# Picturing Sequences

#### Sequences in Music

Music are sounds put together in a pleasing way. There are many interesting mathematics in music. For instance, the Fibonacci sequence also appears in many places in music.

A song is a sequences of musical notes. Each musical note is denoted by a letter (A to G).

For example, for Twinkle Twinkle Little Star, the tune begins with the the following sequence (in C Major):

C C G G A A G F F E E D D C

We can turn a number sequence into music. Let’s do that with the Fibonacci sequence. There are only 12 different notes within an octave. So we must turn each number in the Fibonacci sequence into a number within 1-12, (or 0-11). One way to do this is to divide each number in the sequence by 12, and the remainder is the number we desire:

13 / 12 (remainder = 1) >>>> 13 mod 12 = 1

21 / 12 (remainder = 9) >>>> 21 mod 12 = 9

34 / 12 (remainder = 10) >>>> 34 mod 12 = 10

55 / 12 (remainder = 7) >>>> 55 mod 12 = 7

89/12 (remainder = ?) >>>>. 89 mod 12 = ??

This mathematical shorthand for taking the remainder is “mod.” We would say for example “13 modulo 12 is 1.”

The Fibonacci sequence taking the remainder of 12 becomes:

1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, ….

This can now be set to music. Listen here.