Theta: This brainwave pattern is associated with deep relaxation and with some stages of sleep, including the lighter stages of non-REM (NREM) sleep. REM sleep itself is mostly composed of beta wave and other activity that’s similar to an alert, waking brain. Deep meditation produces theta waves, which are slower and lower frequency (between 5-8 hertz) than Alpha waves. That murky barrier between sleep and wakefulness, when you’re drifting in and out of sleep, and your thoughts feel dreamlike and difficult to remember? That’s a theta-dominant state of consciousness.
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.)
... The goal of the study was to observe the effect of exposure to BB on working memory capacity. As suggested by many studies, BBs corresponding to alpha brain waves can positively influence cognitive processing, namely attention, auditory sequential memory, working memory, working memory storage, and reasoning ability (Carter & Russell, 1993;Cruceanu & Rotarescu, 2013;Foster, 1990;Kennerly, 1994;McMurray, 2006). The results show that a BB of the frequency of 9.55 Hz – which is a representation of the alpha frequency range of the brain activity – had a temporary positive effect on working memory capacity in our sample of healthy, adult university students. ...

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. 
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.
The brain is composed of millions of specialized cells called neurons. Neurons send signals to other neurons using electro-chemical messengers called neuro-transmitters that attach to receiving sites located on the neurons themselves. There is a space between the end of the neuron and the receptor called the synaptic gap. As neuro-transmitter chemicals move across this gap, a small electrical charge is created. 
(Shannahoff-Khalsa, 1991; Webb & Dube, 1981). These naturally occurring shifts may underlie the anecdotal reports of fluctuations in the effectiveness of binaural beats. External factors are also thought to play roles in mediating the effects of binaural beats (Owens & Atwater, 1995). The perception of a binaural beat is, for example, said to be heightened by the addition of white noise to the carrier signal (Oster, 1973), so white noise is often used as background. "Music, relaxation exercises, guided imagery, and verbal suggestion have all been used to enhance the state-changing effects of the binaural beat" (Owens & Atwater, 1995). Other practices such as humming, toning, breathing exercises, autogenic training, and/or biofeedback can also be used to interrupt the homeostasis of resistant subjects (Tart, 1975).
Binaural beats change the frequency of your brainwaves, giving you control over which category you experience at any given moment. And because you’re in the driver’s seat — and producing specific frequencies to induce a specific state of mind — you can use binaural beats to boost performance, increase focus, get better sleep… the possibilities are endless. “There’s an infinite number of variations on how you could use this kind of technology,” says Bill Harris, Director of Centerpointe Research Institute and creator of auditory brainwave training program Holosync.
You won’t recall ever being in this state, but it’s an incredibly important brainwave for your health. In this state, you will be deeply asleep, but not actively dreaming. Your body needs this state to heal and regenerate. On a daily basis, you’ll need to achieve this state when you sleep at night to make sure your body can heal itself. When you’re feeling really sick or your body and mind are working hard, you’ll want to stay in this state a little longer.
... [9] While entrainment by binaural auditory beats in the alpha frequency has also been shown to enhance creativity, cognition, memory, and an improvement in intelligence tests and achievement tests in learning disabled boys. [10][11][12][13] The gamma-band activity has been shown to involve in a variety of functions such as attention, memory, and consciousness. Current literature suggests that entrainment by gamma beats promotes cognitive flexibility, modulates visual attention, and enhances creativity. ...

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.

