Epimorphic Euler genera: Difference between revisions

(6 intermediate revisions by 4 users not shown)

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>2013-12-14 16:01:41 UTC</tt>.<br>~~

Below are listed the [[Periodic_scale#Epimorphic|epimorphic]] [[Euler_genera|Euler genera]] for various numbers of notes.

~~: The original revision id was <tt>477464648</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"~~>Below are listed the [[~~Periodic scale~~#Epimorphic|epimorphic]] [[Euler genera]] for various numbers of notes.

=Eight notes=

==Rank two==

Genus(3^3*11), Genus(13^3*5)

==Rank three==

Genus(3*11*13), Genus(5*11*13), Genus(3*7*11) (patent)

Genus(3*11*13), Genus(5*11*13), Genus(3*5*11) (patent), Genus(3*7*11) (patent)

=Nine notes=

==Rank one==

Genus(11^9)

Line 21:

Line 18:

==Rank two==

Genus(3^2*5^2), Genus(3^2*13^2)

Genus(5^2*7^2), Genus(5^2*11^2),

Genus(7^2*13^2), Genus(11^2*13^2)

=Ten notes=

==Rank one==

Genus(5^9), Genus(13^9)

Line 30:

==Rank two==

Genus(3^4*5), Genus(3^4*11), Genus(3^4*13)

Genus(5^4*7), Genus(5^4*11)

Genus(7^4*5), Genus(7^4*11), Genus(7^4*13)

Genus(13^4*11)

=Twelve notes=

==Rank one==

Genus(3^11) (Pythagorean)

Line 40:

Line 44:

==Rank two==

Genus(3^5*11), Genus(3*7^5)

Genus(3^3*5^2) (Duodene)

Genus(3^2*13^3) (12f), Genus(3^3*13^2) (patent)

==Rank three==

Genus(3*5^2*7), Genus(3*5^2*11), Genus(3*7^2*11)

Genus(5^2*7*13) (12f), Genus(5^2*11*13) (12f), Genus(3*11*13^2) (patent)

Line 52:

Line 59:

=Fifteen notes=

Genus(3^4*11^2), Genus(5^4*11^2)

Genus(5^2*7^4), Genus(5^2*11^4), Genus(5^2*13^4)

=Sixteen notes=

==Rank one==

Genus(5^15), Genus(7^15)

Line 62:

Line 71:

=Eighteen notes=

==Rank two==

Genus(5^2*13^5)

Line 69:

Line 79:

=Twenty notes=

==Rank two==

Genus(7^4*11^3), Genus(13^9*11)

Line 74:

Line 85:

==Rank three==

Genus(7^4*5*11), Genus(7^4*11*13)

=Twenty-one notes=

==Rank one==

Genus(7^20)

==Rank two==

Genus(3^6*7^2), Genus(7^6*5^2), Genus(13^6*5^2)

=Twenty-two notes=

==Rank one==

Genus(5^21)

Line 83:

Line 103:

=Twenty-four notes=

==Rank one==

Genus(11^23)

Line 88:

Line 109:

==Rank two==

Genus(3^11*7) (patent), Genus(3^11*11), Genus(3^11*13)

Genus(5^2*11^7), Genus(5^2*13^7)

==Rank three==

Genus(3^3*5^2*7) (patent), Genus(3^3*5^2*11), Genus(3^3*5^2*13)

Genus(3^2*7*13^3) (24d)

Line 98:

Line 121:

=Twenty-five notes=

==Rank one==

Genus(5^24)

Line 105:

Line 129:

=Twenty-six notes=

==Rank one==

Genus(7^25)

Line 111:

Line 136:

Genus(7^12*5), Genus(11^12*3), Genus(11^12*7)

=Twenty-seven=

=Twenty-seven notes=

==Rank one==

Genus(13^26)

Line 120:

Line 146:

==Rank three==

Genus(5^2*11^2*13^2) (patent)

