And now, as to the ancient Octave system, which has been implicitly followed by the moderns, even in the present mathematical divisions of the scale.

Greek music did not attain so high a level for many centuries after the death of Pythagoras. The Greek scale adopted by the moderns was devised in the second century of the Christian era, and no further improvement has been effected since that date.

It is certain that Pythagoras did but import the Octave system from Egypt or Babylon, where it had existed for ages before his time, yet the vanity of certain Greeks, who were of a different stamp to Herodotus, led them to attribute the discovery to Pythagoras, because he was their countryman. To give circumstance and confirmation to this first fable, they concocted others as to the way in which he had been led to the discovery. These stories are such clumsy inventions, that they carry their own refutation.

The first is, that he was passing a blacksmith's shop, and, hearing the musical consonances of the Fourth, Fifth, and Octave, sounded by the various hammers on the anvils, he was induced to enter and to weigh the hammers. He is then said to have found the cause of the consonances in their respective weights, which were in the proportions of six, eight, nine, and twelve pounds. That of six pounds sounded the Octave to twelve; that of eight, compared with twelve, gave the interval of a Fifth; and those nine and twelve, sounded together, were at the interval of a Fourth. It is surprising how often this childish story has been repeated. Demolish it a thousand times and yet it appears again.