Re: [tuning] Re: naughty and nice [12 note scales]

Paul!
I will try to answer the second question which i think will answer the first, since i can
interpret what you are asking in a few ways. What is on page 3 of the Letter to John Chalmers
is that the 1-3-5-7-9 x 1-3-5-7-9 cross-set can be combined with the subharmonic version of
this cross-set by dividing it by 1-3-5-7 or 9 that is the 5 solutions. he illustrates it with
it divided by 9 showing the 1-3-5-7 hexany being the union. If this doesn't answer your
question let me know.
BTW This article is 51 pages long and we are considering making it available for purchase
as it outside the boundaries of what we can put up. Funds will be used to pay keeping the
archives on-line. those interested should contact me off-list.

Paul Erlich wrote:

> Kraig, I'm fascinated by this and particularly by the depiction of
> the double dekany (in this case, 1-5-7-11-15, but that is of no
> consequence) at http://www.anaphoria.com/dal24.html. The fourteen
> nots come out mapped to the vertices of a rhombic dodecahedron, which
> is fully symmetrical. So if you were to multiply the 2(5 dekany by
> one of the factors before combining it with the 3(5 dekany, you'd get
> the same shape, and hence a transposition of the same scale -- is
> that right?

> Does this contradict what Daniel Wolf was affirming
> earlier, that there are 5 distinct ways to combine the 2(5 and 3(5 to
> get a dekateserany?

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

Kraig!

I can answer my own question now. The reason for the apparant
symmetry is that the factor "1" is placed at the center of the
tetrahedron. But the symmetry is only apparant because in truth the
lattice is four-dimensional and it is only in this particular
projection down to three dimensions, in which "1" appears at the
center of the tetrahedron, that the rhombic dodecahedron shape
results for your "double dekany."

-Paul

Paul!
If you have the 3-5-7-9-11 Double dekany and add the factor 1 to the 2)5 set you have the
Eikosany

not mine by Erv's "double dekany." I just discovered that it was a 14 tone constant
structure. the only other one i found is in the Japanese version of Lou Harrisons' Primer. I
found both in the same week and haven't found any 14 tone scales since. Paul Erlich wrote:

> that the rhombic dodecahedron shape
> results for your "double dekany."
>
> -Paul
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

I apologize in advance for the commercial nature of this message, but I
wanted subscribers to know that a compilation of my videos with free-style
JI scores is available from the Just Intonation Network store, even though
they don't yet appear on the web site (http://www.dnai.com/~jinetwk/). The
price is $18, $16 for JI Network members (shipping info and other details
can be found at the above site). The NTSC VHS video is 25 minutes long and
consists of Static Cling, Collateral Damage, and Hiway 70. The first and
last are abstract computer animations, in which the motion of the elements,
by the way, reflect to some extent the tunings used. More information about
each is available at: http://www2.hmc.edu/~alves/static.html,
http://www2.hmc.edu/~alves/collateral.html, and
http://www2.hmc.edu/~alves/hiway70.html.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

> Paul!
> If you have the 3-5-7-9-11 Double dekany and add the factor 1 to the 2)5
set you have the Eikosany

Can you show this more explicitly?

>not mine by Erv's "double dekany."

Well the rhombic dodecahedron lattice applies equally well whether the
factors are 1-3-5-7-9 (yours) or 1-5-7-11-15 (Erv's).

>I just discovered that it was a 14 tone constant structure. the only other
one i found is in the Japanese version of Lou Harrisons' >Primer. I found
both in the same week and haven't found any 14 tone scales since.

Would you like me to try to find some 14 tone CS scales? In any particular
prime-limit? I think I can do it easily using, yes, that's right, Fokker
periodicity blocks. Let me know.

_________________________________________________

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As of June 26, 2000, Acadian Asset Management will be at a
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Please contact us at:
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All phone, fax and email remain the same.

"Paul H. Erlich" wrote:

> > Paul!
> > If you have the 3-5-7-9-11 Double dekany and add the factor 1 to the 2)5
> set you have the Eikosany
>
> Can you show this more explicitly?

