Re: [tuning] Re: 12-tone tunings for 7-limit harmony (for Joseph Pehr son et al)

Paul!
The hexichord I think of in the same way that Margo might as being of diatonic origin hence my
confusion. Possibly the hexichord comes trivially from the tetrachords. The latter of having
more historical use, the latter of which i know of none (except possibly howards hansons the
Harmonic Material of Modern Music)

Paul Erlich wrote:

> --- In tuning@egroups.com, Kraig Grady <kraiggrady@a...> wrote:
> >
> >
> > Paul Erlich wrote:
> >
> > >
> > > >
> > > Ah yes they are what I would have called hexachords in my paper
> > > (since there are 6 notes spanning a 4:3). So these six octave
> species
> > > of the Centaur scale have identical hexachords a 4:3 apart:
> > >
> > > D#-D#
> > > E-E
> > > G#-G#
> > > A#-A#
> > > A-A
> > > B-B
> >
> > I confused by this. I meant that any type of tetrachord between D#
> and G# is repeated at A#-D#
> >
> > Also those between e-a are reaped between b-e.
>
> Right -- that follows trivially from the hexachords being identical.
> The hexachords being identical means that the 12-tone octave species
> listed above all contain two identical hexachords either a 4:3 apart
> or a 3:2 apart (oops, left that second possibility out before).
> .

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