Cv scales
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From [[http://tech.groups.yahoo.com/group/tuning-math/message/11451]] It turns out there are a lot of five tetrad scales involving only 11 notes (I've got a list of 132 of them) but none I've found are strictly [[Periodic scale|epimorphic]]. Checking for permutation epimorphic scales may be a good plan. Of course, there are even more five tetrad scales with 12 notes, but here I give only ones which are epimorphic--all, as it turns out, with the [[Patent val|standard val]]. I cataloged these in pairs, where the odd numbers have three major and two minor tetrads, and the even pairs the reverse. Marvel tempering removes this distinction, and I only list the odd, with the three major tetrads. I found two scales I've found before, "pris" and "hen12". The latter is an adjusted version of the Hahn reduction of a chain of fifths. ! cv1.scl First 12/5 <12 19 28 34| epimorphic 12 ! 16/15 8/7 7/6 5/4 4/3 7/5 3/2 8/5 5/3 7/4 28/15 2 ! cv3.scl Third 12/5 scale <12 19 28 34| epimorphic = pris 12 ! 16/15 28/25 7/6 5/4 4/3 7/5 3/2 8/5 5/3 7/4 28/15 2 ! cv5.scl Fifth 12/5 scale <12 19 28 34| epimorphic = inverse hen12 12 ! 15/14 9/8 6/5 5/4 21/16 7/5 3/2 8/5 12/7 7/4 15/8 2 ! cv7.scl Seventh 12/5 scale <12 19 28 34| epimorphic 12 ! 21/20 9/8 6/5 9/7 21/16 7/5 3/2 8/5 12/7 9/5 15/8 2 ! cv9.scl Ninth 12/5 scale <12 19 28 34| epimorphic 12 ! 15/14 8/7 7/6 5/4 4/3 10/7 32/21 8/5 5/3 25/14 40/21 2 ! cv11.scl Eleventh 12/5 scale <12 19 28 34| epimorphic 12 ! 15/14 9/8 6/5 9/7 21/16 7/5 3/2 8/5 12/7 9/5 15/8 2 ! cv13.scl Thirteenth 12/5 scale <12 19 28 34| epimorphic 12 ! 16/15 28/25 6/5 5/4 4/3 7/5 3/2 8/5 12/7 7/4 28/15 2
Original HTML content:
<html><head><title>cv scales</title></head><body>From <a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/11451" rel="nofollow">http://tech.groups.yahoo.com/group/tuning-math/message/11451</a><br /> <br /> It turns out there are a lot of five tetrad scales involving only 11 notes (I've got a list of 132 of them) but none I've found are strictly <a class="wiki_link" href="/Periodic%20scale">epimorphic</a>. Checking for permutation epimorphic scales may be a good plan.<br /> <br /> Of course, there are even more five tetrad scales with 12 notes, but here I give only ones which are epimorphic--all, as it turns out, with the <a class="wiki_link" href="/Patent%20val">standard val</a>. I cataloged these in pairs, where the odd numbers have three major and two minor tetrads, and the even pairs the reverse. Marvel tempering removes this distinction, and I only list the odd, with the three major tetrads.<br /> <br /> I found two scales I've found before, "pris" and "hen12". The latter is an adjusted version of the Hahn reduction of a chain of fifths.<br /> <br /> ! cv1.scl<br /> First 12/5 <12 19 28 34| epimorphic<br /> 12<br /> !<br /> 16/15<br /> 8/7<br /> 7/6<br /> 5/4<br /> 4/3<br /> 7/5<br /> 3/2<br /> 8/5<br /> 5/3<br /> 7/4<br /> 28/15<br /> 2<br /> <br /> ! cv3.scl<br /> Third 12/5 scale <12 19 28 34| epimorphic = pris<br /> 12<br /> !<br /> 16/15<br /> 28/25<br /> 7/6<br /> 5/4<br /> 4/3<br /> 7/5<br /> 3/2<br /> 8/5<br /> 5/3<br /> 7/4<br /> 28/15<br /> 2<br /> <br /> ! cv5.scl<br /> Fifth 12/5 scale <12 19 28 34| epimorphic = inverse hen12<br /> 12<br /> !<br /> 15/14<br /> 9/8<br /> 6/5<br /> 5/4<br /> 21/16<br /> 7/5<br /> 3/2<br /> 8/5<br /> 12/7<br /> 7/4<br /> 15/8<br /> 2<br /> <br /> ! cv7.scl<br /> Seventh 12/5 scale <12 19 28 34| epimorphic<br /> 12<br /> !<br /> 21/20<br /> 9/8<br /> 6/5<br /> 9/7<br /> 21/16<br /> 7/5<br /> 3/2<br /> 8/5<br /> 12/7<br /> 9/5<br /> 15/8<br /> 2<br /> <br /> ! cv9.scl<br /> Ninth 12/5 scale <12 19 28 34| epimorphic<br /> 12<br /> !<br /> 15/14<br /> 8/7<br /> 7/6<br /> 5/4<br /> 4/3<br /> 10/7<br /> 32/21<br /> 8/5<br /> 5/3<br /> 25/14<br /> 40/21<br /> 2<br /> <br /> ! cv11.scl<br /> Eleventh 12/5 scale <12 19 28 34| epimorphic<br /> 12<br /> !<br /> 15/14<br /> 9/8<br /> 6/5<br /> 9/7<br /> 21/16<br /> 7/5<br /> 3/2<br /> 8/5<br /> 12/7<br /> 9/5<br /> 15/8<br /> 2<br /> <br /> ! cv13.scl<br /> Thirteenth 12/5 scale <12 19 28 34| epimorphic<br /> 12<br /> !<br /> 16/15<br /> 28/25<br /> 6/5<br /> 5/4<br /> 4/3<br /> 7/5<br /> 3/2<br /> 8/5<br /> 12/7<br /> 7/4<br /> 28/15<br /> 2</body></html>