Math and Music

I love math but I also enjoy playing music.  I usually play french horn in the local community band.  I've often wondered what type of connection music has to math.

It is well known that music helps teach fractions and ratios because its a part of learning to play music. That said, no one is sure whether musical training encourages mathematical ability or mathematical skill promotes musical ability or whether the skills develop at the same time.

Although there is some research to indicate that musicians score higher on standardized tests, it cannot be stated with total certainty it applies to every one. 

It has been suggested this occurs because most students learning to play instruments tend to come from a higher socioeconomic class.

Others have suggested people might have to have  high cognitive processing skills necessary to  drive both skills.  One example is the use of executive functions which helps people adjust to the changing demands of the tasks. Executive functions are defined as the ability to plan, organize, and complete tasks.

 Research has shown that having good executive functions is a good indicator of academic achievement.  Playing music requires a person to determine the key signature, tempo, repeats, etc before playing while completing key and tempo changes during the piece in order to produce the music. 

If you think about it, much of mathematical learning is looking for patterns, just like in music.  So many pieces repeat the melody throughout a piece or in the more daring ones, the tempo changes quite rapidly from 3/4 to 4/4 and back again. 

In addition, in the past music has been mathematically analyzed and created.  It has been broken down into waves each at a specific frequency.  Furthermore, people have noticed the relationship between numerical ratios and fixed sounds.  People have also applied group theory's framework of symmetry to analyzing music.

If you think of musical transposition, inversion, and retrogression as group operations, this can shed new light on older compositions.  It's been found that composers have used geometric type transformations as a device when creating music.  Even those who play the music often have to transpose or translate the notes because the parts are not written in the normal key.

Such a nice interweaving of math and music.  Let me know what you think, I'd love to hear. Have a great day.