Transparent Corp's Research Area is arguably the most comprehensive resource for collated brainwave entrainment research.   Update: the main research area on Transparent Corp's website is currently being updated, so it is offline.  However, you can still access their peer-reviewed research paper as a PDF here: “A Comprehensive Review of the Psychological Effects of Brainwave Entrainment“.

Theta waves have a frequency between 4 and 7.5 hertz, making them slower than more wakeful alpha but faster than the dreamless slumber of delta. Theta brainwaves are the frequencies of nighttime dreams and REM sleep when the brain goes through bursts of activity and eye movement. People also experience theta waves in a state of light sleep, deep relaxation, during meditation and prayer, and when daydreaming. Theta waves produce an experience of inward wakefulness where we become disengaged from the outside world while engaging in inner activity. At the lower frequencies of theta, sleeping states are experienced, and at the higher range of frequency, awake relaxed states are experienced. 

Research: the authors stated that qualitative electroencephalogram signatures needed to be developed for different disorders and tested using standard validated methods of psychological assessment. Larger RCTs were needed with clear inclusion criteria for participants. The RCTs should measure qualitative EEG, hormone levels and the time of day of the intervention. Interventions protocols should be clearly defined and the relationship between session frequency/ duration and outcomes should be explored. More studies of auditory stimulation were needed, as well as studies comparing different types of stimulation, monaural, binaural and isochronic beats and use of white noise versus music.
^ Trost W. and Vuilleumier P., Rhythmic entrainment as a mechanism for emotion induction by music: a neurophysiological perspective. In The Emotional Power of Music: Multidisciplinary Perspectives on Musical Arousal, Expression, and Social Control, Cochrane T., Fantini B., and Scherer K. R., (Eds.), Oxford, UK: Oxford University Press; 2013, pp213–225.
In other words, you give the well a little taste of what it is you want from it, and then the well responds by delivering more of the same back to you. In the case of the water well, you pour a small amount of water down into the pump. This is known as “priming” the pump. Until you do this the pump does not produce the water you’re looking for. Once you prime the pump it sets up the conditions in which that pump can do its job and the water begins to flow.
According to an American Psychological Association (APA) survey, more women than men (one in three) turn to comfort food such as ice cream and cookies to ease stress. It's common for women to deny themselves favorite foods because they're trying to lose weight. But under stress, the urge for them becomes even stronger. In fact, researchers at Montclair State University in New Jersey recently confirmed that dieters are more likely than non-dieters to overeat when under pressure, bingeing on the very same high-fat foods they normally try to avoid. The key is to not deprive yourself. Keep three or four healthy snacks on hand that you know you'll probably want--peanuts, if you like salty; string cheese, if you crave protein; a small piece of chocolate for something sweet--so you aren't tempted to binge.

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.

