Because of the way they are created, there may be a positive benefit from listening to binaural beats without considering the brainwave entrainment aspect, but I haven’t seen any research on that. I first discovered brainwave entrainment through binaural beats about 10 years ago now, but they didn’t do anything for me. So I’ve never been a regular user of them. I believe isochronic tones are a more effective way to produce hemispheric synchronisation because they produce a much stronger response in the brain
In 1973, biophysicist Dr. Gerald Oster published a famous article in Scientific American titled “Auditory Beats in the Brain”, which found that when two pure tones of varying frequencies were combined, a third rhythmic beat was created which he called binaural or monaural beats. According to Oster, monaural beats occur when two tones are combined and sent through a loudspeaker, while binaural beats occur when stereo headphones are used to deliver each tone separately to each ear. Oster concluded that monaural beats were a more effective form of brainwave entrainment.
Beta: These brainwaves are associated with high levels of alertness and arousal. When beta brainwave patterns dominate, we’re primed to focus and concentrate, to make decisions and think analytically. When you’re analyzing an issue at work, you’re probably in a beta-dominant state. Beta waves are fast, with a higher frequency (between 15-40 hertz). At the higher levels of this range, beta waves are associated with anxiety.
In physics, entrainment is the process of two oscillating systems coming to assume the same periodic rhythm, such as is observed when two clocks slowly synchronize their ticking and tick together in harmony after some time. Pendulums also achieve this same synchronicity when swinging in close proximity to one another, a phenomenon first observed and written about in 1665 by Christiaan Huygens, a Dutch scientist.
The Frequency following response (FFR), also referred to as Frequency Following Potential (FFP), is a specific response to hearing sound and music, by which neural oscillations adjust their frequency to match the rhythm of auditory stimuli. The use of sound with intent to influence cortical brainwave frequency is called auditory driving,[39][40] by which frequency of neural oscillation is 'driven' to entrain with that of the rhythm of a sound source.[41][42]

Beating can also be heard between notes that are near to, but not exactly, a harmonic interval, due to some harmonic of the first note beating with a harmonic of the second note. For example, in the case of perfect fifth, the third harmonic (i.e. second overtone) of the bass note beats with the second harmonic (first overtone) of the other note. As well as with out-of tune notes, this can also happen with some correctly tuned equal temperament intervals, because of the differences between them and the corresponding just intonation intervals: see Harmonic series (music)#Harmonics and tuning.

Your brain cells reset their sodium & potassium ratios when the brain is in Theta state. The sodium & potassium levels are involved in osmosis which is the chemical process that transports chemicals into and out of your brain cells. After an extended period in the Beta state the ratio between potassium and sodium is out of balance. This the main cause of what is known as "mental fatigue". A brief period in Theta (about 5 - 15min) can restore the ratio to normal resulting in mental refreshment.  
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“Binaural beats are not very noticeable because the modulation depth (the difference between loud and quiet) is 3 db, a two-to-one ratio. (Isochronic tones and mono beats easily have 50 db difference between loud and quiet, which is a 100,00-to-1 ratio). This means that binaural beats are unlikely to produce an significant entrainment because they don’t activate the thalamus.”

For a few minutes a day, practice being mindful—focusing only on what's going on in the present —whether it's during your workout or taking a break from your work. Try taking a short walk and instead of thinking about what's worrying you, pay attention to your senses—what you see, feel, hear, smell. This can make a huge difference in your emotional and physical well-being when done daily.
In physics, entrainment is the process of two oscillating systems coming to assume the same periodic rhythm, such as is observed when two clocks slowly synchronize their ticking and tick together in harmony after some time. Pendulums also achieve this same synchronicity when swinging in close proximity to one another, a phenomenon first observed and written about in 1665 by Christiaan Huygens, a Dutch scientist.
You don’t have to run in order to get a runner’s high. All forms of exercise, including yoga and walking, can ease depression and anxiety by helping the brain release feel-good chemicals and by giving your body a chance to practice dealing with stress. You can go for a quick walk around the block, take the stairs up and down a few flights, or do some stretching exercises like head rolls and shoulder shrugs.
It’s important to keep in mind; a person’s own experiences will be somewhat relative to their starting point. If you are a person who is completely stressed out, burned out, hanging on the ragged edge, experiencing total adrenal fatigue, and you’ve been at that point for awhile, then to you even a small degree of mental quiet and physical relaxation that meditation and brainwave entrainment bring will feel like a tsunami of relief.
This can help develop the ability to see energy fields around people and in nature, and it will also make it much easier to stay awake during your meditations. When your eyes begin to close, you simply have to open them back up again. Doing the meditations with your eyes open is a serious step up in exercising your brain, so go slow with that technique at first.
Yoga involves a series of both moving and stationary poses, combined with deep breathing. As well as reducing anxiety and stress, yoga can also improve flexibility, strength, balance, and stamina. Since injuries can happen when yoga is practiced incorrectly, it’€™s best to learn by attending group classes, hiring a private teacher, or at least following video instructions. Once you’€™ve learned the basics, you can practice alone or with others, tailoring your practice as you see fit.
Insomnia and PTSD for most of my life are real bears that I wrestle with every night. A brain neural-therapist (for lack of a better description) said that this kind of sound recording may help. It is not music. When I remember to play the disc, I fall asleep within the first 5-8 minutes. One day I played the disc while cleaning and I was very surprised to hear how much of the recording I never recall hearing before. That's why I know how long it takes to fall asleep.
Beginning with greater influence on our health, our connection with the universe will lead to enhanced insight and creativity and our ability to influence the evolution of reality, clearing a pathway towards harmony and peace in our lives and in the world-at-large. Using Sacred Acoustics recordings and other methods, we can discover an inner stillness deep enough to connect with our divine spiritual nature. With Living in a Mindful Universe, we show readers how to achieve this same access to the Collective Mind.
Over-arousal in certain brain areas is linked with anxiety disorders, sleep problems, nightmares, hyper-vigilance, impulsive behaviour, anger/aggression, agitated depression, chronic nerve pain and spasticity. Under-arousal in certain brain areas leads to some types of depression, attention deficit, chronic pain and insomnia. A combination of under-arousal and over-arousal is seen in cases of anxiety, depression and ADHD. more...
That’s why it’s so important to find the proper stress relievers to maintain a strong quality of life. The eight stress relievers above — exercise and yoga, meditation/healing prayer, acupuncture, a nutrient-dense diet, cognitive behavioral therapy, spending more time in nature and being social, keeping a journal and using adaptogen herbs and essential oils — can help you maintain a good mood, remain calm and better handle your day-to-day stress.

Theta brainwaves are next highest in frequency above delta and are especially important for many people using brainwave entrainment and meditation because theta waves are at a threshold, forming a link between wakefulness and the subconscious mind. Theta waves bridge between our awake self and the creative and insightful understandings from below our conscious awareness, and while they are not common in awake adults, they are normative for children under 13 years old. 
Your brain actually has a predominant frequency at which it operates in any given moment; this can be associated with your state of mind. In other words, the emotional state of your mind in any moment, such as feeling happy, sad, frightened, sleepy or excited, can be measured as a frequency and with the right sound technology, you can stimulate the state that you want on command!
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.