To really appreciate music, you must understand this Math & history :
5 notes to 7 notes to 12 notes.
& fractions: 3/2, 3/4, 2/1 (octave)
Music = Math + History
1. Ancient China 600 BC 管仲 (5 notes 宫商角徵\zhǐ羽）
2. Pythagoras 450 BC (7 notes, Chords 和弦)
3. Modern Music: 十二平均律 (明朝 1600 AD 朱载堉- > Bach 1700 AD)
Pythagoras did not believe in Irrational numbers (sqroot 2) , so only 7 integer notes.
17CE Chinese 明朝 Prince invented 12 notes music, using a giant 81-row Abacus to compute the12th root of 2 (picture below) ：
[Greek: Stretch Against]
Pythagoras was a visiting scholar in Egypt where he saw the pyramid workers used a rope construction tool. The closed rope had 3 knots separated at distance apart in ratio 3:4:5. When it was ‘stretch against‘ on 3 poles formed a right-angled triangle.