Our brains follow cues from outside stimuli, and brainwaves mimic the pulse rates of the sounds we expose it to. So, by creating tracks that pulse sound waves at a desired frequency, we can effectively coax our brain into that state. In layman's terms; by listening to some strange sounding brainwave frequency audios, we can literally slip our brain into a state of feeling calm, alert, focused, energized... and the list goes on. Pretty cool, right!?
^ Jump up to: a b Fox, Kieran C.R.; Nijeboer, Savannah; Dixon, Matthew L.; Floman, James L.; Ellamil, Melissa; Rumak, Samuel P.; Sedlmeier, Peter; Christoff, Kalina (June 2014). "Is meditation associated with altered brain structure? A systematic review and meta-analysis of morphometric neuroimaging in meditation practitioners". Neuroscience & Biobehavioral Reviews. 43: 48–73. doi:10.1016/j.neubiorev.2014.03.016. PMID 24705269.

Earlier evidence out of UCLA suggested that meditating for years thickens the brain (in a good way) and strengthens the connections between brain cells. Now a further report by UCLA researchers suggests yet another benefit. Long-term meditators have larger amounts of gyrification ("folding" of the cortex, which may allow the brain to process information faster) than people who do not meditate. A direct correlation was found between the amount of gyrification and the number of meditation years, possibly providing further proof of the brain's neuroplasticity, or ability to adapt to environmental changes.

Our brains follow cues from outside stimuli, and brainwaves mimic the pulse rates of the sounds we expose it to. So, by creating tracks that pulse sound waves at a desired frequency, we can effectively coax our brain into that state. In layman's terms; by listening to some strange sounding brainwave frequency audios, we can literally slip our brain into a state of feeling calm, alert, focused, energized... and the list goes on. Pretty cool, right!?
The same can be applied to the auditory senses, instead of the visual. Think of when you walk around the city with a friend or relative, have you ever noticed that your steps end up synchronized? Or when you walk with music which just happens to have a walkable tempo, before you know it you’re walking to the beat! This is how some insomniacs get treated. Binaural beats or brainwave entrainment aims to naturally help you synchronize yourself to a desired state of mind.
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.
At any rate, I am enjoying the product immensely. I’m keeping a journal in which I’m recording my thoughts & observations as well as memory and cognition scores just as a sort of completely unscientific pet project, out of curiosity. So far, I’ve benefited from being better rested and more focused as a result of your product and that alone is worth the price of admission but I hope to be able to show that over an extended period of time, EquiSync can also improve working memory, cognition, &etc. I’ll be sure to share the data I collect with you if I get anything of statistical significance.
I have received many requests for live sessions and personal support via telephone and video chat (Skype or Facetime). I am proud to announce that you can now schedule your own appointments with me for personal consultations, hypnosis sessions or any general counseling, questions or concerns about your specific needs, life coaching, self-help issues, dream guidance, spiritual matters or just random questions about consciousness or reality in general. I look forward to speaking with you on the phone or video chatting via Skype or Facetime.
The huge problem will all such studies is that there is a clear placebo effect on any kind of mental performance whenever the subject is observed. Do any intervention, then measure performance, and the intervention and measurement are likely to cause an increase in effort and attention which will increase performance. This generic “placebo” effect needs to be factored out of any such study by proper blinding and controls in order for the results to have any meaning at all.
Brain research is beginning to produce concrete evidence for something that Buddhist practitioners of meditation have maintained for centuries: Mental discipline and meditative practice can change the workings of the brain and allow people to achieve different levels of awareness. Those transformed states have traditionally been understood in transcendent terms, as something outside the world of physical measurement and objective evaluation.
Brainwave Entrainment is the process of synchronizing the brain to specific frequencies and patterns embedded in audio tracks. These frequencies correlate to specific emotions, feelings, and even energy levels. Using nothing more than sound, Brainwave Entrainment can enhance creativity, change moods, and even alter behavior like sleep and energy levels.
The gentle pulsating rhythms of Brain Sync audio programs act in a similar fashion, yet because the frequencies are precise and consistent they can be targeted to induce highly specific and desired brain states. Just as you can tune a radio to get a particular station, with Brain Sync technology you can re-tune your consciousness – effectively dialing your mind into a wide variety of brain states.
Theta waves have a frequency between 4 and 7.5 hertz, making them slower than more wakeful alpha but faster than the dreamless slumber of delta. Theta brainwaves are the frequencies of nighttime dreams and REM sleep when the brain goes through bursts of activity and eye movement. People also experience theta waves in a state of light sleep, deep relaxation, during meditation and prayer, and when daydreaming. Theta waves produce an experience of inward wakefulness where we become disengaged from the outside world while engaging in inner activity. At the lower frequencies of theta, sleeping states are experienced, and at the higher range of frequency, awake relaxed states are experienced. 
Binaural beats are not a physical noise or sound per se. Rather binaural beats are a sort of phantom tone which is manufactured by the brain when two different tones are played in each ear. For the binaural beat to be perceived you need stereo headphones and the frequency of the two different tones coming into each ear must be below 1000hz, and no more than 30hz apart. If they are more than 30hz apart you will simply hear a tone in each ear, one louder than the other. But if the difference between the beats is below 30hz you hear the binaural beats.

