Porwell 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>~~2013~~-12-~~06 21~~:45:55 UTC</tt>.<br>

: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2015-02-14 09:47:18 UTC</tt>.<br>

: The original revision id was <tt>~~475389192~~</tt>.<br>

: The original revision id was <tt>540963040</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 porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.

=Hewuermity=

Comma: 6144/6125

7 and 9 limit minimax

[|1 0 0 0>, |0 1 0 0>, |11/5 1/5 2/5 -2/5>,

|11/5 1/5 -3/5 3/5>]

Eigenmonzos: 4/3, 7/5

Line 24:

[[Projection pair]]s: 3 6125/2048 to 2.5.7

=Zeus=

Commas: 121/120, 176/175

Minimax tuning

[|1 0 0 0 0>, |11/9 10/9 -1/3 -2/9 0>,

|22/9 2/9 1/3 -4/9 0>, |22/9 2/9 -2/3 5/9 0>,

|10/3 2/3 0 -1/3 0>]

Eigenmonzos: 2, 9/7, 7/5

Line 45:

Zeus11[22] [[Hobbits|hobbit]] [[transversal]]

33/32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3,

11/8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4,

11/6, 15/8, 64/33, 2

Zeus11[24] hobbit transversal

33/32, 16/15, 11/10, 9/8, 8/7, 77/64, 11/9, 5/4, 21/16, 4/3,

11/8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9,

11/6, 15/8, 64/33, 2

[[genus1155zeus|Euler(1155) genus in zeus temperament]]

==Tridecimal Zeus==

==13-limit (tinia)==

Commas: 66/65, 121/120, 176/175

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

EDOs: 7, 9, 15, 24, 31, 77f, 108ef

Badness: 0.000808

==Tridecimal Zeus==

Commas: 121/120, 176/175, 351/350

13-limit minimax

[|1 0 0 0 0 0>, |11/9 10/9 -1/3 -2/9 0 0>,

|22/9 2/9 1/3 -4/9 0 0>, |22/9 2/9 -2/3 5/9 0 0>,

|10/3 2/3 0 -1/3 0 0>, |14/3 -8/3 1 1/3 0 0>]

Eigenmonzos: 2, 9/7, 7/5

15-limit minimax

[|1 0 0 0 0 0>, |0 1 0 0 0 0>,

|11/5 1/5 2/5 -2/5 0 0>,|11/5 1/5 -3/5 3/5 0 0>,

|13/5 3/5 1/5 -1/5 0 0>, |38/5 -12/5 1/5 -1/5 0 0>]

Eigenmonzos: 2, 4/3, 7/5

Line 73:

Line 80:

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

Map: [<1 0 1 4 2 7|, <0 1 1 -1 1 -2|, <0 0 -2 3 -1 -1|]

Generators: 2, 3, 11/10

Edos: 6, 7, 8, 9, 15, 16, 22, 23, 24, 31, 37, 38, 39, 40, 46, 47, 53, 55, 59, 68, 75, 77, 84, 99, 130e

Line 83:

Line 90:

260/243, 88/81, 11/10, 44/39, 162/143, 11/9, 16/13, 320/243, 4/3, 1040/729, 13/9, 729/520, 3/2, 99/65, 44/27, 18/11, 1280/729, 16/9, 11/6, 24/13, 243/130, 2

~~==Tinia==~~

=Jupiter=

~~Commas: 66/65, 121/120, 176/175~~

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

~~EDOs: 7, 9, 15, 24, 31, 77f, 108ef~~

~~Badness: 0.000808~~

=Jupiter=

Commas: 540/539, 5632/5625

Line 97:

Badness: 0.000562</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>Porwell family</title></head><body><a href="#Zeus">Zeus</a> | <a href="#Jupiter">Jupiter</a>

<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>Porwell family</title></head><body><a href="#Hewuermity">Hewuermity</a> | <a href="#Zeus">Zeus</a> | <a href="#Jupiter">Jupiter</a>

~~<br />~~

The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.<br />

The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.<br />

<br />

Comma: 6144/6125<br />

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

Comma: 6144/6125<br />

<br />

7 and 9 limit minimax<br />

[|1 0 0 0&gt;, |0 1 0 0&gt;, |11/5 1/5 2/5 -2/5&gt;, <br />

[|1 0 0 0&gt;, |0 1 0 0&gt;, |11/5 1/5 2/5 -2/5&gt;,<br />

|11/5 1/5 -3/5 3/5&gt;]<br />

Eigenmonzos: 4/3, 7/5<br />

Line 115:

