Maths & Music: Electric Guitar with Tom Rocks Maths!

In his latest video, popular maths YouTuber Dr. Tom Crawford finally embraces his rock star side and is learning to play the electric guitar! While we can’t wait to learn along with Tom, we can't help but think there must be a few beautiful equations and mathematical applications related to electric guitars! Here are three of our favourites:

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1. Fret Spacing X Pythagoras

Pythagoras’s main legacy is of course his formula of the relationship between the length of sides of a right-angled triangle, mainly thanks to it being named after him. However, there’s a lot more of his work that is well worth noting, particularly in relation to music! He noticed that the pitch of a musical note played on a guitar is inversely proportional to the length of the string. For example, halving the length of a string means it will vibrate twice as frequently, producing a note with a higher pitch - more precisely, the same note but an octave higher. Pythagoras used this concept to determine which fractions of a string would produce melodious-sounding notes, and it’s these exact fractions that are still used to place the frets on an electric guitar!

2.The body shape

In order to produce those beautiful melodies, a guitar's six (and sometimes more) strings have to be pulled pretty tight. This string tension can be up to about 60kg and even 90kg for a guitar with steel strings! For a guitar to support this force over its lifetime its form must be optimised: applying maths and physics allows us to find this ideal shape!

3. Math Rock

Slightly less technical than Pythagoras and frequencies… But still with plenty of maths and the occasional electric guitar, math rock is a whole sub genre of music! And don’t worry, it’s not just geeks singing about their favourite equations (although we’re keen for that too). Described as a progressive indie rock, what defines maths rock is its irregularity. For example, most music, especially rock, sticks to the classic 4/4 time signature but changing frequently between a 5/4 or 11/8 signature is a common feature for math rock. Influenced by musicians who also have PhDs in maths, such as Canada’s Dan Snaith, this genre's sound is also distinctive thanks to its angular melodies, extended chords, atypical rhythmic structures and irregular stops and starts.