Brainwave entrainment is a method to alter the frequency of your brainwaves by listening to audible tones containing the desired frequency. So if you want to sleep, you would listen to audio that begins at your current frequency and slowly descends to a delta frequency. By introducing these new lower frequencies, your mind begins to lower its own brainwaves to match this new frequency.

The brain has two hemispheres that operate somewhat independently from one another. The two hemispheric structures of the brain are connected by a large nerve, called the corpus callosum, which sends information back and forth between the two sides of the brain. In most people, the left hemisphere controls language, logical thinking, and analytic processes and the right side contains the centers for emotion, intuition, and non-linear creative thinking.
When we are mentally active various groups of neurons will be firing and the EEG will look like a jumble of different waves at different frequencies. When we are in a relaxed state, however, our brains settle into a steady rhythm – when fully awake this is the alpha rhythm, which as a frequency of 8-12 hz and other recognizable features. When drowsy our brainwaves slow to the theta range, 6-7hz, and when in deep sleep into the delta range, 4-5hz.
... These factors may be the specific frequency of BB; the targeted population-because it is known that older people have different quality of brainwave activity than, e.g., youngsters (Bazanova & Aftanas, 2008;Clark et al., 2004), and the tests used to detect the possible changes in working memory capacity. Based on the research showing a positive impact of alpha-range BB on cognitive functioning, specifically attention, auditory sequential memory, working memory, working memory storage, reasoning ability, cognitive processing and hemispheric synchronization, (Carter & Russell, 1993;Cruceanu & Rotarescu, 2013;Foster, 1990;Kennerly, 1994;McMurray, 2006) as well as on the wealth of research documenting the important role of alpha brain wave activity on vigilance, in-hibitory processes, attention, filtering out irrelevant information working memory, the visuo-spatial component of working memory, perceptual abilities and information processing speed (Braboszcz & Delorme, 2011;Clark et al., 2004;Engle et al., 1999a;Freunberger et al., 2011;Klimesch et al., 2007;Lachat et al., 2012;Oprisan, 2004;Palva & Palva, 2007;Rihs et al., 2007;Sauseng et al., 2009;Tuladhar et al., 2007;VanRullen & Koch, 2003), we believe that BB of a frequency that corresponds to the alpha range of brain activity has a temporary effect on working memory capacity. In our study, subjects were exposed to 9.55 Hz BB stimulation while we measured their working memory capacity through the Automated Operation Span Task (AOSPAN). ...

You don't have to buy one, though. It's not too hard to make your own binaural beat, and free software is widely available to do just that. The one that I used to make that little sample is an open-source program called Gnaural, available on the Sourceforge website. It's pretty easy to use, though it takes some practice before you can generate some of the really cool, more professional sounding beats. A binaural beat consists of two simple tones, and most people add that background pink noise. Nothing special.
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).  
The functional role of neural oscillations is still not fully understood;[6] however they have been shown to correlate with emotional responses, motor control, and a number of cognitive functions including information transfer, perception, and memory.[7][8][9] Specifically, neural oscillations, in particular theta activity, are extensively linked to memory function, and coupling between theta and gamma activity is considered to be vital for memory functions, including episodic memory.[10][11][12]
…I got curious about the Equisync II CDs and it was the 2nd track that started giving me some body signs that revealed me I was in the alpha state. I never practiced meditation before, however, I follow the Gurdjieff and Ouspensky teachings which, if you are not aware, tell us how to do quite the same thing as meditation in our everyday lives while performing our daily tasks. I also believe that Equisync II was more appropriate for me because my life is also dedicated to collective causes, my personal life is totally under control, but your CDs were able to relieve my severe depression after only 3 days of practicing, my chronic insomnia condition which had been lasting for over 27 years seemed to be finally healed. I am truly amazed, really.