~~</pre></div>~~

~~<h4>Original HTML content:</h4>~~

=Twenty-eight notes=

~~<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>Epimorphic Euler Genera</title></head><body>Below are listed the <a class="wiki_link" href="/Periodic%20scale#Epimorphic">epimorphic</a> <a class="wiki_link" href="/Euler%20genera">Euler genera</a> for various numbers of notes.<br />

~~<br />~~

==Rank one==

~~<h1 id="toc0"><a name="Eight notes"></a><!-- ws:end:WikiTextHeadingRule:0 -~~-~~>Eight~~ notes~~</h1>~~

Genus(5^27)

~~<h2 id="toc1"><a name~~=~~"Eight notes-Rank two"></a>Rank two</h2>~~

~~Genus(3^3*11), Genus(13^3*5)<br />~~

==Rank two==

~~<br />~~

Genus(5^3*13^6)

~~<h2 id~~=~~"toc2"><a name~~=~~"Eight notes-Rank three"></a>Rank three</h2>~~

[[Category:Lists of scales]]

~~Genus(3*11*13), Genus(5*11*13), Genus(3*7*11) (patent)<br />~~

[[Category:Euler-Fokker genera]]

~~<br />~~

~~<h1 id="toc3"><a name="Nine notes"></a>Nine notes</h1>~~

~~<h2 id="toc4"><a name="Nine notes-Rank one"></a>~~Rank one~~</h2>~~

~~Genus(11^9)<br />~~

~~<br />~~

~~<h2 id~~=~~"toc5"><a name~~=~~"Nine notes-Rank two"></a>Rank two</h2>~~

~~Genus(3^2*5^2), Genus(3^2*13^2)<br />~~

~~Genus(5^2*7^2), Genus(5^2*11^2),<br />~~

~~Genus(7^2*13^2), Genus(11^2*13^2)<br />~~

~~<br />~~

~~<h1 id="toc6"><a name="Ten notes"></a>Ten notes</h1>~~

~~<h2 id="toc7"><a name="Ten notes-Rank one"></a>Rank one</h2>~~

~~Genus(5^9), Genus(13^9)<br />~~

~~<br />~~

~~<h2 id="toc8"><a name="Ten notes-Rank two"></a>Rank two</h2>~~

Genus(3^4*5~~), Genus(3^4*11), Genus(3^4*13)<br />~~

~~Genus(5^4*7), Genus(5^4*11)<br />~~

~~Genus(7^4*5), Genus(7^4*11), Genus(7^4*13)<br />~~

~~Genus(13^4*11)<br />~~

~~<br />~~

~~<h1 id="toc9"><a name="Twelve notes"></a>Twelve notes</h1>~~

~~<h2 id="toc10"><a name="Twelve notes-Rank one"></a>Rank one</h2>~~

~~Genus(3~~^~~11) (Pythagorean~~)~~<br />~~

~~<br />~~

~~<h2 id~~=~~"toc11"><a name~~=~~"Twelve notes-Rank two"></a>~~Rank two~~</h2>~~

~~Genus(3^5*11), Genus(3*7^5)<br />~~

~~Genus(3^3*5^2) (Duodene) <br />~~

~~Genus(3^2*13^3) (12f), Genus(3^3*13^2) (patent)<br />~~

~~<br />~~

~~<h2 id~~=~~"toc12"><a name~~=~~"Twelve notes-Rank three"></a>Rank three</h2>~~

Genus(3*5^~~2*7), Genus(~~3*5^2*11), Genus(3*7^2*11)<br />

~~Genus(5^2*7~~*13~~) (12f), Genus(5^2*11*13) (12f), Genus(3*11*13^2) (patent)<br />~~

