Epimorphic Euler genera
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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) =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-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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<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 /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Eight notes"></a><!-- ws:end:WikiTextHeadingRule:0 -->Eight notes</h1> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Eight notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank two</h2> Genus(3^3*11), Genus(13^3*5)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Eight notes-Rank three"></a><!-- ws:end:WikiTextHeadingRule:4 -->Rank three</h2> Genus(3*11*13), Genus(5*11*13), Genus(3*7*11) (patent)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Nine notes"></a><!-- ws:end:WikiTextHeadingRule:6 -->Nine notes</h1> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Nine notes-Rank one"></a><!-- ws:end:WikiTextHeadingRule:8 -->Rank one</h2> Genus(11^9)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Nine notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:10 -->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 /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Ten notes"></a><!-- ws:end:WikiTextHeadingRule:12 -->Ten notes</h1> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="Ten notes-Rank one"></a><!-- ws:end:WikiTextHeadingRule:14 -->Rank one</h2> Genus(5^9), Genus(13^9)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Ten notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:16 -->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 /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="Twelve notes"></a><!-- ws:end:WikiTextHeadingRule:18 -->Twelve notes</h1> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="Twelve notes-Rank one"></a><!-- ws:end:WikiTextHeadingRule:20 -->Rank one</h2> Genus(3^11) (Pythagorean)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="Twelve notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:22 -->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 /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="Twelve notes-Rank three"></a><!-- ws:end:WikiTextHeadingRule:24 -->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 /> <!-- ws:start:WikiTextHeadingRule:26:<h1> --><h1 id="toc13"><a name="Fourteen notes"></a><!-- ws:end:WikiTextHeadingRule:26 -->Fourteen notes</h1> Genus(3^6*7), Genus(13^6*5) (weakly; patent)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h1> --><h1 id="toc14"><a name="Fifteen notes"></a><!-- ws:end:WikiTextHeadingRule:28 -->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 /> <!-- ws:start:WikiTextHeadingRule:30:<h1> --><h1 id="toc15"><a name="Sixteen notes"></a><!-- ws:end:WikiTextHeadingRule:30 -->Sixteen notes</h1> <!-- ws:start:WikiTextHeadingRule:32:<h2> --><h2 id="toc16"><a name="Sixteen notes-Rank one"></a><!-- ws:end:WikiTextHeadingRule:32 -->Rank one</h2> Genus(5^15), Genus(7^15)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h2> --><h2 id="toc17"><a name="Sixteen notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:34 -->Rank two</h2> Genus(5^7*7)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h1> --><h1 id="toc18"><a name="Eighteen notes"></a><!-- ws:end:WikiTextHeadingRule:36 -->Eighteen notes</h1> <!-- ws:start:WikiTextHeadingRule:38:<h2> --><h2 id="toc19"><a name="Eighteen notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:38 -->Rank two</h2> Genus(5^2*13^5)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:40:<h2> --><h2 id="toc20"><a name="Eighteen notes-Rank three"></a><!-- ws:end:WikiTextHeadingRule:40 -->Rank three</h2> Genus(5^2*7*13^2), Genus(5^2*11^2*13)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:42:<h1> --><h1 id="toc21"><a name="Twenty notes"></a><!-- ws:end:WikiTextHeadingRule:42 -->Twenty notes</h1> <!-- ws:start:WikiTextHeadingRule:44:<h2> --><h2 id="toc22"><a name="Twenty notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:44 -->Rank two</h2> Genus(7^4*11^3), Genus(13^9*11)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:46:<h2> --><h2 id="toc23"><a name="Twenty notes-Rank three"></a><!