edge

4. N-SING : usu the N of n

The edge of something, especially something bad, is the point at which it may start to happen.

• They have driven the rhino to the edge of extinction.   
• = verge, brink   

7. N-SING : oft N of n, N to n

If someone's voice has an edge to it, it has a sharp, bitter, or emotional quality.

• But underneath the humour is an edge of bitterness.
  

... Cobuild

1(c). A penetrating, incisive quality: 

• "His simplicity sets off the satire, and gives it a finer edge" William Hazlitt.
• cf. [Collin Essential]4. keenness, sharpness, or urgency: there was a nervous edge to his voice.

3(c). The point at which something is likely to begin: on the edge of war.

6. A provocative or discomforting quality, as from audacity or innovativeness: 

• "Over all, the show will have a grittier edge" Constance C.R. White.
  

... Am Heritage