A word that I like:

tact. noun.

  1. a keen sense of what to say or do to avoid giving offense; skill in dealing with difficult or delicate situations.
  2. a keen sense of what is appropriate, tasteful, or aesthetically pleasing; taste; discrimination.

Or as the OED puts it:

‘Ready and delicate sense of what is fitting and proper in dealing with others, so as to avoid giving offence, or win good will; skill or judgement in dealing with men or negotiating difficult or delicate situations; the faculty of saying or doing the right thing at the right time.’

I recently read a short story in which rhetoric is described as the art of ruling; if so, then tact is the art of conversation.