-- ws:end:WikiTextHeadingRule:46 -->Rank three</h2> Genus(7^4*5*11), Genus(7^4*11*13)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:48:<h1> --><h1 id="toc24"><a name="Twenty-two notes"></a><!-- ws:end:WikiTextHeadingRule:48 -->Twenty-two notes</h1> <!-- ws:start:WikiTextHeadingRule:50:<h2> --><h2 id="toc25"><a name="Twenty-two notes-Rank one"></a><!-- ws:end:WikiTextHeadingRule:50 -->Rank one</h2> Genus(5^21)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:52:<h2> --><h2 id="toc26"><a name="Twenty-two notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:52 -->Rank two</h2> Genus(5^10*7), Genus(7^10*3), Genus(11^10*5), Genus(11^10*13)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:54:<h1> --><h1 id="toc27"><a name="Twenty-four notes"></a><!-- ws:end:WikiTextHeadingRule:54 -->Twenty-four notes</h1> <!-- ws:start:WikiTextHeadingRule:56:<h2> --><h2 id="toc28"><a name="Twenty-four notes-Rank one"></a><!-- ws:end:WikiTextHeadingRule:56 -->Rank one</h2> Genus(11^23)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:58:<h2> --><h2 id="toc29"><a name="Twenty-four notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:58 -->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 /> <!-- ws:start:WikiTextHeadingRule:60:<h2> --><h2 id="toc30"><a name="Twenty-four notes-Rank three"></a><!-- ws:end:WikiTextHeadingRule:60 -->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 /> <!-- ws:start:WikiTextHeadingRule:62:<h2> --><h2 id="toc31"><a name="Twenty-four notes-Rank four"></a><!-- ws:end:WikiTextHeadingRule:62 -->Rank four</h2> Genus(3*5^2*7*13) (24d)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:64:<h1> --><h1 id="toc32"><a name="Twenty-five notes"></a><!-- ws:end:WikiTextHeadingRule:64 -->Twenty-five notes</h1> <!-- ws:start:WikiTextHeadingRule:66:<h2> --><h2 id="toc33"><a name="Twenty-five notes-Rank one"></a><!-- ws:end:WikiTextHeadingRule:66 -->Rank one</h2> Genus(5^24)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:68:<h2> --><h2 id="toc34"><a name="Twenty-five notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:68 -->Rank two</h2> Genus(5^4*7^4)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:70:<h1> --><h1 id="toc35"><a name="Twenty-six notes"></a><!-- ws:end:WikiTextHeadingRule:70 -->Twenty-six notes</h1> <!-- ws:start:WikiTextHeadingRule:72:<h2> --><h2 id="toc36"><a name="Twenty-six notes-Rank one"></a><!-- ws:end:WikiTextHeadingRule:72 -->Rank one</h2> Genus(7^25)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:74:<h2> --><h2 id="toc37"><a name="Twenty-six notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:74 -->Rank two</h2> Genus(7^12*5), Genus(11^12*3), Genus(11^12*7)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:76:<h1> --><h1 id="toc38"><a name="Twenty-seven notes"></a><!-- ws:end:WikiTextHeadingRule:76 -->Twenty-seven notes</h1> <!-- ws:start:WikiTextHeadingRule:78:<h2> --><h2 id="toc39"><a name="Twenty-seven notes-Rank one"></a><!-- ws:end:WikiTextHeadingRule:78 -->Rank one</h2> Genus(13^26)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:80:<h2> --><h2 id="toc40"><a name="Twenty-seven notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:80 -->Rank two</h2> Genus(5^2*13^8)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:82:<h2> --><h2 id="toc41"><a name="Twenty-seven notes-Rank three"></a><!-- ws:end:WikiTextHeadingRule:82 -->Rank three</h2> Genus(5^2*11^2*13^2) (patent)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:84:<h1> --><h1 id="toc42"><a name="Twenty-eight notes"></a><!-- ws:end:WikiTextHeadingRule:84 -->Twenty-eight notes</h1> <!-- ws:start:WikiTextHeadingRule:86:<h2> --><h2 id="toc43"><a name="Twenty-eight notes-Rank one"></a><!-- ws:end:WikiTextHeadingRule:86 -->Rank one</h2> Genus(5^27)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:88:<h2> --><h2 id="toc44"><a name="Twenty-eight notes-Rank two"></a><!-- ws:end:WikiTextHeadingRule:88 -->Rank two</h2> Genus(5^3*13^6)</body></html>