The Collaborative International Dictionary of English v.0.48:

Asperity \As*per"i*ty\, n.; pl. Asperities. [L. asperitas, fr.
   asper rough: cf. F. asp['e]rit['e].]
   1. Roughness of surface; unevenness; -- opposed to
      smoothness. "The asperities of dry bodies." --Boyle.
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   2. Roughness or harshness of sound; that quality which grates
      upon the ear; raucity.
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   3. Roughness to the taste; sourness; tartness.
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   4. Moral roughness; roughness of manner; severity;
      crabbedness; harshness; -- opposed to mildness.
      "Asperity of character." --Landor.
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            It is no very cynical asperity not to confess
            obligations where no benefit has been received.
                                                  --Johnson.
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   5. Sharpness; disagreeableness; difficulty.
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            The acclivities and asperities of duty. --Barrow.
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   Syn: Acrimony; moroseness; crabbedness; harshness; sourness;
        tartness. See Acrimony.
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WordNet (r) 3.0 (2006):

asperity
    n 1: something hard to endure; "the asperity of northern
         winters" [syn: asperity, grimness, hardship, rigor,
         rigour, severity, severeness, rigorousness,
         rigourousness]
    2: harshness of manner [syn: asperity, sharpness] [ant:
       bluntness, dullness]