For my own reference:

Gamma - This could be considered an extension of Beta, as it is said to start at 25 HZ (cycles) and go up to 100, though some say it really starts at 40.  It is said to be the highest clarity of them all.  And some attribute magical qualities to it.

Beta - Highest in frequency and lowest in amplitude.  More desynchronous than other waves. 13- 40 HZ.  This is the stage of maximum mental alertness and concentration.

Alpha (quiet, calm alertness) - During moments of relaxation, while still awake, our brain waves become slower, with higher amplitude and more synchonousity.  When more relaxed and peaceful such as in meditation or biofeedback.  Activities that promote alpha wave activity appear to have positive health benefits. 7-12 HZ.  Good for visualization and creativity, often feeling a sense of peace and well-being.  Good for problem solving, new ideas.  This is deep relaxation but not quite meditation.  L-Theanine, also found in tea, used as a sleep herb, induces an alpha state of relaxation.  L-theanine crosses the blood brain barrier and increase the neurotransmitters serotonin, dopamine and GABA, which help induce the alpha state - and it calms us down.  If someone is stressed and disjointed feeling, unable to concentrate well, this will help one potentially be more focused.  Activity diminished in our stress system.

Theta waves occur in the first two stages of sleep, and are, again, lower in frequency and greater in amplitude. 4-7 HZ. Meditation, intuition, can bring back long forgotten memories.  On the threshold of your subconscious, kind of a twilight state, in a waking dream of sorts.  A good state for super-learning and reprogramming.

Delta.  In stages 3 and 4, delta waves occur, again even slower in frequency and highest in amplitude.  In stage 3, 50% of the waves are theta and in stage 4 has more than 50%.  This is our deepest sleep.  If awakened in these stages, usually we are groggy and disoriented.   Some Human Growth Hormone is released, which helps healing and regeneration.

In REM (rapid eye movement), there is a dramatic loss of muscle tone, with the skeletal muscles being effectively paralyzed.  In REM, a combination of alpha, beta, and desynchronous waves occur.  Most importantly to psychologists, this is the stage of sleep most associated with dreaming.

A sleeper goes from Stage 1 through REM in about 90 minutes, which is called a cycle, of which there are 4 or 5 a night. The length of REM increases in each cycle with the delta sleep decreasing until the delta disappear in the last few cycles. 


4.5 beats per second correspond to the trance-like state of theta brain wave activity.  Drums struck 4.5 time per second and/or the constant drone of Tibetan Buddhist chants transport one into realms of blissful meditation.  

A number of practitioners in the area of largely unknown verifications of "healing" or "seeking super humanness".  One prominent theory that actually makes some sense is that of "entrainment", which is simply that two sets of waves will tend over time to "synchronize", affecting each other, essentially drawing the other toward their brain waves.   Some people sell "entrainment" programs that are said to draw the brain waves toward the sound waves in the program, thereby inducing relaxation or hypnotic states or even gamma waves (to produce "super human" thinking powers).  The extreme versions are not likely to be true, but there is some underlying truth.  

One of the famous series of studies are those that actually prove that women's menstrual cycles will begin to be drawn toward the same timing.  Also, there is the study of a number of clocks in the same room will tend to draw each other toward the exact same time.    

See also:  Music And Its Effects On Our Bodies And Brains.   

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Waves, Frequencies, And Energy - To go deeper and remove some false theories and shortcuts, such as the brain causing "things to come into existence" and other unlikely effects.