuning|POTE generator]]: 316.9999
 
Map: [&lt;4 0 4 7|, &lt;0 6 5 4|]
 
EDOs: 68, 72, 140, 212, 1200(!)</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Kleismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 5-limit parent comma for the kleismic family 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. 14/53 is about perfect as a generator, though 9/34 also makes sense and using &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 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;
<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;Kleismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 5-limit parent comma for the kleismic family 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. 14/53 is about perfect as a generator, though 9/34 also makes sense and using &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 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;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;
The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 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 and catakleismic both have octave period and use the minor third as a generator; catakleismic defines 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 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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Seven limit children-Keemun"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Keemun&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Seven limit children-Keemun"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Keemun&lt;/h3&gt;
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Map: [&amp;lt;1 0 1 2|, &amp;lt;0 6 5 3|]&lt;br /&gt;
Map: [&amp;lt;1 0 1 2|, &amp;lt;0 6 5 3|]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Seven limit children-Clyde"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Clyde&lt;/h3&gt;
EDOs: 19, 91&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Seven limit children-Catakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Catakleismic&lt;/h3&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;
&lt;br /&gt;
Map: [&amp;lt;1 0 1 -3|, &amp;lt;0 6 5 22|]&lt;br /&gt;
&lt;br /&gt;
EDOs: 53, 72, 197&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Seven limit children-Countercata"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Countercata&lt;/h3&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;
&lt;br /&gt;
Map: [&amp;lt;1 0 1 11|, &amp;lt;0 6 5 -31|]&lt;br /&gt;
&lt;br /&gt;
EDOs: 53, 140&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Seven limit children-Hemikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Hemikleismic&lt;/h3&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;
&lt;br /&gt;
Map: [&amp;lt;1 0 1 4|, &amp;lt;0 12 10 -9|]&lt;br /&gt;
EDOs: 53, 121&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-Seven limit children-Clyde"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Clyde&lt;/h3&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;
&lt;br /&gt;
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Map: [&amp;lt;1 6 6 12|, &amp;lt;0 -12 -10 -25|]&lt;br /&gt;
Map: [&amp;lt;1 6 6 12|, &amp;lt;0 -12 -10 -25|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 9/7&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 9/7&lt;br /&gt;
&lt;a class="wiki_link" href="/Edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/49edo"&gt;49&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/155edo"&gt;155&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;a class="wiki_link" href="/Edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/49edo"&gt;49&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/155edo"&gt;155&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-Seven limit children-Tritikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Tritikleismic&lt;/h3&gt;
Commas: 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;
&lt;br /&gt;
Map: [&amp;lt;3 0 3 10|, &amp;lt;0 6 5 -2|]&lt;br /&gt;
&lt;br /&gt;
EDOs: 72, 231&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Seven limit children-Quadritikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Quadritikleismic&lt;/h3&gt;
Commas: 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;
&lt;br /&gt;
Map: [&amp;lt;4 0 4 7|, &amp;lt;0 6 5 4|]&lt;br /&gt;
&lt;br /&gt;
EDOs: 68, 72, 140, 212, 1200(!)&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 14:26, 10 December 2010

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2010-12-10 14:26:27 UTC.
The original revision id was 187190445.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

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. 14/53 is about perfect as a generator, though 9/34 also makes sense and using [[19edo]] is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].

[[POTE tuning|POTE generator]]: 317.007

Map: [<1 0 1|, <0 6 5|]

==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

[[POTE tuning|POTE generator]]: 316.473

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

EDOs: 19, 91

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

[[POTE tuning|POTE generator]]: 316.732

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

EDOs: 53, 72, 197

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

[[POTE tuning|POTE generator]]: 317.121

Map: [<1 0 1 11|, <0 6 5 -31|]

EDOs: 53, 140

===Hemikleismic===
Commas: 4000/3969, 6144/6125

[[POTE tuning|POTE generator]]: 158.649

Map: [<1 0 1 4|, <0 12 10 -9|]
EDOs: 53, 121

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

7 and 9 limit minimax
[|1 0 0 0>, |6/25 0 0 12/25>, |6/5 0 0 2/5>, |0 0 0 1>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7

[[POTE tuning|POTE generator]]: 441.335

Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 [[Cent|cents]]. Associated recurrence relationship quickly converges.

