Music and maths are interlinked!

One of the earliest known applications of maths in music was applied by Pythagoras, a Greek mathematician who is best known for his theory concerning right-angled triangles (Pythagoras’ Theorem). According to sources, Pythagoras was walking past a blacksmiths listening to the sound of hammers on anvils, and after a while, he realised that all of the hammers were in perfect harmony - except one. Upon thorough examination of the hammers, Pythagoras found that when the masses of the hammers were in simple ratios (i.e. 3:1, 4:1, 2:1, etc.), the notes produced were in harmony. However, the mass of the hammer making the dissonance wasn’t in simple ratio with any of the hammers. Although the truth of this is questionable, it still shows an application of maths in music.

The harmonies that Pythagoras was talking about were almost certainly octaves (the same note at a higher pitch). Today, this pattern can be seen in the frequencies of various musical notes.

For instance, the frequency of Middle C has a frequency of 262Hz.

The C an octave above middle C has a frequency of 524Hz, which gives a ratio of 2:1 with the middle C.

This pattern continues for octave intervals no matter what the note (i.e. the ratio of G and G an octave below would be 1:2).

Therefore, all notes can be written as n x 2^i, where n is the frequency one of the octaves of the note, and i is an integer.