If anybody would like to look over the scientific evidence concerning brainwave entrainment and isochronic tones, I’ve done a lot of research over the years which I’ve collected at the PubMed website of NCBI – a branch of the National Institute of Health – that provides access to a large library of medical journal articles. I’ve made my list public so you can look through the journal articles that were published concerning this topic. Here’s the link: http://www.ncbi.nlm.nih.gov/sites/myncbi/1tmDFOl0XtyA4/collections/51531796/public/. Most of the collection only gives access to abstracts or summaries unless you’re at some kind of educational institution that has a subscription to the particular journal that article is in, but I actually find abstracts really helpful. So have at it, read away. And if your psychiatrist/therapist thinks you’re nuts for feeling better after listening to isochronic tones, just whip out your 82-page collection of scientific journal abstracts written by her peers and give it to her to read. 🙂
“One of the best ways to explain how brainwave entrainment works is by observing the effect of a tuning fork on a guitar string,” says Naik. “Hit a tuning fork tuned to a particular sound frequency, such as the note C, and hold it close to the strings of a guitar. You will notice that the C string on the guitar starts to vibrate because it has entrained on to the same frequency of the tuning fork.”
Using a small amount of alcohol in the Pregnancy and Children's lines was a conscious decision. It enables us to keep the strength and efficaciousness of the formula intact but is also gentle and appropriate for women and children. Extracts made with only glycerine or water limit the constituent profile. WishGarden's finished extract contains a minimal amount of alcohol, which, per serving, is at a very low dietary level (similar to what is found in kombucha and ripe bananas). You can also further reduce the alcohol content by stirring your droppers full, or pumps, into hot water or tea for a few minutes.

When you play two separate frequencies in each ear, say 140 Hz and 149 Hz, the difference in frequency is 9 Hz. Your brain compensates for this difference and a third tone of 9 Hz is experienced. This will result in your brain being lowered or raised and tuned into the desired frequency. This is how binaural beats are produced. Headphones are essential for this to work.  
Above is a nice, simple and short chart of the various brainwave ranges and the types of effects they generally have and what sorts of activities they may be able to enhance. There simply is nothing more detailed than what this chart contains about entrainment frequencies and what they are useful for. Those other elaborate lists to be found on the internet are nothing but the product of overactive imaginations.
While the physiological and psychological processes being uncovered by brain science in the study of brainwaves is sometimes complex and still being investigated, certain basic principles are well-established, easily understood, and helpful for achieving the most effectively use of brainwave entrainment when seeking relaxation, improved sleep, lowering of anxiety, or other goals. This important background information and scientific knowledge presented here includes: 
The huge problem will all such studies is that there is a clear placebo effect on any kind of mental performance whenever the subject is observed. Do any intervention, then measure performance, and the intervention and measurement are likely to cause an increase in effort and attention which will increase performance. This generic “placebo” effect needs to be factored out of any such study by proper blinding and controls in order for the results to have any meaning at all.
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. 

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.

Other than that the experience of those brainwave states is no different. Once we achieve a particular brainwave state using entrainment there is one significant difference to the experience and that is that we are usually still at a high level of consciousness. We’re not (hopefully) zoned out as we are when daydreaming or unconscious as we are when we’re sleeping. We maintain awareness and therefore we get to consciously experience what those brainwave states feel like in some detail.
Thanks for your appreciation of what I’m doing. I’ve been asked for help with autism a number of times over the years, so it’s something that I’ve often looked into and tried to find new information about. Unfortunately, I’ve yet to find any specific research relating to it and using the type of brainwave entrainment tones I use. There are a number of opinions and claims out here, but I’ve often found them to be conflicting. While some are recommending higher frequency gamma waves, others are recommending lower frequency alpha and theta waves while meditating.
I call the kind of intuitions and inspirations that come when we meditate and do these kinds of practices my “marching orders.”Okay, this is what I need to do. We’re not using our brilliant linear minds here; that’s not the place wisdom comes from. The place of wisdom is, again, relaxing into these states with loving-kindness, and then all the stuff can come out, whether we are dealing with our shadow issues or dealing with our light issues—the wisdom and gifts we haven’t yet brought forth that need to be birthed.
The I-Doser claims it can emulate prescription drug-like effects by listening to MP3's, to get stoned.[1] This is largely a moral panic by parents who flunked science fueled by the eternal quest by teenagers to get stoned, and stupid ones convincing their friends it works. It is really more of wishful thinking and making yourself disoriented by playing discordant sounds really damn loud. If you want to experience it yourself, you can always listen to Bjork Captain Beefheart dubstep.
Business executive and radio producer Robert Monroe started experimenting with brainwave entrainment and has a series of powerful out of body experiences using it. In 1971 he published his cult classic “Journeys Out of the Body” sharing his experiences. He later created one of the first audio entrainment companies called Hemi Sync, alongside the Monroe Institute of Applied Sciences.
The activity of neurons generate electric currents; and the synchronous action of neural ensembles in the cerebral cortex, comprising large numbers of neurons, produce macroscopic oscillations. These phenomena can be monitored and graphically documented by an electroencephalogram (EEG). The electroencephalographic representations of those oscillations are typically denoted by the term 'brainwaves' in common parlance.[4][5]