publishing consistency work, newest addition

Okay!

I've fixed a minor formatting problem in the chart I created this morning,
updated the code of the first three programs, and created a web page for it
all at http://lumma.org/scheme/.

I've also added my fourth and final program in this series, which I call
consist-badies.

As we saw this morning, searching for consistent subsets returns too much
data to make a chart practical. So my new proggie works only one ET at a
time. I'm looking into getting a complier for Scheme, though, so I may
have a binary for it before too long. For now, you'll have to download
scheme if you want to run it (www.scheme.com). It works like this...

(check ET lev card '(idents))

Where ET is the ET you want to check, lev is the minimum Hahn consistency
level you're willing to accept (you can enter non-integer levels), card is
the number of tones in your basic chord (triad=3, tetrad=4 and so on), and
'(idents) is the list of identities you'd like to check against (the
identities can be in any order). Let's give it a try...

>(check 41 1 4 '(1 3 5 7 9 11 13 15 17))
((23/63 fail) ((17) bad) (() nogood))

The result will always be a list of three lists. In this case, the three
lists are...

1. (23/63 fail)

This means that 23 out of 63 17-limit tetrads are not level-1 consistent in
41tET. That is, about 37% of them (Scheme will reduce this ratio to lowest
terms, as it did in this case) "fail". If we had asked 3 instead of 4
(triads instead of tetrads), this ratio would be Patrick Ozzard-Low's
fractional consistency.

2. ((17) bad)

This means that of identities you listed, 17 is the only one that occurs in
every failing chord. If this list is empty, then there's no identity
common to all the failing chords. Deal is, by leaving out the "bad"
identities, you can eliminate all the failing chords.

3. (() nogood)

This means that there aren't any identities that occur only in failing
chords. If an identity did appear in this list, you won't loose any
consistent chords by getting rid of it.

>>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.

A totally different way of measuring accuracy at a given limit with respect
to step size. The fractional Hahn level should follow the inverse of the
Ozzard-Low consistency fairly well. You can see it by jacking up the Hahn
level in consist_badies, and watching the fail ratio go up.

Thanks, all, for humoring my debugging process! I think we're getting
close to golden on some of these.

-Carl

[I wrote...]
>A totally different way of measuring accuracy at a given limit with respect
>to step size. The fractional Hahn level should follow the inverse of the
>Ozzard-Low consistency fairly well. You can see it by jacking up the Hahn
>level in consist_badies, and watching the fail ratio go up.

Ah, that last sentence isn't quite right. Once you take the Hahn level off
1, the fail ratio will no longer be the Patrick Ozzard-Low consistency.
But I still think the first part is right.

-Carl