Epimorphic Euler genera: Difference between revisions

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**Imported revision 477428412 - Original comment: **
m Fredg999 moved page Epimorphic Euler Genera to Epimorphic Euler genera: WP:NCCAPS
 
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<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 11:08:30 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>477428412</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=
=Eight notes=
==Rank two==
==Rank two==
Genus(3^3*11), Genus(13^3*5)
Genus(3^3*11), Genus(13^3*5)


==Rank three==
==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=
=Nine notes=
==Rank one==
==Rank one==
Genus(11^9)
Genus(11^9)
Line 21: Line 18:
==Rank two==
==Rank two==
Genus(3^2*5^2), Genus(3^2*13^2)
Genus(3^2*5^2), Genus(3^2*13^2)
Genus(5^2*7^2), Genus(5^2*11^2),
Genus(5^2*7^2), Genus(5^2*11^2),
Genus(7^2*13^2), Genus(11^2*13^2)
Genus(7^2*13^2), Genus(11^2*13^2)


=Ten notes=
=Ten notes=
==Rank one==
==Rank one==
Genus(5^9), Genus(13^9)
Genus(5^9), Genus(13^9)
Line 30: Line 30:
==Rank two==
==Rank two==
Genus(3^4*5), Genus(3^4*11), Genus(3^4*13)
Genus(3^4*5), Genus(3^4*11), Genus(3^4*13)
Genus(5^4*7), Genus(5^4*11)
Genus(5^4*7), Genus(5^4*11)
Genus(7^4*5), Genus(7^4*11), Genus(7^4*13)
Genus(7^4*5), Genus(7^4*11), Genus(7^4*13)
Genus(13^4*11)
Genus(13^4*11)


=Twelve notes=
=Twelve notes=
==Rank one==
==Rank one==
Genus(3^11) (Pythagorean)
Genus(3^11) (Pythagorean)
Line 40: Line 44:
==Rank two==
==Rank two==
Genus(3^5*11), Genus(3*7^5)
Genus(3^5*11), Genus(3*7^5)
Genus(3^3*5^2) (Duodene)  
Genus(3^3*5^2) (Duodene)  
Genus(3^2*13^3) (12f), Genus(3^3*13^2) (patent)
Genus(3^2*13^3) (12f), Genus(3^3*13^2) (patent)


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


Line 52: Line 59:
=Fifteen notes=
=Fifteen notes=
Genus(3^4*11^2), Genus(5^4*11^2)
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)
Genus(5^2*7^4), Genus(5^2*11^4), Genus(5^2*13^4)


=Sixteen notes=
=Sixteen notes=
==Rank one==
==Rank one==
Genus(5^15), Genus(7^15)
Genus(5^15), Genus(7^15)
Line 62: Line 71:


=Eighteen notes=
=Eighteen notes=
==Rank two==
==Rank two==
Genus(5^2*13^5)
Genus(5^2*13^5)


==Rank three==
==Rank three==
Genus(5^2*7*13^2), Genus(5^2*11^2*13)</pre></div>
Genus(5^2*7*13^2), Genus(5^2*11^2*13)
<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;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;
=Twenty notes=
&lt;br /&gt;
 
&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;
==Rank two==
&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(7^4*11^3), Genus(13^9*11)
Genus(3^3*11), Genus(13^3*5)&lt;br /&gt;
 
&lt;br /&gt;
==Rank three==
&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;
Genus(7^4*5*11), Genus(7^4*11*13)
Genus(3*11*13), Genus(5*11*13), Genus(3*7*11) (patent)&lt;br /&gt;
 
&lt;br /&gt;
=Twenty-one notes=
&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;
==Rank one==
Genus(11^9)&lt;br /&gt;
Genus(7^20)
&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;
==Rank two==
Genus(3^2*5^2), Genus(3^2*13^2)&lt;br /&gt;
Genus(3^6*7^2), Genus(7^6*5^2), Genus(13^6*5^2)
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;
=Twenty-two notes=
&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;
==Rank one==
&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(5^21)
Genus(5^9), Genus(13^9)&lt;br /&gt;
 
&lt;br /&gt;
==Rank two==
&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(5^10*7), Genus(7^10*3), Genus(11^10*5), Genus(11^10*13)
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;
=Twenty-four notes=
Genus(7^4*5), Genus(7^4*11), Genus(7^4*13)&lt;br /&gt;
 
Genus(13^4*11)&lt;br /&gt;
==Rank one==
&lt;br /&gt;
Genus(11^23)
&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;
==Rank two==
Genus(3^11) (Pythagorean)&lt;br /&gt;
Genus(3^11*7) (patent), Genus(3^11*11), Genus(3^11*13)
&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(5^2*11^7), Genus(5^2*13^7)
Genus(3^5*11), Genus(3*7^5)&lt;br /&gt;
 
Genus(3^3*5^2) (Duodene) &lt;br /&gt;
==Rank three==
Genus(3^2*13^3) (12f), Genus(3^3*13^2) (patent)&lt;br /&gt;
Genus(3^3*5^2*7) (patent), Genus(3^3*5^2*11), Genus(3^3*5^2*13)
&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(3^2*7*13^3) (24d)
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;
==Rank four==
&lt;br /&gt;
Genus(3*5^2*7*13) (24d)
&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;
=Twenty-five notes=
&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;
==Rank one==
Genus(3^4*11^2), Genus(5^4*11^2)&lt;br /&gt;
Genus(5^24)
Genus(5^2*7^4), Genus(5^2*11^4), Genus(5^2*13^4)&lt;br /&gt;
 
&lt;br /&gt;
==Rank two==
&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;
Genus(5^4*7^4)
&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;
=Twenty-six notes=
&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;
==Rank one==
Genus(5^7*7)&lt;br /&gt;
Genus(7^25)
&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;
==Rank two==
&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(7^12*5), Genus(11^12*3), Genus(11^12*7)
Genus(5^2*13^5)&lt;br /&gt;
 
&lt;br /&gt;
=Twenty-seven notes=
&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;/body&gt;&lt;/html&gt;</pre></div>
==Rank one==
Genus(13^26)
 
==Rank two==
Genus(5^2*13^8)
 
==Rank three==
Genus(5^2*11^2*13^2) (patent)
 
=Twenty-eight notes=
 
==Rank one==
Genus(5^27)
 
==Rank two==
Genus(5^3*13^6)
[[Category:Lists of scales]]
[[Category:Euler-Fokker genera]]

Latest revision as of 04:35, 28 April 2023

Below are listed the 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*5*11) (patent), Genus(3*7*11) (patent)

Nine notes

Rank one

Genus(11^9)

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)

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)

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)

Fourteen notes

Genus(3^6*7), Genus(13^6*5) (weakly; patent)

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)

Rank two

Genus(5^7*7)

Eighteen notes

Rank two

Genus(5^2*13^5)

Rank three

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

Twenty notes

Rank two

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

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)

Rank two

Genus(5^10*7), Genus(7^10*3), Genus(11^10*5), Genus(11^10*13)

Twenty-four notes

Rank one

Genus(11^23)

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)

Rank four

Genus(3*5^2*7*13) (24d)

Twenty-five notes

Rank one

Genus(5^24)

Rank two

Genus(5^4*7^4)

Twenty-six notes

Rank one

Genus(7^25)

Rank two

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

Twenty-seven notes

Rank one

Genus(13^26)

Rank two

Genus(5^2*13^8)

Rank three

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

Twenty-eight notes

Rank one

Genus(5^27)

Rank two

Genus(5^3*13^6)

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