EquiSync’s design is based on the 100’s of studies performed on the effectiveness of brainwave entrainment technology, and 1000’s of studies on the powerful benefits of meditation. If you are interested in better understanding the power of this technology and rapidly expanding field of research, then here is a very abbreviated bibliography, a very small sample of the studies out there:
Many people experienced in using alpha brainwave entrainment report that the state of mind associated with alpha waves is a time when they feel most consciously connected to their subconscious mind. The intense experience of hypnagogic sleep, reported by some people as a feeling of being awake and asleep at the same time, is also associated with alpha brainwaves.
“When you play two separate frequencies in each ear, say 140 Hz and 149 Hz, the difference in frequency is 9 Hz. Your brain compensates for this difference, and a third tone of 9 Hz is experienced,” says Niraj Naik, founder of Trpynaural, a resource for binaural tracks. “This will result in your brain being raised or lowered and tuned into the desired frequency. This is how binaural beats are produced.”

After buying a new bed and feeling restless in a new home, I decided to buy a few meditation tracks. I have to say, for the last 2 months, I play this mp3 every night and fall asleep within 5-10 minutes when earlier it took me much longer. I am more relaxed when I sleep! Only hiccup is sometimes I wake up in the night, however, I fall back asleep quickly since the music is on repeat mode. A great purchase and highly recommended for people with insomnia!

3. Alpha State: (9 — 13Hz) Brain waves start to slow down out of thinking mind. We feel more calm, peaceful and grounded. We often find ourselves in an “alpha state” after a yoga class, a walk in the woods, a pleasurable sexual encounter or during any activity that helps relax the body and mind. We are lucid, reflective, have a slightly diffused awareness. The hemispheres of the brain are more balanced (neural integration).
So to summarize their claim, they're saying that entrainment means that a binaural beat will cause your brain's electroencephalogram to match the pattern of the phantom beat. Well, if it did, entrainment certainly doesn't apply and would not be part of the equation, so we can scratch that off the list. But it doesn't make the claimed observation wrong. We do know that certain electroencephalogram waveforms are often associated with certain kinds of activity. For example, physical activity or REM sleep often produces an electroencephalogram with a sine wave of between 4 and 8 Hz, which we term a theta pattern. Waking relaxation with eyes closed often produces a pattern from 8 to 12 Hz, which is called an alpha pattern. There are only a few characterized patterns, and pretty general descriptions of what kinds of activities go with them. The claim made by the binaural beat sellers depends on much more granular and specific matches. For example, the claim that a binaural beat with a frequency of X produces the same effect in your brain as Vicodin is wholly implausible. Such claims presume that we know the exact frequency of the electroencephalogram in each of these desired conditions, and the fact is that brain waves don't work that way. It is wholly and absolutely implausible to say that desired brain condition X will occur if we get your EEG to read exactly X Hz.
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 most common way to use a brainwave entrainment is for a short-term benefit, to help guide your brain into a particular mental state at the time you need it.  In a similar way to how you might take a sleeping pill before bed to help you get to sleep, or maybe drink some coffee or an energy drink to help wake you up and give you a boost of energy.
Since it’s humble beginnings, the science of brainwave entrainment has evolved to be one of the most potent and powerful ways to unlock the full potential of the human mind. Our audios have been created by brainwave entrainment engineer, Ashton Aiden, and his years of research, expertise, personal experience, and creativity. We are confident that the audios we offer on this site are of the best quality you will ever find, anywhere.
Basically, "two ears." One usage of the word is "binaural recording," which is a form of stereo recording meant to take advantage of the spatial perception of the human ear. Recordings are usually done using a pair of microphones mounted to a dummy head with roughly accurate models of the human outer ear, and the result when played back through headphones is extremely realistic and comparable to surround sound, though following an entirely different recording model. Binaural recordings aren't woo at all, and have nothing to do with binaural beats.[citation needed]
In Theta, you are in a waking dream, receptivity is heightened and you are able to access knowledge and information that normally lies beyond your conscious awareness. As flashes of vivid imagery dance before your mind's eye, you may feel a "floating" sensation as your mind expands beyond the boundaries of your body. In this deeply relaxed state don't be surprised to receive sudden insights, inspiration or a sense of knowing.

