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Noun: abrasiveness  u'brey-siv-nus
  1. The roughness of a substance that causes abrasions
    "The abrasiveness of the wool sweater irritated her skin";
    - harshness, scratchiness
     
  2. The quality of being sharply disagreeable
    "The abrasiveness of his comments offended many people"

Type of: disagreeableness, raggedness, roughness