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

Joseph Pehrson wrote:

> Hexany 1.3.5.7: 32/35 5/4 21/16 3/2 7/4 15/8

Another 1-3-5-7 at a 3/2 above the above. (That is so nice to say)
105/64 15/8 63/32 9/8 21/16 45/32
Unfortunately this is not a constant structure but the 1-3-5-7-9 double dekany at 14 tones is
(my discovery too) !
c 1-3
d- 3-5-7
d 3-9
d# 1-7
e 3-5
f- 7-9
f# 3-5-9
g- 5-7
g 1-9
a- 5-7-9
a 1-5
a# 3-7
b 5-9
c- 3-7-9
c 1-3

this has the 1-3-5-7 hexany 3 times
3-7 1-7 3-7 1-3 3-5 1-5
3-5-7 3-7 7-9 1-9 5-9 3-5
5-7-9 1-7-9 3-7-9 3-9 3-5-9 5-9
the 1-3-5-9 hexany 2 times
5-7 3-5-7 5-7-9 3-7 7-9 3-7-9
1-5 3-5 5-9 1-3 1-9 3-9
the 1-3-7-9 hexany 2 times
5-7 3-5-7 5-7-9 3-5 5-9 3-5-9
1-7 3-7 7-9 1-3 1-9 3-9
the 1-5-7-9 hexany 2 times
5-7 1-5 1-7 1-9 7-9 5-9
3-5-7 3-5 3-7 3-9 3-7-9 3-5-9
the 3-5-7-9 hexany just once
5-7 3-5 5-9 3-7 7-9 3-9
a good buy for the extra dollar

>
>
> Hexany 1.3.5.9: 9/8 5/4 45/32 3/2 27/16 15/8
>
> Hexany 1.3.7.9: 9/8 21/16 3/2 27/16 7/4 63/32
>
> Hexany 1.5.7.9: 35/32 9/8 5/4 45/32 7/4 63/32
>
> Hexany 3.5.7.9: 35/32 21/16 45/32 27/16 15/8 63/32
>
> Whoopie!
>
> This means, of course, that the pre-compositional composer can have a
> "field day..." One can begin with a certain hexany and then "mutate" it
> to another near form... one can "transpose" by LINKED common-notes
> between hexanys, etc.
>
> Or, one could just listen to the sounds... not entirely prohibited, but
> for some, perhaps unadvisable.
>
> A funny property of this scale for the "keyboard fixated" is the fact
> that our keyboard "major chord" C-E-G-C comes out as the subdominant
> (using a "narrow fourth" and a "septimal neutral sixth") and the "major
> triad" of the root can be easily made by C-Eb-Gb-C (a just major third
> and perfect fifth!)... so there can be a kind of "plagal cadence" action
> going on... although I doubt seriously I would use the scale like
> that...
>
> It also doesn't seem that hard to "transcribe" to traditional 12-tET
> staff notation, using quartertones and cents deviation... but I know
> there are people on this list who feel this is very "naughty, naughty!"
>
> ____________ ______ ___ __ __
> Joseph Pehrson
>
> tuning-normal@egroups.com - change your subscription to individual emails.

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

--- In tuning@egroups.com, Kraig Grady <kraiggrady@a...> wrote:

> Unfortunately this is not a constant structure but the 1-3-5-7-9
double dekany at 14 tones is
> (my discovery too) !
> c 1-3
> d- 3-5-7
> d 3-9
> d# 1-7
> e 3-5
> f- 7-9
> f# 3-5-9
> g- 5-7
> g 1-9
> a- 5-7-9
> a 1-5
> a# 3-7
> b 5-9
> c- 3-7-9
> c 1-3

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?