The usage I have heard is that a crooked tune doesn't fall on normal 16 bar contra dance template. There is either a short part, or a longer part, or the first half of the A part is longer than the second half so the B part comes in "early", you know what I mean. A friend of mine, an accomplished OT fiddler, calls it a "burl" in the rhythm.
When listening, a crooked tune is cool because it punctures your expectations of the normal "dramatic arc" of the tune. Playing a crooked tune is really fun because, once you get it, the "burl" can be addicting.
I would never put up a crooked tune at a contra dance.
But... there are many tunes that get ambiguous here and there, and while they are firmly 16 bar (four square regular), they can sound crooked in the emphasis. I like these tunes (I am trying to come up with an example, but my coffee cup is empty), thrown in at a contra dance because they are eminantly dancible, especially for experienced dancers, but have that little drama, that little threat of chaos in them.
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