, that is, the average of the two frequencies. It can be noted that every second burst in the modulation pattern is inverted. Each peak is replaced by a trough and vice versa. However, because the human ear is not sensitive to the phase of a sound, only its amplitude or intensity, only the magnitude of the envelope is heard. Therefore, subjectively, the frequency of the envelope seems to have twice the frequency of the modulating cosine, which means the audible beat frequency is:[5]
Critics, like Owen Flanagan, PhD, believe that Hanson, and those like him, are overextending the results of current scientific studies.[citation needed] In his book Bodhisattva’s Brain: Buddhism Naturalized, Flanagan presents a more conservative viewpoint of current scientific research and cautions readers against the seemingly exciting results of recent studies.[20] Flanagan does not believe current science supports the idea that positive emotion can be strengthened in the same way that stroke victims can recover use of limbs with use.[20] Flanagan does acknowledge that meditation may be beneficial in some way, but the mechanism of how meditation affects the brain is still clouded.[20] Similarly, Awasthi argues that Meditation is non-specific to the research studies showing clinical efficacy in some cases, though mechanisms remain unclear.[21] Flanagan and Hanson use many of the same scientific studies to attempt to support their differing viewpoint, but both authors identify the need and importance of future studies investigating meditation.
A good recording will also not immediately start with tones that produce the theta range, but will begin higher up, in the beta range (which is associated with anxiety, but also active concentration and other waking states of being), and gradually move down, through the alpha range (which is the ideal meditative wavelength, but is also associated with falling asleep) before moving into the final, theta, range. If you get a binaural beat that goes directly into the theta range, you might find yourself distracted or unable to sync up as easily.
Theta waves have another interesting characteristic. The Earth has a measurable resonance of 7.83 hertz known as the Schumann resonance. Because the Schumann resonance is a constant background frequency surrounding all life, it may play a special role in biological activity. The Schumann resonance frequency falls within the range of theta brainwaves and may have something to do with why these brainwave frequencies are so powerful. 
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