Hello Jason, this is an unusually thoughtful discussion. Thank you for all your expertise and your kind manner of presenting and moderating it. I’m wondering if you have any experience with this: ever since I’ve been exposed to theta wave music, without headphones, I have found it irritating. And this is in spite of the fact that when I was first handed a CD by someone I knew well and trusted he was so confident I’d love it It didn’t occur to either of us that I might not. This happened again recently, which is about 10 years later, when I heard it playing overhead at an acupuncture clinic. I felt restless and even irritated, unable to zone out, which is unusual for me, during the treatment. I realized that the quality of my irritation was similar to what I’d felt listening to that CD a decade ago.So I asked if it was theta wave music and she said yes. The acupuncturist said that some people, but a vast minority, really dislike the music. She said that the few people who dislike it are not simply neutral, but actively dislike it. And she also said, but most people like it a lot. I’m just wondering what kind of factors might be present that would make a person feel so irritated by this music?
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.
Beta brainwaves are further divided into three bands; Lo-Beta (Beta1, 12-15Hz) can be thought of as a 'fast idle', or musing. Beta (Beta2, 15-22Hz) is high engagement or actively figuring something out. Hi-Beta (Beta3, 22-38Hz) is highly complex thought, integrating new experiences, high anxiety, or excitement. Continual high frequency processing is not a very efficient way to run the brain, as it takes a tremendous amount of energy. 
Go behind the scenes of brainwave entrainment technology creation with Joseph Kao, developer of the extraordinary meditation tool Journey to the Center of the Self. Here, in an interview with John Dupuy, CEO of iAwake Technologies, Joe describes the amazing complexity of the brainwave entraining soundscape he created to both accompany his deeply inductive, 30-minute, guided meditation on the first track of Journey, and also stand alone as a music-only track that holds you in a profoundly relaxed, still, yet clear place on the theta/delta border. To find out all that went into the making of the inductive guided meditation on the first track of Journey, see A Guide to Transpersonal Meditation: Journey to the Center of the Self, part I of this interview.
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.[13]

In the meta-analysis performed by Fox et al., several sources of bias were indicated which bring into question the validity of meditation studies which use neuroimaging. Fox et al. suggests a publication bias may be leading to the over-reporting of significant results.[18] Despite this, however, Fox et al. found "consistent differences in prefrontal cortex and body awareness regions" in "areas key to meta-awareness..., exteroceptive and interoceptive body awareness..., memory consolidation and reconsolidation..., self and emotion regulation..., and intra- and interhemispheric communication..." and that changes were significant with "moderate" global median effect size and "consistent and medium-sized brain structure differences."[18]
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.
In Philadelphia, a researcher discovers areas of the brain that are activated during meditation. At two other universities in San Diego and North Carolina, doctors study how epilepsy and certain hallucinogenic drugs can produce religious epiphanies. And in Canada, a neuroscientist fits people with magnetized helmets that produce "spiritual" experiences for the secular. The work is part of a broad new effort by scientists around the world to better understand religious experiences, measure them, and even reproduce them. Using powerful brain imaging technology, researchers are exploring what mystics call nirvana, and what Christians describe as a state of grace. Scientists are asking whether spirituality can be explained in terms of neural networks, neurotransmitters and brain chemistry.
A therapy that slows brainwave activity, helping to produce low frequency waves, is likely to aid relaxation and sleep. But it’s not only lowering brainwave frequency that binaural beats may offer to sleep and relaxation. A small study (19 people) has found that exposure to binaural beats is associated with changes to three hormones important to sleep and well being:
Today, EEG machines are used for diagnosing epilepsy and sleep disorders, for determining dosages for anesthesia, and measuring the brain activity of people in comas or suffering from brain trauma. EEG machines also continue to play a role in researching and understanding brainwave entrainment and developing new and better methods for delivering the benefits of this form of brainwave modification. 
Theta brainwaves in the frequency range of 6 to 9 hertz are known as thalpha waves because of their proximity to alpha waves. They are seen during states of high suggestibility, during hypnosis, and during paranormal experience and are also connected to an increase in human growth hormone (HGH) levels and higher blood flow to the brain. Theta brainwaves sit between the realms of the subconscious and conscious mind, making them an especially useful brainwave state for developing creative thinking, working through emotional problems, and integrating subconscious and conscious experience. 
Go behind the scenes of brainwave entrainment technology creation with Joseph Kao, developer of the extraordinary meditation tool Journey to the Center of the Self. Here, in an interview with John Dupuy, CEO of iAwake Technologies, Joe describes the amazing complexity of the brainwave entraining soundscape he created to both accompany his deeply inductive, 30-minute, guided meditation on the first track of Journey, and also stand alone as a music-only track that holds you in a profoundly relaxed, still, yet clear place on the theta/delta border. To find out all that went into the making of the inductive guided meditation on the first track of Journey, see A Guide to Transpersonal Meditation: Journey to the Center of the Self, part I of this interview.
“…humans have always been intrigued by the possibilities for influencing mental functioning that emerge from combining rhythmic sound and rhythmic light stimulation. Ancient rituals for entering trance states often involved both rhythmic sounds in the form of drum beats, clapping, or chanting and flickering lights produced by candles, torches, bonfires, or long lines of human bodies passing before the fire and chopping the light into mesmerizing rhythmic flashes. From Greek plays to Western opera, our most popular entertainment forms have made use of combinations of lights and sounds. Some composers, such as the visionary Scriabin, actually created music intended to be experienced in combination with rhythmic light displays.”
As a relatively new technology, fMRI has only recently been used to assess brain state changes during meditation. Recent studies have shown heightened activity in the anterior cingulate cortex, frontal cortex, and prefrontal cortex, specifically in the dorsal medial prefrontal area during Vipassana meditation.[7] Similarly, the cingulate cortex and frontal cortex areas were shown to have increased activity during Zen meditation.[8] Both studies comment on the possibility that these findings could indicate some state of heightened voluntary control over attention during mindfulness meditation. Review works by Cahn and Chiesa state that these results indicate consistency in meditation’s effect on these regions of the brain, citing a multitude of other studies spanning other meditative disciplines, but mention the need for further investigation with better controls.[4][6]
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However, yoga and meditation take time to learn and master, and until the student becomes proficient, progress can be slow and frustrating, leading many people to abandon the effort before they see the benefits. Brainwave entrainment has the potential for helping a person enter the relaxing and rejuvenating mind-states brought about by yoga and meditation without the learning curve and time needed for mastering these other techniques. Brainwave entrainment may even facilitate learning other mindfulness methods by helping a person achieve success faster and more reliably. 

