Synchronized brain waves have long been associated with meditative and hypnogogic states, and audio with embedded binaural beats has the ability to induce and improve such states of consciousness. The reason for this is physiological. Each ear is "hardwired" (so to speak) to both hemispheres of the brain (Rosenzweig, 1961). Each hemisphere has its own olivary nucleus (sound-processing center) which receives signals from each ear. In keeping with this physiological structure, when a binaural beat is perceived there are actually two standing waves of equal amplitude and frequency present, one in each hemisphere. So, there are two separate standing waves entraining portions of each hemisphere to the same frequency. The binaural beats appear to contribute to the hemispheric synchronization evidenced in meditative and hypnogogic states of consciousness. Brain function is also enhanced through the increase of cross-collosal communication between the left and right hemispheres of the brain.
These are very similar to binaural beats, except that instead of the audio being fed through two different channels containing two different tones, monaural beats put both tones together on a single channel. The difference is that instead of your brain producing the effect of cancelling out the wave and producing the low frequency beat, it instead mixes in the air where it is perceived by the ears, with no brain processing involved.
The reason this rule of thumb is so useful is because there is a huge market for simple answers. A genuine elegant solution (one that accomplishes more with less) is highly valuable in the marketplace. We are used to technology delivering new easy solutions to previously difficult tasks. While most improvements are incremental, there are occasional breakthroughs that transform our lives.
There’s a growing body of research suggesting that binaural beats can reduce different forms of anxiety, from mild to chronic. One especially interesting study looked at the effects of binaural beats on anxiety among patients preparing to undergo surgery—a life circumstance that is pretty anxiety provoking for most anyone. Over a period of six months, patients spent 30 minutes on the day of their surgery listening to binaural beats. Compared to patients who listened to a soundtrack that did not include binaural beats—and patients who received no “beats” therapy at all—the binaural beat listeners experienced significantly greater reductions in their anxiety levels.
Your brain cells reset their sodium & potassium ratios when the brain is in Theta state. The sodium & potassium levels are involved in osmosis which is the chemical process that transports chemicals into and out of your brain cells. After an extended period in the Beta state the ratio between potassium and sodium is out of balance. This the main cause of what is known as "mental fatigue". A brief period in Theta (about 5 - 15min) can restore the ratio to normal resulting in mental refreshment.  
Why is exposure to these soundwaves helpful to sleep and relaxation? Science shows that exposure to binaural beats can create changes in the brain’s degree of arousal. Listening to these sounds that create a low-frequency tone, research indicates, triggers a slow-down to brainwave activity—and that may help you relax, lower your anxiety, and can make it easier for you to fall asleep and sleep more soundly.
Our relaxing music is perfect for Deepak Chopra Meditations, Buddhist meditation, Zen meditation, Mindfulness meditation, Kundalini meditation, Qi Gong Meditation, Zazen Meditation and more. Our music is influenced by Japanese meditation music, Indian meditation music, Tibetan music and Shamanic music. Our instrumental music has been designed to encourage and enhance relaxation, meditation, brain function and concentration, spa and massage therapy, and healing music therapy. In addition, we use binaural beats (Delta, Alpha and Theta Waves) to naturally reach a state of relaxation perfect for concentration, meditation or deep sleep. Our music playlists are perfect for your daily meditation and relaxation. Our music videos use soundscapes such as nature sounds, animals, oceans, rain sounds, thunder sounds and many more).
Beating can also be heard between notes that are near to, but not exactly, a harmonic interval, due to some harmonic of the first note beating with a harmonic of the second note. For example, in the case of perfect fifth, the third harmonic (i.e. second overtone) of the bass note beats with the second harmonic (first overtone) of the other note. As well as with out-of tune notes, this can also happen with some correctly tuned equal temperament intervals, because of the differences between them and the corresponding just intonation intervals: see Harmonic series (music)#Harmonics and tuning.

There were no significant differences between the experimental and control conditions in any of the EEG measures. There was an increase of the Profile of Mood States depression subscale in the experimental condition relative to the control condition (p = 0.02). There was also a significant decrease in immediate verbal memory recall (p = 0.03) in the experimental condition compared to control condition.
Slightly higher-frequency entrainment can lead to hyper suggestive states of consciousness. Still higher-frequency EEG states are associated with alert and focused mental activity needed for the optimal performance of many tasks. Perceived reality changes depending on the state of consciousness of the perceiver (Tart, 1975). Some states of consciousness provide limited views of reality, while others provide an expanded awareness of reality. For the most part, states of consciousness change in response to the ever-changing internal environment and surrounding stimulation. For example, states of consciousness are subject to influences like drugs and circadian and ultradian rhythms (Rossi, 1986; Shannahoff-Khalsa, 1991; Webb & Dube, 1981). Specific states of consciousness can also be learned as adaptive behaviors to demanding circumstances (Green and Green, 1986).  
If you search the Internet for "binaural beats" you'll quickly find there's a whole industry built on the idea that listening to binaural beats can produce all kinds of desired effects in your brain. It can alter your mood, help you follow a diet or stop smoking, get you pumped up for a competition, calm you down, put you to sleep, enhance your memory, act as an aphrodisiac, cure headaches, and even balance your chakra. Binaural-Beats.com offers a $30 CD that they call the world's first "digital drug". They claim it can get you drunk without the side effects. I-Doser.com offers a range of music tracks that they say simulates a variety of actual pharmaceuticals, such as Demerol, Oxycontin, and Vicodin. Suffice it to say that no matter what superpower you're looking for, someone on the Internet sells a binaural beat audio file claimed to provide it.
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