Binaural beats are the playing of two sine waves of close, but not the same, frequency into different earpieces of a set of headphones. The "beat" is heard as the brain tries to process them as a distinct sound, while taking into account the constructive/destructive interference. It is said to migrate brain waves to be closer to that frequency, like a sort of biological resonance, which is true. Of course the same can be said for listening to relaxing music help you relax, up tempo music to help you feel energetic, etc...
Most of these websites give some brief explanation of entrainment. The example you hear most often is that of Dutch polymath Christiaan Huygens, who in 1665, hung two pendulum clocks next to each other on a wall. He noticed that the pendulums eventually matched each others' frequency, but always in antiphase, opposite to each other, as if canceling each other out. He'd try disturbing one or setting them in sync, but they'd always return to the same antiphase synchronization. Huygen's experience is widely touted on binaural beat websites as a demonstration of how systems can become spiritually connected through some energy field. However, they misunderstand what happened, and have not read the full story. Huygens also tried taking one clock off the wall, and as soon as they were no longer physically connected to one another via the actual wall, the effect disappeared. It was not the proximity of the clocks to one another that created the entrainment; it was their physical, mechanical connection to one another. As each pendulum swung it imparted an infinitesimal equal and opposite reaction to the wall itself. With two clocks on the wall, the system naturally sought the lowest energy level, according to the laws of thermodynamics; and both pendulums would thus swing exactly counter to each other, minimizing the system's total energy.
Infra-Low brainwaves (also known as Slow Cortical Potentials), are thought to be the basic cortical rythms that underlie our higher brain functions. Very little is known about infra-low brainwaves. Their slow nature make them difficult to detect and accurately measure, so few studies have been done. They appear to take a major role in brain timing and network function. 
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.
Generally speaking, the brain will usually entrain to the strongest stimulus which would be isochronic tones over binaural beats. So when you see people add binaural beats at a different frequency to the isochronic tones, that would not produce additional brainwave entrainment at another frequency. If they are both at the same frequency I haven’t seen any research to indicate whether that would be beneficial or not, but my belief is that it would weaken the potential for entrainment. When you look at the waveform of an isochronic tone there is a distinct empty space between each beat, making it very pronounced and effective. When you add binaural beats at the same frequency it looks like this: http://www.mindamend.com/wp-content/uploads/2017/11/isochronic-tones-binaural-beats-combined-waveform.jpg. The depth of the waveform is now half as deep and less effective. This is before the binaural beats are formed inside your head, where the waveform is hard to determine and measure. From listening to that type of combination the beats sound much less pronounced, which has to make them much less effective in terms of a brainwave entrainment stimulus, compared to isochronic tones on their own.

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Recent research at the University of Lisbon finally uncovered the reason for the 350 year-old mystery, finding that the resonance of sound is the mechanism for entrainment of swinging pendulums and ticking clocks, and it seems likely that the energy transferred by sound is also responsible for other observations of entrainment, including brainwave entrainment.
By the 1980s, entrainment technology had merged with advancements in microelectronics technology, making it possible to develop even more sophisticated audio and visual brainwave entrainment products for the marketplace. In the last two decades, a number of scientific studies have reported brainwave entrainment as an effective remedy for ADD, academic learning problems, and improving memory and cognition.
Brainwave entrainment also happens with the use of pulsating light, and visual and auditory stimuli are sometimes combined for additional effect and visual stimuli is used alone. Using brainwave entrainment techniques is safe for almost everyone, the exception being pregnant women and people who have seizure disorders who should check with their physician before using these methods.
This music encourages a state of delta relaxation. Delta brainwaves are most prevalent during deep, dreamless sleep. The delta state is a mostly unconscious state that is essential to one’s physical, emotional, psychological and spiritual wellbeing. People who are able to achieve a state of delta relaxation through meditation will sometimes describe spiritual encounters and out of body experiences. The delta state is perfect for inducing profound spiritual experiences, healing and deep subconscious repatterning. Delta frequency brainwave entrainment music is also a fantastic cure for insomnia.
