How "infinite" the tonal lattice?

As a sub-amateur in tuning, I'd like to ask the following question.

After having read the _JI Primer_, much is made out of the "infinite" tonal
lattice. But, clearly, their are limits, both physical and perceptional,
on how fine an increment can be discerned. And, since some intervals are
indiscernible, it would seem that the _practically_ the lattice is finite.

Is it reasonable to superimpose a "discernability grid" or a "precision
grid", or some other such grid, on top of the tonal lattice, thereby
joining like-tones (hmm..., 'homotones'?), into a finite, practical
lattice?

Best regards,

Polychroni Moniodis
Ypsilanti, MI

Dear Paul H. Erlich, et. al. respondents,

Thank much for the references. (And, here I thought I was on to something
with my discovery!). I've begun working my way through them; but these
will take some time after having read them to assimulate. Fancinating
work.

Best regards,

Polychroni Moniodis
Ypsilanti Michigan

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On 19 Apr 00, at 10:00, "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
wrote:

> Polychroni wrote,
>
> >After having read the _JI Primer_, much is made out of the "infinite"
> >tonal
>
> >lattice. But, clearly, their are limits, both physical and perceptional,
> > on how fine an increment can be discerned. And, since some intervals
> >are indiscernible, it would seem that the _practically_ the lattice is
> >finite.
>
> >Is it reasonable to superimpose a "discernability grid" or a "precision
> >grid", or some other such grid, on top of the tonal lattice, thereby
> >joining like-tones (hmm..., 'homotones'?), into a finite, practical
> >lattice?
>
> This is exactly the concept of _finity_ that forms one of Joe Monzo's main
> interests. He's been kind enough to put lots of material on the subject on
> the Web, and will no doubt be adding more once he gets settled in
> California. You could start with
> http://www.ixpres.com/interval/dict/finity.htm.
>
> Also go to http://www.ixpres.com/interval/dict/pblock.htm and follow the
> links from there. When Joe visited me in Boston, he made it a point to ask
> me about finity and I mentioned that Fokker's periodicity block formalism
> seemed to get at the same idea. Since then, I've looked into the concept
> more deeply and posted many articles on it (search the archives for
> "periodicity").
>
> I'd be happy to help you if any of the material you find is unclear.