Page "Acoustics" Paragraph 6

In the 6th century BC, the ancient Greek philosopher Pythagoras wanted to know why some musical intervals seemed more beautiful than others, and he found answers in terms of numerical ratios representing the harmonic overtone series on a string.

He is reputed to have observed that when the lengths of vibrating strings are expressible as ratios of integers ( e. g. 2 to 3, 3 to 4 ), the tones produced will be harmonious.

If, for example, a string sounds the note C when plucked, a string twice as long will sound the same note an octave lower.

The tones in between are then given by 16: 9 for D, 8: 5 for E, 3: 2 for F, 4: 3 for G, 6: 5 for A, and 16: 15 for B, in ascending order.

Aristotle ( 384-322 BC ) understood that sound consisted of contractions and expansions of the air " falling upon and striking the air which is next to it ...", a very good expression of the nature of wave motion.

In about 20 BC, the Roman architect and engineer Vitruvius wrote a treatise on the acoustic properties of theatres including discussion of interference, echoes, and reverberation — the beginnings of architectural acoustics.