* Sharpness: This is the most common and general abstract noun for "sharp." It refers to the quality of being sharp, whether in terms of a physical object's edge, a mind's intellect, or a sound's pitch.
* Acuity: This noun specifically refers to sharpness of perception, especially in terms of vision or mental understanding.
* Keenness: This noun emphasizes a strong and intense form of sharpness, particularly in terms of senses, intellect, or emotions.
The best choice depends on the specific nuance you want to convey.