That is generally where the science ends and the pseudoscience begins. A number of companies and individuals have then extrapolated from the phenomenon of entrainment to claim that altering the brain waves changes the actual functioning of the brain. There is no theoretical or empirical basis for this, however. Entrainment is a temporary effect on the synchronization of neuronal firing – it does not improve or increase brain functioning, it does not change the hardwiring, nor does it cure any neurological disorder. There is no compelling evidence for any effect beyond the period of entrainment itself.

Binaural beats require two separate tones from two sources that are combined inside the listener’s brain to form the target tone. The lower frequency sound is called the carrier tone, and it is combined with a higher frequency sound known as the offset tone. Because of this, binaural beats must be listened to with stereo headphones or the effect is lost. Binaural beats create a hypnotic effect, but they are not the most effective tool for brainwave entrainment, and binaural beats are often ineffective for people with hearing loss.
All you need to experiment with binaural beats is a binaural beat audio and a pair of headphones or earbuds. You can easily find audio files of binaural beats online, such as on YouTube, or you can purchase CDs or download audio files directly to your mp3 player or other device. As mentioned earlier, for a binaural beat to work, the two tones have to have frequencies of less than 1000 Hz, and the difference between the two tones can’t be more than 30 Hz.
Similar to research into state changes in brain function, older studies make more specific claims about trait changes in meditators versus non-meditators. Changes to the alpha wave were indicated to be a trait, as well as state, phenomena. Studies have reported an increase in the specific frequencies expressed in the alpha range, increased alpha band power, and an overall slowing (reduction in frequency) in EEG activity in experienced meditators versus less experienced meditators while meditating.[5][10] The alpha blocking phenomena, observed as a state change in brain function, was investigated as a possible trait change as well. One study that examined a variety of meditation techniques tried to show that alpha blocking was affected by the long term practice of meditation by testing response to auditory stimuli.[11] Review works, however, comment on inconsistent findings as well as a lack of repeated results in this, and other studies. They further remark that, similar to observations in brain state changes, only general assertions can be made about brain trait changes: some change in the electroencephalographic profile exists but with some inconsistency.[4][12] It is also important to note that these trait changes were observed during meditation, and although it does indicate that a practitioner’s electroencephalographic profile is modified by the practice of meditation, these EEG studies have not yet shown changes in non-meditating brains, even of experienced meditators.
The authors concluded that preliminary evidence suggested that brainwave entrapment was an effective therapeutic tool, but further research was required. The evidence presented appeared to justify the recommendation for further research. In view of the lack of controlled evidence and problems with methodology and reporting in the review, the authors’ conclusions regarding efficacy did not appear reliable.
For many years this principle of entrainment has been used as a part of neurofeedback to help patients change their brain wave patterns in the hope of ameliorating the symptoms of dysregulated brain processes that are hypothesized to contribute to various disorders such as ADHD, anxiety, and depression. There is some evidence that neurofeedback combined with photic stimulation (e.g. Hammond, 2000) can help depression and that auditory and visual stimulation can help cognitive abilities in children with learning disabilities (e.g. Olmstead, 2005). 
Well, except for one reason: The power of suggestion. If I give you a music track and tell you that it will cure your headache, you're more likely to report that it cured your headache than you are to say "Well it didn't effect my headache, but it made my short-term memory better." An interesting experiment would be to buy a binaural track claimed to induce drunkenness, for example; play it for five friends without telling them the claim, and then ask how it made each of them feel. Give them multiple choices to select from. Chances are they're going to respond all over the map. If you have a friend who is a believer in binaural beats, I suggest going ahead and setting up this little test.