A Doubt Concerning Pythagoras’s Discovery

Now upon the said discovery of Pythagoras a doubt arises: in what manner could concord issue from those two hammers which contained the Sesquioctave proportion, which is the form of the Tone, an interval that is without any doubt dissonant? To this one may answer and say that it is a reasonable thing that the Smiths of those times did not strike all at one and the same time in beating with their hammers, but rather one after another, as we see and hear done at the present day.

Whence it is credible that, when the Philosopher passed by chance near the smiths’ workshop, the first thing which presented itself to his perception was a certain harmonic order of sound, and that it was very pleasing to him; by which he was moved to wish to investigate the reason of the harmonic concords.

But because, the hammers striking one after another, the Tone could not offend his hearing as it would have offended it had they all struck at a single stroke — seeing that Consonance and Dissonance are heard between two sounds which strike the hearing at one and the same time — it cannot therefore be said that Pythagoras in that act heard anything dissonant such as might offend him; and the more so since he had first removed the Fifth hammer, as Boethius says, because it did not agree with the others.

And that this is true, Macrobius manifests clearly, saying that as Pythagoras passed by chance along a public way, there came to his ears certain sounds which answered one another in a certain order, and which arose from the hammers of certain Smiths who were beating a piece of red-hot iron. And he says that they were sounds which answered one another in a certain order; and he does not say that they were consonant sounds.

For which cause we may see that such an interval could give him no annoyance, just as we may hear from ourselves in every modulation of our own that not only in proceeding by a like interval, but by any other whatsoever, provided it arise from sonorous and harmonic numbers, the sense is not offended.

The Philosopher having then found that this proceeded from the quantity of the weight of each hammer, he began from the weights he had found to investigate the musical proportions and the harmonic numbers, making the experiment of one sound against the other by their weight; and he found their reason in the numbers named, and came to know those proportions which gave the consonances, and those which made the dissonances.

Whence Boethius, in chapter 10 of the first book of his Music, wishing to show in fact those proportions which were the true forms of the consonances, in speaking of each one of them adds to it one of these words, Consonantia or Concinentia; but when he comes to the Sesquioctave, without adding anything to it, he says only that the Tone sounded — meaning to infer that such a proportion was not placed by the Philosopher in the number of those which make Consonance.