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Entrainment in the biomusicological sense refers to the synchronization of organisms (only humans as a whole, with some particular instances of a particular animal) to an external perceived rhythm, such as human music and dance such as foot tapping.
Beat induction is the process in which a regular isochronous pulse is activated while one listens to music (i.e. the beat to which one would tap one's foot). It was thought that the cognitive mechanism that allows us to infer a beat from a sound pattern, and to synchronize or dance to it, was uniquely human. No primate tested so far--with exception of the human species--can dance or collaboratively clap to the beat of the music. Humans know when to start, when to stop, when to speed up or to slow down, in synchronizing with their fellow dancers or musicians. Although primates do not appear to display beat induction, some parrots do. The most famous example, Snowball was shown to display genuine dance, including changing his movements to a change in tempo (Patel et al., 2009)
Beat induction can be seen as a fundamental cognitive skill that allows for music (e.g., Patel, 2008; Honing, 2007; 2012). We can hear a pulse in a rhythmic pattern while it might not even be explicitly in there: The pulse is being induced (hence the name) while listening--like a perspective can be induced by looking at an arrangement of objects in a picture.
Neuroscientist Ani Patel proposes beat induction--referring to it as "beat-based rhythm processing"--as a key area in music-language research, suggesting beat induction "a fundamental aspect of music cognition that is not a byproduct of cognitive mechanisms that also serve other, more clearly adaptive, domains (e.g. auditory scene analysis or language)" (Patel, 2008).
Joseph Jordania recently suggested that the human ability to be entrained was developed by the forces of natural selection as an important part of achieving the specific altered state of consciousness, battle trance. Achieving this state, in which humans lose their individuality, do not feel fear and pain, are united in a shared collective identity, and act in the best interests of the group, was crucial for the physical survival of our ancestors against the big African predators, after hominids descended from the safer trees to the dangerous ground and became terrestrial.