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.  
Other entrainment methods sometimes used include autopan modulation that moves sound in an 180º arc to create a desired tone. Harmonic box entrainment, invented by James Mann, uses a layering of binaural and monaural tones that alternate between ears, requiring headphones. Sound modulation and filtering, amplitude modulation, and pitch panning use diverse sounds to create rhythmic pulses matched to the desired brainwave frequency. 

As strange as it may sound, vocal toning is a special technique that reduces the stress hormones adrenaline and cortisol. Try sneaking off to a quiet place to spend a few minutes toning before a meeting with your boss and see how much more relaxed and focused you feel. It works by exercising the tiny muscles of the inner ear that help you detect the higher frequencies of human speech that impart emotion and tell you what someone is really trying to say. Not only will you feel more relaxed in that meeting, you’ll also be better able to understand what he’s trying to communicate.
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.

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. 
A study by Tina Huang, PhD, and Christine Charyton, published in the September 2008 issue of the journal, Alternative Therapies examined the results of twenty previous studies measuring the effectiveness of brainwave entrainment for improvements in cognitive dysfunction and deficits, stress reduction, pain management, migraine and headache control, pre-menstrual syndrome, and behavioral difficulties, and all showed significant improvement in symptoms using entrainment techniques.
Hi Ulka, thanks for your compliment on my article. Unfortunately, I haven’t come across any studies or much discussion about the problem with habituation and isochronic tones and how to overcome it. The consensus among experienced users is to regularly change the frequencies and music soundtracks you listen to. Adding music to the tones does change the waveform you are stimulated with, so that’s one of the main reasons why I provide different soundtracks for my isochronic tones sessions. I have released some tracks which use amplitude modulations in the music, instead of isochronic tones. It might be worth giving them a try if you haven’t already. I have them in a playlist on YouTube https://www.youtube.com/watch?v=Lj5tHl2cuWw&list=PLveg0IEcZWN6OIRZyLkv0BJADY7Q6xFCl.
♥ ← 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.

Binaural beats are pretty simple. Basically, you take two frequencies that are similar and play each one through it’s own stereo headphone. The two competing frequencies will work together in your mind to produce a pulsing. That pulse will be a certain frequency that corresponds to a number in hertz that is linked to what your brain produces when you are in certain states of consciousness.
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.
Over the long term, traditional eastern methods (such as meditation and yoga) train your brainwaves into balance. Of the newer methods, brainwave entrainment is an easy, low-cost method to temporarily alter your brainwave state. If you are trying to solve a particular difficulty or fine-tune your brainwave function, state-of-the-art brain training methods like neurofeedback and pEMF deliver targeted, quick, and lasting results.  
Robert Monroe, a radio producer and executive published a popular book called Journeys Out of the Body about his out-of-body experiences when using brainwave entrainment. He later founded an original brainwave entrainment audio company, Hemi Sync. In 1981, the book Mega Brain by Michael Hutchison brought brainwave entrainment information, techniques, and terminology into the popular press.
Another very useful application for the Theta & Delta frequencies is to keep your eyes open while listening to the entrainment recordings. Simply pick a spot on the wall and look beyond it as if you were looking at the view beyond the wall. Keeping your eyes open while in Theta and Delta brainwave states stimulates connections between the visual information processing centers of your brain and the "dream vision" centers that normally only function with the eyes closed.
It is important to note that not all stress is bad. Everyone experiences a certain amount of stress on an almost daily basis, and it cannot be completely eliminated. Stress becomes a problem when too much is experienced, and it has a negative impact on behaviors, relationships, and health. The term “eustress” refers to positive stress that is associated with improved performance and productivity. “Distress” is negative stress that is associated with performance decrement and negative health consequences. The individual’s perception of the stressor and coping resources determine whether a situation is eustress or distress. College graduation is a stressor for most. The student who has a job or who has been accepted to a graduate program likely perceives the stress of graduation as eustress, whereas the student who has student loans and no immediate plans of a job or further education perceives distress.
These sounds in these musical tracks are presented through monaural beats, binaural beats, isochronic tones, or a mixture involving combinations of all three of these modalities, described in detail below. Choose alpha brainwave tracks for calming anxiety and relaxing body and mind, and choose theta tracks for help in getting to sleep and for bringing hidden feelings to the surface. Some people also report out-of-body type experiences when in theta brainwave states.
The exact physiological mechanisms to explain how exercise improves stress have not been delineated. Human and animal research indicates that being physically active improves the way the body handles stress because of changes in the hormone responses, and that exercise affects neurotransmitters in the brain such as dopamine and serotonin that affect mood and behaviors (9,11). In addition to the possible physiological mechanisms, there also is the possibility that exercise serves as a time-out or break from one’s stressors. A study that tested the time-out hypothesis used a protocol that had participants exercise but did not allow a break from stress during the exercise session (5). Participants were college-aged women who reported that studying was their biggest stressor. Self-report of stress and anxiety symptoms was assessed with a standard questionnaire before and after four conditions over 4 days. The conditions were quiet rest, study, exercise, and studying while exercising. These conditions were counterbalanced across participants, and each condition was 40 minutes in duration. The “exercise only” condition had the greatest calming effect (5). When participants were not given a break from their stressor in the “studying while exercising” condition, exercise did not have the same calming effect.
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  That said, you achieve the best results when you listen to the tones in a relaxed, quiet environment, investing your complete attention to the tones and the effect they have on your inner self. Experts recommend that even isochronic tones be heard via headphones to cut out distractions from external noises. The best thing to do is give it your entire, undivided attention, so that you can experience the outcomes quickly and easily.

