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Brainwave entrainment is any practice that aims to cause brainwave frequencies to fall into step with a periodic stimulus having a frequency corresponding to the intended brain-state (for example, to induce sleep), usually attempted with the use of specialized software. It purportedly depends upon a "frequency following" response on the assumption that the human brain has a tendency to change its dominant EEG frequency towards the frequency of a dominant external stimulus. Such a stimulus is often aural, as in the case of binaural or monaural beats and isochronic tones, or else photic (visual), as with a dreamachine, a combination of the two with a mind machine, or even electromagnetic radiation.
Hemispheric synchronization, a potential and generally desired result of brainwave entrainment, refers to a state when the brainwave pattern of the right and left hemispheres become alike. A person with similar activity in both hemispheres is alleged (typically by companies trying to sell a product) to be happier, more optimistic, more emotionally stable and less prone to mental illness. Increased levels of synchronization are found naturally in people who meditate regularly and people who are very content with their lives in general.
While there have been many small-scale studies done (see below for some samples), there has not yet been a large-scale or long-term study of brainwave entrainment.
Enthusiasts of brainwave entrainment claim that it has been noted or used in one form or another for centuries (long before the invention of EEG equipment), from shamanistic societies' use of drum beats to Ptolemy noting in 200 AD the effects of flickering sunlight generated by a spinning wheel. In the 1930s and '40s, with then-new EEG equipment and strobe lights, William Grey Walter performed some of the first scientific research on the subject. Later, in the 1960s and '70s, interest in altered states led some artists to become interested in the subject, most notably Brion Gysin who, along with a Cambridge math student, invented the Dreamachine. From the 1970s to date there have been numerous studies and various machines built that combine light and sound. These efforts were aided by continued development of micro-circuitry and other electronic breakthroughs which allowed for ever more sophisticated equipment. One of the more frequently noted scientific results claimed for brainwave entrainment was the discovery of binaural beats, published in Scientific American in 1973 by Gerald Oster. However, Oster's research actually makes no mention of brainwaves. With the development of isochronic tones by Arturo Manns, combined with more sophisticated equipment, these discoveries led to many attempts to use claimed brainwave entrainment techniques in the treatment of numerous psychological and physiological conditions.
Binaural beats deserve special mention because of the manner in which the desired frequencies are obtained. Brainwave entrainment may be achieved when audio signals are introduced to the brain causing a response directly related to the frequency of the signal introduced, called binaural beats. Two tones close in frequency generate a beat frequency at the difference of the frequencies, which is generally subsonic. For example, a 495 Hz tone and 505 Hz tone will produce a subsonic 10 Hz beat, roughly in the middle of the alpha range. The "carrier frequency" (e.g., the 505 Hz in the example above), is also said by some to affect the quality of the transformative experience. This effect is achieved without either ear hearing the pulse when headphones are used. Instead, the brain produces the pulse by combining the two tones. Each ear hears only a steady tone. Although some have claimed that these frequencies do provide help in treating certain medical conditions, there is not a wide acceptance by the medical community to adopt the practice of brainwave entrainment for emotional/mental disorders. A fixed, constant frequency of synchronization is less helpful than techniques such as classical neurofeedback or learning meditation, which naturally generate brainwave frequencies that differ from person to person and may vary from minute to minute.
Binaural beats were first discovered in 1839 by H. Dove, a German experimenter. At that time, binaural beats were considered to be a special case of monaural beats. Binaural beats are not the same as monaural beats. Binaural beats are perceived by presenting two different tones at slightly different pitches (or frequencies) separately into each ear. This effect is produced in the brain, not in the ears as with monaural beats. It is produced by the neural output from the ears and created within the olivary body within the brain, in its attempt to "locate" the direction of the sound based on phase.
Only monaural beats are the result of the arithmetic (vector) sum of the waveforms of the two tones as they add or subtract from one another, becoming louder and quieter and louder again.
Monaural and binaural beats are rarely encountered in nature, but in man-made objects, monaural beats occur frequently. For example, two large engines running at slightly different speeds will send "surges" of vibrations through the deck of a ship or jet plane. The lower pitched tone is called the carrier and the upper tone is called the offset.
Monaural beats occur in the open air and external to the ears. For example, when two guitar strings of slightly different frequencies are plucked simultaneously, monaural beats strike the ear as beats and therefore excite the thalamus, an action crucial for entrainment. Binaural beats played through loudspeakers become monaural beats. Binaural tones require headphones to be effective.
To hear monaural beats, both tones must be of the same amplitude. However binaural beats can be heard when the tones have different amplitudes. They can even be heard if one of the tones is below the hearing threshold. Noise reduces the perceived volume of monaural beats whereas noise actually increases the loudness of binaural beats.
"Isochronic tones are evenly spaced tones which turn on and off quickly." Unlike binaural and monaural beats, isochronic tones do not rely on the combination of two tones – the "beat" is created manually by turning a tone on and off. 
Modulating sound is a way to produce brainwave entrainment using something as complex as a musical track. In effect, this is "embedding" brainwave entrainment into the audio. Any sound can be used, from nature sounds to white noise to a full classical symphony.
Modulation works by rhythmically adjusting a component in the sound. For example, volume modulation would be used to increase and decreases the volume to create the rhythmic stimulus necessary for entrainment to occur.
The problem with modulation (above) is that it can often distort the audio, particularly when used with music or certain nature sounds like rain. Frequency band selection solves this problem by selectively modulating certain parts of an audio file, instead of the whole of it.
The brainwave entrainment is embedded into a lower frequency range only – affecting parts of the bass, but leaving the mid and treble alone. Frequency band selection can be used to affect only one part of a sound file. Multiple frequency bands can also be selected.
Frequency band selection is an important advancement, allowing entrainment to be embedded into any sound file with virtually no negative effect on the existing audio. Because it allows for much higher intensity levels, the effectiveness of the session is actually increased.
Audio–visual entrainment (AVE), a subset of brainwave entrainment, uses flashes of lights and pulses of tones to guide the brain into various states of brainwave activity. AVE devices are often termed light and sound machines or mind machines. Altering brainwave activity may aid in the treatment of psychological and physiological disorders.