A newer alternative to binaural beats is isochromatic tones. These are tones that are interspersed with periods of brief silence, creating a similar effect to binaural beats but without the two frequencies playing in different ears. Because isochromatic tones do not need headphones, they are gaining popularity as the newest method of brainwave entertainment.
The composer Alvin Lucier has written many pieces that feature interference beats as their main focus. Italian composer Giacinto Scelsi, whose style is grounded on microtonal oscillations of unisons, extensively explored the textural effects of interference beats, particularly in his late works such as the violin solos Xnoybis (1964) and L'âme ailée / L'âme ouverte (1973), which feature them prominently (note that Scelsi treated and notated each string of the instrument as a separate part, so that his violin solos are effectively quartets of one-strings, where different strings of the violin may be simultaneously playing the same note with microtonal shifts, so that the interference patterns are generated). Composer Phill Niblock's music is entirely based on beating caused by microtonal differences.
When we are mentally active various groups of neurons will be firing and the EEG will look like a jumble of different waves at different frequencies. When we are in a relaxed state, however, our brains settle into a steady rhythm – when fully awake this is the alpha rhythm, which as a frequency of 8-12 hz and other recognizable features. When drowsy our brainwaves slow to the theta range, 6-7hz, and when in deep sleep into the delta range, 4-5hz.

Theta waves also have been observed in moments when a person recalls information from the past, and this may be what links them also to improvement in learning ability. We also experience theta waves when we go into automatic pilot mode, such as when doing a repetitive task like driving a familiar route where the mind become disconnected while you still drive safely toward your destination.
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.
♥ ← This set of tones with the bird calls from Aotearoa is keeping me awake while I finish an essay I've been working on for the past four days. Focus beats + sounds I associate with morning = wakefulness. Still craving the bed, but at least I'm not falling asleep at my desk. Thanks myNoise, without you I'd probably be listening to music and distracted.
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).
With digital upgrades, Berger’s machine is still in use today, known as an electroencephalography machine, or EEG. Berger used his machine to study the brains of psychologically normal and abnormal people and discovered the first brainwave, called the alpha wave and also known as the Berger wave, along with the faster beta wave, which he observed suppressing the alpha wave when subjects opened their closed eyes. 

As a relatively new technology, fMRI has only recently been used to assess brain state changes during meditation. Recent studies have shown heightened activity in the anterior cingulate cortex, frontal cortex, and prefrontal cortex, specifically in the dorsal medial prefrontal area during Vipassana meditation.[7] Similarly, the cingulate cortex and frontal cortex areas were shown to have increased activity during Zen meditation.[8] Both studies comment on the possibility that these findings could indicate some state of heightened voluntary control over attention during mindfulness meditation. Review works by Cahn and Chiesa state that these results indicate consistency in meditation’s effect on these regions of the brain, citing a multitude of other studies spanning other meditative disciplines, but mention the need for further investigation with better controls.[4][6]

But the question is: Does it have a special effect on the brain? A lot of people think so. The basic claim being made for binaural beats is "resonant entrainment". Entrainment, in physics, is when two systems which oscillate at different frequencies independently are brought together, they synchronize with one another, at whatever the combined system's resonant frequency is. Examples of entrainment occur in animals in nature; for example the chirping of crickets or the croaking of frogs. Synchronization of menstrual cycles in women is another example. Even people coming together and dancing with one another is a type of entrainment. The basic claim for binaural beats is that the perceived low-frequency beat will entrain your brain wave pattern, thus forcing your brain into some desired state.