Humans have known about the octave at least since Sumerian times, i.e., that its sound is pleasing and harmonious. Chimps and some other animals enjoy it, as well. Perception first discovered the octave - perhaps even before there were homo sapiens - and Sumerians were sufficiently captivated to write about it beginning around 3,000 BCE.
Starting around 4,700 years later, the calculus was invented, the existence of sound waves was discovered, and devices to measure frequency were invented. Science was astonished to discover that the octave is a doubling of the frequency of a sound wave, and that the octave is the first harmonic in a series of overtones. The octave has been called "the basic miracle of music."
So, that is the short history of the octave, which was perceived to be harmonious, and has been used to tune instruments in most musical systems, long before it was measured. See this for more:
http://proaudioencyclopedia.com/the-history-of-audio-and-sound-measurement/
Starting around 4,700 years later, the calculus was invented, the existence of sound waves was discovered, and devices to measure frequency were invented. Science was astonished to discover that the octave is a doubling of the frequency of a sound wave, and that the octave is the first harmonic in a series of overtones. The octave has been called "the basic miracle of music."
So, that is the short history of the octave, which was perceived to be harmonious, and has been used to tune instruments in most musical systems, long before it was measured. See this for more:
http://proaudioencyclopedia.com/the-history-of-audio-and-sound-measurement/