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Definition of asperity : 1. Moral roughness; roughness of manner; severity; crabbedness; harshness; - opposed to mildness.
2. Roughness of surface; unevenness; - opposed to smoothness.
3. Roughness or harshness of sound; that quality which grates upon the ear; raucity.
4. Roughness to the taste; sourness; tartness.
5. Sharpness; disagreeableness; difficulty.

Synonyms:

hard knocks, fury, acridness, badness, temper, stiffness, validity, roughness, virulence, acrimony, keenness, sourness, rigour, easy, causticity, bile, raciness, malignity, ghastliness, mood, poignance, severeness, virulency, gruesomeness, sharpness, difficulty, moroseness, resentment, severity, harshness, rigourousness, hardness, cattiness, acuity, acerbity, vicissitude, vitriol, hardship, edge, acridity, bite, pungency, acidness, irritation, bitterness, rigor, acuteness, austereness, inclemency, rigorousness, rudeness, distinctness, poignancy, ill temper, rage, acidity, unkindness, heavy sledding, anger, outrage, cogency, tartness, mordancy, luridness, corrosiveness, annoyance, grimness, acrimoniousness, adversity

unevenness

Usage examples:

• And it seems that there was somthing in the Forms of Asperity that was requisite to the Distinction of Colours, besides the Degree of it, since he found it so difficult to distingush Black and White from one another, though not from other Colours. - "Experiments and Considerations Touching Colours (1664)", Robert Boyle.
• I have often observed that when one female shows asperity, nearly all the others do the same. - "Erema My Father's Sin", R. D. Blackmore.
• " No," said Tom, with some asperity, for he felt too much exhausted to speak. - "Hunting the Lions", R.M. Ballantyne.