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Pythagoras on Harmony
Pythagoras

Pythagoras was the first person to devote a great deal of time and effort to work out a "theory of music" and much of what we use now is based on his research.

He realised that when a blacksmith struck his anvil, different notes were produced according to the weight of the hammer. That is, the “amount of weight” seemed to govern musical tone.

Next, he realised that if you take two strings with the same degree of tension, and then divide one of them exactly in half, when they are plucked the pitch of the shorter string is exactly one octave higher than the longer one.

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He also discovered that if the length of the two strings are in relation to each other 2:3, the difference in pitch is called a fifth.
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And if the length of the strings are in relation to each other 3:4, then the difference is called a fourth.

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Thus the musical notation of the Greeks, which people all over the world have inherited, can be expressed mathematically as 1:2:3:4.

Check that you understand what these words mean in this document
Blacksmith: a man working with iron.
Anvil: the tool on which the blacksmith places a piece of red hot iron and strikes it with his hammer.
Degree of tension: level of force.
To pluck (a musical instrument): to pull a string and release it quickly.
To inherit: to receive something that a person has left it to you.