SymmetricalJustTunings

The CPS's when reduced to a single octave will have at least two places of mirroring. These are the points where opposite products are adjacent scale wise. It is quite easy and sometimes advantageous to use a template such as 1,3,5,7,9,11 and space the structure this way. This application can be seen in the generation of the tuning for the 31 tone marimba in Xen. XI page 60 fig 4. here Wilson used the series 6,8,9,10,11,14.
The instrument which i recently mentioned THE TREE would suspend bars in a the 10 sided lattice (centered hexad) and using a like method, one could have a symmetrical spacing that could exceed the octave. The advantage is the arrangement will predetermine the exact spacing of every chord (triad or tetrad) in such a way that no other inversions will occur.
Also as a symmetrical scale structures are all the pure MOS scales and as well as all the Lambdomas. Let us no forget the Euler genii (SP?)

tuning@yahoogroups.com wrote:_

>
> Message: 11
> Date: Tue, 07 May 2002 23:46:01 -0000
> From: "jpehrson2" <jpehrson@rcn.com>
> Subject: Re: SymmetricalJustTunings Yahoo Group:
>
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
>
> /tuning/topicId_36852.html#36867
>
> > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> >
> > > ***Oh... I finally think I see where this is going... So, in
> other
> > > words, the Erv Wilson "combinatorial product set" tunings would
> fit
> > > into this category??
> >
> > These are octave equivalent scales of rational numbers q such
> > that if q is in the scale, so is 2/q. Because of octave
> > equivalence, this is the same as saying if q is in the scale, so
> > is 1/q. It gives radial symmetry in a lattice, and is a type of
> > symmetry exhibited by many scales, which can have more--eg,
> > major/minor symmetry.
>
> ***Thanks, Gene!
>
> Well, I wish I could hear some examples of these, if anybody has done
> any...
>
> J. Pehrson
>
> ________________________________________________________________________
>

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