Binaural beats are the playing of two sine waves of close, but not the same, frequency into different earpieces of a set of headphones. The "beat" is heard as the brain tries to process them as a distinct sound, while taking into account the constructive/destructive interference. It is said to migrate brain waves to be closer to that frequency, like a sort of biological resonance, which is true. Of course the same can be said for listening to relaxing music help you relax, up tempo music to help you feel energetic, etc...
Although getting organized and staying organized is not often thought of as a stress management technique per se, this is an activity that can reduce the stress you face in your life, and can even be calming as you are engaged in the act. (See how cleaning can be a stress reliever in itself.) By working through the clutter of your life, you can eliminate those energy drains that can make you feel like you're 'being pecked to death by ducks' and reserve that energy for dealing with life's more important challenges. Read more on being organized and eliminating extra stress from your life. 
Looking for an even more impactful way to feel the benefits of exercise? Do so while listening to uplifting music. Research findings indicate that music listening positively impacts the psycho-biological stress system, helps activate the parasympathetic nervous system, improves recovery time, and has benefits for hormonal balance and brain functioning overall. (4)

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.
In fact just having a particular range of brainwaves running through our grey matter is also not “meditation”. Brainwaves are not the cause of the meditative state. They are only an indicator that we might be in a meditative state. And then again we might be in some other state as well. Those exact same brainwave frequencies are present during many different activities and states of consciousness, not just during meditation.
Once you begin to experience the beneficial aspects of brainwave entrainment, you may be tempted to have these tracks playing all the time during your waking and sleeping hours. This is NOT advisable, nor is it necessary. Remember, brainwave entrainment is exercise for your brain so your brain will need to rest and integrate the new changes that your entrainment regime is creating.
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.

This music encourages a state of delta relaxation. Delta brainwaves are most prevalent during deep, dreamless sleep. The delta state is a mostly unconscious state that is essential to one’s physical, emotional, psychological and spiritual wellbeing. People who are able to achieve a state of delta relaxation through meditation will sometimes describe spiritual encounters and out of body experiences. The delta state is perfect for inducing profound spiritual experiences, healing and deep subconscious repatterning. Delta frequency brainwave entrainment music is also a fantastic cure for insomnia.
In addition to the exercise prescription, other characteristics of the exercise session (e.g., group vs. individual) and the individual also are important considerations. Because of health consequences associated with stress, high-stress clients are likely to be at increased risk for cardiovascular disease and cardiovascular events during exercise. Therefore, using the preexercise screening procedures outlined and endorsed by the American College of Sports Medicine is essential (1). Monitoring exercise intensity for those looking to “blow off steam” to reduce stress might be a concern when the client has high blood pressure or other cardiovascular risk factors that further the risk increase for cardiovascular events.

Beta: These brainwaves are associated with high levels of alertness and arousal. When beta brainwave patterns dominate, we’re primed to focus and concentrate, to make decisions and think analytically. When you’re analyzing an issue at work, you’re probably in a beta-dominant state. Beta waves are fast, with a higher frequency (between 15-40 hertz). At the higher levels of this range, beta waves are associated with anxiety.

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.
When you play a tone with a slightly different frequency into your left and right ear — say, 200 hertz (Hz) in one and 210 Hz in the other — they travel separately to your inferior colliculus, the part of your brain that gathers auditory input. There, the tones “squelch” together into a so-called “beat” at a perceived new frequency. (In this case, it would be 10 Hz.)
Your brain actually has a predominant frequency at which it operates in any given moment; this can be associated with your state of mind. In other words, the emotional state of your mind in any moment, such as feeling happy, sad, frightened, sleepy or excited, can be measured as a frequency and with the right sound technology, you can stimulate the state that you want on command!

Stressed out after work? Need to relax and be focused before a test, exam, or interview?. This CD is for you. Wish I could explain how this CD works on your brain's "entrainment" but they do enclose a benefits description inside the CD case. It's amazing to listen to and see/feel the results after hearing the entire CD with a quality set of headphones on. Note: also works well with earbuds. I couldn't tell if the last track had played or not on the Nexus 6p...it just takes you away then brings you back ... into something more structured and coherent.
People who meditate regularly enjoy many benefits such as increased sense of well being, happiness, contentment, and far less anxiety that many other people. Some believe that this is due to both hemispheres of the brain being in sync with each other, which meditative practice can provide. Therefore, a goal of using technology to entrain the brain and align the frequencies of the brain hemispheres has become a very interesting avenue of science and experimentation.
Alpha (12hz – 8hz) – Awake, but deeply relaxed. Simply closing your eyes will produce alpha brainwaves. This category is associated with daydreaming, visualization, imagination, light meditation. Brainwave expert Anna Wise called the alpha range the bridge between beta and theta. (More information can be found in Wise’ book The High-Performance Mind)
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