Binaural beats are acoustically generated frequencies that match the frequency bands of brain waves and are therefore considered a means to inducing neurophysiological relaxation. There is, however, large dispute on the scientific quality and validity of extant research on binaural beats. Thus, the effect of a binaural 10Hz (Alpha) stimulation on subjective and physiological parameters... [Show full abstract]

Beating can also be heard between notes that are near to, but not exactly, a harmonic interval, due to some harmonic of the first note beating with a harmonic of the second note. For example, in the case of perfect fifth, the third harmonic (i.e. second overtone) of the bass note beats with the second harmonic (first overtone) of the other note. As well as with out-of tune notes, this can also happen with some correctly tuned equal temperament intervals, because of the differences between them and the corresponding just intonation intervals: see Harmonic series (music)#Harmonics and tuning.
Isochronic tones work just the same in delta as they do in alpha, theta and beta and they are widely used in the brainwave entrainment community to help people sleep. Like you, I’ve also seen some websites saying they don’t work in delta, but it’s a bit like the game of Chinese Whispers, where someone makes a comment and then after it gets passed around and shared a lot the message gets distorted and appears to be a fact. I don’t know of any scientific reason why they wouldn’t work in delta. I remember some people talking about this on a brainwave entrainment forum many years ago. They were saying they found isochronic tones a bit too abrupt for using to help them sleep and they preferred binaural beats, as they thought they were a more soothing sound. That was just a personal preference shared by a couple of prominent forum members at the time and some people then took that as a fact for everyone. That’s where I think that belief originated from.
In addition to potentially boosting sleep-promoting hormones, binaural beats may also reduce our perceptions of pain. A 2017 study found binaural beats used in combination with visual stimulation led to reductions in patients’ perception of acute pain. Other recent research showed binaural beats helped improve pain perception in patients with chronic pain.
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.
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.
With almost 100 years of research validating the effectiveness of brainwave entrainment, it’s no wonder why it’s used by thousands of people all over the world. What does the future entail in this exciting field? With the adoption of smartphones, virtual and augmented reality, and advancements in technology reducing the cost of EEG and other forms of biofeedback devices, the entrainment possibilities are endless.
When signals of two different frequencies are presented, one to each ear, the brain detects phase differences between these signals. "Under natural circumstances a detected phase difference would provide directional information. The brain processes this anomalous information differently when these phase differences are heard with stereo headphones or speakers. A perceptual integration of the two signals takes place, producing the sensation of a third "beat" frequency. The difference between the signals waxes and wanes as the two different input frequencies mesh in and out of phase. As a result of these constantly increasing and decreasing differences, an amplitude-modulated standing wave -the binaural beat- is heard. The binaural beat is perceived as a fluctuating rhythm at the frequency of the difference between the two auditory inputs. Evidence suggests that the binaural beats are generated in the brainstem's superior olivary nucleus, the first site of contra-lateral integration in the auditory system (Oster, 1973). Studies also suggest that the frequency-following response originates from the inferior colliculus (Smith, Marsh, & Brown, 1975)" (Owens & Atwater, 1995). This activity is conducted to the cortex where it can be recorded by scalp electrodes.  

Entrainment is a phenomenon by which some external sensory stimulation synchronizes brainwaves differently than the native rhythm. The most obvious example of this is photic driving – during an EEG the subject will have a strobe light flashed before them at various frequencies. The purpose of this is to see if it will trigger seizure activity. In many normal subjects the brain wave rhythm in the occipital lobes, which is the visual part of the cortex, will match its frequency to the frequency of the strobe light. This specifically is called photic driving, but the phenomenon in general is called entrainment.
Delta brainwaves are slow, loud brainwaves (low frequency and deeply penetrating, like a drum beat). They are generated in deepest meditation and dreamless sleep. Delta waves suspend external awareness and are the source of empathy. Healing and regeneration are stimulated in this state, and that is why deep restorative sleep is so essential to the healing process.
Brain waves are electrical activity patterns caused by the neurons of the brain communicating with each other. Brain waves can be detected using sensitive medical equipment such as an electroencephalogram (EEG) monitor. Brain waves provide an indication of the mental state of an individual. In other words, the appearance of brain waves is directly connected to what a person is doing, thinking or feeling. The different Brain states are: Gamma, Beta, Alpha, Theta, Delta. You have your own unique brain wave patterns that function habitually. Some of these brain wave habits are useful, and others need some fine-tuning. When your brain is functioning efficiently, your brain waves are “in sync” with your activity, but stress or lack of sleep can interfere with this natural harmonious relationship. To restore this harmony, at Gaia Meditation, we have developed a wide range of free audio programs, including meditation music, relaxation music, sleep music and plenty other Sound Healing programs.
It takes slightly more time to practice guided imagery, but this is a great way to leave your stress behind for a while and relax your body. Some find it easier to practice than meditation, as it allows more engagement of the conscious mind. You can focus on imagining relaxing environments you would love to visit, or on memories of your "happy place" for when you're stressed. You can play natural sounds in the background as you practice, to promote a more immersive experience.
Because the brain filters and interprets reality in a split-brained way, we tend to see things as separate and opposed, rather than as connected and part of the oneness spoken of by the great spiritual teachers (and, in the last few decades, by quantum mechanical physicists). Thus, at a deep level, the dual structure of our brain, in conjunction with brain lateralization, predisposes us to see and experience ourselves as separate from, and often in opposition to, the rest of the world—instead of experiencing the elegant interconnectedness between us and everything else. Our childhood associations and programming build on this inborn tendency by training us to seek this and avoid that, to move toward pleasure and away from pain, to do good and not bad, and so on. The greater the lateralization in the brain, the greater the feelings of separation—and the greater the feelings of separation, the greater the fear, stress, anxiety, and isolation.
If brainwave entrainment leaves you with unwanted side-effects (see below) or discomfort, you’re probably encouraging a range of brainwaves that are already excessive in some area of your brain. The way around this is to get a brain map to see what your brain’s strengths and weaknesses are, and see what (if any) brainwaves could use some encouragement. 
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