One of the earliest known applications of mathematics in music is
attributed to Pythagoras, a Greek mathematician best known for his theorem concerning
right-angled triangles.
According to the myth, Pythagoras was walking past a blacksmiths,
listening to the sound of the hammers on the anvils. After a while, he realised that
all but one of the hammers were sounding in harmony. Curious as to the reason,
Pythagoras made a thorough examination of the hammers and discovered that when their
masses were simple ratios i.e. 2:1 or 4:1, then the respective notes produced were in
harmony. On the other hand, the mass of the hammer producing the discordant note
wasn't in a simple ratio with any of the other hammers.
Although the absolute truth of this myth is questionable, it
illustrates the first real application of maths in music.
