re: consistency parts?

>Cool! Maybe you should print out Patrick Ozzard Low's "fractional
>consistency" measure; that is, what percentage of the triads succeed.

Aeeh- I prefer Hahn's levels, if I'm going to think about levels.

>>Wait a minute! Those are pairs, not triads! The "1" is implied. So the
>>best 11/1 in 5tET is not the sum of the best 5/1 and 11/5.
>
>You also need to check triads that don't include the 1.

Really? Paul Hahn's algorithm doesn't seem to do that. Checking...

-Carl

On Fri, 14 Jan 2000, Carl Lumma wrote:
>>>Wait a minute! Those are pairs, not triads! The "1" is implied. So the
>>>best 11/1 in 5tET is not the sum of the best 5/1 and 11/5.
>>
>>You also need to check triads that don't include the 1.
>
> Really? Paul Hahn's algorithm doesn't seem to do that. Checking...

My algorithm doesn't bother because I'm only interested in absolute
consistency and don't need to took at the individual triads. It works
because given a triad (A,B,C) and some random other pitch X, if (A,B,C)
is inconsistent then at least one of (A,B,X), (A,X,C), and (X,B,C) will
be inconsistent as well. But for your purposes, Carl, Paul E. is right;
you should check _all_ the triads.

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

>You also need to check triads that don't include the 1.

D'oh! Of course that's right. Fortunately, way I've done things, it only
takes about 10 seconds to fix. The consist_triad files at
ftp://lumma.org/pub/ are corrected.

I hesitated because I was still turning up the right stop limits -- you'd
think there'd be places where a triad without a 1 would cause consistency
to fail, and I'd have missed it.

I forgot that to save time, I had the program checking for overall
consistency in the normal way, before calculating subsets.

Funny thing is, taking that failsafe out and still checking only for triads
with 1's, I can't find such a spot. If you'd like to try it, the procedure
is called only_1s (also at my ftp site).

A corrected version of the chart I posted yesterday appears at:
http://lumma.org/consist_fail.txt

I admit it's getting a little crowded.

Thanks!
-Carl

>>Cool! Maybe you should print out Patrick Ozzard Low's "fractional
>>consistency" measure; that is, what percentage of the triads succeed.

>Aeeh- I prefer Hahn's levels, if I'm going to think about levels.

It's a totally different concept -- for one thing, this will increase the
number of ETs under consideration as opposed to strict consistency, while
Hahn's higher-level criteria only decrease the number of ETs under
consideration.