~~<br />~~

~~<h1 id="toc13"><a name="Fourteen notes"></a>Fourteen notes</h1>~~

~~Genus(3~~^6*7)~~, Genus(13^6*5) (weakly; patent)<br />~~

~~<br />~~

~~<h1 id="toc14"><a name="Fifteen notes"></a>Fifteen notes</h1>~~

~~Genus(3^4*11^2), Genus(5^4*11^2)<br />~~

~~Genus(5^2*7^4), Genus(5^2*11^4), Genus(5^2*13^4)<br />~~

~~<br />~~

~~Sixteen notes</h1>~~

~~<h2 id="toc16"><a name="Sixteen notes-Rank one"></a>Rank one</h2>~~

~~Genus(5^15), Genus(7^15)<br />~~

~~<br />~~

~~<h2 id="toc17"><a name="Sixteen notes-Rank two"></a>Rank two</h2>~~

~~Genus(5^7*7)<br />~~

~~<br />~~

~~<h1 id="toc18"><a name="Eighteen notes"></a>Eighteen notes</h1>~~

~~<h2 id="toc19"><a name="Eighteen notes-Rank two"></a>Rank two</h2>~~

~~Genus(5^2*13^5)<br />~~

~~<br />~~

<h2 id="toc20"><a name="Eighteen notes-Rank three"></a>Rank three</h2>

~~Genus(5^2*7*13^2), Genus(5^2*11^2*13)<br />~~

~~<br />~~

~~<h1 id="toc21"><a name="Twenty notes"></a>Twenty notes</h1>~~

~~<h2 id="toc22"><a name="Twenty notes-Rank two"></a>Rank two</h2>~~

~~Genus(7^4*11^3), Genus(13^9*11)<br />~~

~~<br />~~

<h2 id="toc23"><a name="Twenty notes-Rank three"></a>Rank three</h2>

~~Genus(7^4*5*11), Genus(7^4*11*13)<br />~~

~~<br />~~

~~<h1 id="toc24"><a name="Twenty-two notes"></a>Twenty-two notes</h1>~~

<h2 id="toc25"><a name="Twenty-two notes-Rank one"></a>Rank one</h2>

~~Genus(5^21)<br />~~

~~<br />~~

<h2 id="toc26"><a name="Twenty-two notes-Rank two"></a>Rank two</h2>

~~Genus(5^10*7), Genus(7^10*3), Genus(11^10*5), Genus(11^10*13)<br />~~

~~<br />~~

<h1 id="toc27"><a name="Twenty-four notes"></a>Twenty-four notes</h1>

<h2 id="toc28"><a name="Twenty-four notes-Rank one"></a>Rank one</h2>

~~Genus(11^23)<br />~~

~~<br />~~

<h2 id="toc29"><a name="Twenty-four notes-Rank two"></a>Rank two</h2>

~~Genus(3^11*7) (patent), Genus(3^11*11), Genus(3^11*13)<br />~~

~~Genus(5^2*11^7), Genus(5^2*13^7)<br />~~

~~<br />~~

<h2 id="toc30"><a name="Twenty-four notes-Rank three"></a>Rank three</h2>

~~Genus(3^3*5^2*7) (patent), Genus(3^3*5^2*11), Genus(3^3*5^2*13)<br />~~

~~Genus(3^2*7*13^3) (24d)<br />~~

~~<br />~~

<h2 id="toc31"><a name="Twenty-four notes-Rank four"></a>Rank four</h2>

~~Genus(3*5^2*7*13) (24d)<br />~~

~~<br />~~

<h1 id="toc32"><a name="Twenty-five notes"></a>Twenty-five notes</h1>

<h2 id="toc33"><a name="Twenty-five notes-Rank one"></a>Rank one</h2>

~~Genus(5^24)<br />~~

~~<br />~~

<h2 id="toc34"><a name="Twenty-five notes-Rank two"></a>Rank two</h2>

~~Genus(5^4*7^4)<br />~~

~~<br />~~

~~<h1 id="toc35"><a name="Twenty-six notes"></a>Twenty-six notes</h1>~~

<h2 id="toc36"><a name="Twenty-six notes-Rank one"></a>Rank one</h2>

~~Genus(7^25)<br />~~

~~<br />~~

<h2 id="toc37"><a name="Twenty-six notes-Rank two"></a>Rank two</h2>

~~Genus(7^12*5), Genus(11^12*3), Genus(11^12*7)<br />~~

~~<br />~~

~~<h1 id="toc38"><a name="Twenty-seven"></a>Twenty-seven</h1>~~

~~<h2 id="toc39"><a name="Twenty-seven-Rank one"></a>Rank one</h2>~~

~~Genus(13^26)<br />~~

~~<br />~~

~~<h2 id="toc40"><a name="Twenty-seven-Rank two"></a>Rank two</h2>~~

~~Genus(5^2*13^8)<br />~~

~~<br />~~

<h2 id="toc41"><a name="Twenty-seven-Rank three"></a>Rank three</h2>

~~Genus(5^2*11^2*13^2) (patent)</body></html></pre></div>~~

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+<div style="float:right">__TOC__</div>
-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>2013-12-14 16:01:41 UTC</tt>.<br>
+Below are listed the [[Periodic_scale#Epimorphic|epimorphic]] [[Euler_genera|Euler genera]] for various numbers of notes.