<a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 3 6125/2048 to 2.5.7<br />

<br />

<h1 id="~~toc0~~"><a name="Zeus"></a>Zeus</h1>

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

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

<br />

Minimax tuning<br />

[|1 0 0 0 0&gt;, |11/9 10/9 -1/3 -2/9 0&gt;, <br />

[|1 0 0 0 0&gt;, |11/9 10/9 -1/3 -2/9 0&gt;,<br />

|22/9 2/9 1/3 -4/9 0&gt;, |22/9 2/9 -2/3 5/9 0&gt;, <br />

|22/9 2/9 1/3 -4/9 0&gt;, |22/9 2/9 -2/3 5/9 0&gt;,<br />

|10/3 2/3 0 -1/3 0&gt;]<br />

Eigenmonzos: 2, 9/7, 7/5<br />

Line 136:

<br />

Zeus11[22] <a class="wiki_link" href="/Hobbits">hobbit</a> <a class="wiki_link" href="/transversal">transversal</a><br />

33/32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3, <br />

33/32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3,<br />

11/8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4, <br />

11/8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4,<br />

11/6, 15/8, 64/33, 2<br />

Zeus11[24] hobbit transversal<br />

33/32, 16/15, 11/10, 9/8, 8/7, 77/64, 11/9, 5/4, 21/16, 4/3,<br />

11/8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9, <br />

11/8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9,<br />

11/6, 15/8, 64/33, 2<br />

<a class="wiki_link" href="/genus1155zeus">Euler(1155) genus in zeus temperament</a><br />

<br />

<h2 id="~~toc1~~"><a name="Zeus-Tridecimal Zeus"></a>Tridecimal Zeus</h2>

<h2 id="toc2"><a name="Zeus-13-limit (tinia)"></a>13-limit (tinia)</h2>

Commas: 121/120, 176/175, 351/350<br />

Commas: 66/65, 121/120, 176/175<br />

<br />

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

EDOs: 7, 9, 15, 24, 31, 77f, 108ef<br />

Badness: 0.000808<br />

<br />

<h2 id="toc3"><a name="Zeus-Tridecimal Zeus"></a>Tridecimal Zeus</h2>

Commas: 121/120, 176/175, 351/350<br />

<br />

13-limit minimax<br />

[|1 0 0 0 0 0&gt;, |11/9 10/9 -1/3 -2/9 0 0&gt;, <br />

[|1 0 0 0 0 0&gt;, |11/9 10/9 -1/3 -2/9 0 0&gt;,<br />

|22/9 2/9 1/3 -4/9 0 0&gt;, |22/9 2/9 -2/3 5/9 0 0&gt;, <br />

|22/9 2/9 1/3 -4/9 0 0&gt;, |22/9 2/9 -2/3 5/9 0 0&gt;,<br />

|10/3 2/3 0 -1/3 0 0&gt;, |14/3 -8/3 1 1/3 0 0&gt;]<br />

Eigenmonzos: 2, 9/7, 7/5<br />

<br />

15-limit minimax<br />

[|1 0 0 0 0 0&gt;, |0 1 0 0 0 0&gt;, <br />

[|1 0 0 0 0 0&gt;, |0 1 0 0 0 0&gt;,<br />

|11/5 1/5 2/5 -2/5 0 0&gt;,|11/5 1/5 -3/5 3/5 0 0&gt;, <br />

|11/5 1/5 2/5 -2/5 0 0&gt;,|11/5 1/5 -3/5 3/5 0 0&gt;,<br />

|13/5 3/5 1/5 -1/5 0 0&gt;, |38/5 -12/5 1/5 -1/5 0 0&gt;]<br />

Eigenmonzos: 2, 4/3, 7/5<br />

Line 164:

Line 171:

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

<br />

Map: [&lt;1 0 1 4 2 7|, &lt;0 1 1 -1 1 -2|, &lt;0 0 -2 3 -1 -1|]<br />

Generators: 2, 3, 11/10<br />

Edos: 6, 7, 8, 9, 15, 16, 22, 23, 24, 31, 37, 38, 39, 40, 46, 47, 53, 55, 59, 68, 75, 77, 84, 99, 130e<br />

Line 174:

Line 181:

260/243, 88/81, 11/10, 44/39, 162/143, 11/9, 16/13, 320/243, 4/3, 1040/729, 13/9, 729/520, 3/2, 99/65, 44/27, 18/11, 1280/729, 16/9, 11/6, 24/13, 243/130, 2<br />

