Though ancient Chinese, Indians, Egyptians and Mesopotamians are known to have studied the mathematical principles of sound,[4] the Pythagoreans (in particular Philolaus and Archytas)[5] of ancient Greece were the first researchers known to have investigated the expression of musical scales in terms of numerical ratios,[6] particularly the ratios of small integers. Their central doctrine was that "all nature consists of harmony arising out of numbers".[7]