The reason this rule of thumb is so useful is because there is a huge market for simple answers. A genuine elegant solution (one that accomplishes more with less) is highly valuable in the marketplace. We are used to technology delivering new easy solutions to previously difficult tasks. While most improvements are incremental, there are occasional breakthroughs that transform our lives.
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.

Anyone who has sought out different methods for enhancing cognitive ability will probably have come across a technique known as Brainwave Entrainment. However, it is a fairly niche area of brain training, meaning that this form of stimulation is often overlooked in favour of more mainstream methods. The following outlines what Brainwave Entrainment actually is, how it is used, and some of the benefits attributed to it.
When you hit a tuning fork, tuned to a particular sound frequency such as the note B, and hold it close to the strings of a guitar, you will notice that the B string on the guitar will vibrate because it has entrained on to the same frequency of the tuning fork. Interesting enough, the other strings will not vibrate. Only the one with the same tuning as the tuning fork.

I have read something different about theta waves and learning languages. A University of Washington study tested students resting brainwave activity before learning French. They found that students with a higher amount beta/gamma and a lower amount of delta/theta activity were better at acquiring a second language. When you are dominant in theta, that is the lowest and most deeply relaxed awakened state you can be in. I think it would be much harder to really concentrate, fully understand and learn new information while in a theta state, so I would personally consider using theta while studying.
4. Be hesitant committing to any BWE system making wild claims. Profit fueled marketers with little to no experience in the BWE field have created a slew of low-quality entrainment systems on the market. These products typically make outrageous promises such as permanently enhancing the brain within minutes of use. Although BWE is a powerful method to improve the mind, it’s not a magic bullet.
So, what we’re doing is combining these two parts, the awakening of complete stillness and deep relaxation with the rhythmic sounds, and embedding all frequencies within the music from right at the upper limits of human hearing to the lower limits. There is multi-level entrainment within Journey—I’ve layered in everything I know about audio brainwave entrainment into this track. 
Tracks that move from alpha to theta can be a perfect vehicle for transitioning from a hectic day into a relaxing and rejuvenating sleep. Beginning with alpha waves takes you into a light but still alert meditative mind state where the difficulties of the day can be resolved and put to rest. Later, theta waves go deeper into the unconscious, preparing you for sleep and dreams.
By simultaneously combining the sounds of two didgeridoos, a desired state of consciousness can be induced in the listener. For example, when one didgeridoo is played in the key of Bb (fundamental frequency of 58 Hz) and a second didgeridoo is played in the key of C (65 Hz), the difference between the frequencies is manifested as a subtle pulsing (in this case 7 Hz). The listener’s dominant brainwave state will sync with this pulsation in a frequency-following response known as brainwave entrainment.
Beta brainwaves are further divided into three bands; Lo-Beta (Beta1, 12-15Hz) can be thought of as a 'fast idle', or musing. Beta (Beta2, 15-22Hz) is high engagement or actively figuring something out. Hi-Beta (Beta3, 22-38Hz) is highly complex thought, integrating new experiences, high anxiety, or excitement. Continual high frequency processing is not a very efficient way to run the brain, as it takes a tremendous amount of energy. 
“Stress” is a commonly used term, and it is often used with different meanings. The standard definition for stress that will be used in this article is the disruption of the body’s homeostasis or a state of disharmony in response to a real or perceived threat or challenge (8). The threatening or challenging situation is referred to as a “stressor.” When a person encounters a stressor, the body prepares to respond to the challenge or threat. The autonomic nervous and endocrine systems respond by producing the hormones epinephrine, norepinephrine, and cortisol. The result of this hormone production is a cascade of physiological reactions that make up the stress response. Epinephrine and norepinephrine are involved in the initial changes that take place to prepare the body to react and to prepare for a challenge. These responses include increases in heart and respiration rates, blood pressure, perspiration, and energy production (8). There also is a suppression of immune function, production of β-endorphin (the body’s natural pain killer), and increased acuity of the senses. These changes make up the fight-or-flight response, which prepares the body to cope with the stressor. If the stressor is perceived as negative or more as a threat than as a challenge, cortisol production is increased. Cortisol is involved in energy production but also suppresses immune function.
The pitch frequency measures and describes what a beat sounds like, i.e. does the isochronic beat have a deeper bass sound, or is it high pitched and sharper sounding? The beat waveform frequency describes how many times the beat is repeating per second, i.e. how fast it is beating. You don’t really need to concern yourself about the pitch frequency, as that doesn’t have a direct influence on brainwave entrainment and doesn’t play a part on the measurement on an EEG. I only mentioned it because you were referring to humans not being able to hear below 20Hz. I change the pitch frequency just to suit the mood of the track. For tracks that are to be relaxing, for meditation or sleep, I tend to use a lower pitch frequency so it sounds deeper and more relaxing and I never have that lower than 100Hz. For an energizing, high focus track I might use a more higher pitched 200Hz isochronic tone, because that is sharper sounding and less likely to make you feel sleepy. That’s all you really need to know about the pitch frequency.
Theta brain waves occur most often in sleep but are also dominant in deep meditation. Theta is known to be a dreamlike state with vivid imagery, intuition and information beyond your normal conscious awareness. This state of mind is excellent for psychic experiences to occur, as well as astral projection and extended remote viewing. To reach this state without falling asleep while meditating takes practice.
Everyone experiences stress, and not all stress is bad. Individuals who experience acute episodic or chronic stress are at increased risk for developing stress-related health problems. Research supports the idea that exercise can improve the way the body handles stress, and it can provide a time-out from stressors. Exercise programs meeting the current recommendations for health included within a stress management program can be effective in stress reduction. However, it is important to consider the client’s stressors and physical activity barriers, activities the client will enjoy, and the exercise setting. Prescribing exercise for clients seeking stress management is recommended, but fitness professionals should recognize that some clients will need additional assistance for managing stress and major life stressors.
Since opening their online store in 2011, Binaural Beats Meditation has served “hundreds of thousands” of customers, according to James Matthews, the site’s customer happiness manager. “We continue to see an increase in interest… from individuals, but increasingly so from therapists using the music to help clients, health and wellness organizations, and businesses around the world.”
way of describing it—at both theta brainwave frequencies. And then there are also 40-Hz gamma frequencies, the frequency that came through a lot when the Dalai Lama sent some Buddhist monks to have their brain waves studied as they were meditating and doing loving-kindness practices. Gamma is associated both with heightened awareness and also with loving-kindness practices, metta practices.