Map: [<1 6 6 12|, <0 -12 -10 -25|]
[[Generator|Generators]]: 2, 9/7
[[Edo|Edos]]: [[19edo|19]], [[49edo|49]], [[68edo|68]], [[87edo|87]], [[155edo|155]]

===Tritikleismic===
Commas: 15625/15552, 1029/1024

[[POTE tuning|POTE generator]]: 316.872

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

EDOs: 72, 231

===Quadritikleismic===
Commas: 15625/15552, 2401/2400

[[POTE tuning|POTE generator]]: 316.9999

Map: [<4 0 4 7|, <0 6 5 4|]

EDOs: 68, 72, 140, 212, 1200(!)

Original HTML content:

<html><head><title>Kleismic family</title></head><body>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. 14/53 is about perfect as a generator, though 9/34 also makes sense and using <a class="wiki_link" href="/19edo">19edo</a> 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 />
<br />
Map: [&lt;1 0 1|, &lt;0 6 5|]<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2>
The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> 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.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Seven limit children-Keemun"></a><!-- ws:end:WikiTextHeadingRule:2 -->Keemun</h3>
<a class="wiki_link" href="/Comma">Commas</a>: 49/48, 126/125<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.473<br />
<br />
Map: [&lt;1 0 1 2|, &lt;0 6 5 3|]<br />
<br />
EDOs: 19, 91<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Catakleismic"></a><!-- ws:end:WikiTextHeadingRule:4 -->Catakleismic</h3>
<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 />
<br />
Map: [&lt;1 0 1 -3|, &lt;0 6 5 22|]<br />
<br />
EDOs: 53, 72, 197<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Seven limit children-Countercata"></a><!-- ws:end:WikiTextHeadingRule:6 -->Countercata</h3>
<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 />
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Map: [&lt;1 0 1 11|, &lt;0 6 5 -31|]<br />
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EDOs: 53, 140<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Seven limit children-Hemikleismic"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hemikleismic</h3>
Commas: 4000/3969, 6144/6125<br />
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 158.649<br />
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Map: [&lt;1 0 1 4|, &lt;0 12 10 -9|]<br />
EDOs: 53, 121<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-Seven limit children-Clyde"></a><!-- ws:end:WikiTextHeadingRule:10 -->Clyde</h3>
<a class="wiki_link" href="/Comma">Commas</a>: 245/243, 3136/3125<br />
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7 and 9 limit minimax<br />
[|1 0 0 0&gt;, |6/25 0 0 12/25&gt;, |6/5 0 0 2/5&gt;, |0 0 0 1&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7<br />
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 441.335<br />
<br />
Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 <a class="wiki_link" href="/Cent">cents</a>. Associated recurrence relationship quickly converges.<br />
<br />
Map: [&lt;1 6 6 12|, &lt;0 -12 -10 -25|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 9/7<br />
<a class="wiki_link" href="/Edo">Edos</a>: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/49edo">49</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/155edo">155</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x-Seven limit children-Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:12 -->Tritikleismic</h3>
Commas: 15625/15552, 1029/1024<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.872<br />
<br />
Map: [&lt;3 0 3 10|, &lt;0 6 5 -2|]<br />
<br />
EDOs: 72, 231<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="x-Seven limit children-Quadritikleismic"></a><!-- ws:end:WikiTextHeadingRule:14 -->Quadritikleismic</h3>
Commas: 15625/15552, 2401/2400<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.9999<br />
<br />
Map: [&lt;4 0 4 7|, &lt;0 6 5 4|]<br />
<br />
EDOs: 68, 72, 140, 212, 1200(!)</body></html>
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