Focus, relaxation, creativity and problem solving are at their peak when the mind is relaxed. Similarly meditation and sense of well being are deeper when the mind is not filled with too many thoughts. All these are sometimes referred to as "Peak Performance" states of a person's brain. The brain is not a muscle but scientists find that in many ways it mimics certain nuances of muscles. One builds up strength and dexterity by training the muscles over a period of time. Repetitions are important. Similarly, the peak performance states when achieved daily trains the brain cells such that one can on-demand achieve these states.
All human beings feel calmer listening to the sound of waves or a gentle rain fall. Different sounds contain different combinations of frequencies. Some are soothing and some are jarring. Evolution appears to have trained the human brain to settle into relaxed states with some of the gentle sounds of nature, to an extent. When the thoughts in one's head exceed a threshold even these sounds loose their ability to relax. The ancient people figured out that certain chants appear to be far more effective in leading the brain to peak performance states. The relationship between such practices and the brain waves were not known a century back. The first recording of brainwaves was only done in 1924 by Hans Berger.
All ancient civilizations included chanting as an important part of their rituals. Settlers in to the American continent found Shamans in almost all red Indian tribes. The knowledge of most of these have disappeared. More people in the west are aware of the custom of chants of Tibetan monks due Hollywood celebrity following of Tibetan Buddhism. Gregorian chants are still heard in the Vatican. The Vedic chants are even more ancient and can still be heard in India. Brain waves of a listener of vedic chants show simultaneous activation of multiple activity centers in the brain, namely, alertness, relaxation, visiualization. The amazement about this is that these observations were in the brains that had no clue about the Vedas.