Transparent Corp's Research Area is arguably the most comprehensive resource for collated brainwave entrainment research.   Update: the main research area on Transparent Corp's website is currently being updated, so it is offline.  However, you can still access their peer-reviewed research paper as a PDF here: “A Comprehensive Review of the Psychological Effects of Brainwave Entrainment“.
In order to understand brainwave entrainment you first have to understand something about brain waves and electroencephalograms (EEG). Neurons are cells that communicate with each other through electrical conduction. When a neuron fires it creates a small electrical and magnetic field. These fields are far too small to measure by placing electrodes on the scalp, or even on the surface of the brain. The only reason we can detect the electrical fields of the brain is because many neurons are firing together – in synchrony. All brain waves that are measured by an EEG, therefore, represent a large group of neurons firing together.
... [9] While entrainment by binaural auditory beats in the alpha frequency has also been shown to enhance creativity, cognition, memory, and an improvement in intelligence tests and achievement tests in learning disabled boys. [10][11][12][13] The gamma-band activity has been shown to involve in a variety of functions such as attention, memory, and consciousness. Current literature suggests that entrainment by gamma beats promotes cognitive flexibility, modulates visual attention, and enhances creativity. ...
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.
Maya Mendoza is a published author of 3 personal development books. She has run an NLP / EFT Practice for 29 years helping clients transform problems into personal power. Maya is also a accomplished copywriter and well known Digital Marketing & Social Social Media Strategist - Specializing in Google+ for business. She was named "best marketing consultant" in Glasgow, UK in 2013.  
All brainwave frequencies are useful and beneficial at certain times – there is no brainwave that is intrinsically better than another. However, by deliberately choosing to attain a particular brainwave state, a corresponding mental state can be brought about at the same time. For example, a working person who has been in an overly alert beta brainwave pattern for many hours can quickly shift their mind and body into a relaxed state by listening to a few minutes of brainwave entrainment music for inducing alpha or theta brainwaves.
Despite the vast differences between each individual, our brain’s inner workings are remarkably similar. Brainwave Entrainment was built around these fundamental similarities and has equally powerful effects for almost everyone who uses it. While each situation may require a different frequency or audio track, Brainwave Love has one of the most complete, effective libraries to cover your every need. Take a look now:
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These select frequencies and tones reduce the brain's filtering effect and allows consciousness to be set free. Each recording includes binaural beats, monaural beats, isochronic tones and other sound patterns, combined to deliver a range of delta, theta and alpha rhythms that draw your brain into hypnagogia, the transitional state between wakefulness and sleep.
The activity of neurons generate electric currents; and the synchronous action of neural ensembles in the cerebral cortex, comprising large numbers of neurons, produce macroscopic oscillations. These phenomena can be monitored and graphically documented by an electroencephalogram (EEG). The electroencephalographic representations of those oscillations are typically denoted by the term 'brainwaves' in common parlance.[4][5]
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