-: The original revision id was <tt>477464648</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">Below are listed the [[Periodic scale#Epimorphic|epimorphic]] [[Euler genera]] for various numbers of notes.
 =Eight notes=
 ==Rank two==
 Genus(3^3*11), Genus(13^3*5)
 ==Rank three==
-Genus(3*11*13), Genus(5*11*13), Genus(3*7*11) (patent)
+Genus(3*11*13), Genus(5*11*13), Genus(3*5*11) (patent), Genus(3*7*11) (patent)
 =Nine notes=
 ==Rank one==
 Genus(11^9)
@@ Line 21: / Line 18: @@
 ==Rank two==
 Genus(3^2*5^2), Genus(3^2*13^2)
 Genus(5^2*7^2), Genus(5^2*11^2),
 Genus(7^2*13^2), Genus(11^2*13^2)
 =Ten notes=
 ==Rank one==
 Genus(5^9), Genus(13^9)
@@ Line 30: / Line 30: @@
 ==Rank two==
 Genus(3^4*5), Genus(3^4*11), Genus(3^4*13)
 Genus(5^4*7), Genus(5^4*11)
 Genus(7^4*5), Genus(7^4*11), Genus(7^4*13)
 Genus(13^4*11)
 =Twelve notes=
 ==Rank one==
 Genus(3^11) (Pythagorean)
@@ Line 40: / Line 44: @@
 ==Rank two==
 Genus(3^5*11), Genus(3*7^5)
 Genus(3^3*5^2) (Duodene)
 Genus(3^2*13^3) (12f), Genus(3^3*13^2) (patent)
 ==Rank three==
 Genus(3*5^2*7), Genus(3*5^2*11), Genus(3*7^2*11)
 Genus(5^2*7*13) (12f), Genus(5^2*11*13) (12f), Genus(3*11*13^2) (patent)
@@ Line 52: / Line 59: @@
 =Fifteen notes=
 Genus(3^4*11^2), Genus(5^4*11^2)
 Genus(5^2*7^4), Genus(5^2*11^4), Genus(5^2*13^4)
 =Sixteen notes=
 ==Rank one==
 Genus(5^15), Genus(7^15)
@@ Line 62: / Line 71: @@
 =Eighteen notes=
 ==Rank two==
 Genus(5^2*13^5)
@@ Line 69: / Line 79: @@
 =Twenty notes=
 ==Rank two==
 Genus(7^4*11^3), Genus(13^9*11)
@@ Line 74: / Line 85: @@
 ==Rank three==
 Genus(7^4*5*11), Genus(7^4*11*13)
+=Twenty-one notes=
+==Rank one==
+Genus(7^20)
+==Rank two==
+Genus(3^6*7^2), Genus(7^6*5^2), Genus(13^6*5^2)
 =Twenty-two notes=
 ==Rank one==
 Genus(5^21)
@@ Line 83: / Line 103: @@
 =Twenty-four notes=
 ==Rank one==
 Genus(11^23)
@@ Line 88: / Line 109: @@
 ==Rank two==
 Genus(3^11*7) (patent), Genus(3^11*11), Genus(3^11*13)
 Genus(5^2*11^7), Genus(5^2*13^7)
 ==Rank three==
 Genus(3^3*5^2*7) (patent), Genus(3^3*5^2*11), Genus(3^3*5^2*13)
 Genus(3^2*7*13^3) (24d)
@@ Line 98: / Line 121: @@
 =Twenty-five notes=
 ==Rank one==
 Genus(5^24)
@@ Line 105: / Line 129: @@
 =Twenty-six notes=
 ==Rank one==
 Genus(7^25)
@@ Line 111: / Line 136: @@
 Genus(7^12*5), Genus(11^12*3), Genus(11^12*7)
-=Twenty-seven=
+=Twenty-seven notes=
 ==Rank one==
 Genus(13^26)
@@ Line 120: / Line 146: @@
 ==Rank three==
 Genus(5^2*11^2*13^2) (patent)
-</pre></div>
-<h4>Original HTML content:</h4>
+=Twenty-eight notes=
-<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;Epimorphic Euler Genera&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are listed the &lt;a class="wiki_link" href="/Periodic%20scale#Epimorphic"&gt;epimorphic&lt;/a&gt; &lt;a class="wiki_link" href="/Euler%20genera"&gt;Euler genera&lt;/a&gt; for various numbers of notes.&lt;br /&gt;
-&lt;br /&gt;
+==Rank one==
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Eight notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Eight notes&lt;/h1&gt;
+Genus(5^27)
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Eight notes-Rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Rank two&lt;/h2&gt;
-Genus(3^3*11), Genus(13^3*5)&lt;br /&gt;
+==Rank two==
-&lt;br /&gt;
+Genus(5^3*13^6)
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Eight notes-Rank three"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Rank three&lt;/h2&gt;
+[[Category:Lists of scales]]
-Genus(3*11*13), Genus(5*11*13), Genus(3*7*11) (patent)&lt;br /&gt;
+[[Category:Euler-Fokker genera]]
