Cv scales: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
From [http://tech.groups.yahoo.com/group/tuning-math/message/11451 http://tech.groups.yahoo.com/group/tuning-math/message/11451]
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>2011-03-02 12:54:26 UTC</tt>.<br>
: The original revision id was <tt>206542286</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">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.
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.


! 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
2


! 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
2


! 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


! 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
2


! 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
2


! 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
2


! 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
2
</pre></div>
<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;cv scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;From &lt;a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/11451" rel="nofollow"&gt;http://tech.groups.yahoo.com/group/tuning-math/message/11451&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
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 &lt;a class="wiki_link" href="/Periodic%20scale"&gt;epimorphic&lt;/a&gt;. Checking for permutation epimorphic scales may be a good plan.&lt;br /&gt;
&lt;br /&gt;
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 &lt;a class="wiki_link" href="/Patent%20val"&gt;standard val&lt;/a&gt;. 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.&lt;br /&gt;
&lt;br /&gt;
I found two scales I've found before, &amp;quot;pris&amp;quot; and &amp;quot;hen12&amp;quot;. The latter is an adjusted version of the Hahn reduction of a chain of fifths.&lt;br /&gt;
&lt;br /&gt;
! cv1.scl&lt;br /&gt;
First 12/5 &amp;lt;12 19 28 34| epimorphic&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
16/15&lt;br /&gt;
8/7&lt;br /&gt;
7/6&lt;br /&gt;
5/4&lt;br /&gt;
4/3&lt;br /&gt;
7/5&lt;br /&gt;
3/2&lt;br /&gt;
8/5&lt;br /&gt;
5/3&lt;br /&gt;
7/4&lt;br /&gt;
28/15&lt;br /&gt;
2&lt;br /&gt;
&lt;br /&gt;
! cv3.scl&lt;br /&gt;
Third 12/5 scale &amp;lt;12 19 28 34| epimorphic = pris&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
16/15&lt;br /&gt;
28/25&lt;br /&gt;
7/6&lt;br /&gt;
5/4&lt;br /&gt;
4/3&lt;br /&gt;
7/5&lt;br /&gt;
3/2&lt;br /&gt;
8/5&lt;br /&gt;
5/3&lt;br /&gt;
7/4&lt;br /&gt;
28/15&lt;br /&gt;
2&lt;br /&gt;
&lt;br /&gt;
! cv5.scl&lt;br /&gt;
Fifth 12/5 scale &amp;lt;12 19 28 34| epimorphic = inverse hen12&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
15/14&lt;br /&gt;
9/8&lt;br /&gt;
6/5&lt;br /&gt;
5/4&lt;br /&gt;
21/16&lt;br /&gt;
7/5&lt;br /&gt;
3/2&lt;br /&gt;
8/5&lt;br /&gt;
12/7&lt;br /&gt;
7/4&lt;br /&gt;
15/8&lt;br /&gt;
2&lt;br /&gt;
&lt;br /&gt;
! cv7.scl&lt;br /&gt;
Seventh 12/5 scale &amp;lt;12 19 28 34| epimorphic&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
21/20&lt;br /&gt;
9/8&lt;br /&gt;
6/5&lt;br /&gt;
9/7&lt;br /&gt;
21/16&lt;br /&gt;
7/5&lt;br /&gt;
3/2&lt;br /&gt;
8/5&lt;br /&gt;
12/7&lt;br /&gt;
9/5&lt;br /&gt;
15/8&lt;br /&gt;
2&lt;br /&gt;
&lt;br /&gt;
! cv9.scl&lt;br /&gt;
Ninth 12/5 scale &amp;lt;12 19 28 34| epimorphic&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
15/14&lt;br /&gt;
8/7&lt;br /&gt;
7/6&lt;br /&gt;
5/4&lt;br /&gt;
4/3&lt;br /&gt;
10/7&lt;br /&gt;
32/21&lt;br /&gt;
8/5&lt;br /&gt;
5/3&lt;br /&gt;
25/14&lt;br /&gt;
40/21&lt;br /&gt;
2&lt;br /&gt;
&lt;br /&gt;
! cv11.scl&lt;br /&gt;
Eleventh 12/5 scale &amp;lt;12 19 28 34| epimorphic&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
15/14&lt;br /&gt;
9/8&lt;br /&gt;
6/5&lt;br /&gt;
9/7&lt;br /&gt;
21/16&lt;br /&gt;
7/5&lt;br /&gt;
3/2&lt;br /&gt;
8/5&lt;br /&gt;
12/7&lt;br /&gt;
9/5&lt;br /&gt;
15/8&lt;br /&gt;
2&lt;br /&gt;
&lt;br /&gt;
! cv13.scl&lt;br /&gt;
Thirteenth 12/5 scale &amp;lt;12 19 28 34| epimorphic&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
16/15&lt;br /&gt;
28/25&lt;br /&gt;
6/5&lt;br /&gt;
5/4&lt;br /&gt;
4/3&lt;br /&gt;
7/5&lt;br /&gt;
3/2&lt;br /&gt;
8/5&lt;br /&gt;
12/7&lt;br /&gt;
7/4&lt;br /&gt;
28/15&lt;br /&gt;
2&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

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 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 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

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