Around 500 B.C. Pythagoras studied the musical scale connecting the sounds
with the length of the string that produces them, by using a simple mechanical
tool called monochord. Pythagoras determined a seven notes scale using just
three ratios between notes: 2:1 called octave (because it is the eighth note in
a seven-note scale), 3:2 called a perfect fth (because it is the position of the
fth note in a modern scale), 4:3 called a perfect fourth (because it is the posi-
tion of the fourth note in a modern scale). After he created the second note by
increasing the fth of another fth (9:4), and by using the 1=2 rule in order to
remain in the same octave, hence the second note corresponds to 9:8. Similarly: