The Connection Between Math and Music

Since ancient times, the Chinese, Hindus, Persians, Egyptians, Israelites, and Greeks experimented in music. The word music comes from the Latin word musica, which was derived from the Ancient Greek word mousike, meaning “the art of Muses.” Greek Mythology portrays the Muses as the Greek Goddesses of the Arts and Sciences. Gottfried Leibniz, a philosopher and mathematician, stated that “music is a secret exercise in arithmetic of the soul, unaware of its act of counting.” Greek philosophers, such as Plato and Aristotle, are credited with discovering music’s mathematical foundation, and registering music in the quadrivium of mathematical arts alongside geometry, arithmetic, and astronomy. They assigned various geometric shapes different tones, numbers, names, colors, and forms to create drawings which described the musical notes that constituted a melody. In addition to mathematical properties embedded in music theory, there are contentious implications that have already influenced many aspects of musical composition.

Pythagoras (6^th Century B.C.) was the first Greek Philosopher to take notice of the harmonic ratios between different pairs of notes to create the diatonic scale (the traditional western scale). He thought that harmonies were controlled by mathematical proportions. Pythagoras used a monochord to test frequency ratios. This instrument features a single string with adjustable bridges that allow the string to be proportionately divided.  A 2:1 ratio produced similar sounds and therefore became the interval of an octave and the basis for the other 11 pitches between each octave. By experimenting with his theories, Pythagoras deducted that music follows a series of natural laws and can be broken down into an exact science. Therefore it was widely believed by the Pythagoreans of ancient Greece that the laws of harmonic intervals could be applied to all characteristics of nature. The Pythagoreans central belief was that “all of nature consists of harmony arising out of numbers.” Many objects in nature approximate another one of Pythagoras’ discoveries: the gold ratio (1.618 or “phi”; pronounced fee). Another example is found in the progression of natural elements in science according the ascending order of their atomic weights substantiated that every eighth element possessed similar properties. In modern chemistry, this pattern is called the Law of Octaves. 

Patterns are evident throughout music. The Greek Philosopher, Plato, once said, “Mathematics was born from music.” Aside from time, rhythm, and meter, music consists of many other calculated principles that are exemplified in areas of math such as abstract algebra, set theory and number theory. The mathematical structure of a single piece of music commonly features underlying patterns. For instance, Pachelbel’s Cannon in D features a repetitive structure, rhythmic beats and looping breaks that construct the song. Composers can musically vary themes by rearranging a single melodic phrase over and over again. Studies have been conducted on the relationship between the aesthetics of harmonic ratios and the patterns in songs. The results show that some music becomes popular due to its mathematical structure. 

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