Beware simple answers to complex problems, or easy methods for accomplishing difficult goals. If you combine this maxim with the advice to be skeptical of any claims that are being made in order to sell you something – then ironically you have a simple method (perhaps I should call it an “elegant” method) for protecting yourself from most scams and cons. Actually the application of this combination of maxims can be complex, but what it does do is trigger doubt and skeptical analysis. (And to be clear I am not saying that all simple solutions must be wrong – you should just beware them, meaning your skeptical senses should be tingling.)
The effects are strongest while you are listening to the tones because your brainwaves are synchronized and tuned into the frequency range you desire at that time.  After you've stopped listening the effects can still linger for a while afterwards.  The timescale will vary from person to person and be affected by what you do after you've stopped listening.
Science shows that massages reduce stress, but you don’t have to go to the spa—you can give yourself one right now. “Learning how to self-massage your foot, head, neck, or shoulders reduces the stress hormone cortisol, boosts your immune system, and increases the feel-good hormones oxytocin, dopamine, and serotonin,” Dr. Serani says. You can even use a tennis ball or cold water bottle on your feet or neck. In addition, try rubbing pressure points like the webbing between your thumb and index finger, or your inner wrist. Another technique is the EFT tapping technique, literally tapping certain points on your body such as in between your eyes, your temples, and the center of your collarbone. “Tapping brings cleansing energy to the meridian points, as your mind directs the energy to what’s unbalanced in the body,” Whitaker says. “This restores your mind and body’s natural balance, which aids in releasing stress, worry, fears, and disharmony.”
Isochronic tones work just the same in delta as they do in alpha, theta and beta and they are widely used in the brainwave entrainment community to help people sleep. Like you, I’ve also seen some websites saying they don’t work in delta, but it’s a bit like the game of Chinese Whispers, where someone makes a comment and then after it gets passed around and shared a lot the message gets distorted and appears to be a fact. I don’t know of any scientific reason why they wouldn’t work in delta. I remember some people talking about this on a brainwave entrainment forum many years ago. They were saying they found isochronic tones a bit too abrupt for using to help them sleep and they preferred binaural beats, as they thought they were a more soothing sound. That was just a personal preference shared by a couple of prominent forum members at the time and some people then took that as a fact for everyone. That’s where I think that belief originated from.

The reason this rule of thumb is so useful is because there is a huge market for simple answers. A genuine elegant solution (one that accomplishes more with less) is highly valuable in the marketplace. We are used to technology delivering new easy solutions to previously difficult tasks. While most improvements are incremental, there are occasional breakthroughs that transform our lives.

OK – so some of this is pretty common marketing hype. Consumers have become almost numb to such hyperbole. But still we see some of the common – almost ubiquitous – elements of pseudoscientific scams. The company claims that the device is “effort-free”, that the results are “rapid and long-lasting,” that it is the “most effective” method of its kind, and that it is useful for a broad range of applications (hey, why limit the market). I am used to such hype about dishwashing detergent, but find it intolerable when applied to a pseudoscientific device with medical applications.

In 1956, the famous neuroscientist W. Gray Walter published the results of studying thousands of test subjects using photic stimulation, showing their change in mental and emotional states. He also learned that photic stimulation not only altered brainwaves, but that these changes were occurring in areas of the brain outside of vision. In Walter’s words:
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Theta frequencies have long been viewed as the doorway to the subconscious mind. Heightened intuition, deep relaxation, extrasensory perception, and vivid dreaming are all connected to this frequency. There is a distinctly dreamy and otherworldly feel that accompanies the Theta brainwave. Many therapists and hypnotherapists make use of the Theta frequency to tap into the subconscious mind and heal core issues. As such, this frequency is a powerful way to change limiting beliefs and do deep inner work.
2. The other thing you cannot afford to do is evaluate whether or not a technique is having an effect based upon having (or not having) any of those superficial, irrelevant, distracting phenomena discussed above, like face flushing, seeing light swirls, having sensations of this, that or the other thing, etc. Those kinds of phenomena will just lead you down the wrong path and steer you away from the true benefits of meditation. If you’ve already fallen into the trap of this sort of conditioning, using something like the Release Technique, the Sedona Method, or even EFT can be helpful in breaking established conditioned associations.
Changes in neural oscillations, demonstrable through electroencephalogram (EEG) measurements, are precipitated by listening to music,[20][21][22][23][24][25] which can modulate autonomic arousal ergotropically and trophotropically, increasing and decreasing arousal respectively.[26] Musical auditory stimulation has also been demonstrated to improve immune function, facilitate relaxation, improve mood, and contribute to the alleviation of stress.[27][28][29][30][31][32][27][33] These findings have contributed to the development of neurologic music therapy, which uses music and song as an active and receptive intervention, to contribute to the treatment and management of disorders characterized by impairment to parts of the brain and central nervous system, including stroke, traumatic brain injury, Parkinson's disease, Huntington's disease, cerebral palsy, Alzheimer's disease, and autism.[34][35][36]