# Music and Modular Arithmetic and their Similarities

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For many “right-brained” people, like myself, math is not an enjoyable concept. Aside from just counting, it seems that there is no correlation between people who practice differential calculus and people who practice Violin Concertos. When I am working on learning a piece of music, the only numbers I need to know are measure numbers and note numbers. But without realizing it, there is a pattern of numbers that is present in most all music, a basic scale. Though it is different for each key, most pieces stick to a basic eight note scale. Musicians understand the concept of the musical alphabet. It begins at A and ends on G and is repeated over and over. But this concept of the musical alphabet is the concept of modular arithmetic. If a piece is in the key of C major, the C~scale would begin on C and go up. Each semitone between the beginning C and the next octave could be numbered 1 to 12. However, at the number 13, the scale starts over at C again. The next whole tone, D, would be numbered 14. But there are only 12 notes in the chromatic scale so this new, higher D is 14-12 which equals 2. Therefore, 14 is 2 modulated 12.
This diagram shows a three octave scale beginning on a C and ending on an E. The original line of numbers is how all the notes would be counted without repetition. Each new line of numbers begins at 1 again at a new octave C. So without knowing it, musicians have incorporated modular arithmetic into the very fabric of musical theory through the musical