Sharpness, n.
Etymology: [AS. scearpness.]
The quality or condition of being sharp; keenness; acuteness.
Shades of meaning
Fernald has no entry of its own for sharpness; he lists it under acrimony, acumen.
Where he writes about it:
Acerbity is a sharpness, with a touch of bitterness, which may arise from momentary annoyance or habitual impatience; asperity is keener and more pronounced, denoting distinct irritation or vexation; in speech asperity is often manifested by the tone of voice rather than by the words that are spoken. — from acrimony
Sharpness, acuteness, and insight, however keen, and penetration, however deep, fall short of the meaning of acumen, which implies also ability to use these qualities to advantage. — from acumen
Acumen is sharpness to some purpose, and belongs to a mind that is comprehensive as well as keen. — from acumen