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How composers from Mozart to Bach made their music add up

Article by Marcus du Sautoy. The Guardian, Friday 5 April 2013

“Works from The Marriage of Figaro and The Magic Flute to Schumann’s Lyric Suite betray their creators’ fascination with numbers.”

 

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Mozart and Mathematics

Article by Patrick Hunt. 

“Because it is so accepted and no coincidence how much music and mathematics intertwine, it would be possibly fruitful and definitely fascinating to note whether and how mathematicians and physicists themselves enjoy the music of Mozart and Bach perhaps above all others; vice versa, it is well known that many musicians also train in mathematics. It must not be forgotten that Pythagoras devised a musical tuning based on mathematical harmonics in frequency ratios of whole number intervals…”

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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.”