Above is a nice, simple and short chart of the various brainwave ranges and the types of effects they generally have and what sorts of activities they may be able to enhance. There simply is nothing more detailed than what this chart contains about entrainment frequencies and what they are useful for. Those other elaborate lists to be found on the internet are nothing but the product of overactive imaginations.

Think about it for a moment...your mind is at work all day, every day. Every decision you make, every challenge that you face, every moment you go through in life, your mind is your constant companion, and it can be your best friend or your worst enemy. Your mind is something you need to take good care of, because your quality of life is directly related to your "quality of mind".

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.
So to summarize their claim, they're saying that entrainment means that a binaural beat will cause your brain's electroencephalogram to match the pattern of the phantom beat. Well, if it did, entrainment certainly doesn't apply and would not be part of the equation, so we can scratch that off the list. But it doesn't make the claimed observation wrong. We do know that certain electroencephalogram waveforms are often associated with certain kinds of activity. For example, physical activity or REM sleep often produces an electroencephalogram with a sine wave of between 4 and 8 Hz, which we term a theta pattern. Waking relaxation with eyes closed often produces a pattern from 8 to 12 Hz, which is called an alpha pattern. There are only a few characterized patterns, and pretty general descriptions of what kinds of activities go with them. The claim made by the binaural beat sellers depends on much more granular and specific matches. For example, the claim that a binaural beat with a frequency of X produces the same effect in your brain as Vicodin is wholly implausible. Such claims presume that we know the exact frequency of the electroencephalogram in each of these desired conditions, and the fact is that brain waves don't work that way. It is wholly and absolutely implausible to say that desired brain condition X will occur if we get your EEG to read exactly X Hz.

When signals of two different frequencies are presented, one to each ear, the brain detects phase differences between these signals. "Under natural circumstances a detected phase difference would provide directional information. The brain processes this anomalous information differently when these phase differences are heard with stereo headphones or speakers. A perceptual integration of the two signals takes place, producing the sensation of a third "beat" frequency. The difference between the signals waxes and wanes as the two different input frequencies mesh in and out of phase. As a result of these constantly increasing and decreasing differences, an amplitude-modulated standing wave -the binaural beat- is heard. The binaural beat is perceived as a fluctuating rhythm at the frequency of the difference between the two auditory inputs. Evidence suggests that the binaural beats are generated in the brainstem's superior olivary nucleus, the first site of contra-lateral integration in the auditory system (Oster, 1973). Studies also suggest that the frequency-following response originates from the inferior colliculus (Smith, Marsh, & Brown, 1975)" (Owens & Atwater, 1995). This activity is conducted to the cortex where it can be recorded by scalp electrodes.  
In one study, researchers had a group of participants relax alone in a quiet, low-light environment following an exercise session. They split the group in two — one spent 20 minutes listening to theta-frequency binaural beats while the other listened to a carrier tone and monitored their parasympathetic (rest and relaxation) and sympathetic (fight or flight) nervous system activity. Researchers found the group that listened to binaural beats experienced an increase in parasympathetic activity and a decrease in sympathetic activity, along with higher rates of self-reported relaxation.
Brainwave entrainment is a simple concept. It’s simply causing your brainwave frequency to align with some intended frequency in order to produce some intended result. It’s a way of modulating your brainwaves to resonate at a certain frequency. Being that there are certain dominant frequencies associated with different states of consciousness, this is being researched as a quick and effective way to induce states such as sleep, alertness, concentration, and even meditative and deep sleep states.

Think about it for a moment...your mind is at work all day, every day. Every decision you make, every challenge that you face, every moment you go through in life, your mind is your constant companion, and it can be your best friend or your worst enemy. Your mind is something you need to take good care of, because your quality of life is directly related to your "quality of mind".

There are many ways to reduce tension and relax, but some are more effective than others. Some techniques are difficult to learn while others are challenging to practice. Others have negative consequences that almost outweigh their effectiveness or can create bigger problems. Here are ten stress relievers proven to be among the most effective for the amount of work and time involved. Most can be learned in the time it takes to read this page and will help you to feel more relaxed almost immediately. And even more exciting, the ​stress relief benefits will increase with regular practice. Try as many as you can—there's something here for everyone.

