Alpha is the resting state for the brain; it is “The Power Of Now”, being here in the present. The Alpha state is the relaxed state of consciousness essential to stress reduction. It is intensely pleasurable: you are awake but relaxed and not processing much information, with a sort of floating feeling. According to Alpha researcher Dr. Joe Kamiya, the Alpha state is “something like letting go of anxieties”.

Aside from Brain Evolution, this is another good resource for brainwave entrainment products that I recommend. They have binaural beats and isochronic tones for many different applications. The nice thing is that they are inexpensive, so you can experiment with different types and find ones that work for you. They also have a membership plan that makes experimenting even more affordable. It’s probably the best bang for the buck that I can find for brainwave entrainment.
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Gamma brainwaves occur during creative thinking and processing of memory and language and in many learning activities. These brainwaves are not present at all when a person is under anesthesia, but return as soon as the person becomes conscious again. Multiple scientific studies have shown gamma brainwave entrainment to be helpful for reducing distractibility, improving short-term memory, improving motor coordination, and relieving migraine headaches.
While a practical understanding of brainwaves has been around for as long as people have been singing, chanting, and drumming, a scientific view of the electrical activity inside the human brain was not published until 1924 when German psychiatrist Hans Berger developed a machine for sensing and recording activity in the brain by attaching small electrical sensors to the scalp of his patients and recording the resulting electrical activity. Berger’s inventions and discoveries were built upon the earlier work of Richard Caton who published animal studies on brainwave oscillations in 1875.
Beta brainwaves are typically those we experience when we are wide awake and full of energy. You can think of this frequency as the equivalent of taking stimulants like caffeine, Adderall, or various nootropics. The Beta frequency is good for generating a concentrated, focused, and analytical mind. In fact, the brainwave you probably possess while reading this is of the Beta frequency.

