Re : CS implies EPIMORPHISM

Paul wrote:
i'm confused as to what you mean. rotating the progression so as to
begin and end on ii -- ii-V-I-vi-ii -- should tell you what i'm
talking about (i hope). rewriting in terms of dorian functions, it's
i-IV-VII-v-i, a progression one can find many examples of in pop and
rock music.

what's your "scientific" assessment of this progression?
I know very few things in music as such. I seeked an analogy of the progression used by Asselin
in which there was generally two common intervals between successive chords. Now, It seems
easy to propose a similitude for an intonation where the comma wouldn't be distributed. Naturally,
I don't advocate something here and it's not a "scientific" assessment, since it's above all a matter
of music. I use only tools to show a certain similarity with the Asselin solution. In such cases, it
would have nothing to do with a second "commatic" tonic.

First, rather than using, a "dorian" which would be, as seen in a precedent post, an exact translation
(9/8 or 10/9) of the Zarlino scale S = < 1 9/8 5/4 4/3 3/2 5/3 15/8 2 > in the space
...U
UooooooU
.oooTooo
.UooooooU
.....U
generated by the scale S or equivalently G = < 1 3 5 9 15 27 45 > (said its harmonic generator),
one can use the unique "dorian" mode ( 2 1 2 2 2 1 2 ) in the Zarlino gammier, i.e. the restricted
space
...U
UooooooU
.oooTooo
.UooooooU
.....U
whose generator is the very low < 1 3 5 9 15 >. That scale is < 1 9/8 6/5 4/3 3/2 5/3 16/9 2 >.

(Note that the modes in a gammier are not restricted to horizontal and vertical lines).

The intervals 10/9 and 9/5 aren't here an alternative as melodic steps (while 10/9 was an alternative
between 1 and 5/4), but nothing prevent to use it as optional harmonic intervals, in link with consonance
and functions.

I use here conveniently the tonic D for there is no alteration. The scale is in red and the harmonic alternative
in black.
...U
UoEB..oU
.oCGDAEo
.Uo..FCoU
.....U
(Unhappily, the ideas here will remain hidden from now without the color using)

Before to restrict at this space, I will use the larger space to show more clearly which of the possible
alternative chord corresponds to a function : is it located in tonic, subdominant or dominant region. So,
I will use first the following matrix, generated by < 1 3 5 9 15 27 45 >
D.A.E.B
.DFACEG
GBD.A.E
.G.DFAC
CEGBD.A
.C.G.DF
FACEGBD
for the choice of the chords, and then that simpler generated by < 1 3 5 9 15 >
D.A.E
.DFAC
GBD.A
.G.DF
CEGBD
Locating first, all chord variants DFA, GBD, CEG, ACE in the larger matrix
-------
D.A.E.B
.DFACEG
GBD.A.E
.G.DFAC
CEGBD.A
.C.G.DF
FACEGBD
-------
D.A.E.B
.DFACEG
GBD.A.E
.G.DFAC
CEGBD.A
.C.G.DF
FACEGBD
-------
D.A.E.B
.DFACEG
GBD.A.E
.G.DFAC
CEGBD.A
.C.G.DF
FACEGBD
-------
D.A.E.B
.DFACEG
GBD.A.E
.G.DFAC
CEGBD.A
.C.G.DF
FACEGBD
-------
It seems clear that the functional region are
-------
D.A.E.B
.DFACEG
GBD.A.E
.G.DFAC
CEGBD.A
.C.G.DF
FACEGBD
-------
D.A.E.B
.DFACEG
GBD.A.E
.G.DFAC
CEGBD.A
.C.G.DF
FACEGBD
-------
D.A.E.B
.DFACEG
GBD.A.E
.G.DFAC
CEGBD.A
.C.G.DF
FACEGBD
-------
D.A.E.B
.DFACEG
GBD.A.E
.G.DFAC
CEGBD.A
.C.G.DF
FACEGBD
-------
One can thus easily visualize that dorian progression in the matrix with these simplified views
-----
D.A.E
.DFAC
GBD.A
.G.DF
CEGBD
-----
D.A.E
.DFAC
GBD.A
.G.DF
CEGBD
-----
D.A.E
.DFAC
GBD.A
.G.DF
CEGBD
-----
D.A.E
.DFAC
GBD.A
.G.DF
CEGBD
-----
D.A.E
.DFAC
GBD.A
.G.DF
CEGBD
-----
completed with these views in the Z-module < 2 5 > ZxZ
---------
...U
UoEB..oU
.oCGDAEo
.Uo..FCoU
.....U
---------
...U
UoEB..oU
.oCGDAEo
.Uo..FCoU
.....U
---------
...U
UoEB..oU
.oCGDAEo
.Uo..FCoU
.....U
---------
...U
UoEB..oU
.oCGDAEo
.Uo..FCoU
.....U
---------
...U
UoEB..oU
.oCGDAEo
.Uo..FCoU
.....U
---------
I imagine that the simultaneous comma shift on E and C could be more disturbingly than the
Asselin example, so requiring even more its distribution. I'm not a musician and can't appreciate that.

Pierre

i'm sorry, but i can't understand your reply below. can anyone?

p.s. i don't think "i am not a musician" excuses one from having to
consider the relevance of musical situations if one's theory claims
to pertain to music.

p.p.s. keep up the good work and ignore my whining.

