RE: [tuning] Re: Tetrads :) Do you promote dualism ?

Pierre wrote,

><< The only difference is that I've produced numbers for the dyadic case
but
>not the chordal case. If I give you some numbers, will you reconsider
>dualism? Everyone, listen to the experiment Joseph Pehrson put up. Who
>thinks 1/7:1/6:1/5:1/4 and 4:5:6:7 are equally consonant? >>

>I didn't want to defend dualism but show that total sum of entropy give
>dual results. It's just funny that acousticians can't yet produce
>asymmetric results. I'm not in doubt for perception but seek for principle
>which will permit asymmetrical results.

The principle is, chordal harmonic entropy. We need a multidimensional
analogue of mediants and then we can calculate it. CAN YOU HELP??

Pierre wrote,

>Hermite would have say that this problem (analogue of mediants in Z^3)
>didn't cease worring and desesperating him during 50 years. I would seek a
>less direct approach but I need to read about harmonic entropy.

I've proposed a voronoi cell approach which should be good enough for large
N. However I can't currently implement it (not enough programming skill).

>I thank you
>for following reference :

><< See Parncutt's book _Harmony -- A Psychoacostic Approach_
>(Springer-Verlag) for a taste of where I'm coming from. >>

>I can't buy books but I'll try to find it at library. For the moment I take
> information only on web. Also, if you know good reference on web about
>that, I would appreciate to know it.

See http://www.mmk.ei.tum.de/persons/ter/top/muscons.html.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> http://www.egroups.com/message/tuning/12930
>
> The principle is, chordal harmonic entropy. We need a
> multidimensional analogue of mediants and then we can calculate
> it. CAN YOU HELP??

Paul, every time I see something like this my brain keeps
insisting that something resembling our multi-dimensional
trigonometric prime- or odd-based lattice formulas is the key.

Unfortunately the math is hopelessly beyond my capabilities.

... ?????

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
> --- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/12961

> > http://www.egroups.com/message/tuning/12930
> >
> > The principle is, chordal harmonic entropy. We need a
> > multidimensional analogue of mediants and then we can calculate
> > it. CAN YOU HELP??
>
>
> Paul, every time I see something like this my brain keeps
> insisting that something resembling our multi-dimensional
> trigonometric prime- or odd-based lattice formulas is the key.
>
> Unfortunately the math is hopelessly beyond my capabilities.
>
> ... ?????
>

You know, if David Keenan can't figure this out, maybe we could post
to some scientific or mathematics list for a "cross post"(??) Maybe
somebody would "dig" working on a new problem related to numbers and
music... Just a thought.
_________ ___ __ __ _
Joseph Pehrson