Aristotle has said that “[beauty] is the principal object of reasoning in the sciences and in their proofs.” Science and math are used to understand the world, from the planets, to the things we create, like music. People have studied songs and found mathematical patterns, like the use of phi, in many songs. Phi, or 1.618033988749895, is a ratio discovered by the greek architect Phidias, who used the ratio for building (The Geometry Center). The ratio is most commonly found in Fibonacci numbers, or 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. They were found by Leonardo Fibonacci, through a hypothetical scenario with rabbits. The scenario starts with one pair of rabbits. They take one month to mature, then another to have two kids. After each generation,
The general construction of music tends to use φ in either the timing of different sections, or the notes used. Playing notes corresponding to Fibonacci numbers is said to have a “growing” sort of sound. This can be useful depending on the mood of the piece. Many songs place their climax at about 61% of the way through the song, or 20 bars into a 32 bar song (Meisner). Most composers who use φ in their music do so based on timing. “There are even claims that Mozart used the golden mean in one of his compositions and that Beethoven used it in his fifth symphony”(Ayoub). For example, Mozart’s “Sonata n. 1 in C Major” has movements divided between 38 and 62 measures, around 61% into the song, and Beethoven’s Fifth Symphony has sections at around 61%. Bartok’s “Music for strings, percussion and celesta” has 55 measures before it’s climax, and 34 after, for a total of 89 measures; all three of these are Fibonacci numbers. The xylophone progressions also correlate to Fibonacci numbers. Erik Satie’s “Sonneries de la Rose+Croix” uses beat counts corresponding to the golden ratio, and in Claude Debussy’s “Dialogue du vent et de la mer”, Debussy divides his song into sections where the number of bars in each section is a Fibonacci number