I came across following article and found it very informative. It highlights the findings of research in the field of brainwave entrainment. Epsilon is the frequency range which is the lowest(below Delta) and hypergamma(above Gamma) is the frequency range which is the highest, but two of them are interrelated via inter-modulation in brainwaves, suggesting that the entrainment done with the help of either epsilon or hypergamma tends towards the same ends. Quite handful of information for those willing to meditate deep with the aid of binaural beats. Article has been reproduced here in its entirety along with references from: this source.
New evidence has emerged of brainwave states above the highest recognized brainwave frequencies of Beta (30 Hz). Higher-than Beta frequencies are called Gamma. These Gamma brainwaves resonate around 40 Hz and are associated with the brain function which holographically synthesizes all the bits of individual data from various areas of the brain and fuses them all together in a higher perspective.
Gamma is a ‘newer’ brainwave only because it is difficult to get instrumentation to accurately measure it. It is thought the Gamma is the harmonizing frequency – for example when you are observing an object, its colour, size, texture etc are all perceived and processed by different parts of the brain, it is thought that Gamma allows for unification of all the different information.
This brainwave activity is associated with states of self awareness, higher levels of insight and information, psychic abilities and out of body experiences. This new region of brain activity and states of consciousness associated with it is called EPSILON.
Theta and gamma rhythms also interact helping the brain to package information into coherent images, thought and memories.
EEG researchers are noticing extremely high brainwave frequencies above Gamma, at up to 100 Hz. Totally opposite speed brainwave frequencies – some at 100 Hz and others at less than 0.5 Hz – have exactly the same states of consciousness associated with them. These high-range brain frequency states are named HyperGamma. Later information showed new evidence of frequencies even higher than this, at almost 200 Hz.named: Lambda brainwave frequencies and states of consciousness.
These HyperGamma, Lambda and Epsilon frequencies, are linked together in a circular relationship -where if you looked with a magnifying glass at an extremely slow Epsilon brain frequency, you would see hidden within it a modulation frequency of 100 – 200 Hz. If you stand back far enough from an extremely fast 200 Hz brainwave frequency, you would see that is it riding on the crest of a slow motion modulating wave of Epsilon.
This Epsilon state of consciousness (the state Yogi’s go into when they achieve “suspended animation”) is where western medical doctors can perceive no heart beat, respiration or pulse. HyperGamma and Lambda states of consciousness are the states associated with the ability of certain sects of Tibetan monks who can mediate in the Himalayan mountains in sub-zero temperatures with scanty clothing and melt the snow all around them.
Fast, gamma rhythms range from 30 to 100 Hz, and may vary in frequency during a response. The 20-100 Hz range we consider here overlaps the beta band (15 to 30 Hz), but we will ignore the finer points of EEG classification here. The natural history and functional roles of synchronous gamma oscillations have been reviewed recently [5,10,12,22]. Below is a potted history.
Gamma rhythms occur in humans and other mammals following sensory stimuli. They often occur in brief runs in these responses. “Induced rhythms” at 50-60 Hz were first described in olfactory bulb by Adrian . They have since been found in: olfactory , visual [3a,3b,6-8,11,22], auditory [13,16], somatosensory  and motor cortex [17,19,21]. Gamma oscillations also occur in the hippocampus [3,24], where the link with external sensory stimuli is less direct, but may still exist in the multimodal inputs it receives from higher order sensory cortices. Hippocampal gamma tends to occur during the theta (4-12 Hz) EEG that is a prominent feature of the hippocampus in vivo [3,23], especially during exploration.
In Man the auditory response includes brief “40 Hz transient responses” [18,25], which increase when the subject pays attention and which disappear with loss of consciousness during anaesthesia . Repetitive auditory stimulation at ~40 Hz generates a large “40 Hz steady state response” . MEG recordings in Man suggest that gamma rhythms can be very widespread , both during waking and dream states. Other MEG measurements in Man suggest that gamma rhythms may be organised to sweep across the whole brain, perhaps providing “temporal binding …. into a single cognitive experience” .
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