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.
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.
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.
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)
When tuning instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a unison will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception[1], the beating starts to sound like a note, and a combination tone is produced. This combination tone can also be referred to as a missing fundamental, as the beat frequency of any two tones is equivalent to the frequency of their implied fundamental frequency.
Regarding split hemisphere isochronic tones. Think of this as two separate isochronic tones tracks playing independently of each other, one playing in one ear and the other one in the opposite ear. Better still, imagine someone playing and recording a drum beat at a rate of 5 taps per second (5Hz – 5 cycles per second). Then a separate recording of a drum beat is made at a rate of 10 taps per second (10 Hz). You then make an audio track where the left ear/channel hears the 5 drum beats recording and the right ear/channel hears the 10 beat recording. With headphones on, each ear can only hear each respective drum beat and not the other. So you are hearing two different beat recordings at the same time, but it’s different in each ear. A split hemisphere isochronic tones track works just the same. You hear two beats at the same time, not two tones as with binaural beats that create a single beat, but two different speeds of beats in each ear. This is what enables you to stimulate and influence each side of the brain with a different frequency of beat. Binaural beats can only stimulate and influence a whole brain effect using a single beat.
If brainwave entrainment leaves you with unwanted side-effects (see below) or discomfort, you’re probably encouraging a range of brainwaves that are already excessive in some area of your brain. The way around this is to get a brain map to see what your brain’s strengths and weaknesses are, and see what (if any) brainwaves could use some encouragement. 
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