I first heard L. Shankar playing against a 9.5 beat tala, and the concept blew my mind. In western terms, it means that the relationship between the rythm and melody (plus any harmony if there is any) shifts 0.5 beats every cycle: for one cycle, the rythm may feel ahead, or on time, and for the next it may feel on time, or late. It's a fascinating technique that I think has no true analog in western music.

It is true that many forms of african-derived music in the US will shift the precise position of beats to create swing/syncopation/dilla-time, but this is generally done on a per-note basis, not on a per-cycle basis as happens with a half-beat tala.