Musical Math

Oct 26, 2021 | Littleton

Musical Math

 

Math and music may seem like an odd couple, but they actually have a lot in common.  Without math, music as we know it would not exist. A music composer creates music for others to enjoy and perform by using standard musical symbols that give instructions to the performer, just as the math symbols give us instructions on how to solve an equation. Understanding the counts and symbols in music helps us better understand math concepts.  Let's take a look at some of the ways math partners with music.

 

Math in Musical Notes

If you've ever learned to play an instrument or read music, you first learn what the symbols written on your sheet music represent and how they sound. But you may not realize how learning math can help you learn to read music. There are various formations of musical notes, but in this blog we will focus on the basics:

 

To start simply, say a quarter note equals one beat. Then, how many quarter notes do you think would equal two beats?  If you said "2," correct! (1+1 = 2). This is also known as a half note.

 

How many half beats equal a whole note? Using our basic math skills again, how many halves equal a whole?

 

 ½ + ½ = 1.

 

Two halves equal a whole. if one half note equals two beats, two half notes equal to 4 beats, or a whole note.

 

To make it a little more advanced, you can also have an eighth note and a sixteenth note.

An eighth note is half a beat- or ½ of a quarter note – or â…› of a whole note. So how many eighth notes would it take to equal 1 quarter note (or one beat in this example)? As we were just reminded, 2 halves make a whole, so 2 eighth notes would equal to one quarter note (â…› + â…› = ¼). A sixteenth note equals one quarter of a beat – or quarter note - or 1/16 of a whole note.

 

Music Timing and Math

Music is broken up into measures, or sections of a song. Each measure is then broken down further into beats. Now, how does the musician know how many beats to play in each section without guessing? The music will indicate a time signature, which you will always see written as a fraction. For example, you may see a time signature written as 4/4. The top number tells the musician the number of times that note is found in each measure, while the bottom number tells the musician the note that gets only one beat.

 

So, 4/4 means that there are 4 beats per measure and that each quarter note, ¼, is equal to one beat. So, 4 quarter notes will be played per measure, or 1,2,3,4 beats.  An 8/8 time signature means there are 8 beats per measure and the eighth note gets the one beat.

 

One example of a song in 4/4 time signature is the nursery rhyme, Old MacDonald.

 

Old--Mac--Don--ald--had--a--farm (pause)

"1"     "2"    "3"    "4"  "1"   "2"   "3"     "4"

 

There are 4 quarter note beats in each measure.

 

The same time signature is also used for another nursery rhyme favorite, Twinkle, Twinkle Little Star:

 

Twin--kle--Twin--kle--lit--tle--star.  (pause)

"1"     "2"     "3"   "4"  "1" "2"  "3"      "4"

How--I--won--der--what--you--are. (pause)

"1"   "2" "3"    "4"   "1"       "2"   "3"     "4"

 

The Fibonacci Sequence

The last math concept we will discuss that's connected to music is the Fibonacci sequence. In the sequence, the sum of the first two numbers equals the third, the sum of the second and third number equals the fourth, the sum of the third and fourth number equals the fifth, and so on.

 

The sequence is written as 1,1,2,3,5,8,13,21, and so on. You can see this sequence in music by looking at piano keys, as the piano has eight white keys and five black keys, each numbers in the Fibonacci sequence. Each set of 13 keys equals an octave, which is the distance between repeating notes on a piano, while 8 notes equal a scale (Do, Re, Mi, Fa, So, La, To, Do!). So the Fibonacci sequence of numbers is an integral part of math and music!

 

 

Math and music have a true connection, as both fields activate the same part of our brain. Listening to music has even been shown to help a student's ability to learn and perform better in math.

 

If you are a music lover who wants to learn to love math too, our Mathnasium center is here to help. We offer in-person and online live individualized math instruction for students in grades 2 through 12. Give us a call today or reach out to us online to schedule your child's no-risk free math assessment!

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