There are many aspects shared by traditional African music: movement of the body through dance when listening to music, existence of a regular beat underlying these movements and a tendency for musical events to be placed against this regular beat, a feature called "contrametricity". The perception of the beat both has a physiological dimension (since movement of the body when listening to music seems to be universal) and a cultural one since contrametricity is developped to a high degree in African music. We will show how "contrametricity" contredicts theories of the perception of beats derived from Lerdahl and Jackendoff hypothesis. We will furthermore investigate the comparison between African music and jazz, and discuss aspects of jazz ...