--- In tuning-math@y..., "Pierre Lamothe" <plamothe@a...> wrote:
> Paul wrote:
> i'm confused as to what you mean. rotating the progression so as
to
> begin and end on ii -- ii-V-I-vi-ii -- should tell you what i'm
> talking about (i hope). rewriting in terms of dorian functions,
it's
> i-IV-VII-v-i, a progression one can find many examples of in pop
and
> rock music.
>
> what's your "scientific" assessment of this progression?
> I know very few things in music as such. I seeked an analogy of the
progression used by Asselin
> in which there was generally two common intervals between
successive chords. Now, It seems
> easy to propose a similitude for an intonation where the comma
wouldn't be distributed. Naturally,
> I don't advocate something here and it's not a "scientific"
assessment, since it's above all a matter
> of music. I use only tools to show a certain similarity with the
Asselin solution. In such cases, it
> would have nothing to do with a second "commatic" tonic.
>
> First, rather than using, a "dorian" which would be, as seen in a
precedent post, an exact translation
> (9/8 or 10/9) of the Zarlino scale S = < 1 9/8 5/4 4/3 3/2 5/3 15/8
2 > in the space
> ...U
> UooooooU
> .oooTooo
> .UooooooU
> .....U
> generated by the scale S or equivalently G = < 1 3 5 9 15 27 45 >
(said its harmonic generator),
> one can use the unique "dorian" mode ( 2 1 2 2 2 1 2 ) in the
Zarlino gammier, i.e. the restricted
> space
> ...U
> UooooooU
> .oooTooo
> .UooooooU
> .....U
> whose generator is the very low < 1 3 5 9 15 >. That scale is < 1
9/8 6/5 4/3 3/2 5/3 16/9 2 >.
>
> (Note that the modes in a gammier are not restricted to horizontal
and vertical lines).
>
> The intervals 10/9 and 9/5 aren't here an alternative as melodic
steps (while 10/9 was an alternative
> between 1 and 5/4), but nothing prevent to use it as optional
harmonic intervals, in link with consonance
> and functions.
>
> I use here conveniently the tonic D for there is no alteration. The
scale is in red and the harmonic alternative
> in black.
> ...U
> UoEB..oU
> .oCGDAEo
> .Uo..FCoU
> .....U
> (Unhappily, the ideas here will remain hidden from now without the
color using)
>
> Before to restrict at this space, I will use the larger space to
show more clearly which of the possible
> alternative chord corresponds to a function : is it located in
tonic, subdominant or dominant region. So,
> I will use first the following matrix, generated by < 1 3 5 9 15
27 45 >
> D.A.E.B
> .DFACEG
> GBD.A.E
> .G.DFAC
> CEGBD.A
> .C.G.DF
> FACEGBD
> for the choice of the chords, and then that simpler generated by <
1 3 5 9 15 >
> D.A.E
> .DFAC
> GBD.A
> .G.DF
> CEGBD
> Locating first, all chord variants DFA, GBD, CEG, ACE in the larger
matrix
> -------
> D.A.E.B
> .DFACEG
> GBD.A.E
> .G.DFAC
> CEGBD.A
> .C.G.DF
> FACEGBD
> -------
> D.A.E.B
> .DFACEG
> GBD.A.E
> .G.DFAC
> CEGBD.A
> .C.G.DF
> FACEGBD
> -------
> D.A.E.B
> .DFACEG
> GBD.A.E
> .G.DFAC
> CEGBD.A
> .C.G.DF
> FACEGBD
> -------
> D.A.E.B
> .DFACEG
> GBD.A.E
> .G.DFAC
> CEGBD.A
> .C.G.DF
> FACEGBD
> -------
> It seems clear that the functional region are
> -------
> D.A.E.B
> .DFACEG
> GBD.A.E
> .G.DFAC
> CEGBD.A
> .C.G.DF
> FACEGBD
> -------
> D.A.E.B
> .DFACEG
> GBD.A.E
> .G.DFAC
> CEGBD.A
> .C.G.DF
> FACEGBD
> -------
> D.A.E.B
> .DFACEG
> GBD.A.E
> .G.DFAC
> CEGBD.A
> .C.G.DF
> FACEGBD
> -------
> D.A.E.B
> .DFACEG
> GBD.A.E
> .G.DFAC
> CEGBD.A
> .C.G.DF
> FACEGBD
> -------
> One can thus easily visualize that dorian progression in the matrix
with these simplified views
> -----
> D.A.E
> .DFAC
> GBD.A
> .G.DF
> CEGBD
> -----
> D.A.E
> .DFAC
> GBD.A
> .G.DF
> CEGBD
> -----
> D.A.E
> .DFAC
> GBD.A
> .G.DF
> CEGBD
> -----
> D.A.E
> .DFAC
> GBD.A
> .G.DF
> CEGBD
> -----
> D.A.E
> .DFAC
> GBD.A
> .G.DF
> CEGBD
> -----
> completed with these views in the Z-module < 2 5 > ZxZ
> ---------
> ...U
> UoEB..oU
> .oCGDAEo
> .Uo..FCoU
> .....U
> ---------
> ...U
> UoEB..oU
> .oCGDAEo
> .Uo..FCoU
> .....U
> ---------
> ...U
> UoEB..oU
> .oCGDAEo
> .Uo..FCoU
> .....U
> ---------
> ...U
> UoEB..oU
> .oCGDAEo
> .Uo..FCoU
> .....U
> ---------
> ...U
> UoEB..oU
> .oCGDAEo
> .Uo..FCoU
> .....U
> ---------
> I imagine that the simultaneous comma shift on E and C could be
more disturbingly than the
> Asselin example, so requiring even more its distribution. I'm not a
musician and can't appreciate that.
>
>
> Pierre