[tuning-math] Re: Modulatoy topology in 22-TET
- From: "emotionaljourney22" <paul@xxxxxxxxxxxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Wed, 03 Jul 2002 11:40:52 -0000
--- In tuning-math@xxxx, "hs" <straub@xxxx> wrote:
> >> >thanks, hans! this topology is already implied in the appendix
to my
> >> >paper, isn't it? just roll the page around so that the bottom
meets
> >> >the top, and you have it!
> >>
> >> Oops - looks like I should get the habit of readiong reports to
> >their _very_
> >> end...
> >
> >you can also see in that diagram how the *symmetrical* modes fit
> >nicely into the overall modulatory topology -- see it?
>
> Errm... After having a closer look at the diagrams, I think not.
The diagram
> axes are fifth, major third and harmonic seventh:
no, not those diagrams!
>I see no hint that the
> easiest modulation steps are semitone and tritone.
i said the appendix!
> The dimension of the whole diagram has no importance in this
aspect - in
> ET12, you probably can find chord systems with easiest modulation
steps
> 4 and 3 (I already found one with 4).
that would be systems related to the augmented scale (3 1 3 1 3 1).
for easiest modulation step 3, try systems related to the diminished
scale (1 2 1 2 1 2 1 2).
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