Pythagoras

2500 years ago Pythagoras discovered musical harmony in simple ratios of frequency. The blacksmiths' hammer attack sounded harmony at half the weight the (Pitch) frequency was twice as fast (Octave; 2/1), a pair at 2 to 3 sounded harmony (Perfect 5th; 2/3).

Pythagorean Temperament

Pythagoras made a system to divide the Octave through multiplying by 3/2 to get the Circle of Fifths and multiplying by 4/3 to get the Circle of Fifths in reverse order (Fourths).

Pythagorean Temperament worked nicely for music in those Medieval times. The Root, Fifth, and Octave were recognized, other Intervals, and changing key were of the devil!

• The Notes are the simpler ratio derived from either Fifths, or Fourths.
The system has what you might call... interesting features:

• Derived from either Fifths or Fourths the 13th note, instead of an Octave, is 531441:524288, and is called the Pythagorean Comma.

• Chords made with a Root and its Fifth sound more in tune compared to 12 Tone Equal Temperament!!! A Roots' Third however, is out to lunch!

Links:
•Pythagorean Comma Sound-Physics.com
•Music of the Spheres Here attributed to Johannes Kepler