*by kathyz, This post originally appeared at Function of a Rubber Duck.*

Music… almost everyone likes it, whether it is jazz, rap, country, or classical. Music is a form of art, because it is expressive and free in style, allowing individuals to compose different songs and listeners to interpret the same piece of music in different ways. However, music is more than just an art. Is it also a science.

In order for notes to sound good together, their frequencies have to be a specific multiple of another. For example, octaves have frequencies factors of two apart: middle C is 256 Hertz while an octave up, C is 512 Hertz. (Although this value can vary with tuning notes to slightly different standards.) The perfect fifth, a “nice sounding” interval, has a ratio of 3:2 for the two notes. In contrast, when you have a not-so-perfect ratio such as 29:7, the two notes probably won’t sound that good together.

(above: since the frequencies form a geometric sequence, it graphs as a curved line.) |

Each note on a piano is tuned so that no matter what key you play a scale in, the notes will always sound nice together. This is made possible by equal temperament, meaning that in a scale, starting at frequency X, the next note would have a frequency of Xa, the one after that Xa^2, followed by Xa^3, Xz^4, etc. We can use logs and some algebra to find the exact value of a: 2 to the power of 1/12. Therefore, even if we start at a higher note, the ratio between every two notes will always be the same, and the scale will sound the same as well.

Music is an art and a science, and for more information on how it relates to math, visit my next blog post when it comes out! (:

*About this contributor: An idoyncratic gr10 student who loves playing the piano, flute and violin and enjoys reading historical fiction and Edgar Allan Poe. She completes jigsaw puzzles in her spare time and aspires to learn Latin as well as publish a children's book in the near future.*
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