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Message: 5375 Date: Mon, 21 Oct 2002 13:29:23 Subject: Re: Epimorphic From: manuel.op.de.coul@xxxxxxxxxxx.xxx Gene wrote: >Not so far as I can see. I haven't found a CS and non-epimorphic counterexample yet. Manuel
Message: 5378 Date: Mon, 21 Oct 2002 16:02:29 Subject: Re: Epimorphic From: manuel.op.de.coul@xxxxxxxxxxx.xxx >Try 1/1--2700/2401--5/4--4/3--3/2--5/3--2401/2400--2/1 Allright, but are there any monotonic examples? Manuel
Message: 5379 Date: Mon, 21 Oct 2002 16:22:00 Subject: Re: Epimorphic From: manuel.op.de.coul@xxxxxxxxxxx.xxx >By the way, if you decide to impliment the epimorphism feature, I'd suggest "Scale is epimorphic with val >---" or "Scale is epimorphic with mapping ---" Yes, it will show that. Manuel
Message: 5381 Date: Mon, 21 Oct 2002 13:31:21 Subject: Re : CS implies EPIMORPHISM From: Pierre Lamothe 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 [This message contained attachments]
Message: 5384 Date: Mon, 21 Oct 2002 14:04:01 Subject: Re: Epimorphic From: Pierre Lamothe Gene wrote: Try 1/1--2700/2401--5/4--4/3--3/2--5/3--2401/2400--2/1 Do you consider that unordered list as a scale ? Need correction or reordering. Pierre [This message contained attachments]
Message: 5385 Date: Mon, 21 Oct 2002 14:36:23 Subject: Re: CS implies EPIMORPHISM From: Pierre Lamothe Maybe it would have been better I precise the generator order used to generate the matrices in my precedent post. There was successively < 1 5 3 15 9 45 27 > and < 1 5 3 15 9 >. [This message contained attachments]
Message: 5395 Date: Tue, 22 Oct 2002 01:45:48 Subject: Re: Epimorphic From: Carl Lumma >>Try 1/1--2700/2401--5/4--4/3--3/2--5/3--2401/2400--2/1 > >Allright, but are there any monotonic examples? Why does this fail? The stronger argument against CS /-> Epimorphic is that CS doesn't require JI, as Gene pointed out. -C.
Message: 5397 Date: Tue, 22 Oct 2002 11:36:49 Subject: Re: Epimorphic From: manuel.op.de.coul@xxxxxxxxxxx.xxx Yes that scale is indeed not epimorphic. So I'll add the additional integer test to the code. So doesn't that need to be added to the definition in Joe's dictionary too, since all components being integer doesn't follow automatically from h(qn)=n for n = 1 .. (number of notes - 1)? Manuel
Message: 5399 Date: Tue, 22 Oct 2002 12:30:31 Subject: Re: Epimorphic From: manuel.op.de.coul@xxxxxxxxxxx.xxx So I may conclude that the simplest example of a JI, CS and non-epimorphic scale is this one: 1/1--4/1 Manuel
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