Resonant entrainment of oscillating systems is a well-understood principle within the physical sciences. If a tuning fork designed to produce a frequency of 440 Hz is struck (causing it to oscillate) and then brought into the vicinity of another 440 Hz tuning fork, the second tuning fork will begin to oscillate. The first tuning fork is said to have entrained the second or caused it to resonate. The physics of entrainment apply to bio-systems as well. Of interest here are the electromagnetic brain waves. The electrochemical activity of the brain results in the production of electromagnetic wave forms which can be objectively measured with sensitive equipment. Brain waves change frequencies based on neural activity within the brain. Because neural activity is electrochemical, brain function can be modified through the introduction of specific chemicals (drugs), by altering the brain's electromagnetic environment through induction, or through resonant entrainment techniques.
Brainwave entrainment also happens with the use of pulsating light, and visual and auditory stimuli are sometimes combined for additional effect and visual stimuli is used alone. Using brainwave entrainment techniques is safe for almost everyone, the exception being pregnant women and people who have seizure disorders who should check with their physician before using these methods.
Different people have different requirements when it comes to frequency changes in the music and it's quite impossible for us to anticipate them all. We would need to produce so many different variants of all our music productions that it would be impractical to manage and confusing for our customers. For example, if we were to start raising the frequency from theta up to alpha between the 50-60 minute mark of a piece of music, this would be useless to someone who used the music for a guided meditation that was only 45 minutes long. In the early stages of the development of our brainwave entrainment music we had so many different requests from different people that we could only opt for the simplest solution, which is to use a consistent frequency throughout. It might not be the absolute "perfect ideal", but this is still a very effective technique and the feedback we've received on our brainwave entrainment music has always been exceptionally positive.
I was failing to achieve deep physical relaxation and looking for ways to shift my consciousness. After trying out many ‘solutions’ - including some truly bizarre ones - I decided to stop for a while and take a break before my next attempts at astral projection. That’s when I was recommended X. I must say it has been instrumental in helping me enter the state of relaxation and vibration necessary to a satisfactory OBE.

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:
When you hit a tuning fork, tuned to a particular sound frequency such as the note B, and hold it close to the strings of a guitar, you will notice that the B string on the guitar will vibrate because it has entrained on to the same frequency of the tuning fork. Interesting enough, the other strings will not vibrate. Only the one with the same tuning as the tuning fork.
You’ve heard the “om” sound yogis make when they meditate, right? Well, Joshi says using a buzzing sound is another way to use your voice to calm yourself in the midst of a freakout. “Bhramari, a humming bee sound, can be done by closing the eyes and making the humming sound like a bee,” she says. “These sound vibrations calm down the thought waves and relax the entire nervous system. External sound frequency resonates with the internal rhythm of the body and mind, creating peace and tranquility within.” Research from India has shown Bhramari to improve cardiovascular patterns. Press your ears closed for an even stronger vibration.
The advice “take a deep breath” may seem like a cliché, but it holds true when it comes to stress. For centuries, Buddhist monks have been conscious of deliberate breathing during meditation. For an easy three- to five-minute exercise, sit up in your chair with your feet flat on the floor and hands on top of your knees. Breathe in and out slowly and deeply, concentrating on your lungs as they expand fully in your chest. While shallow breathing causes stress, deep breathing oxygenates your blood, helps center your body, and clears your mind.
Slumping can be an outward sign of stress—not to mention that bad posture actually puts more physical stress on your body. “People who are overly stressed often display their worries in their body carriage,” Whitaker says. “Those who are weighed down with stress commonly have a poor posture or struggle with aches and pains in their body. They often slouch when sitting or concave their body inwards with rounded shoulders as they go about their business under the weight of the burdens they carry.” Taking a few seconds when you feel stressed to check your posture and sit up straight (like your mother told you) can help you feel better. “Studies show that poor posture is related to anxiety, depression, helplessness, and irritability, so keeping your chin up and shoulders back will help,” Dr. Serani says. Happy and confident people naturally tend to stand a bit taller. Here are the other stressors you didn’t know you had.
Turns out, science says there is something to needing “fresh air”—even opening a window can help get more oxygen to your brain, soothing stress. “We live so much of our lives indoors, that when stress hits, one of my go-to techniques is to get outside or open a window,” Dr. Serani says. “Taking in a nice deep breath of crisp fresh air can immediately shift your neurochemistry.” If you’re overwhelmed with work, it can seem hard to take a break; but a quick step outside is even recommended by the American Psychological Association. When you come back, you’ll be recharged and ready to take on the challenge.
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.
As to the second question raised in the above paragraph, audio with embedded binaural beats alters the electrochemical environment of the brain. This allows mind-consciousness to have different experiences. When the brain is entrained to lower frequencies and awareness is maintained, a unique state of consciousness emerges. This state is often referred to as hypnogogia "mind awake/body asleep."  
Absolutely. Binaural beats were first discovered over 150 years ago, and their use in brainwave entrainment audio has been the subject of a great deal of scientific exploration over the last 35 years in particular. Millions of people use brainwave entrainment music to enhance their quality of life and to experience deep relaxation. In fact, brainwave entrainment technology is now used for more than just meditation. It is also used by a variety of practitioners and private users for improving self-confidence, stress relief, pain management, relaxation, improving and concentration and improving the quality of one's sleep. If you would like to read an objective third party report on binaural beats, please refer to this Wikipedia article.
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]
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