Brainwaves are electromagnetic pulses produced by the (human?) brain. They were discovered in 1924 by the German psychiatrist Hans Berger. Their measurement is called electroencephalography. An electroencephalogram (EEG) is used by physicians as a diagnostic tool for the identification of various ailments. Four different frequency bands of brainwaves have been found. From lower to higher they are called the delta, theta, alpha, beta bands. An even higher Gamma band is applied by some. The strongest brainwave frequency corresponds to the current state of consciousness, being deep sleep, dreaming, waking, or focusing. Each of these rythms is produced in a specific area in the brain.
Typically binaural beats are two tones of different frequencies, one is heard through the left side of a set of headphones, the other through the right side. The brain puts these two signals together, and we hear only one tone. The brain is stimulated to adjust its brainwave patterns to the frequency closest to the difference between the two tones. For example if we have 12 Hz on the left, and 22 Hz on the right, the brain tries to synchronize its own frequency to 10 Hz, which is in the alpha range. This principle can be used to influence the brain to move to the desired brainstate.
Example of 10 Hz binaural beat 
This example has 12 Hz on the left channel and 22 Hz on the right channel. The resulting sound is a 10 Hz pulsating tone. The binaural beat effect is demonstrated by turning off one of the speakers. Either of the composing non-pulsating tones remains.
Experimenting with brainwave stimulation (i.e. listening to the sounds presented here) is not without risk. For example people who suffer from epilepsy should not practice brainwave stimulation without consulting a physician. Only you are responsible for the results of listening to these sound fragments. There is a lot of information about brainwaves on the web: read about it before you start experimenting. The Mp3 sound files presented here were created with the help of Brainwaves Generator Software.
Relaxed, tranquil, unfocused, being awake. Super learning, positive thinking, pleasant drifting feelings, inward awareness.
Relaxing meditation. Alpha rythm with sounds of sea and birds. This particular frequency stimulates the release of serotonin in the blood, and works as a mood elevator. It is the safest frequency.
This particular frequency can be used for stress reduction.
Physical relaxation. (SMR = sensorimotor rhythm)
Dream (REM) sleep, deep relaxation, creative inspiration, mental imagery, Zen meditation.
Theta 4.5 Hz Tibetan Buddhist Chants 
This frequency seems to play a role in some forms of Buddhist chanting.
Deep sleep (dreamless, restorative), deep trance or hypnosis. Diminishes the level of cortisol in the blood, responsible for many of the negative symptoms of burnout and stress. Increases the levels of DHEA and melatonin.
Normal wakefulness, alert state of mind, focused. Outer awareness, problem solving, worry, anger, fear, intellectual thinking, verbal communication, working with computers, watching TV etc.
This frequency seems to stimulate general mental ability.
This frequency can be used for desensitization.
This frequency can be helpful for practicing astral projection techniques. Use with care.
Hans Berger (history of the discovery of brainwaves)
OpenEEG Project: how to make your own EEG measuring device
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