Insomnia and PTSD for most of my life are real bears that I wrestle with every night. A brain neural-therapist (for lack of a better description) said that this kind of sound recording may help. It is not music. When I remember to play the disc, I fall asleep within the first 5-8 minutes. One day I played the disc while cleaning and I was very surprised to hear how much of the recording I never recall hearing before. That's why I know how long it takes to fall asleep.
The pitch frequency measures and describes what a beat sounds like, i.e. does the isochronic beat have a deeper bass sound, or is it high pitched and sharper sounding? The beat waveform frequency describes how many times the beat is repeating per second, i.e. how fast it is beating. You don’t really need to concern yourself about the pitch frequency, as that doesn’t have a direct influence on brainwave entrainment and doesn’t play a part on the measurement on an EEG. I only mentioned it because you were referring to humans not being able to hear below 20Hz. I change the pitch frequency just to suit the mood of the track. For tracks that are to be relaxing, for meditation or sleep, I tend to use a lower pitch frequency so it sounds deeper and more relaxing and I never have that lower than 100Hz. For an energizing, high focus track I might use a more higher pitched 200Hz isochronic tone, because that is sharper sounding and less likely to make you feel sleepy. That’s all you really need to know about the pitch frequency.
There's nothing like anxiety to annihilate your sense of humor. It would follow, then, that it's impossible to feel stressed when you're hunched over in a fit of giggles. Studies have shown, in fact, that laughter not only relieves tension, but actually improves immune function. Swap jokes with your friends. Rent a funny movie. Stop taking things so seriously!
How does brainwave entrainment work? Consistent, precisely engineered audio frequencies in the form of binaural beats cause the brain’s frequencies to match the stimulus. Your brain perceives two beats with slightly different frequencies (which are inaudible to the ear) through your headphones. It takes the difference between the two, and matches its own frequency to it. This is called the “frequency following” response.
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