^ Trost W. and Vuilleumier P., Rhythmic entrainment as a mechanism for emotion induction by music: a neurophysiological perspective. In The Emotional Power of Music: Multidisciplinary Perspectives on Musical Arousal, Expression, and Social Control, Cochrane T., Fantini B., and Scherer K. R., (Eds.), Oxford, UK: Oxford University Press; 2013, pp213–225.
Our everyday, waking brain used for active intelligence operates at approximately 13 hertz, which is in the range of high alpha or low beta frequencies. People who have certain learning disabilities and problems with attention often have low levels of 13 hertz frequency brainwaves in crucial areas of the brain used for sequencing tasks and doing simple math calculations. This is one concrete example of how brainwaves are associated with thinking and behavior. Each identified brainwave frequency has a different effect on a person’s ability to think, act, and feel.
Both brainwave entrainment and neurofeedback deal with brainwaves, but the similarity stops there. Entrainment pushes your whole brain into a pre-determined state, while neurofeedback teaches you how to move specific parts of your brain on your own. It is the differeence between forcing the brain into a given position, and skills building so you can move it there yourself. 
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