<br />

<h2 id="toc2"><a name="Zeus-Tinia"></a>Tinia</h2>

<h1 id="toc4"><a name="Jupiter"></a>Jupiter</h1>

~~Commas: 66/65, 121/120, 176/175<br />~~

Commas: 540/539, 5632/5625<br />

~~<br />~~

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

~~EDOs: 7, 9, 15, 24, 31, 77f, 108ef<br />~~

~~Badness: 0.000808<br />~~

~~<br />~~

~~<h1 id="~~toc3"><a name="Jupiter"></a>Jupiter</h1>

Commas: 540/539, 5632/5625<br />

<br />

Map: [&lt;1 0 1 4 -5|, &lt;0 1 1 -1 6|, &lt;0 0 2 -3 8|]<br />

EDOs: 9, 22, 31, 53, 99e, 108, 121, 130, 152, 282, 434de, 465d, 617de, 747def, 899def<br />

Badness: 0.000562</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>2013-12-06 21:45:55 UTC</tt>.<br>
+: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2015-02-14 09:47:18 UTC</tt>.<br>
-: The original revision id was <tt>475389192</tt>.<br>
+: The original revision id was <tt>540963040</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 porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.
+=Hewuermity=
 Comma: 6144/6125
 and 9 limit minimax
 [|1 0 0 0&gt;, |0 1 0 0&gt;, |11/5 1/5 2/5 -2/5&gt;,
 |11/5 1/5 -3/5 3/5&gt;]
 Eigenmonzos: 4/3, 7/5
@@ Line 24: / Line 24: @@
 [[Projection pair]]s: 3 6125/2048 to 2.5.7
 =Zeus=
 Commas: 121/120, 176/175
 Minimax tuning
 [|1 0 0 0 0&gt;, |11/9 10/9 -1/3 -2/9 0&gt;,
 |22/9 2/9 1/3 -4/9 0&gt;, |22/9 2/9 -2/3 5/9 0&gt;,
 |10/3 2/3 0 -1/3 0&gt;]
 Eigenmonzos: 2, 9/7, 7/5
@@ Line 45: / Line 45: @@
 Zeus11[22] [[Hobbits|hobbit]] [[transversal]]
 /32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3,
 /8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4,
 /6, 15/8, 64/33, 2
 Zeus11[24] hobbit transversal
 /32, 16/15, 11/10, 9/8, 8/7, 77/64, 11/9, 5/4, 21/16, 4/3,
 /8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9,
 /6, 15/8, 64/33, 2
 [[genus1155zeus|Euler(1155) genus in zeus temperament]]
-==Tridecimal Zeus==
+==13-limit (tinia)==
+Commas: 66/65, 121/120, 176/175
+Map: [&lt;1 0 1 4 2 2|, &lt;0 1 1 -1 1 1|, &lt;0 0 -2 3 -1 -1|]
+EDOs: 7, 9, 15, 24, 31, 77f, 108ef
+Badness: 0.000808
+==Tridecimal Zeus==
 Commas: 121/120, 176/175, 351/350
 -limit minimax
 [|1 0 0 0 0 0&gt;, |11/9 10/9 -1/3 -2/9 0 0&gt;,
 |22/9 2/9 1/3 -4/9 0 0&gt;, |22/9 2/9 -2/3 5/9 0 0&gt;,
 |10/3 2/3 0 -1/3 0 0&gt;, |14/3 -8/3 1 1/3 0 0&gt;]
 Eigenmonzos: 2, 9/7, 7/5
 -limit minimax
 [|1 0 0 0 0 0&gt;, |0 1 0 0 0 0&gt;,
 |11/5 1/5 2/5 -2/5 0 0&gt;,|11/5 1/5 -3/5 3/5 0 0&gt;,
 |13/5 3/5 1/5 -1/5 0 0&gt;, |38/5 -12/5 1/5 -1/5 0 0&gt;]
 Eigenmonzos: 2, 4/3, 7/5
@@ Line 73: / Line 80: @@
 Map to lattice: [&lt;0 1 -1 2 0 -3|, &lt;0 1 1 -1 1 -2|]
-Map: [&lt;1 0 1 4 2 7|, &lt;0 1 1 -1 1 -2|, &lt;0 0 -2 3 -1  -1|]
+Map: [&lt;1 0 1 4 2 7|, &lt;0 1 1 -1 1 -2|, &lt;0 0 -2 3 -1 -1|]
 Generators: 2, 3, 11/10
 Edos: 6, 7, 8, 9, 15, 16, 22, 23, 24, 31, 37, 38, 39, 40, 46, 47, 53, 55, 59, 68, 75, 77, 84, 99, 130e
@@ Line 83: / Line 90: @@
 /243, 88/81, 11/10, 44/39, 162/143, 11/9, 16/13, 320/243, 4/3, 1040/729, 13/9, 729/520, 3/2, 99/65, 44/27, 18/11, 1280/729, 16/9, 11/6, 24/13, 243/130, 2
-==Tinia==
+=Jupiter=
-Commas: 66/65, 121/120, 176/175
-Map: [&lt;1 0 1 4 2 2|, &lt;0 1 1 -1 1 1|, &lt;0 0 -2 3 -1 -1|]
-EDOs: 7, 9, 15, 24, 31, 77f, 108ef
-Badness: 0.000808
-=Jupiter=
 Commas: 540/539, 5632/5625
