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.
      [1913 Webster]

   2. Roughness or harshness of sound; that quality which grates
      upon the ear; raucity.
      [1913 Webster]

   3. Roughness to the taste; sourness; tartness.
      [1913 Webster]

   4. Moral roughness; roughness of manner; severity;
      crabbedness; harshness; -- opposed to mildness.
      "Asperity of character." --Landor.
      [1913 Webster]

            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.
      [1913 Webster]

            The acclivities and asperities of duty. --Barrow.
      [1913 Webster]

   Syn: Acrimony; moroseness; crabbedness; harshness; sourness;
        tartness. See Acrimony.
        [1913 Webster]

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]

Moby Thesaurus II by Grady Ward, 1.0:

85 Moby Thesaurus words for "asperity":
   acerbity, acid, acidity, acidness, acidulousness, acridity,
   acrimony, anger, animosity, astringency, austerity, bad humor,
   bad temper, bile, biliousness, bitingness, bitter resentment,
   bitterness, bitterness of spirit, bumpiness, causticity,
   causticness, choler, choppiness, corrosiveness, cragginess,
   cuttingness, discontent, edge, gall, gnashing of teeth,
   granulation, grimness, hard feelings, hardness, hardship,
   harshness, heartburning, hispidity, ill humor, ill nature,
   ill temper, incisiveness, inclemency, inequality, irregularity,
   irritability, jaggedness, joltiness, keenness, mordacity, mordancy,
   nonuniformity, piercingness, piquancy, poignancy, pungency,
   raggedness, rancor, rankling, rigor, rough air, roughness,
   ruggedness, rugosity, scraggliness, severity, sharpness, slow burn,
   snappishness, soreness, sourness, spleen, stabbingness, stringency,
   tartness, tooth, trenchancy, turbulence, unevenness, unsmoothness,
   ununiformity, vicissitude, virulence, waspishness