Brain Wave Entrainment is any procedure that causes one's brainwave frequencies to synchronize with a periodic stimulus (sound, vibration or light) having a frequency corresponding to the intended brain-state (for example, to induce a trance, dreams, sleep or relaxation.) It is also called the Flicker-response because of how staring at a campfire or the flickering of a burning candle can lull you into a state of calmness and serenity. There was an extensive article on this phenomenon by Gerard Oster in Scientific American in 1973. It may sound novel, but in many ways, this is old tech.
This music encourages a state of alpha relaxation. The alpha state is a pleasant state of relaxed alertness. It’s a state that many people experience when they are waking up in the morning or when they are just beginning to drift off to sleep at night. While in a state of alpha relaxation, the mind is quite clear and receptive to information, learning is accelerated and one’s sense of creativity is enhanced. The mind is also very open to positive suggestions during this state.
Today we're going to put on our headphones, kick back in the beanbag, and get mellow to the soothing sounds of the latest digital drug: binaural beats. These computer generated sound files are said to massage your brain and produce all sorts of effects, everything from psychedelic experiences to behavior modification. Let's point our skeptical eye at the science of binaural beats, and especially at some of the claims made for them.
A popular opinion in the brainwave entrainment community is that listening to isochronic tones without music produces a much stronger effect. However, in the study by Doherty, Cormac. “A comparison of alpha brainwave entrainment, with and without musical accompaniment” (2014), it was concluded that brainwave entrainment was equally effective for isochronic tones, both with and without music.
Entrainment is a principle of physics which appears in biology, chemistry, neurology, medicine, astronomy etc. It is defined as the synchronization of two or more rhythmic cycles. In the seventeenth century, Dutch scientist Christian Huygens found out that by placing two unsynchronized clocks side by side on a wall, they would slowly synchronize to each other in a very accurate way. The clocks were the first example of spontaneous synchronization, a phenomenon found throughout nature from cells to the Solar System.
...  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.  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. ...
Cognitive behavioral therapy (CBT) is a type of therapeutic practice that has been proven to lower anxiety, stress and multiple disorders — including addiction, eating disorders, insomnia and depression. Knowing that at least 50 percent of the time experiencing a mental disorder is due mostly to chronic, untreated stress reactions, therapists use CBT to train all types of people to better react to situations that are stressful.
There are five main categories of brainwave frequencies: Gamma (40Hz+), Beta (13 – 40Hz), Alpha (7 – 13Hz), Theta (4 – 7Hz), and Delta (<4Hz). Each category is associated with a different state of mind; so, for example, when you’re in a peak state of performance, your brain produces Alpha Waves, and when you’re in a deep sleep, your brain produces Delta Waves.
If brainwave entrainment leaves you with unwanted side-effects (see below) or discomfort, you’re probably encouraging a range of brainwaves that are already excessive in some area of your brain. The way around this is to get a brain map to see what your brain’s strengths and weaknesses are, and see what (if any) brainwaves could use some encouragement.