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Nine notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Nine notes&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Nine notes-Rank one"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Rank one&lt;/h2&gt;
-Genus(11^9)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Nine notes-Rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Rank two&lt;/h2&gt;
-Genus(3^2*5^2), Genus(3^2*13^2)&lt;br /&gt;
-Genus(5^2*7^2), Genus(5^2*11^2),&lt;br /&gt;
-Genus(7^2*13^2), Genus(11^2*13^2)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Ten notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Ten notes&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Ten notes-Rank one"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Rank one&lt;/h2&gt;
-Genus(5^9), Genus(13^9)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Ten notes-Rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Rank two&lt;/h2&gt;
-Genus(3^4*5), Genus(3^4*11), Genus(3^4*13)&lt;br /&gt;
-Genus(5^4*7), Genus(5^4*11)&lt;br /&gt;
-Genus(7^4*5), Genus(7^4*11), Genus(7^4*13)&lt;br /&gt;
-Genus(13^4*11)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Twelve notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Twelve notes&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Twelve notes-Rank one"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Rank one&lt;/h2&gt;
-Genus(3^11) (Pythagorean)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Twelve notes-Rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Rank two&lt;/h2&gt;
-Genus(3^5*11), Genus(3*7^5)&lt;br /&gt;
-Genus(3^3*5^2) (Duodene) &lt;br /&gt;
-Genus(3^2*13^3) (12f), Genus(3^3*13^2) (patent)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Twelve notes-Rank three"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Rank three&lt;/h2&gt;
-Genus(3*5^2*7), Genus(3*5^2*11), Genus(3*7^2*11)&lt;br /&gt;
-Genus(5^2*7*13) (12f), Genus(5^2*11*13) (12f), Genus(3*11*13^2) (patent)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Fourteen notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Fourteen notes&lt;/h1&gt;
-Genus(3^6*7), Genus(13^6*5) (weakly; patent)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Fifteen notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Fifteen notes&lt;/h1&gt;
-Genus(3^4*11^2), Genus(5^4*11^2)&lt;br /&gt;
-Genus(5^2*7^4), Genus(5^2*11^4), Genus(5^2*13^4)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Sixteen notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Sixteen notes&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Sixteen notes-Rank one"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Rank one&lt;/h2&gt;
-Genus(5^15), Genus(7^15)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Sixteen notes-Rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Rank two&lt;/h2&gt;
-Genus(5^7*7)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Eighteen notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Eighteen notes&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Eighteen notes-Rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Rank two&lt;/h2&gt;
-Genus(5^2*13^5)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Eighteen notes-Rank three"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Rank three&lt;/h2&gt;
-Genus(5^2*7*13^2), Genus(5^2*11^2*13)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Twenty notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Twenty notes&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Twenty notes-Rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Rank two&lt;/h2&gt;
