...  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. ...
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.
A warning: Be sure to listen to these two tracks no more than twice each per day. Any more and your beta-thought centers can have TOO much energy in them, causing you to feel like you are on a stimulant. Some people may only be able to listen to each track once per day without feeling over-stimulated. That's fine, just go with what works for you. Sometimes less is more when it comes to brainwave entrainment. Don't push too hard trying to force-grow your brain cells. :-)
The mantra technique as taught by Michael at Project Meditation is an excellent example of an outward technique. Since the vast majority of people have somewhat active minds, this mantra technique is a good bet for most of us. Even mantra techniques have some differences. Some require rigid concentration while others are more relaxed, such as Michael’s technique. There are some that use chanting which is helpful for a person whose mind is hyperactive.
Entrainment is a term originally derived from complex systems theory, and denotes the way that two or more independent, autonomous oscillators with differing rhythms or frequencies, when situated in a context and at a proximity where they can interact for long enough, influence each other mutually, to a degree dependent on coupling force, such that they adjust until both oscillate with the same frequency. Examples include the mechanical entrainment or cyclic synchronization of two electric clothes dryers placed in close proximity, and the biological entrainment evident in the synchronized illumination of fireflies.