@@ Line 97: / Line 97: @@
 Badness: 0.000562</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;Porwell family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:8:&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:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;a href="#Zeus"&gt;Zeus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt; | &lt;a href="#Jupiter"&gt;Jupiter&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&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;Porwell family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:10:&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:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt;&lt;a href="#Hewuermity"&gt;Hewuermity&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt; | &lt;a href="#Zeus"&gt;Zeus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Jupiter"&gt;Jupiter&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:16 --&gt;The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.&lt;br /&gt;
-The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.&lt;br /&gt;
 &lt;br /&gt;
-Comma: 6144/6125&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Hewuermity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Hewuermity&lt;/h1&gt;
+ Comma: 6144/6125&lt;br /&gt;
 &lt;br /&gt;
 and 9 limit minimax&lt;br /&gt;
-[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |11/5 1/5 2/5 -2/5&amp;gt;, &lt;br /&gt;
+[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |11/5 1/5 2/5 -2/5&amp;gt;,&lt;br /&gt;
 |11/5 1/5 -3/5 3/5&amp;gt;]&lt;br /&gt;
 Eigenmonzos: 4/3, 7/5&lt;br /&gt;
@@ Line 115: / Line 115: @@
 &lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 3 6125/2048 to 2.5.7&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="Zeus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Zeus&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Zeus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Zeus&lt;/h1&gt;
-Commas: 121/120, 176/175&lt;br /&gt;
+ Commas: 121/120, 176/175&lt;br /&gt;
 &lt;br /&gt;
 Minimax tuning&lt;br /&gt;
-[|1 0 0 0 0&amp;gt;, |11/9 10/9 -1/3 -2/9 0&amp;gt;, &lt;br /&gt;
+[|1 0 0 0 0&amp;gt;, |11/9 10/9 -1/3 -2/9 0&amp;gt;,&lt;br /&gt;
-|22/9 2/9 1/3 -4/9 0&amp;gt;, |22/9 2/9 -2/3 5/9 0&amp;gt;, &lt;br /&gt;
+|22/9 2/9 1/3 -4/9 0&amp;gt;, |22/9 2/9 -2/3 5/9 0&amp;gt;,&lt;br /&gt;
 |10/3 2/3 0 -1/3 0&amp;gt;]&lt;br /&gt;
 Eigenmonzos: 2, 9/7, 7/5&lt;br /&gt;
@@ Line 136: / Line 136: @@
 &lt;br /&gt;
 Zeus11[22] &lt;a class="wiki_link" href="/Hobbits"&gt;hobbit&lt;/a&gt; &lt;a class="wiki_link" href="/transversal"&gt;transversal&lt;/a&gt;&lt;br /&gt;
-/32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3, &lt;br /&gt;
+/32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3,&lt;br /&gt;
-/8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4, &lt;br /&gt;
+/8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4,&lt;br /&gt;
 /6, 15/8, 64/33, 2&lt;br /&gt;
 Zeus11[24] hobbit transversal&lt;br /&gt;
 /32, 16/15, 11/10, 9/8, 8/7, 77/64, 11/9, 5/4, 21/16, 4/3,&lt;br /&gt;
-/8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9, &lt;br /&gt;
+/8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9,&lt;br /&gt;
 /6, 15/8, 64/33, 2&lt;br /&gt;