Today we're going to put on our headphones, kick back in the beanbag, and get mellow to the soothing sounds of the latest digital drug: binaural beats. These computer generated sound files are said to massage your brain and produce all sorts of effects, everything from psychedelic experiences to behavior modification. Let's point our skeptical eye at the science of binaural beats, and especially at some of the claims made for them.
“Stress” is a commonly used term, and it is often used with different meanings. The standard definition for stress that will be used in this article is the disruption of the body’s homeostasis or a state of disharmony in response to a real or perceived threat or challenge (8). The threatening or challenging situation is referred to as a “stressor.” When a person encounters a stressor, the body prepares to respond to the challenge or threat. The autonomic nervous and endocrine systems respond by producing the hormones epinephrine, norepinephrine, and cortisol. The result of this hormone production is a cascade of physiological reactions that make up the stress response. Epinephrine and norepinephrine are involved in the initial changes that take place to prepare the body to react and to prepare for a challenge. These responses include increases in heart and respiration rates, blood pressure, perspiration, and energy production (8). There also is a suppression of immune function, production of β-endorphin (the body’s natural pain killer), and increased acuity of the senses. These changes make up the fight-or-flight response, which prepares the body to cope with the stressor. If the stressor is perceived as negative or more as a threat than as a challenge, cortisol production is increased. Cortisol is involved in energy production but also suppresses immune function.

Many of our common symptom-soothing formulas are designed to take effect within 5-10 minutes if used properly. To get these fast-acting results, we recommend 3-4 droppers full, or 6-8 pumps, per use to start. If you are not yet feeling the full effect within the first 5 minutes, repeat the original serving. You can do this up to 4 servings back to back. Note that some of our formulas are tonics and are meant to work over longer periods of time.
Escape from a stressful situation by remembering a favorite vacation spot or a place where you feel cozy and at home. “Make sure to take note of every detail of your favorite spot—the more detailed your visualization, the more stress gets kicked to the curb,” Dr. Serani says. “For me, it’s a beautiful spot on the beach in my native Long Island. But it’s not just the white velvet sand of the beach or the teal blue ocean water; it’s the sounds of the surf, the tang of the salt water, the feel of the sun, the waves in the distance, and the imagined walk I take along the water.” You can combine this with a three-word mantra like “blue-ocean-water,” Serani suggests. Miller calls the visualization of a memory that evokes a positive association an “anchor.” She remembers watching beautiful sunsets in Costa Rica. “Now that I am back in the hustle and bustle of life, I will often pause and take mini-retreats, bringing up the anchored experience of inner calm that I felt watching the sunsets,” she says.
Unlike many traditional therapies for dealing with stress, anxiety, depression or cognitive impairment, entrainment does not require a focused effort from the person having the therapy, as the brain instinctively follows the frequency. This makes it a much more effective therapy for managing some of these challenging conditions, by automatically inducing a sense of relaxation and a reduction in negative physical and emotional patterns.
There are five main categories of brainwave frequencies: Gamma (40Hz+), Beta (13 – 40Hz), Alpha (7 – 13Hz), Theta (4 – 7Hz), and Delta (<4Hz). Each category is associated with a different state of mind; so, for example, when you’re in a peak state of performance, your brain produces Alpha Waves, and when you’re in a deep sleep, your brain produces Delta Waves.
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.
Passively listening to binaural beats may not spontaneously propel you into an altered state of consciousness. One's subjective experience in response to binaural-beat stimulation may also be influenced by a number of mediating factors. For example, the willingness and ability of the listener to relax and focus attention may contribute to binaural-beat effectiveness in inducing state changes. "Ultradian rhythms in the nervous system are characterized by periodic changes in arousal and states of consciousness (Rossi, 1986).
However, with this integration will come upheavals as the mind is forced to integrate areas of the brain that were previously sequestered. Repressed memories and unpleasant emotions from the past will often rise to the surface of the mind to be processed and healed. This is sometimes referred to as "processing the shadow" within one's mind and emotions.
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To get a full answer you should really get in touch with the owner of the app, because it does really depend on how their track is constructed and how they intend it to work. I have one 50-minute sleep track which takes you down into delta (http://www.mindamend.com/shop/sleeping-and-dreaming/sleep-induction-isochronic-tones/) and that is designed to just get you to sleep, so you just let play until the end. If you played that track on repeat it might make you jump and wake you up, as the track begins at a higher frequency. I have another 8-hour sleep track which is meant to be played all throughout the night (http://www.mindamend.com/shop/sleeping-and-dreaming/deep-sleep-8-hour-sleep-cycle/). So it does depend on the individual track you are using.

