Pythagoras, an Ancient Greek philosopher who is known mostly for his mathematical findings, did much active research to understand music. He wanted to understand the effects of harmonics upon human behavior and intervals within music and their linkage to the cosmos. For instance, the flute was believed to cause stress or madness and strings (the lyre) brought out serenity. In addition, the only harmonious intervals in music were considered to be the octave, the fourth and the fifth.
| 8 : 16 or 1 : 2 | Octave | diapason |
| 4 : 6 or 2 : 3 | Fifth | diapente |
| 9 : 12 or 3 : 4 | Fourth | diatesseron |
The Pythagoreans supposedly found them by experimenting with a single string with a moveable bridge, and found these pleasant intervals could be expressed as the ratio of whole numbers.