“Like the pulses of vibration that produce sound on a guitar string, your brain also creates pulses of vibrations. These vibrations are electrical impulses,” continues Naik. “Their activity can be measured by using an EEG (electroencephalogram), which measures the frequency of these pulses [which is measured in Hertz]. Your brain actually has a predominant frequency at which it operates in any given moment; this can be associated with your state of mind.”
Gamma was dismissed as 'spare brain noise' until researchers discovered it was highly active when in states of universal love, altruism, and the ‘higher virtues’. Gamma is also above the frequency of neuronal firing, so how it is generated remains a mystery. It is speculated that gamma rhythms modulate perception and consciousness, and that a greater presence of gamma relates to expanded consciousness and spiritual emergence.
I wouldn’t personally recommend listening to delta wave frequencies for depression, so I’m not sure who advised you to do that? People with depression usually have a higher ratio of theta and delta wave activity, so I would normally recommend listening to high alpha wave and low beta wave frequencies, to help balance things. I have some 10Hz alpha tracks for serotonin release, which you can try for free on my YouTube channel here: https://www.youtube.com/watch?v=3NSUcuzpRcY&list=PLveg0IEcZWN6T86nhmSrdwG2kMQtcLRou. I also recommend you give these SMR (low beta wave) tracks a try: https://www.youtube.com/watch?v=HGTvBbrEwZQ&list=PLveg0IEcZWN7yaMaKr8F-eWHALk2_zGqY. I hope that helps.
Meditation and its effect on brain activity and the central nervous system became a focus of collaborative research in neuroscience, psychology and neurobiology during the latter half of the 20th century. Research on meditation sought to define and characterize various practices. Meditation’s effect on the brain can be broken up into two categories: state changes and trait changes, respectively alterations in brain activities during the act of meditating and changes that are the outcome of long-term practice.

The Transparent Corp forum – This forum is an invaluable resource for any brainwave entrainment user or enthusiast.  Most of the feedback is obviously focused on the Transparent Corp software, but with over 20,000+ posts now you can find answers to the whole array of brainwave entrainment questions on there.  (UPDATE: Sadly, the Transparent Corp forum has now been taken offline)

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).  

There is a lot to like about this technology as a potential treatment for sleep problems. It’s low impact and non-invasive, it doesn’t rely on chemical drugs, it’s inexpensive and for most people likely easy to adopt and maintain. In this way, it’s similar to the other behavioral therapies for sleep that I like so much, including meditation and relaxation techniques, and other mind-body therapies.
A 2008 study at Hofstra University played two different binaural beats and a control sound (a babbling brook) to patients with high blood pressure. There was no difference between the groups. In one small study from Japan that was published in the Journal of Neurophysiology in 2006, they played various binaural beats to nine subjects, and observed the resulting EEGs. They found great variability in the results. Their conclusion was that listening to binaural beats can produce activity on the human cerebral cortex, however the cause was more likely a conscious auditory reaction and was not correlated to the frequency of the binaural beat. However, a 2005 study published in Clinical Neurophysiology found that they were able to induce a desired frequency in the EEG matching the phantom beat frequency encoded in a binaural beat, however this was with a single subject and was neither blinded nor controlled.