I recently applied for a Canada transit visa and was denied. The reason for the refusal was 'Purpose of visit.'
Now I want to apply for a visitor visa. How long is the normal time to wait before making another application?
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Everything I've read from Citizenship and Immigration Canada on visa denials emphasizes that you should only apply if your situation has materially changed (e.g. see a short note on this here) - waiting does not matter. However, in your situation, it's a bit more complicated:
The trick is, of course, proving that the two trips "A" and "B" are completely unrelated (that you didn't lie about the original application, and that instead you have some new need to visit Canada, completely unrelated to the previous need to transit through Canada). If the visitor visa application is soon after the transit one, it does look very suspicious... Here's what I would do (but please take with a grain of salt, I am not a lawyer by any means):
If it's really clear that the two trips are completely unrelated, and you have really clear documentation for both trips, and you have a very clear explanation for why the desire to visit Canada arose all of a sudden (why you only wanted to transit before but want to visit now), then go ahead and apply right now, showing all these clear explanations in your application. (E.g.: 1st application was transit via Vancouver with a ticket that clearly showed the transit route, and since the denial you've been invited to a conference in Toronto with clear evidence of that fact)
If the facts are not as clear, spend the money on a lawyer before you submit any other application. Lawyer may suggest appealing the 1st denial in some way, or directly addressing the open questions remaining from your 1st application in your 2nd application, or something else entirely... (And especially if you did in fact lie on your 1st application - definitely talk to a lawyer before even thinking about reapplying).