数学物理的第一个记录The first recorded facts in mathematical physics

36° The first recorded facts in mathematical physics. A remarkable discovery about numbers, claimed to have been made by Pythagoras, is the dependence of musical intervals upon simple numerical ratios. Thus Pythagoras is said to have found that for like strings under the same tension, the lengths should be 2 to 1 for the octave, 3 to 2 for the fifth, and 4 to 3 for the fourth. These results, apparently the first recorded facts in mathematical physics, are said to have led the Pythagoreans to initiate the scientific study of musical scales.

The manner of the above discovery by Pythagoras has been told repeatedly over the ages and runs as follows. While passing a blacksmith's shop one day, Pythagoras was arrested by the clang of four hammers swung in succession by four slaves pounding a piece of red-hot iron. All but one of the hammers clanged in harmony. Upon investigation, Pythagoras found that the differences in pitch of the four sounds were due to the different weights of the hammers. He persuaded the blacksmith to let him borrow the hammers for a short time. Taking the hammers home, he weighed them and then hung them individually to four strings of the same length and thickness. On plucking the strings, he noted that the emitted sounds corresponded to those made by the hammers striking the red-hot iron. By sticking a small lump of clay on the hammer responsible for the dissonance, he brought the emitted note for this hammer into harmony with the other three.

Now, curiously enough, there is a grave flaw in this often-repeated story, namely: the tone of a hammer striking a given anvil is independent of the weight of the hammer. A couple of minutes in a blacksmith's shop would have convinced any one of the erudite scholars who passed this legend on to their successors that the whole story is physically absurd.