Math Vs Music

For centuries two distinct subject, mathematics and music, have coexisted rather harmoniously but still separate. Often this two subjects find themselves on opposite ends of the academic and social spectrum. Mathematics seem to give the world a sense of order. Formulas, algorithms, logarithms, geometry, etc., all fit into daily life on earth with out much effort and with great appreciation. Music on the other hand gives the world an escape from order and allows expression and individuality to take place. Whether it is classical or contemporary, rap or rondo, every person on earth has a form of music they like that seems to define them socially (at least in a musical sense). But what if these two distant relatives could come together. Can mathematics really live in music, and music in mathematics? Is it possible for such an ordered concept to be reflective and expressive, while at that same time maintaining order? Of the many mathematical principles that in this world, find those that fit to music can be hard. But take the idea of beautiful music and apply it to mathematics. What is beautiful in math? Some people may answer that question be saying the golden ratio holds the beauty in math. But take that a step backwards and one lands on the numerical sequence that gives us that golden ratio. That sequence is the well known Fibonacci sequence. This sequence, first mentioned by the Leonardo Fibonacci in his Liber Abaci in 1202 AD. From there however it was not really followed or talked about until the Frenchman Edouard Lucas in the nineteenth century named them and began using these numbers along (Debnath 355). The sequence, as determined and listed by Lucas begins 1,1,2,3,5,8,13... The sequence continues as the current number and the number just before it are added to get the next number (i.e. 3+5=8, 5+8=13, etc). But along with the Fibonacci sequence, Lucas found a sequence that still led to the golden ration, but it started 2,1,3,4,7,11. The same addition is used in Lucas numbers but the starting point of the sequence is different. But what about these numbers makes them beautiful mathematically? When these numbers are used consecutively they create patterns that are not only useful and convenient but also seemingly pleasing to the eye. For instance, a sunflower, a flower many see as beautiful contains seeds packed into spirals of consecutive Fibonacci numbers. And architecturally these same numbers create visually appealing and structurally sound buildings. The Ancient Greek Parthenon, The Eden Project in England, and the College of Engineering at the California Polytechnic State University, San Louis Obispo, used Fibonacci number and golden ratios in the building plans and many find these buildings visually appealing. But can a mathematical beauty like Fibonacci be transferred to music? Many, from musicians to mathematicians alike, seem to think so. …show more content…
Mathematician James J. Sylvester described Music “...as the Mathematic of Sense, Mathematics as the Music of Reason... The soul of each the same! Thus the musician feels Mathematic, the mathematician thinks Music,-Music the dream, Mathematics the working life, -each to receive its consummation from the other” (Fauvel). And famed composer Claude Debussy echoed “Music is the arithmeic of sounds as optics the geometry of light” (Fauvel). Both men, respected in their fields, had equal feelings about the relationship between mathematics and music. They not only live together, but feed each other, and complement each other. How many have not studied these relationships, but a few have and made it known that math and music can in fact be related and are related. Mario Livio in his work “The Golden Ratio” listed several instances where Fibonacci numbers are used in music. Livio looks at tuning styles, piano and violin building, and compositions that use mathematics. Most commonly associated with Fibonacci is the works Béla Bartók (1881-1945). A study of Bartok by musicologist Ernö Lendvai, concluded that “the chief feature of his chromatic technique is obedience to the laws of the Golden Section in every movement” (Livio 188). And while Bartók may have used these numbers, and he definitely lived in the time after they are named, some go back to J.S. Bach and claim the he used