Binaural-beat perception originates in the inferior colliculus of the midbrain and the superior olivary complex of the brainstem, where auditory signals from each ear are integrated and precipitate electrical impulses along neural pathways through the reticular formation up the midbrain to the thalamus, auditory cortex, and other cortical regions.[6]
Recent research at the University of Lisbon finally uncovered the reason for the 350 year-old mystery, finding that the resonance of sound is the mechanism for entrainment of swinging pendulums and ticking clocks, and it seems likely that the energy transferred by sound is also responsible for other observations of entrainment, including brainwave entrainment.
... Several studies have looked at the possible effects of binaural beats within the alpha range on cognitive abilities. A significant improvement in cognitive processing, as measured by the Stroop Effect exercise, was found by a BB stimulation of 10.2 Hz frequency (Cruceanu & Rotarescu, 2013).Carter and Russell (1993)exposed 8 to 12 year old boys with learning disabilities to 8-week long 10 and 18 Hz BB stimulation sessions, and they found an improvement in Raven's progressive matrices and in a subtest of auditory sequential memory (Carter & Russell, 1993).McMurray (2006)assessed the effect of 7 and 11 Hz BB on alpha brainwave activity, working memory, and attention in healthy elderly people, who are known for experiencing gradual decrease in physiological alpha activity. The 2 minutes exposure to BB resulted in an altered electrical activity in the brain. ...

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.
Your brainwave activity during sleep is largely distinct from your brain activity when you’re awake. (REM sleep is one exception to this—during REM, your brain is active in ways very much like when you’re awake.) During non-REM sleep, the slower, lower frequency theta and delta waves dominate, compared to the alpha and beta waves that are prominent when you’re alert and active.
Most programs start at a work/life busy brain Beta frequency of twenty light flashes per second (20Hz) and slowly ramp them down to Alpha (relaxation and meditation) at 8-12 HZ, Theta (deep relaxation and dreaming) at 4-8 Hz) and Delta (dreamless deep relaxation) of .5-4Hz. We have taken measurements at Mass General with state of the art EEG equipment and have seen a slowing of the brain waves from Beta to Theta in two minutes and complete brain wave harmonization in the left, right, anterior, posterior and occipital regions of the brain.
"These methods are often described as nondirective, because practitioners do not actively pursue a particular experience or state of mind. They cultivate the ability to tolerate the spontaneous wandering of the mind without getting too much involved. Instead of concentrating on getting away from stressful thought and emotions, you simple let them pass in an effortless way."

The aim of this study is to identify tendencies in the effectiveness of relaxing audio stimuli that could be verified through further focused experiments. A series of brainwave entrainment (BWE) techniques for inducing relaxation will be presented consisting of different binaural phenomena (BP). The BP will derive from the binaural sine wave beat, widely acknowledged in rhythmic BWE... [Show full abstract]
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 were first discovered in 1839. The effects of using audio instead of light for brainwave entrainment were noted in 1959. Oster’s research paper in 1973 brought attention to the use of binaural beats in a medical setting and this inspired a range of studies in the 1980s indicating very positive findings. The effects of brainwave entrainment using binaural beats has become of a hot topic of research ever since but despite their reported successes, they have never quite shook off the sometimes negative connotations of being an “alternative medicine”.

Rather than discontinuing my meditation practice altogether, I instead began researching methods of increasing the effectiveness of meditative practice. This seemed an inevitable decision for me in light of the undeniable improvements I had witnessed in response to previous experience with meditation. This resulted in my eventual re-discovery of brainwave meditation programs brainwave synchronization. I had used a few different such products previously, but none that seemed effectively designed to meet my specific needs. After deciding to try a particular brainwave meditation program, I found it to greatly assist me in producing all of the previously experienced benefits of meditation, but in a shorter period of time and in a much more focused manner.
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!?

In addition to potentially boosting sleep-promoting hormones, binaural beats may also reduce our perceptions of pain. A 2017 study found binaural beats used in combination with visual stimulation led to reductions in patients’ perception of acute pain. Other recent research showed binaural beats helped improve pain perception in patients with chronic pain.
You listen to binaural beats using headphones. In each ear, you receive sound at a slightly different frequency (often accompanied by some relaxing background sounds). If your left ear receives a 300-hertz tone and your right ear receives a 280-hertz tone, your brain will process and absorb a 10-hertz tone. That’s a very low-frequency soundwave—one you can’t actually hear. But you don’t need to hear the sound for your brain to be affected by it.

Theta also plays an important part in behavior modification programs and has been used in the treatment of drug and alcohol addiction. Because theta brainwave activity induces an "endorphin high" it can reduce the desire for mind altering substances. Also, because theta is associated with heightened receptivity, it is the ideal state to reprogram your mind with positive thoughts that assist in changing habits and behaviors.

Once you have a good recording, start listening to your binaural beats while in bed, and try to be sure you’re undisturbed so your brain can sync up. If you have chronic insomnia, be sure to listen on a regular basis so you train yourself to fall asleep at the same time every night. If you like, you can even invest in a pair of comfortable sleep headphones.

There is a solution, which, although you may not have heard about it, has been around (and scientifically tested!) for decades now. By using binaural beats, you can ease your brain from its active state into a more restful state simply by listening to a different frequency wavelengths of sound in each ear. Because two different wavelengths are entering through two different entrances (your ears), that difference is perceived as a “beat” (though it may sound like a warble to some) that resonates at the frequency equal to the difference. The brain will entrain (match) itself to the beat produced by the difference in wavelengths. If the difference between the two wavelengths is less than seven hertz, your brain will fall into a state of deep relaxation, also known at the theta range.

Did you ever wonder why someone who "has everything" could be depressed and unhappy and why someone who has very little can be so happy? Of course, we can answer that material wealth, beauty, situation, good environments aren't everything. (Sure are nice though :+)) But that explanation ends up seeming like a rationalization and not an explanation. Consider the idea that the answer could reside in our brainwaves. Certain brain frequencies promote a feeling of well being and certain frequencies promote a feeling of depression. The state of our brainwaves also influences our tendency to be overly reactive or detached.
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. 
Research: the authors stated that qualitative electroencephalogram signatures needed to be developed for different disorders and tested using standard validated methods of psychological assessment. Larger RCTs were needed with clear inclusion criteria for participants. The RCTs should measure qualitative EEG, hormone levels and the time of day of the intervention. Interventions protocols should be clearly defined and the relationship between session frequency/ duration and outcomes should be explored. More studies of auditory stimulation were needed, as well as studies comparing different types of stimulation, monaural, binaural and isochronic beats and use of white noise versus music.

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