One way to determine the pitch on a threaded hole is to force-screw a soft wood dowel of appropriate size into the hole. It will take the impression of the threads and then you can use a thread checker to try to determine the pitch. Once it is determined it may or may not yield a result that is easy to match. In replacing a stripped screw on a drilling's sidelock I once did this, but then had to drill and tap to another size, anyway.

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