Harmony in mathematics
Try the following experiment. Fill a jar with water. Bang the jar.
Now take the same jar half filled with water. Bang the jar.
Repeat but taking the jar a third full, a quarter full…

Pythagoras discovered the notes all seemed to have a beautiful harmonic relationship.

Our bodies seem tuned to recognize some inherent beauty in the series of fractions 1, 1/2, 1/3… The sequence of notes are called the harmonics of the lowest note.

Harmonics are responsible for why a clarinet sounds different from a violin.