consisting of parts?

All-

I've just finished a LISP run that evaluates ET's for consistency at a
given limit, and at all subsets of the given limit. Specifically, the ET
is rated by the largest cardinality it can consistently represent. So if
12tET isn't consistent at the 19-limit, maybe it would be consistent with
respect to all 19-limit tetrads. In that case, I would call it "4-part
consistent at the 19-limit".

Funny thing is, I've searched the first 50 ET's at all limits up to 19, and
no intermediate results have shown up. That is, at each limit, the ET is
either consistent with respect to the whole set, or not at all. IOW, while
12tET is consistent with the [1 7 15 19] tetrad, it is not consistent with
_all_ 19-limit tetrads. At least, that is what my software is telling me.
There's a good possibility it's wrong; I haven't looked it over carefully
since writing it. My question is, does this result sound surprising?
Reasonable? Trivial?

-Carl

[I wrote...]
>My question is, does this result sound surprising? Reasonable? Trivial?

Hmm. Maybe it is trivial. A failure of consistency means there's at least
one triad that's failing, and that triad will turn up if you take all the
subsets (down to, of course, triads) of the saturated chord. That sound
right? I keep forgetting that consistency doesn't really involve anything
bigger than a triad!

-Carl

On Thu, 13 Jan 2000, Carl Lumma wrote:
> Hmm. Maybe it is trivial. A failure of consistency means there's at least
> one triad that's failing, and that triad will turn up if you take all the
> subsets (down to, of course, triads) of the saturated chord. That sound
> right? I keep forgetting that consistency doesn't really involve anything
> bigger than a triad!

That's exactly right, Carl.

--pH <manynote@library.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o

Carl, triadic consistency is logically equivalent to tetradic consistency,
pentadic consistency, etc. See Patrick Ozzard Low's paper for a full
explanation.