Confucius, like Pythagoras, regarded the small numbers 1,2,3,4 as the source of all perfection. The area of mathematics called combinatorics enables one to count the many ways of combining pitches, i.e. The discrete whole numbers::: 2 1 0 1 2::: are particularly well suited for labelling the pitches, or the keys of the piano. Early Indian and Chinese theorists show similar approaches: all sought to show that the mathematical laws of harmonics and rhythms were fundamental not only to our understanding of the world but to human well-being. Music theorists often draw on the formidable powers of mathematics in their creation of conceptual categories. R.s awesomely fun elementary math site Read a math poem or learn a math song Challenge your students with a math story, poem, lesson, or exemplar. Their central doctrine was that "all nature consists of harmony arising out of numbers".įrom the time of Plato, harmony was considered a fundamental branch of physics, now known as musical acoustics. Though ancient Chinese, Indians, Egyptians and Mesopotamians are known to have studied the mathematical principles of sound, the Pythagoreans (in particular Philolaus and Archytas) of ancient Greece were the first researchers known to have investigated the expression of musical scales in terms of numerical ratios, particularly the ratios of small integers. Some composers have incorporated the golden ratio and Fibonacci numbers into their work. The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory. Elements of music such as its form, rhythm and metre, the pitches of its notes and the tempo of its pulse can be related to the measurement of time and frequency, offering ready analogies in geometry. Music theory has no axiomatic foundation in modern mathematics, although some interesting work has recently been done in this direction (see the External Links), yet the basis of musical sound can be described mathematically (in acoustics) and exhibits "a remarkable array of number properties".
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