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.

“In order to get into a flow state, you have to calm a part of the brain, the posterior cingulate cortex, which is the source of what brain scientists call the default state, which is the non-focused state,” says Harris. “At any rate, it turns out that Holosync [binaural beats], when you listen to it, [calms that part of the brain] and so does traditional meditation. It’s just Holosync does it faster and more easily and more effortlessly. It turns down the posterior cingulate cortex and it enhances the other part of the brain that, when it’s enhanced, you can easily go into a flow state.”
Theta waves have another interesting characteristic. The Earth has a measurable resonance of 7.83 hertz known as the Schumann resonance. Because the Schumann resonance is a constant background frequency surrounding all life, it may play a special role in biological activity. The Schumann resonance frequency falls within the range of theta brainwaves and may have something to do with why these brainwave frequencies are so powerful. 
♥ I admit that I do not know much about brainwaves and can be swayed by suggestion (ah, the fickle subconscious), but since using this machine and sort of hiding the noise with other sounds or my own music so it is not so obvious to me, it has helped me get through my email correspondences and other online tasks with the focus that I need. Thank you so much for making this!
So using the example track above, the right ear is sent a 20Hz beat, compared to a 10Hz beat in the left ear.  As the right ear receives the higher frequency of beat, this works to increase the speed of the ‘left' brain hemisphere, which can be helpful for people with conditions like ADD, who are often found to have an abundance of slow wave activity in the left brain.
Alpha (12hz – 8hz) – Awake, but deeply relaxed. Simply closing your eyes will produce alpha brainwaves. This category is associated with daydreaming, visualization, imagination, light meditation. Brainwave expert Anna Wise called the alpha range the bridge between beta and theta. (More information can be found in Wise’ book The High-Performance Mind)

The quickest way to relieve stress is to release endorphins through exercise. An easy way to do this is through shaking and dancing, a form of expressive meditation that loosens your joints as well as clears the mind. It’s one of our favorite techniques to teach in conflict and disaster areas, such as Haiti. Start by standing with your feet shoulder-width apart, knees slightly bent, shoulders relaxed, and shake your whole body for a few minutes (we recommend 7-8 minutes). Then, stop for a minute or two and pay attention to your breathing and physical sensations. Finally, turn on fast music – anything that gets you energized, and allow the music to move you. Don’t feel the need to follow any specific dance moves, just do whatever feels good for you in the moment (it might help to close your eyes). Dance for about 5 minutes, or until you feel satisfied.

I wouldn’t personally recommend listening to delta wave frequencies for depression, so I’m not sure who advised you to do that? People with depression usually have a higher ratio of theta and delta wave activity, so I would normally recommend listening to high alpha wave and low beta wave frequencies, to help balance things. I have some 10Hz alpha tracks for serotonin release, which you can try for free on my YouTube channel here: https://www.youtube.com/watch?v=3NSUcuzpRcY&list=PLveg0IEcZWN6T86nhmSrdwG2kMQtcLRou. I also recommend you give these SMR (low beta wave) tracks a try: https://www.youtube.com/watch?v=HGTvBbrEwZQ&list=PLveg0IEcZWN7yaMaKr8F-eWHALk2_zGqY. I hope that helps.
A common element in recordings incorporating alpha and theta frequencies is a steady but barely perceptible rhythm of the frequencies themselves. This subtle and calming pulse mixes with sounds of gentle breezes, distant bird songs, and the slow progression of deep synth notes. Underneath this, below the audible sounds at sub 16 hertz levels, other frequencies intermingle, deepening the merging of conscious and unconscious mind.

Changes in neural oscillations, demonstrable through electroencephalogram (EEG) measurements, are precipitated by listening to music,[20][21][22][23][24][25] which can modulate autonomic arousal ergotropically and trophotropically, increasing and decreasing arousal respectively.[26] Musical auditory stimulation has also been demonstrated to improve immune function, facilitate relaxation, improve mood, and contribute to the alleviation of stress.[27][28][29][30][31][32][27][33] These findings have contributed to the development of neurologic music therapy, which uses music and song as an active and receptive intervention, to contribute to the treatment and management of disorders characterized by impairment to parts of the brain and central nervous system, including stroke, traumatic brain injury, Parkinson's disease, Huntington's disease, cerebral palsy, Alzheimer's disease, and autism.[34][35][36]