Did Mozart use the Golden Section?
“Considerable evidence suggests that Mozart dabbled in mathematics. According to his sister, Wolfgang “talked of nothing, thought of nothing but figures” during his school days. Moreover, he jotted mathematical equations in the margins of some of his compositions, including Fantasia and Fugue in C Major, where he calculated his odds of winning a lottery. Although these equations did not relate to his music, they do suggest an attraction to mathematics….”
“To describe the golden section, imagine a line that is one unit long. Then divide the line in two unequal segments, such that the shorter one equals x, the longer one equals (1 – x) and the ratio of the shorter segment to the longer one equals the ratio of the longer segment to the overall line; that is, x/(1 – x) = (1 – x)/1. That equality leads to a quadratic equation that can be used to solve for x, and substituting that value back into the equality yields a common ratio of approximately 0.618. That value has been given many names, including the golden ratio, the golden number and even the divine proportion.”
mathemusic 