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Binaural beats or binaural tones are auditory processing artifacts, that is, apparent sounds, the perception of which arises in the brain independent of physical stimuli. This effect was discovered in 1839 by Heinrich Wilhelm Dove.
The brain produces a phenomenon resulting in low-frequency pulsations in the loudness of a perceived sound when two tones at slightly different frequencies are presented separately, one to each of a subject's ears, using stereo headphones. A beating tone will be perceived, as if the two tones mixed naturally, out of the brain. The frequency of the tones must be below about 1,000 to 1,500 hertz for the beating to be heard. The difference between the two frequencies must be small (below about 30 Hz) for the effect to occur; otherwise the two tones will be heard separately and no beat will be perceived.
Interest in binaural beats can be classified into two categories. First, they are of interest to neurophysiologists investigating the sense of hearing. Second, that binaural beats may influence the brain in more subtle ways through the entrainment of brainwaves   and can be used to produce relaxation and other health benefits.
Heinrich Wilhelm Dove discovered binaural beats in 1839. While research about them continued after that, the subject remained somewhat of a scientific curiosity until 134 years later, with the publishing of Gerald Oster's article "Auditory Beats in the Brain" (Scientific American, 1973). Oster's article identified and assembled the scattered islands of relevant research since Dove, offering tremendous fresh insight (and new laboratory findings) to research on binaural beats.
In particular, Oster saw binaural beats as a powerful tool for cognitive and neurological research, addressing questions such as how animals locate sounds in their three-dimensional environment, and also the remarkable ability of animals to pick out and focus on specific sounds in a sea of noise (what is known as the "cocktail party effect").
Oster also considered binaural beats to be a potentially useful medical diagnostic tool, not merely for finding and assessing auditory impairments, but also for more general neurological conditions. (Binaural beats involve different neurological pathways than ordinary auditory processing.) For example, Oster found that a number of his subjects that could not perceive binaural beats suffered from Parkinson's disease. In one particular case, Oster was able to follow the subject through a week-long treatment of Parkinson's disease; at the outset the patient couldn't perceive binaural beats, but by the end of the week of treatment, the patient could hear them again.
In corroborating an earlier study, Oster also reported gender differences in the perception of beats. Specifically, women seemed to experience two separate peaks in their ability to perceive binaural beats- peaks possibly correlating with specific points in the menstrual cycle (onset of menstruation and approx. 15 after). This data led Oster to wonder if binaural beats could be used as a tool for measuring relative levels of estrogen. 
The sensation of binaural beats is believed to originate in the superior olivary nucleus, a part of the brain stem. They appear to be related to the brain's ability to locate the sources of sounds in three dimensions and to track moving sounds, which also involves inferior colliculus (IC) neurons.  Regarding entrainment, the study of rhythmicity provides insights into the understanding of temporal information processing in the human brain. Auditory rhythms rapidly entrain motor responses into stable steady synchronization states below and above conscious perception thresholds. Activated regions include primary sensorimotor and cingulate areas, bilateral opercular premotor areas, bilateral SII, ventral prefrontal cortex, and, subcortically, anterior insula, putamen, and thalamus. Within the cerebellum, vermal regions and anterior hemispheres ipsilateral to the movement became significantly activated. Tracking temporal modulations additionally activated predominantly right prefrontal, anterior cingulate, and intraparietal regions as well as posterior cerebellar hemispheres.
Hypothetical Effects on Brain Function
Binaural beats may influence functions of the brain besides those related to hearing. This phenomenon is called frequency following response. The concept is that if one receives a stimulus with a frequency in the range of brain waves, the predominant brain wave frequency is said to be likely to move towards the frequency of the stimulus (a process called entrainment). In addition, binaural beats have been credibly documented to entrain brainwave rhythms, according to the frequency following response, at various sites in the brain.    
The stimulus does not have to be aural; it can also be visual or a combination of aural and visual. (One such example would be Dreamachine.) However, using alpha frequencies with such stimuli can trigger photosensitive epilepsy.
Perceived human hearing is limited to the range of frequencies from 20 Hz to 20,000 Hz, though Infrasound - sound below 20Hz - still have scientifically observable effects on humans, however, it is not readily audible, especially at low volume levels. While the frequencies of human brain waves are below about 40 Hz. To account for this lack of perception, binaural beat frequencies are used. Beat frequencies of 40 Hz have been produced in the brain with binaural sound and measured experimentally.
