Howdy Ian,

It would be good to have at least part of the file, so that the surrounding musical context is present. Composer doesn't just analyze a chord in exclusion to it's surroundings. As you mentioned above, context can affect whether one reads a given chord as one thing or another. Since there are an infinite variety of "contexts" we could test (in my spare time, mind you ;) ), it would be helpful if you've got a case that is clearly in need of tweaking that we could use to do the tweaking

So I guess the answer is "enough context to help us see where the chord analysis can pick up enough clues to make a better chord name guess." If the piece is one you don't want to post publicly, please feel free to send it to me at the helpdesk (support@notation.com) or directly to me my email (just click on my post name to the left here.)

ttfn,
Sherry