3-5
3-7
3-9
3-11
5-7
5-9
5-11
7-9
7-11
9-11
3-5

>
>
> >not mine by Erv's "double dekany."
>
> Well the rhombic dodecahedron lattice applies equally well whether the
> factors are 1-3-5-7-9 (yours) or 1-5-7-11-15 (Erv's).
>
> >I just discovered that it was a 14 tone constant structure. the only other
> one i found is in the Japanese version of Lou Harrisons' >Primer. I found
> both in the same week and haven't found any 14 tone scales since.
>
> Would you like me to try to find some 14 tone CS scales? In any particular
> prime-limit? I think I can do it easily using, yes, that's right, Fokker
> periodicity blocks. Let me know.
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

>I just discovered that it was a 14 tone constant structure. the only other
one i found is in the Japanese version of Lou Harrisons' >Primer. I found
both in the same week and haven't found any 14 tone scales since

For 7-limit, have a look at these:

4 -1 -4
0 -2 -3
2 -1 -3
1 -1 -2
3 0 -2
-1 -1 -1
2 0 -1
-2 -1 0
0 0 0
3 1 0
-1 0 1
1 1 1
-3 0 2
-2 1 3

and

-3 3 -3
1 1 -2
-2 2 -2
2 0 -1
-1 1 -1
3 -1 0
0 0 0
-3 1 0
4 -2 1
1 -1 1
-2 0 1
2 -2 2
-1 -1 2
3 -3 3

where the first column is the power of 3, the second column is the power of
5, and the third column is the power of 7.

These are the Fokker periodicity blocks using unison vectors

3 -1 -3
-7 -1 3
0 3 5

for the first scale and

-4 3 -2
8 -4 2
-1 -2 4

for the second scale. Many, many other 14-note scales are possible by
transposing one or more notes by one or more unison vectors.

_________________________________________________

We are Moving!

As of June 26, 2000, Acadian Asset Management will be at a
new location in Boston's financial district.

Please contact us at:
Acadian Asset Management
Ten Post Office Square, 8th Floor
Boston, MA 02109.

All phone, fax and email remain the same.

"Paul H. Erlich" wrote:

> > Paul!
> > If you have the 3-5-7-9-11 Double dekany and add the factor 1 to the 2)5
> set you have the Eikosany
>
> Can you show this more explicitly?

(1)-3-5
(1)-3-7
(1)-3-9
(1)-3-11
(1)-5-7
(1)-5-9
(1)-5-11
(1)-7-9
(1)-7-11
(1)-9-11
------------------------
3-5-7
3-5-9
3-5-11
3-7-9
3-7-11
3-9-11
5-7-9
5-7-11
5-9-11
7-9-11

> Would you like me to try to find some 14 tone CS scales?

Do what thy wilt! It is an area worth exploring and might yeild some interesting results. the
more the better. the limit is yours!

> In any particular
> prime-limit? I think I can do it easily using, yes, that's right, Fokker
> periodicity blocks. Let me know.
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

OK, Kraig, now it seems obvious . . . what was confusing me was that I was
expecting the double dekany to have 14 notes but that is only the case when
one of the factors is 1 . . . with 3-5-7-9-11 the double dekany has, of
course, 20 notes . . . I should've had a V8!

_________________________________________________

We are Moving!

As of June 26, 2000, Acadian Asset Management will be at a
new location in Boston's financial district.

Please contact us at:
Acadian Asset Management
Ten Post Office Square, 8th Floor
Boston, MA 02109.

All phone, fax and email remain the same.

"Paul!
never broke this code, would like ratios!

"Paul H. Erlich" wrote:

> >I just discovered that it was a 14 tone constant structure. the only other
> one i found is in the Japanese version of Lou Harrisons' >Primer. I found
> both in the same week and haven't found any 14 tone scales since
>
> For 7-limit, have a look at these:
>
>
> 4 -1 -4
> 0 -2 -3
> 2 -1 -3
> 1 -1 -2
> 3 0 -2
> -1 -1 -1
> 2 0 -1
> -2 -1 0
> 0 0 0
> 3 1 0
> -1 0 1
> 1 1 1
> -3 0 2
> -2 1 3
>
> and
>
>
> -3 3 -3
> 1 1 -2
> -2 2 -2
> 2 0 -1
> -1 1 -1
> 3 -1 0
> 0 0 0
> -3 1 0
> 4 -2 1
> 1 -1 1
> -2 0 1
> 2 -2 2
> -1 -1 2
> 3 -3 3
>
> where the first column is the power of 3, the second column is the power of
> 5, and the third column is the power of 7.
>
> These are the Fokker periodicity blocks using unison vectors
>
> 3 -1 -3
> -7 -1 3
> 0 3 5
>
> for the first scale and
>
> -4 3 -2
> 8 -4 2
> -1 -2 4
>
> for the second scale. Many, many other 14-note scales are possible by
> transposing one or more notes by one or more unison vectors.
>
> _________________________________________________
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com