 &lt;a class="wiki_link" href="/genus1155zeus"&gt;Euler(1155) genus in zeus temperament&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Zeus-Tridecimal Zeus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Tridecimal Zeus&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Zeus-13-limit (tinia)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit (tinia)&lt;/h2&gt;
-Commas: 121/120, 176/175, 351/350&lt;br /&gt;
+ Commas: 66/65, 121/120, 176/175&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 0 1 4 2 2|, &amp;lt;0 1 1 -1 1 1|, &amp;lt;0 0 -2 3 -1 -1|]&lt;br /&gt;
+EDOs: 7, 9, 15, 24, 31, 77f, 108ef&lt;br /&gt;
+Badness: 0.000808&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Zeus-Tridecimal Zeus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Tridecimal Zeus&lt;/h2&gt;
+ Commas: 121/120, 176/175, 351/350&lt;br /&gt;
 &lt;br /&gt;
 -limit minimax&lt;br /&gt;
-[|1 0 0 0 0 0&amp;gt;, |11/9 10/9 -1/3 -2/9 0 0&amp;gt;, &lt;br /&gt;
+[|1 0 0 0 0 0&amp;gt;, |11/9 10/9 -1/3 -2/9 0 0&amp;gt;,&lt;br /&gt;
-|22/9 2/9 1/3 -4/9 0 0&amp;gt;, |22/9 2/9 -2/3 5/9 0 0&amp;gt;, &lt;br /&gt;
+|22/9 2/9 1/3 -4/9 0 0&amp;gt;, |22/9 2/9 -2/3 5/9 0 0&amp;gt;,&lt;br /&gt;
 |10/3 2/3 0 -1/3 0 0&amp;gt;, |14/3 -8/3 1 1/3 0 0&amp;gt;]&lt;br /&gt;
 Eigenmonzos: 2, 9/7, 7/5&lt;br /&gt;
 &lt;br /&gt;
 -limit minimax&lt;br /&gt;
-[|1 0 0 0 0 0&amp;gt;, |0 1 0 0 0 0&amp;gt;, &lt;br /&gt;
+[|1 0 0 0 0 0&amp;gt;, |0 1 0 0 0 0&amp;gt;,&lt;br /&gt;
-|11/5 1/5 2/5 -2/5 0 0&amp;gt;,|11/5 1/5 -3/5 3/5 0 0&amp;gt;, &lt;br /&gt;
+|11/5 1/5 2/5 -2/5 0 0&amp;gt;,|11/5 1/5 -3/5 3/5 0 0&amp;gt;,&lt;br /&gt;
 |13/5 3/5 1/5 -1/5 0 0&amp;gt;, |38/5 -12/5 1/5 -1/5 0 0&amp;gt;]&lt;br /&gt;
 Eigenmonzos: 2, 4/3, 7/5&lt;br /&gt;
@@ Line 164: / Line 171: @@
 Map to lattice: [&amp;lt;0 1 -1 2 0 -3|, &amp;lt;0 1 1 -1 1 -2|]&lt;br /&gt;
 &lt;br /&gt;
-Map: [&amp;lt;1 0 1 4 2 7|, &amp;lt;0 1 1 -1 1 -2|, &amp;lt;0 0 -2 3 -1  -1|]&lt;br /&gt;
+Map: [&amp;lt;1 0 1 4 2 7|, &amp;lt;0 1 1 -1 1 -2|, &amp;lt;0 0 -2 3 -1 -1|]&lt;br /&gt;
 Generators: 2, 3, 11/10&lt;br /&gt;
 Edos: 6, 7, 8, 9, 15, 16, 22, 23, 24, 31, 37, 38, 39, 40, 46, 47, 53, 55, 59, 68, 75, 77, 84, 99, 130e&lt;br /&gt;
@@ Line 174: / Line 181: @@
 /243, 88/81, 11/10, 44/39, 162/143, 11/9, 16/13, 320/243, 4/3, 1040/729, 13/9, 729/520, 3/2, 99/65, 44/27, 18/11, 1280/729, 16/9, 11/6, 24/13, 243/130, 2&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Zeus-Tinia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Tinia&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Jupiter"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Jupiter&lt;/h1&gt;
-Commas: 66/65, 121/120, 176/175&lt;br /&gt;
+ Commas: 540/539, 5632/5625&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 1 4 2 2|, &amp;lt;0 1 1 -1 1 1|, &amp;lt;0 0 -2 3 -1 -1|]&lt;br /&gt;
-EDOs: 7, 9, 15, 24, 31, 77f, 108ef&lt;br /&gt;
-Badness: 0.000808&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Jupiter"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Jupiter&lt;/h1&gt;
-Commas: 540/539, 5632/5625&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1 4 -5|, &amp;lt;0 1 1 -1 6|, &amp;lt;0 0 2 -3 8|]&lt;br /&gt;
 EDOs: 9, 22, 31, 53, 99e, 108, 121, 130, 152, 282, 434de, 465d, 617de, 747def, 899def&lt;br /&gt;
 Badness: 0.000562&lt;/body&gt;&lt;/html&gt;</pre></div>