## The Connection Between Music and Mathematics

The famous Greek philosopher and mathematician Pythagoras once said, “there is geometry in the humming of the strings, there is music in the spacing of the spheres.” Although some may interpret this statement as mere poetry, Pythagoras was actually making a direct statement on the relationship between music and mathematics. You see, music is entirely intertwined with mathematics, so much so that even a basic major chord can be described mathematically. To further highlight the connection between music and mathematics, lets examine the mathematics in common musical concepts, such as wave frequencies, scales, intervals and tones.

## History of Studying Music & Mathematics

It’s common knowledge that music has long played for performance and pleasure, yet the study of music, particularly its relation to mathematics, has been going on for equally as long as music for performance. From Greeks to Egyptians to Indians to Chinese, nearly every ancient civilized culture has examined the connection between music and mathematics. Famous philosopher Plato was known to have an extreme interest in music, particularly harmonies, and helped highlight their importance within both an individual and society. Plato wasn’t the only philosopher who found the importance of studying the relationship between music and mathematics – ancient Chinese philosopher Confucius is said to have stated that within music are a number of fundamental truths.

## Wave Frequencies

When we listen to music, we assume that we are hearing a song or a collection of notes, but what our brains are actually processing are sound waves. For example, when a note is played, sound waves travel from an instrument or amplifier and reverberates on our ear drums, and it’s the frequency of this sound wave that tells our brain which pitch or note is being played (e.g. the E above middle C reverberates at approximately 329.63 Hz). Understanding sound waves, particularly the difference between octave notes, requires a bit of mathematics and physics. To find the frequency of a given note, take a constant note (which traditionally is the A above middle C, which contains a frequency of 440Hz) and multiply it by the twelfth root of 2 to the power of the amount of half steps away your desired note is from middle A (if the note is below middle A, make the power a negative). If that confuses you, don’t worry! Below is an example of how to find the frequency of middle C:

- Frequency of Middle C
- = 440Hz * 2 (1/12) to the negative 9th power (middle C is 9 half steps below A)
- =440Hz * 0.59460
- = ~261.625

- =440Hz * 0.59460

- = 440Hz * 2 (1/12) to the negative 9th power (middle C is 9 half steps below A)

## Intervals & Tones

If you were wondering why certain notes or intervals sound pleasing when played together, there is a mathematical explanation for this as well! As shown above, each note has a unique frequency, yet when combined, not all of these frequencies will make a beautiful harmonic chord. In fact, some note combinations can sound quite piercing and harsh. So what gives? Well, intervals that make a beautiful sounding chord tend to have sound waves that reverberate in similar patterns. Let’s look at a middle A major interval, which is A (440 Hz) and E (659.25 Hz). If examining each sound wave, with A on the bottom and E on the top, it will become clear that the frequency of E is approximately 3/2 larger than that of A, making an easy, digestible fraction. This simple mathematically relationship is largely why the two notes sound so pleasing together, whereas a more abstract fraction would result in a more dissonant, less pleasing sound.

## Music & Math in the Classroom

The connections between music and math can appear vast and complex, so to help, here are a few different ways to examine the relationship between music and math in the classroom:

- Pattern activities
- Have students analyze a pattern, then communicate the pattern’s rule
- Next, have them use the rule to predict what’s next

- Add and subtract notes and rests
- Examine compositions to better understand fractions
- Analyze time signatures to understand patterns, fractions, ratios, sorting and combinations

Music teachers can help combine music and math to bring a more holistic take on music and why notes sound the way that they do. Simply teaching the connection in class may inspire a new career or adventures in other kid students

## Learn More

Are you passionate about music and education? Well, why not share your passion with others by becoming the next graduate of Kent State’s online Master of Music in music education program. You can study entirely online and graduate in as few as 23 months – find out more today!

Image source: http://98five.com/wp-content/uploads/2016/03/maths-and-music.jpg

Source: http://www.ams.org/samplings/math-and-music

https://plus.maths.org/content/magical-mathematics-music

http://www.phy.mtu.edu/~suits/chords.html

http://www.phy.mtu.edu/~suits/NoteFreqCalcs.html

https://plato.stanford.edu/entries/confucius/

http://rdmodernresearch.org/wp-content/uploads/2015/11/94.pdf