Let’s say you’re listening to a sound in your left ear that’s at a frequency of 132 Hertz (Hz). And in your right ear, you’re listening to a sound that’s at a frequency of 121 Hz. Your brain, however, gradually falls into synchrony with the difference — or 11 Hz. Instead of hearing two different tones, you instead hear a tone at 11 Hz (in addition to the two tones given to each ear).
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.

When you listen to binaural beats/tones, you are actually listening to two slightly different pitched frequencies. Each frequency goes to each of your ears independently. When this happens your brain responds by creating a third tone, making up the difference between the two frequencies. This shift in frequency then shifts your brain’s consciousness and changes your state.
There are many advantages and disadvantages with binaural beats. One of the major advantages is hemispheric synchronization. Since both hemispheres are required to create the beat within the brain, this method is an excellent way to create greater harmony between areas of the mind typically functioning independently. Binaural beats are also known to have effective hypnotic and relaxing effects.
Why is exposure to these soundwaves helpful to sleep and relaxation? Science shows that exposure to binaural beats can create changes in the brain’s degree of arousal. Listening to these sounds that create a low-frequency tone, research indicates, triggers a slow-down to brainwave activity—and that may help you relax, lower your anxiety, and can make it easier for you to fall asleep and sleep more soundly.
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.
A common element in recordings incorporating alpha and theta frequencies is a steady but barely perceptible rhythm of the frequencies themselves. This subtle and calming pulse mixes with sounds of gentle breezes, distant bird songs, and the slow progression of deep synth notes. Underneath this, below the audible sounds at sub 16 hertz levels, other frequencies intermingle, deepening the merging of conscious and unconscious mind.
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.

Binaural beats are a type of brain entrainment technology. Entrainment, by the way, is a fancy way of saying "matching". The beats influence your brainwaves, which in turn alter the states of your consciousness. They were first discovered in 1839 by Heinrich Wilhelm Dove, but were considered a scientific oddity until 1973, when Gerald Oster published an article called, "Auditory Beats in the Brain". Oster's work offered new insights, as well as some laboratory findings, to Dove's research; hence, a revolution was started in the field of neurophysiology. Binaural beats are of interest to neurophysiologists investigating the sense of hearing.

Alpha (12hz – 8hz) – Awake, but deeply relaxed. Simply closing your eyes will produce alpha brainwaves. This category is associated with daydreaming, visualization, imagination, light meditation. Brainwave expert Anna Wise called the alpha range the bridge between beta and theta. (More information can be found in Wise’ book The High-Performance Mind)
James Austin, a neurologist, began practicing Zen meditation during a visit to Japan. After years of practice, he found himself having to re-evaluate what his professional background had taught him. "It was decided for me by the experiences I had while meditating," said Austin, author of the book "Zen and the Brain" and now a philosophy scholar at the University of Idaho. "Some of them were quickenings, one was a major internal absorption ­ an intense hyper-awareness, empty endless space that was blacker than black and soundless and vacant of any sense of my physical bodily self. I felt deep bliss. I realized that nothing in my training or experience had prepared me to help me understand what was going on in my brain. It was a wake-up call for a neurologist."
Using new scanning techniques, neuroscientists have discovered that certain areas of the brain light up constantly in Buddhists, which indicates positive emotions and good mood. "We can now hypothesize with some confidence that those apparently happy, calm Buddhist souls one regularly comes across in places such as Dharamsala, India, really are happy,"
Brainwave entrainment is a method to alter the frequency of your brainwaves by listening to audible tones containing the desired frequency. So if you want to sleep, you would listen to audio that begins at your current frequency and slowly descends to a delta frequency. By introducing these new lower frequencies, your mind begins to lower its own brainwaves to match this new frequency.
The results of using EquiSync for only 3 months have been phenomenal! Profound and positive changes have occurred , and continue to occur, in my being. These transformations have become obvious to family and friends as well. I am 71 yrs old and feel better than when I was in my thirties. My energy levels remain high with less sleep. I work out at the gym vigorously five days a week – bicycling and swimming are part of the regimen as well. I volunteer services at Hospice and nursing homes. My short term memory has improved to the point that others remark on my remembering their names after meeting them only once several weeks in the past. Sometimes I find that I’m reading fine print without my glasses. I spent the greater portion of my “productive” years as a monk but had lost the ability to meditate due to the development of A.D.D. Now my ability to stay focused and concentrate has remarkably returned and am reaching meditative states that I’ve not reached in years. Each new day is now seen as another opportunity to serve.

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.)
A study published in Electroencephalography and Clinical Neurophysiology by Paul Williams and Michael West in 1975 examined the brainwave states of people experienced in meditation while using photic stimulation, and another study by Leonard, Telch, and Harrington in 1999 examined the successful use of brainwave entrainment techniques for attaining meditative states in subjects.
Binaural beats between 1 and 30 Hz are alleged to create the same brainwave pattern that one would experience during meditation. When you listen to a sound with a certain frequency, your brain waves will synchronize with that frequency. The theory is that binaural beats can help create the frequency needed for your brain to create the same waves commonly experienced during a meditation practice. The use of binaural beats in this way is sometimes called brainwave entrainment technology.
Slightly higher-frequency entrainment can lead to hyper suggestive states of consciousness. Still higher-frequency EEG states are associated with alert and focused mental activity needed for the optimal performance of many tasks. Perceived reality changes depending on the state of consciousness of the perceiver (Tart, 1975). Some states of consciousness provide limited views of reality, while others provide an expanded awareness of reality. For the most part, states of consciousness change in response to the ever-changing internal environment and surrounding stimulation. For example, states of consciousness are subject to influences like drugs and circadian and ultradian rhythms (Rossi, 1986; Shannahoff-Khalsa, 1991; Webb & Dube, 1981). Specific states of consciousness can also be learned as adaptive behaviors to demanding circumstances (Green and Green, 1986).  
If you are reading this, it is likely that your Beta brainwaves are dominating your mind. Beta brainwaves are present when your attention is focused on a problem, whether that is working something complex out in your head, Focusing on a video game or having a conversation with another person. Beta waves are also experienced during anxiety, stress and excitement.2
A 2008 study at Hofstra University played two different binaural beats and a control sound (a babbling brook) to patients with high blood pressure. There was no difference between the groups. In one small study from Japan that was published in the Journal of Neurophysiology in 2006, they played various binaural beats to nine subjects, and observed the resulting EEGs. They found great variability in the results. Their conclusion was that listening to binaural beats can produce activity on the human cerebral cortex, however the cause was more likely a conscious auditory reaction and was not correlated to the frequency of the binaural beat. However, a 2005 study published in Clinical Neurophysiology found that they were able to induce a desired frequency in the EEG matching the phantom beat frequency encoded in a binaural beat, however this was with a single subject and was neither blinded nor controlled.
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