Monaural beats have similarities to binaural beats, but the two separate frequencies are delivered through a pulse pattern and mixed before they reach the listeners ears, resulting in the advantage of being audible without stereo headphones. However, using stereo headphones intensifies the effectiveness of monaural beats and is recommended for the best effect. 
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.
For a little variety, you can use the 60 minute Delta Ultra Deep Standalone Meditation which takes you down into Delta and holds you there for an extended period of time. If you can stay awake during this entire time, you will have some amazing meditative experiences. (If you fall asleep, don't worry! It's natural and with practice you will be able to stay awake more often.)
Well … to understand the role entrainment plays in meditation, think of a water pump. Most of you have lived in areas where you have access to city water. You turn the knob on the tap, water comes out, end of story. If you grew up like I did, on a farm with a local well, then you probably know that in order to get the water flowing from a well you must first “prime the pump”. (Those of you who remember the days when cars all had carburetors rather than fuel injectors might also remember running out of gas and needing to prime the carburetor with a little gasoline. It’s the same principle.)
Because the brain filters and interprets reality in a split-brained way, we tend to see things as separate and opposed, rather than as connected and part of the oneness spoken of by the great spiritual teachers (and, in the last few decades, by quantum mechanical physicists). Thus, at a deep level, the dual structure of our brain, in conjunction with brain lateralization, predisposes us to see and experience ourselves as separate from, and often in opposition to, the rest of the world—instead of experiencing the elegant interconnectedness between us and everything else. Our childhood associations and programming build on this inborn tendency by training us to seek this and avoid that, to move toward pleasure and away from pain, to do good and not bad, and so on. The greater the lateralization in the brain, the greater the feelings of separation—and the greater the feelings of separation, the greater the fear, stress, anxiety, and isolation.
There are various reasons we seek this sort of validation. Many of us first try meditation to find relief from all sorts of different problems. Some seek relief from physical or emotional ailments; for solutions to personality shortcomings, such as a short temper or a tendency towards jealousy, etc. Some problems may be quite serious, even life threatening. Our search for relief may have been going on for a very long time without having found exactly what we were searching for.
They came to the table with the idea that the entrainment track would “cause” them to be in meditation, which it doesn’t. Or they thought that having the specific brainwaves the entrainment program promotes would “cause” them to be in meditation. It doesn’t. If you really understand the principles above, you’ll understand why. If you don’t grasp why yet, read these principles again and consider what they really mean. The answer is there.
Slumping can be an outward sign of stress—not to mention that bad posture actually puts more physical stress on your body. “People who are overly stressed often display their worries in their body carriage,” Whitaker says. “Those who are weighed down with stress commonly have a poor posture or struggle with aches and pains in their body. They often slouch when sitting or concave their body inwards with rounded shoulders as they go about their business under the weight of the burdens they carry.” Taking a few seconds when you feel stressed to check your posture and sit up straight (like your mother told you) can help you feel better. “Studies show that poor posture is related to anxiety, depression, helplessness, and irritability, so keeping your chin up and shoulders back will help,” Dr. Serani says. Happy and confident people naturally tend to stand a bit taller. Here are the other stressors you didn’t know you had.
Delta brainwaves have the slowest frequencies, ranging between 0.1 and 4 hertz, and these are the brainwave states associated with deep sleep, trance states, and unconsciousness. Few people can remain awake during delta brainwaves states, although this state is recorded in awake infants between ages of three months and one year and also in babies just before birth. Delta waves are also linked with increased production of HGH, DHEA, and the neuro-transmitter serotonin.
It cannot be any wonder then that we are almost desperate to find some sign, some indication that meditation and brainwave entrainment is having tangible, definable effects. We seize on these odd little experiences like ‘flushing of the face’ or ‘seeing spirals of color’ when our eyes are closed, hoping these are signs suggesting the elusive relief we’ve been after is finally within our grasp. We ask others to validate our experiences so that we can reassure ourselves we’re on the right track at last.
In fact just having a particular range of brainwaves running through our grey matter is also not “meditation”. Brainwaves are not the cause of the meditative state. They are only an indicator that we might be in a meditative state. And then again we might be in some other state as well. Those exact same brainwave frequencies are present during many different activities and states of consciousness, not just during meditation.
Are you someone who has turned to meditation or yoga as a way of relieving stress and improving your overall well-being? Yoga and meditation are time-proven methods, used for centuries, which restore mental, physical, and spiritual balance in people’s lives, and brainwave entrainment can be used in conjunction with these practices for even deeper levels of benefit. 
Most of the tips we’ve suggested provide immediate relief, but there are also many lifestyle changes that can be more effective in the long run. The concept of “mindfulness” is a large part of meditative and somatic approaches to mental health, and has become popular in modern psychotherapy. From yoga and tai chi to meditation and Pilates, these systems of mindfulness incorporate physical and mental exercises that prevent stress from becoming a problem. Try joining a class.
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.
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Entrainment is a principle of physics which appears in biology, chemistry, neurology, medicine, astronomy etc. It is defined as the synchronization of two or more rhythmic cycles. In the seventeenth century, Dutch scientist Christian Huygens found out that by placing two unsynchronized clocks side by side on a wall, they would slowly synchronize to each other in a very accurate way. The clocks were the first example of spontaneous synchronization, a phenomenon found throughout nature from cells to the Solar System.
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.