The main gist of brainwave entrainment audios, without getting too technical here, is that they effortlessly guide one’s brain (when listened to with stereo headphones) into a specifically targeted state, as designated by the creator of the audio. They are able to alter your brainwave states through the use of specific audio frequencies, and specific beats-the most common of which being binaural beats (though there are other types of beats being used as well).  When one frequency is played into one ear- let’s say 1115 Hz- and a slightly different frequency is played into the other-say 1125 Hz- the brain is forced to reconcile the two, and creates its own “phantom” frequency that is the difference between the two- in this case 10 Hz.  Not only does this allow the brain to be led into specific brainwave states, but it also allows the two hemispheres of the brain to synchronize with each other, stimulating and promoting whole-brain functioning.
However, yoga and meditation take time to learn and master, and until the student becomes proficient, progress can be slow and frustrating, leading many people to abandon the effort before they see the benefits. Brainwave entrainment has the potential for helping a person enter the relaxing and rejuvenating mind-states brought about by yoga and meditation without the learning curve and time needed for mastering these other techniques. Brainwave entrainment may even facilitate learning other mindfulness methods by helping a person achieve success faster and more reliably. 
As Dawkins explains, ideas spread through the behavior that they produce in their hosts, which is what enables them to be transmitted from one brain to another. For example, an ideology — such as a religion — that causes its inhabitants to practice its rituals and communicate its beliefs will be transmitted to others. Successful ideas are those that are best able to spread themselves, while those that fail to self-replicate go extinct. In this way, some religious ideologies persist while others fade into oblivion.
Sleep improvement: There is significant anecdotal evidence that sleep induction and/or quality may be improved as a result of brainwave entrainment. While it is important to consider the placebo effect or simply the effect of a relaxing sound, many people have reported noticeable improvements in their ability to fall asleep and wake up feeling refreshed as a result of entrainment. Entraining frequencies within the slower wave ranges such as alpha, theta, or delta, may help individuals transition more quickly to those states.

I was diagnosed with “acute high anxiety, major clinical depression,and ptsd” 16 years ago. I have clinically addressed these disorders with a number of medications, which none have helped. I am so lucky I have found this simple easy to practice method of practice, that I have found these beats and tones so essential that I indoctrinated them into my daily life, and have come to the realization, that someday very soon I will awake and will not suffer from these burdens these disorders ever again.
By exposing the brain to special computer generated tones that are pulsed at a specific rhythmic frequency, the brain will synchronize its own electrical impulses to that same frequency. This means the brain becomes "entrained", or matched, to the specific frequency of the pulses, which gives you the ability to choose the primary frequency you want to experience in your brain. By guiding the brain into deeper (slower) frequency brainwave patterns, you can induce a profoundly deep state of relaxation and meditation with almost no effort.
When blended with musical sounds, brainwave entrainment frequencies induce specific states of mind, which are the result of those brainwaves, delivering them in pleasing and relaxing audio tracts for use with and without stereo headphones. For example, alpha and theta waves, because they exist at the borders between conscious and unconscious thought, are especially rich and useful for tapping into and stimulating subconscious processes.
This unique session works the opposite to most sessions. It attempts to to ‘dis-entrain’ the brain, breaking stuck thinking patterns and allowing a fresh way of thinking. The recording contains random and chaotic isochronic tones spanning 7.83 to 18 Hz, played over a background of gamma-embedded noise. Use this session to sit back and allow fresh ideas and new connections to form. Finishes at the illuminating14Hz sensorimotor rhythm frequency.
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