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Cv scales: Difference between revisions

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From [http://tech.groups.yahoo.com/group/tuning-math/message/11451 http://tech.groups.yahoo.com/group/tuning-math/message/11451]
From [http://tech.groups.yahoo.com/group/tuning-math/message/11451 http://tech.groups.yahoo.com/group/tuning-math/message/11451] {{dead link}}


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.
"''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.
''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.
''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.''"


<pre>
! cv1.scl
! cv1.scl
First 12/5 &lt;12 19 28 34| epimorphic
First 12/5 &lt;12 19 28 34| epimorphic
12
12
!
!
16/15
16/15
8/7
8/7
7/6
7/6
5/4
5/4
4/3
4/3
7/5
7/5
3/2
3/2
8/5
8/5
5/3
5/3
7/4
7/4
28/15
28/15
2/1
</pre>


2
<pre>
 
! cv3.scl
! cv3.scl
Third 12/5 scale &lt;12 19 28 34| epimorphic = pris
Third 12/5 scale &lt;12 19 28 34| epimorphic = pris
12
12
!
!
16/15
16/15
28/25
28/25
7/6
7/6
5/4
5/4
4/3
4/3
7/5
7/5
3/2
3/2
8/5
8/5
5/3
5/3
7/4
7/4
28/15
28/15
2/1
</pre>


2
<pre>
 
! cv5.scl
! cv5.scl
Fifth 12/5 scale &lt;12 19 28 34| epimorphic = inverse hen12
Fifth 12/5 scale &lt;12 19 28 34| epimorphic = inverse hen12
12
12
!
!
15/14
15/14
9/8
9/8
6/5
6/5
5/4
5/4
21/16
21/16
7/5
7/5
3/2
3/2
8/5
8/5
12/7
12/7
7/4
7/4
15/8
15/8
2
2
</pre>


<pre>
! cv7.scl
! cv7.scl
Seventh 12/5 scale &lt;12 19 28 34| epimorphic
Seventh 12/5 scale &lt;12 19 28 34| epimorphic
12
12
!
!
21/20
21/20
9/8
9/8
6/5
6/5
9/7
9/7
21/16
21/16
7/5
7/5
3/2
3/2
8/5
8/5
12/7
12/7
9/5
9/5
15/8
15/8
2/1
</pre>


2
<pre>
 
! cv9.scl
! cv9.scl
Ninth 12/5 scale &lt;12 19 28 34| epimorphic
Ninth 12/5 scale &lt;12 19 28 34| epimorphic
12
12
!
!
15/14
15/14
8/7
8/7
7/6
7/6
5/4
5/4
4/3
4/3
10/7
10/7
32/21
32/21
8/5
8/5
5/3
5/3
25/14
25/14
40/21
40/21
2/1
</pre>


2
<pre>
 
! cv11.scl
! cv11.scl
Eleventh 12/5 scale &lt;12 19 28 34| epimorphic
Eleventh 12/5 scale &lt;12 19 28 34| epimorphic
12
12
!
!
15/14
15/14
9/8
9/8
6/5
6/5
9/7
9/7
21/16
21/16
7/5
7/5
3/2
3/2
8/5
8/5
12/7
12/7
9/5
9/5
15/8
15/8
2/1
</pre>


2
<pre>
 
! cv13.scl
! cv13.scl
Thirteenth 12/5 scale &lt;12 19 28 34| epimorphic
Thirteenth 12/5 scale &lt;12 19 28 34| epimorphic
12
12
!
!
16/15
16/15
28/25
28/25
6/5
6/5
5/4
5/4
4/3
4/3
7/5
7/5
3/2
3/2
8/5
8/5
12/7
12/7
7/4
7/4
28/15
28/15
 
2/1
2
</pre>
[[Category:Lists of scales]]
[[Category:Pages with Scala files]]
[[Category:Todo:cleanup]]
Retrieved from "https://en.xen.wiki/w/Cv_scales"