Each pitch corresponds to a particular frequency, expressed in hertz (Hz), sometimes referred to as cycles per second (c.p.s.). The most important scale in the Western tradition is the diatonic scale but many others have been used and proposed in various historical eras and parts of the world. ( Ernst Chladni, Acoustics, 1802)Ī musical scale is a discrete set of pitches used in making or describing music. Musical form Ĭhladni figures produced by sound vibrations in fine powder on a square plate. The elements of musical form often build strict proportions or hypermetric structures (powers of the numbers 2 and 3).

Modern musical use of terms like meter and measure also reflects the historical importance of music, along with astronomy, in the development of counting, arithmetic and the exact measurement of time and periodicity that is fundamental to physics. Without the boundaries of rhythmic structure – a fundamental equal and regular arrangement of pulse repetition, accent, phrase and duration – music would not be possible. Confucius, like Pythagoras, regarded the small numbers 1,2,3,4 as the source of all perfection. 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. įrom the time of Plato, harmony was considered a fundamental branch of physics, now known as musical acoustics. Their central doctrine was that 'all nature consists of harmony arising out of numbers'. 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. 7 Musicians who were or are also mathematicians.

Music math pdf