There is geometry in the humming of the strings; there is music in the spacing of the spheres. —Pythagoras
Music and mathematics overlap in many different ways and have a close relationship that goes back thousands of years.
You do not need to know your times tables to play more beautifully, but numbers and patterns tell us much information about a piece of music.
Music is divided into sections called measures, and each measure has equal amounts of beats.
Each piece of music has a time signature that gives rhythmic information about the piece, such as how many beats are in each measure. A time signature is like a fraction, with one number on top and one on the bottom.
All of the notes and rests in music have numerical connections because they each have a certain amount of beats. Musicians need to understand the value of these fractions and notes to count the music correctly.
Pythagoras realized that different sounds could be made up with different weights and vibrations. This led to the discovery that a string’s vibrating length can control its pitch. The shorter the string, the higher the pitch, and the longer the string, the lower the pitch.
Probably the closest connection between music and math is that they both use patterns. Music has repeating choruses and sections of songs. You can study everything in music from different mathematical perspectives, including geometry, number theory, trigonometry, differential calculus and signal processing.
An article researched by Dr. Frances Rauscher says that when young children are provided with instruction on musical instruments, they score much higher on tasks measuring spatial-temporal cognition, hand-eye coordination and arithmetic. Part of this is because of the overlap between math skills and music skills.
A literate musician is required to continually subdivide beats to arrive at the correct interpretation of rhythmic notation. The visual and special skills that a child exercises every time they practice strengthens their mental-physical connection. The slow work of practice, paying attention to details and the discipline it takes to learn an instrument are preparations for building strong math skills.
The next time you hear or play classical, rock, folk, religious, ceremonial, jazz, opera, pop or contemporary types of music, think of what mathematics and music have in common and how mathematics is used to create the music you enjoy.