It may surprise you that maths plays an integral part in producing music.
Every tune that blasts through your radio include elements of geometry, fractions, numeric patterns and wave frequency. Research even suggests that music with a prominent mathematical structure tends to become more popular.
Many mathematical theories are embedded into our music without our knowledge.
The “circle of fifths” is a mathematical formula for understanding tonal chord progression and exploring relationships between musical intervals. This theory assists in creating music that will be pleasing to the ears. It uses an actual circle diagram similar to the colour wheel learnt in primary school. It’s a way to visualise the 12 musical keys and put them in the best-suited order. It’s also used in music to help remember the notes that make up each key and groups similar notes together. This use of geometry is based on a theory created around 600BCE – that’s more than 2600 years ago! and even though music has enhanced dramatically since that point, it is still a fundamental theory used in music production.
According to legend, music was basically invented by none other than (‘the father of maths’) Pythagoras. The Greek philosopher was the first to identify that the pitch of a musical note directly correlates to the length of the string that produces it. Using an instrument like a guitar, creating a shorter string will create a higher pitch, whereas a longer string will create a lower pitch. Therefore, making the string different fractions in length will differ the sound.
Pythagoras even believed that these harmonious frequencies, so basically music, could be prescribed as a medicine if it followed the correct mathematical formula.
The use of different pitches isn’t the only time fractions pop into music.
Musical notes can be easily related back to fractions. The semibreve is worth four beats and is noted as a whole fraction. The minim is worth two beats, and so is half a fraction. The crotchet is worth one beat and is therefore equivalent to a quarter of a fraction. Understanding these equations and having the ability to read them will help create something beautiful, music. Interestingly, the human brain can interpret sounds as either ‘pleasant’ or ‘unpleasant’ by using fractions within music.
Patterns and rhythm are not only fun and make you want to dance; it’s also maths. These elements are another example of mathematics enhancing a positive cognitive response. The use of patterns is probably the strongest correlation between music and maths. Ed Sheeran’s biggest hit is “Shape of You”, which calls on the most repetition from any of his songs. As his’ ‘Mathematics (+–=÷x) Tour’ starts, perhaps this is a subtle ‘thank you’ to the art of maths.
The mathematics behind wave frequencies and how we actually hear music is quite interesting. A sound wave creates high or low air pressure, and all the sounds we hear are caused by these pressure changes. With music, the frequency at which these pockets strike your eardrums creates the pitch you hear.
For example, the trumpet has a frequency of about 500 Hertz. When the trumpet is played, 500 pockets of high air pressure pound against your eardrum each second. The air pockets arrive so quickly that one pocket strikes your ear every 0.002 seconds.
Maybe Pythagoras was right with his theory ‘that everything could be reduced to numbers and that the whole universe has been built using mathematics’.
It’s not uncommon for people to be good at both disciplines; maths and music. Learning music generally helps improve maths skills through signatures, beats per minute and formulaic progressions. Performing music reinforces parts of the brain used when doing maths. Music can also help decrease anxiety when learning maths. When children learn addition, subtraction, multiplication, or division (which can all be difficult), rapping and/or singing a lyric has been proven to help. It’s also a lot of fun!
ORIGO Education is focused on making learning mathematics fun, meaningful, and accessible for everyone.
So don’t be afraid to pick up an instrument and follow along with a song’s beat.