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Websters gives several pronunciations, including reference to the one with two syllables I was about to mention: too-er.
They all sound fine to me.
This may be a north-south division. I first started drinking Coors beer in Oklahoma. When I moved to Kansas, I found more Cores than Coors.
There’s another highly specific pronunciation of tour: Tower, as in Eiffel. Bus drivers refer to their morning and evening shifts as Towers…. but the overnight shift is the Night Train, not the Night Tower.
As a British English-speaker, I find this interesting. To me, there is no difference in pronunciation between tore and toor! (To give an example of actual words, in British English the words more and moor are pronounced the same.) In Britain, we pronounce tour pretty much as the French tour (as in Tour Eiffel) or, as has also been mentioned, as too-er (but as one syllable, if that makes sense).
An ex-girlfriend would constantly nag me for pronouncing it “toor” or probably more closely to “too-er” as mentioned above. That’s the way I had learned it in Southern California. I started to pay a little more attention and almost everyone in Utah pronounced it “tore” as well.
That’s not saying much, since Utah pronounces a handful of things strangely:
milk = melk
pillow = pellow
mountain = mount’n
If you want to see a real argument over pronunciation, ask people to pronounce buoy. Some will say boo-wee, others will say it exactly the way they say boy. And to complicate the matters, add Bowie (as in musician David, or frontiersman Jim and his knife). On one of the Smothers Brothers’ albums, Tommy makes it clear that he’s from Southern California by declaring that Jim Bowie “had a big Bowie knife, and all the other guys just had girl knives”. In a lot of regional dialects, that joke doesn’t work at all.