You may recognize the "binaural recording" from ASMR, where the technique is often used. This explains why, if you search for "binaural" on YouTube, you get a mixture of two entirely different kinds of results: binaural beats and binaural ASMR recordings. It gets especially confusing in that there's some questionable and/or unexplored science surrounding each one.
Absolutely. Binaural beats were first discovered over 150 years ago, and their use in brainwave entrainment audio has been the subject of a great deal of scientific exploration over the last 35 years in particular. Millions of people use brainwave entrainment music to enhance their quality of life and to experience deep relaxation. In fact, brainwave entrainment technology is now used for more than just meditation. It is also used by a variety of practitioners and private users for improving self-confidence, stress relief, pain management, relaxation, improving and concentration and improving the quality of one's sleep. If you would like to read an objective third party report on binaural beats, please refer to this Wikipedia article.
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.
Hello Jason, this is an unusually thoughtful discussion. Thank you for all your expertise and your kind manner of presenting and moderating it. I’m wondering if you have any experience with this: ever since I’ve been exposed to theta wave music, without headphones, I have found it irritating. And this is in spite of the fact that when I was first handed a CD by someone I knew well and trusted he was so confident I’d love it It didn’t occur to either of us that I might not. This happened again recently, which is about 10 years later, when I heard it playing overhead at an acupuncture clinic. I felt restless and even irritated, unable to zone out, which is unusual for me, during the treatment. I realized that the quality of my irritation was similar to what I’d felt listening to that CD a decade ago.So I asked if it was theta wave music and she said yes. The acupuncturist said that some people, but a vast minority, really dislike the music. She said that the few people who dislike it are not simply neutral, but actively dislike it. And she also said, but most people like it a lot. I’m just wondering what kind of factors might be present that would make a person feel so irritated by this music?

Binaural beats are acoustically generated frequencies that match the frequency bands of brain waves and are therefore considered a means to inducing neurophysiological relaxation. There is, however, large dispute on the scientific quality and validity of extant research on binaural beats. Thus, the effect of a binaural 10Hz (Alpha) stimulation on subjective and physiological parameters... [Show full abstract]
way of describing it—at both theta brainwave frequencies. And then there are also 40-Hz gamma frequencies, the frequency that came through a lot when the Dalai Lama sent some Buddhist monks to have their brain waves studied as they were meditating and doing loving-kindness practices. Gamma is associated both with heightened awareness and also with loving-kindness practices, metta practices.

Our brainwave states are natural. Guiding the brain into those states intentionally by using entrainment is just another way of experiencing those same natural states. Nothing “unnatural” is produced by the brain as a result of using entrainment. The only thing that is different is that when using entrainment we often go into the experience with either general expectations, or a well defined laundry list of specific expectations that we associate with entrainment. We have no such list going throughout our normal day when we’re not using entrainment.

Doing almost any routine, repetitive activity (like vacuuming, shredding paper or knitting), or reciting a word that represents how you wish you felt (such as calm) is a quick way to achieve a Zen-like state. Studies show the effects lower blood pressure and slow heart rate and breathing. The crucial elements are to focus on a word, your breathing or a movement and to bring your attention back to your task if your mind wanders or negative thoughts intrude. Or look to your faith for a mantra: A recent study published in the Journal of Advanced Nursing found that repeating phrases with spiritual meanings helped participants cope with a range of problems, from anxiety to insomnia.
Exercise and stress research has typically focused on aerobic exercise. There have been consistent findings that people report feeling calmer after a 20- to 30-minute bout of aerobic exercise, and the calming effect can last for several hours after exercise. Recently, there has been an increased amount of research on the role of mind-body types of exercise such as yoga or Tai Chi. Unfortunately, there is somewhat limited research on the role of resistance exercise in stress management.

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.