The Beauty of Mathematics in Music : Mathematics behind Musical Instruments

The attempt to structure and communicate new ways of composing and hearing music has led tomusical applications of set theory, abstract algebra and number theory. Some composers haveincorporated the golden ratio and Fibonacci numbers into their work.Though ancient Chinese, Indians, Egyptians and Mesopotamians are known to have studied themathematical principles of sound, the Pythagoreans (in particular Philolaus and Archytas) ofancient Greece were the first researchers known to have investigated the expression of musicalscales in terms of numerical ratios, particularly the ratios of small integers. Their centraldoctrine was that all nature consists of harmony arising out of numbers.From the time of Plato, harmony was considered a fundamental branch of physics, now knownas musical acoustics. Early Indian and Chinese theorists show similar approaches: all sought toshow that the mathematical laws of harmonics and rhythms were fundamental not only to ourunderstanding of the world but to human well-being. Confucius, like Pythagoras, regarded thesmall numbers 1,2,3,4 as the source of all perfection.