-Genus(7^4*11^3), Genus(13^9*11)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Twenty notes-Rank three"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Rank three&lt;/h2&gt;
-Genus(7^4*5*11), Genus(7^4*11*13)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Twenty-two notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Twenty-two notes&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Twenty-two notes-Rank one"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Rank one&lt;/h2&gt;
-Genus(5^21)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Twenty-two notes-Rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Rank two&lt;/h2&gt;
-Genus(5^10*7), Genus(7^10*3), Genus(11^10*5), Genus(11^10*13)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Twenty-four notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Twenty-four notes&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Twenty-four notes-Rank one"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Rank one&lt;/h2&gt;
-Genus(11^23)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Twenty-four notes-Rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Rank two&lt;/h2&gt;
-Genus(3^11*7) (patent), Genus(3^11*11), Genus(3^11*13)&lt;br /&gt;
-Genus(5^2*11^7), Genus(5^2*13^7)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Twenty-four notes-Rank three"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;Rank three&lt;/h2&gt;
-Genus(3^3*5^2*7) (patent), Genus(3^3*5^2*11), Genus(3^3*5^2*13)&lt;br /&gt;
-Genus(3^2*7*13^3) (24d)&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="Twenty-four notes-Rank four"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;Rank four&lt;/h2&gt;
-Genus(3*5^2*7*13) (24d)&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="Twenty-five notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;Twenty-five notes&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Twenty-five notes-Rank one"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;Rank one&lt;/h2&gt;
-Genus(5^24)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="Twenty-five notes-Rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;Rank two&lt;/h2&gt;
-Genus(5^4*7^4)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="Twenty-six notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Twenty-six notes&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Twenty-six notes-Rank one"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;Rank one&lt;/h2&gt;
-Genus(7^25)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc37"&gt;&lt;a name="Twenty-six notes-Rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;Rank two&lt;/h2&gt;
-Genus(7^12*5), Genus(11^12*3), Genus(11^12*7)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc38"&gt;&lt;a name="Twenty-seven"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;Twenty-seven&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Twenty-seven-Rank one"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;Rank one&lt;/h2&gt;
-Genus(13^26)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc40"&gt;&lt;a name="Twenty-seven-Rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;Rank two&lt;/h2&gt;
-Genus(5^2*13^8)&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc41"&gt;&lt;a name="Twenty-seven-Rank three"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;Rank three&lt;/h2&gt;
-Genus(5^2*11^2*13^2) (patent)&lt;/body&gt;&lt;/html&gt;</pre></div>