You are already far beyond the need for using an entrainment product as a meditation aid. Those who sincerely believe this to be the case would not have come searching for a meditation site such as Project Meditation to help them learn and practice meditation and brainwave entrainment. They would probably not even bother with using an entrainment aid; hence this entire discussion would be irrelevant to them. The fact that you are here, reading this, seeking to benefit from incorporating meditation and brainwave entrainment to aid in your existing meditation practice suggests you are not one of these folks whose development is so advanced that entrainment is of no use to you.
How does brainwave entrainment work? Consistent, precisely engineered audio frequencies in the form of binaural beats cause the brain’s frequencies to match the stimulus. Your brain perceives two beats with slightly different frequencies (which are inaudible to the ear) through your headphones. It takes the difference between the two, and matches its own frequency to it. This is called the “frequency following” response.
Brainwave entrainment music can be used almost anywhere and anytime, making this mood and self-improvement method versatile and flexible enough to do at work, while traveling, or at other times during the day. When used in the workplace during short rest periods, brainwave entrainment techniques can enhance concentration, communication, and work productivity.
A binaureal beat is created by playing a different tone in each ear, and the interference pattern between the slightly differing frequencies creates the illusion of a beat. It's intended to be heard through headphones, so there's no cross-channel bleed across both ears. Listen to this, I'll play a simple binaural beat, and I'll slide the pan control back and forth from one ear to the other. You can see that there isn't actually any beat, it's just an acoustic illusion:
Pure tones played together interfere with each other when they are close in pitch but not identical. When each tone is sent to a different ear, there will not be any physical interaction between the waves, yet your brain still creates an interference inside your head: the so-called binaural beat. In order to create a binaural beat, each ear must receive its dedicated signal. Therefore, binaural beats only work through headphones.
Hi EJ, at the moment, there hasn’t been any research to give an indication of how long you should or shouldn’t listen for. Over time, I’ve seen people use my tracks for longer and longer. I started off providing 30-minute study tracks, but through demand, I extended them to 3-hours. I know from the many thousands of comments I’ve had on YouTube that a large number of people play those 3-hour tracks on repeat, or listen to different ones, one after the other throughout the day. I’ve also seen apps where you can play tracks like mine on continuous repeat. So it’s common for people to listen to them all day while they are studying.
Controversies concerning the brain, mind, and consciousness have existed since the early Greek philosophers argued about the nature of the mind-body relationship, and none of these disputes has been resolved. Modern neurologists have located the mind in the brain and have said that consciousness is the result of electrochemical neurological activity. There are, however, growing observations to the contrary. There is no neuro-physiological research which conclusively shows that the higher levels of mind (intuition, insight, creativity, imagination, understanding, thought, reasoning, intent, decision, knowing, will, spirit, or soul) are located in brain tissue (Hunt, 1995). A resolution to the controversies surrounding the higher mind and consciousness and the mind-body problem in general may need to involve an epistemological shift to include extra-rational ways of knowing (de Quincey, 1994) and cannot be comprehended by neuro-chemical brain studies alone. We are in the midst of a revolution focusing on the study of consciousness (Owens, 1995). Penfield, an eminent contemporary neurophysiologist, found that the human mind continued to work in spite of the brain's reduced activity under anesthesia. Brain waves were nearly absent while the mind was just as active as in the waking state. The only difference was in the content of the conscious experience. Following Penfield's work, other researchers have reported awareness in comatose patients (Hunt, 1995) and there is a growing body of evidence which suggests that reduced cortical arousal while maintaining conscious awareness is possible (Fischer, 1971;West 1980; Delmonte, 1984; Goleman 1988; Jevning, Wallace, & Beidenbach, 1992; Wallace, 1986; Mavromatis, 1991). These states are variously referred to as meditative, trance, altered, hypnogogic, hypnotic, and twilight-learning states (Budzynski, 1986). Broadly defined, the various forms of altered states rest on the maintenance of conscious awareness in a physiologically reduced state of arousal marked by parasympathetic dominance (Mavromatis, 1991). Recent physiological studies of highly hypnotizable subjects and adept meditators indicate that maintaining awareness with reduced cortical arousal is indeed possible in selected individuals as a natural ability or as an acquired skill (Sabourin, Cutcomb, Crawford, & Pribram, 1993). More and more scientists are expressing doubts about the neurologists' brain-mind model because it fails to answer so many questions about our ordinary experiences, as well as evading our mystical and spiritual ones. The scientific evidence supporting the phenomenon of remote viewing alone is sufficient to show that mind-consciousness is not a local phenomenon (McMoneagle, 1993).  

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. 
A crossover RCT of a single session of theta stimulation in four healthy adults reported no significant improvement in verbal fluency or attention associated with the intervention and a reduction in immediate recall. Controlled comparisons reported significant benefit from the intervention in all three outcomes measured. Six pre/post studies reported significant benefit from the intervention for 19 of 28 cognitive outcomes.
Thanks to e-mail, cell phones, and BlackBerrys, it seems like your job never ends. The increasingly blurry boundaries between work and home life leave us with less downtime than ever before (and in some cases, no downtime!). Advances in technology are a leading source of chronic stress, putting many of us in a constant state of alert. Not to mention the effect it has on family ties. A recent study published in the Journal of Marriage and Family found a link between the use of cell phones and pagers at home and increased stress, which spills over into family life. To make technology work for you, screen calls with caller ID or, better yet, limit your cell phone and e-mail use to working hours only. Can't kick the BlackBerry habit? Set a regular time you'll check it in the evening (say, after dinner), so you're not constantly disrupting home life to keep tabs on work. (The one exception: using your device to breathe with this anxiety-reducing GIF.)
A popular opinion in the brainwave entrainment community is that listening to isochronic tones without music produces a much stronger effect.  However, in the study by Doherty, Cormac. “A comparison of alpha brainwave entrainment, with and without musical accompaniment” (2014),  it was concluded that brainwave entrainment was equally effective for isochronic tones, both with and without music.
Both brainwave entrainment and neurofeedback deal with brainwaves, but the similarity stops there. Entrainment pushes your whole brain into a pre-determined state, while neurofeedback teaches you how to move specific parts of your brain on your own. It is the differeence between forcing the brain into a given position, and skills building so you can move it there yourself.