Binaural beats can easily be heard at the low frequencies (< 30 Hz) that are characteristic of the EEG spectrum (Oster, 1973). This perceptual phenomenon of binaural beating and the objective measurement of the frequency-following response (Hink, Kodera, Yamada, Kaga, & Suzuki, 1980) suggest conditions which facilitate entrainment of brain waves and altered states of consciousness. There have been numerous anecdotal reports and a growing number of research efforts reporting changes in consciousness associated with binaural-beats. "The subjective effect of listening to binaural beats may be relaxing or stimulating, depending on the frequency of the binaural-beat stimulation" (Owens & Atwater, 1995). Binaural beats in the delta (1 to 4 Hz) and theta (4 to 8 Hz) ranges have been associated with reports of relaxed, meditative, and creative states (Hiew, 1995), and used as an aid to falling asleep. Binaural beats in the alpha frequencies (8 to 12 Hz) have increased alpha brain waves (Foster, 1990) and binaural beats in the beta frequencies (typically 16 to 24 Hz) have been associated with reports of increased concentration or alertness (Monroe, 1985) and improved memory (Kennerly, 1994).
Hi Et, In all the feedback and studies I’ve read and looked into over the years, I’ve seen lots of feedback from people talking about how they don’t like the sound of the tones, or they find them irritating in some way. Unfortunately, there doesn’t seem to be any particular reason why one person likes it and the next doesn’t. It’s a bit like normal music, one person’s sweet symphony is another person pneumatic drill. It’s common for people to find it weird and maybe annoying at first, which is how I felt in the beginning. But usually after a few listens you can start to get used to it and appreciate the sound, and especially the feeling it gives you. Personally, I think it can help if you try to embrace the sound, psychologically speaking beforehand. It can also help to have the sound playing at a very low volume, to begin with, then building it up as you get more used to it.

A person might wonder what the problem with looking for validation is; why we shouldn’t seek to compare our experiences with those others have had. Shouldn’t there be some sort of indicators that our practice is producing an effect? There are indicators, but they are not the high profile, odd phenomena most frequently looked for, and they may not become apparent immediately. Some things do take a little time.
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.
There’s an aesthetic element to the music and there are a lot of drone-based sounds and time-stretched sounds, deep, rich bass sounds—there’s a spectrum of sounds within there—and what’s more, there’s a load of 3D processing that goes on to ensure that the mind doesn’t become habituated to them. There’s also a constant, subtle sense, a slow and gradual sense, of the sounds shifting around. And, there are layers of binaural beats.
Just as stress can increase the risk for chronic diseases and other health problems, dealing with chronic conditions and poor health can increase the amount of stress one experiences. Stress also influences behaviors that affect health. Diet choices, sleep habits, and drug use are behaviors that are often negatively affected by stress (3). The APA’s 2011 survey showed that 39% percent of respondents reported overeating or eating unhealthy food because of stress, and 29% reported skipping a meal (3). In addition, 44% reported lying awake at night because of stress (3). On a positive note, 47% of respondents reported walking or exercise as a way of managing stress (3).
Reading can be a wonderful (and healthy) escape from the stress of everyday life. Simply by opening a book, you allow yourself to be invited into a literary world that distracts you from your daily stressors. Reading can even relax your body by lowering your heart rate and easing the tension in your muscles. A 2009 study at the University of Sussex found that reading can reduce stress by up to 68%. It works better and faster than other relaxation methods, such as listening to music or drinking a hot cup of tea. This is because your mind is invited into a literary world that is free from the stressors that plague your daily life.
Subsequently, the term 'entrainment' has been used to describe a shared tendency of many physical and biological systems to synchronize their periodicity and rhythm through interaction. This tendency has been identified as specifically pertinent to the study of sound and music generally, and acoustic rhythms specifically. The most ubiquitous and familiar examples of neuromotor entrainment to acoustic stimuli is observable in spontaneous foot or finger tapping to the rhythmic beat of a song.
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