1 : roughness
2 : harshness of manner or of temper
I've taken to calling those who generally speak with ASPERITY abrasive. (This last/first sentence sounds incredibly awkward to me, but I'm to tired/frustrated to attempt to rephrase.) If ASPERITY had a proper adjective form (ASPERITIOUS? ASPERTIOUS? ASPERCIOUS?) I might consider using that, although I love the way abrasive sounds. It's almost a case of onomatopoeia—but rather in tactility than sound—as though you can feel the roughness every time the word is spoken.
The tone of ASPERITY does not strike me as rough as much as it does harsh. ASPERITY is the verbal slap in the face, the coldness of indifference. Abrasive, on the other hand, describes one who rubs you the wrong way, whose temperament feels like steel wool scraping against your ego.
Let's think of an example. The other day an old boyfriend called, returning a rather spontaneous call I had made a couple weeks ago. I had rambled something to his voicemail about "wanting to say hi." I was hoping he wouldn't call back, but alas. He's still in a state of resenting me (to be fair, I'm still in the pathetic state of desiring his approval). When he called, his conversational tone was as cold as a steel railing in a snowstorm. At the end of our ten or so minute conversation, I thanked him for calling:
It was really good to hear from you, I said.
Yeah, well, just returning your call. (ASPERITY)
The tone would have been more abrasive had he said something like:
Yeah, well, you might hear from me more often if I gave a fuck about you.
But, I mean, that's really just one example of many potential examples.