Binaural beats between 1 and 30 Hz are alleged to create the same brainwave pattern that one would experience during meditation. When you listen to a sound with a certain frequency, your brain waves will synchronize with that frequency. The theory is that binaural beats can help create the frequency needed for your brain to create the same waves commonly experienced during a meditation practice. The use of binaural beats in this way is sometimes called brainwave entrainment technology.
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BrainwavePowerMusic has been the leaders of Lucid Dreaming, Astral Projection and Deep Sleep Music on Youtube for the last 5 years. The First Channel to focus on creating music specifically for dreaming and falling asleep. Unique music tracks dedicated to help you to fall asleep, getting a deep sleep that will leave you recharged and refreshed. Our astral and lucid dreaming tracks are all carefully formulated to make sure that you can achieve subconscious awareness and have helped millions of people to achieve a lucid dreaming state. Most of our sleep music mainly use Delta and Theta Waves. Mixing in soft instrumental music to help you achieve deep relaxation, and fall asleep fast. Our relaxing sleep music can be used as background music, meditation music, relaxation music, peaceful music and sleep music.
There is also evidence to suggest meditation plays a protective role against the natural reduction in grey matter volume associated with aging. One study found evidence that Zen meditators experienced a slower age related decline rate for cerebral gray matter volume in the putamen which plays a role in learning, cognitive flexibility and attentional processing [14] This could suggest a better attentiveness in aging meditators versus non-meditators.
Infra-Low brainwaves (also known as Slow Cortical Potentials), are thought to be the basic cortical rythms that underlie our higher brain functions. Very little is known about infra-low brainwaves. Their slow nature make them difficult to detect and accurately measure, so few studies have been done. They appear to take a major role in brain timing and network function. 
Binaural beats are created when two tones are played simultaneously, one in each ear. As long as the difference between the two frequencies is less than 30 hertz, the brain perceives the difference in the tones as a “beat” which, if listened to with enough focus, the brain will begin to follow (this is known as the “frequency following response”). By changing the difference between the two beats, the brain will change its wavelength and enter into different “states” of being.
In 1956, the famous neuroscientist W. Gray Walter published the results of studying thousands of test subjects using photic stimulation, showing their change in mental and emotional states. He also learned that photic stimulation not only altered brainwaves, but that these changes were occurring in areas of the brain outside of vision. In Walter’s words:

The binaural-beat appears to be associated with an electroencephalographic (EEG) frequency-following response in the brain (3). Many studies have demonstrated the presence of a frequency-following response to auditory stimuli, recorded at the vertex of the human brain (top of the head). This EEG activity was termed "frequency-following response" because its period corresponds to the fundamental frequency of the stimulus (Smith, Marsh, & Brown, 1975). Binaural-beat stimulation appears to encourage access to altered states of consciousness.


While originally brainwave entrainment was achieved by using pure tones of sound, it is now possible to take these tones and blend them with music, rhythms, and natural sounds, such as the sounds of flowing water, bird sounds, or waves lapping on a beach, creating extended tracts of varied and intriguing brainwave entrainment music for everyday use.
♥ ← This set of tones with the bird calls from Aotearoa is keeping me awake while I finish an essay I've been working on for the past four days. Focus beats + sounds I associate with morning = wakefulness. Still craving the bed, but at least I'm not falling asleep at my desk. Thanks myNoise, without you I'd probably be listening to music and distracted.
When delta waves are present, our awareness of the external world decreases and shuts off. People with ADD have problems with delta waves occurring when they are trying to focus, and focus and attention become increasingly impossible with stronger delta waves. Studies show a reduction of anxiety, improvements in insomnia, and elimination of headaches when people engage in sessions of delta brainwave entrainment.
Many psychologists, doctors, teachers, and other professionals have endorsed the technology while personally taking advantage of the limitless benefits that accompany EquiSync's precisely designed brainwave synchronization/ entrainment technology. It is such a profound field of study that many of the metaphysical benefits, those beyond our current scientific measure and technological & philosophical understanding, have yet to be discovered.
Theta is an ideal state for super learning, storing information in long term memory, re-programming your mind, dream recall, and self-hypnosis. The theta frequency is recognized as the gateway to learning and memory. What is learned in theta get's stored in long term memory. Children under the age of 5 learn more in their first few years of life, because they are primarily in the theta state.
If you’re operating in Alpha mode, you’ll feel very present and in the moment. You might be somewhat reactive to the world around you, but you’ll feel like you have time to process what’s going on rather than just react on instinct. This is a wonderful state to achieve when meditating or doing something that requires coordination, focus and learning.
Are you someone who has turned to meditation or yoga as a way of relieving stress and improving your overall well-being? Yoga and meditation are time-proven methods, used for centuries, which restore mental, physical, and spiritual balance in people’s lives, and brainwave entrainment can be used in conjunction with these practices for even deeper levels of benefit. 
Brain trait changes have also been observed in neuroimaging studies, most often employing fMRI. In a meta-analysis of 21 neuroimaging studies, eight brain regions were found to be consistently altered, including areas key to meta-awareness (frontopolar cortex/Brodmann area 10), exteroceptive and interoceptive body awareness (sensory cortex and insular cortex), memory consolidation and reconsolidation (hippocampus), self and emotion regulation (anterior cingulate cortex and orbitofrontal cortex), and intra- and interhemispheric communication (superior longitudinal fasciculus; corpus callosum)[13] These changes were distinguished by density increases in grey matter regions and white matter pathways in the brains of individuals who meditate in comparison to individuals who do not. Of all areas with reported findings, a greater number of structural changes were found in the left hemisphere.
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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