Visual physics and mathematics/Pythagoras and the origin of harmony



The waves propagate but the sphere and the air around it oscillate around their equilibrium position and do not propagate. A vibration, or oscillation, is a periodic movement, a movement that returns to its starting point and starts again. The period $$T$$ is the duration of the repeating movement, the duration of a round trip. The frequency $$f$$ is the number of periods per unit of time, therefore the inverse of the period:

$$f = 1/T$$

If the unit of time is the second (s) then the unit of frequency is the Herz (Hz).

The movement above has a period equal to 3 s and a frequency equal to 1/3 Hz.

Even circular motion is an oscillation:



The human ear perceives as sounds vibrations whose frequency is higher than a few tens of Herz (the lowest sounds) and lower than approximately 20,000 Hz (the highest pitched sounds).

The fundamental mode of vibration of a string is the widest and the slowest: a single belly and no node. Its period is proportional to the length of the string:



Pythagoras discovered that musical chords appear when the lengths of the vibrating strings are in simple ratios (for strings that are equally taut and have the same mass per unit length). The octave is the chord between two strings whose lengths are in the ratio of 2 to 1, as in the animation above. The perfect fifth is caused by a ratio of 3 to 2:



The perfect fourth, 4/3:



The major sixth, 5/3:



The major third, 5/4:



Numbers are the cause of music which is the cause of everything that is, since all beings dance and sing. Numbers are therefore the cause of everything that is. “Everything is number” is the principle of the Pythagoreans.