When the perceived beat frequency corresponds to the delta, theta, alpha, beta, or gamma range of brainwave frequencies, the brainwaves entrain to or move towards the beat frequency. For example, if a 315 Hz sine wave is played into the right ear and a 325 Hz one into the left ear, the brain is entrained towards the beat frequency (10 Hz, in the alpha range). Since alpha range is associated with relaxation, this has a relaxing effect or if in the beta range, more alertness. An experiment with binaural sound stimulation using beat frequencies in the Beta range on some participants and Delta/Theta range in other participants, found better vigilance performance and mood in those on the awake alert state of Beta range stimulation.
Binaural beat stimulation has been used fairly extensively to induce a variety of states of consciousness, there has been some work done in regards to the effects of these stimuli on relaxation, focus, attention, and states of consciousness. Studies have shown that with repeated training to close frequency sounds that a plastic reorganization of the brain occurs for the trained frequencies and is capable of asymmetric hemispheric balancing.
|Frequency range||Name||Usually associated with:|
|> 40 Hz||Gamma waves||Higher mental activity, including perception, problem solving, fear, and consciousness|
|13–40 Hz||Beta waves||Active, busy or anxious thinking and active concentration, arousal, cognition|
|7–13 Hz||Alpha waves||Relaxation (while awake), pre-sleep and pre-wake drowsiness|
|4–7 Hz||Theta waves||Dreams, deep meditation, REM sleep|
|< 4 Hz||Delta waves||Deep dreamless sleep, loss of body awareness|
(The precise boundaries between ranges vary among definitions, and there is no universally accepted standard.)
The dominant frequency determines your current state. For example, if in someone's brain alpha waves are dominating, they are in the alpha state (this happens when one is relaxed but awake). However, also other frequencies will be present, albeit with smaller amplitudes.
The brain entraining is more effective if the entraining frequency is close to the user's starting dominant frequency. Therefore, it is suggested to start with a frequency near to one's current dominant frequency (likely to be about 20 Hz or little less for a waking person), and then slowly decreasing it towards the desired frequency.
Some people find pure sine waves unpleasant, so a pink noise or another background (e.g. natural sounds such as river noises) can also be mixed with them. In addition to that, as long as the beat is audible, increasing the volume should not necessarily improve the effectiveness, therefore using a low volume is usually suggested. One theory is to reduce the volume so low that the beating should not even be clearly audible, but this does not seem to be the case (see the next paragraph).
In addition to lowering the brain frequency to relax the listener (or to raise it to help focusing), there are other controversial, alleged uses for binaural beats. For example, that by using specific frequencies an individual can stimulate certain glands to produce desired hormones. Beta-endorphin has been modulated in studies using alpha-theta brain wave training,  and dopamine with binaural beats. Among other alleged uses, there are reducing learning time and sleeping needs (theta waves are thought to improve learning, since children, who have stronger theta waves, and remain in this state for a longer period of time than adults, usually learn faster than adults; and some people find that half an hour in the theta state can reduce sleeping needs up to four hours; however, this is supposed to happen with any way to get into theta state, e.g. meditation); some use them for lucid dreaming and even for attempting out-of-body experiences, astral projection, telepathy and psychokinesis. However, the role of alpha-wave activity in lucid dreaming is subject to ongoing research.  .) Alpha-theta brainwave training has also been used successfully for the treatment of addictions,    for the recovery of repressed memories, but as with other techniques this can lead to false memories. 
A trial of Delta binaural beat technology over 60 days has shown positive effect on self-reported psychologic measures, especially anxiety. There was significant decrease in trait anxiety, an increase in quality of life, and a decrease in insulin-like growth factor-1 and dopamine  and has been successfully trialled to lessen hospital acute pre-operative anxiety. 
Another claimed effect for sound induced brain synchronization is enhanced learning ability. It was proposed in the 1970's that induced alpha brain waves enabled students to assimilate more information with greater long term retention.  In more recent times has come more understanding of the role of theta brain waves in behavioural learning  The presence of theta patterns in the brain has been associated with increased receptivity for learning and decreased filtering by the left hemisphere.   Based on the association between theta activity (4-7 Hz) and working memory performance, biofeedback training suggests that normal healthy individuals can learn to increase a specific component of their EEG activity, and that such enhanced activity may facilitate a working memory task and to a lesser extent focused attention.
- Brainwave synchronization
- Human enhancement
- Neural oscillations
- Evoked potential
- Event-related potential
- Induced activity
- Ongoing brain activity
- Lucid Dream
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- University thesis, reveiw of literature on brainwave entrainment; Chapter 4 binaural sound Stanford
- Gnaural - GNU General Public License binaural beat generator for Win/Linux (Java version)
- SBaGen - GNU General Public License binaural beat generator for Win/Mac/Linux
- Free and Open Source Binaural Beat Examples
- Binaural beat examples from diydharma.org
- Explanation of binaural beats using examples
- Hearing Lecture Notes (5): Binaural hearing and localization from University of Sussex