It is my (layman's) understanding that a domestic cat learns to meow in a specific tone (I've even read that it can resemble a human baby crying) in order to get the owner's attention.
Regardless of the factual accuracy of this specific claim (which is referenced here, here and was even challenged in Skeptics.se), the fact is that an attention-seeking cat's meowning can be really unsettling.
Again, speaking as a layman - and to give a practical example -, when I'm trying to concentrate on something and my cat meows two or three times (even at a great distance), it is more than enough to disrupt my attention completely.
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My strategy to deal with this has been mixed: Sometimes I'll ignore him for a moment - which is incredibly hard; sometimes (if it won't stop) I'll yell (not too loud, but very firmly): STOP. And it works.
As of lately I've been interested in dealing with the root cause. Precautions have been taken to assure that the cat is getting enough food, water, grooming, and indeed, enough attention.* I've been struggling to not scream (because a) it makes me feel bad, and b) it sure reinforces the cat's behavior).
(*) While this could be debated, because one would think that the cat wouldn't meow if he didn't need to, I'm quite sure he's getting at least the most attention I can provide. From my research it should be more than enough. And it is enough for my _other_ cat, as a matter of fact.
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To be pragmatic, while the cat's behavior cannot be effectively resolved, it is of my utmost interest to learn if the owner can "recondition" him/herself not to be bothered by the sound of the meowning so much.
I'm wondering if a person can be made to simply "observe" the distressing sound, like a Zen Master observes the sound of the wind rustling the leaves of a tree, without her brain generating an immediate distress signal like it does.
Or, maybe, some tones are just "hardwired" to always trigger such reaction, no matter how much cognitive effort a person puts in?