The relationship of the 7 primitive colors to the 7 musical tones

A very long time before Descartes, people had noticed that a prism exposed to the sun gives the colors of the rainbow.

We had often seen these colors painted on a white cloth or paper, in an order that is always the same.

Soon, from experiment to experiment, we went so far as to measure the space that each of these colors occupies.

Finally, we noticed that these spaces are to each other the same as those of the lengths of a string that gives the seven musical tones.

“I had always heard that it was from Kircher that Newton had drawn this discovery of the analogy of light and sound. Kircher in his Ars magna lucis et umbrœ, and in other books, calls sound the monkey of light. Some people inferred that Kircher had known these relationships; but it is good, for fear of misunderstanding, to put here before your eyes what Kircher says, pages 146 and following. ‘Those,’ he says, ‘who have a high and strong voice come from the nature of the donkey: they are indiscreet and petulant, as we know donkeys are; and this voice resembles the color black. Those whose voice is first deep, and then acute, come from the ox: they are, like him, sad and angry, and their voice corresponds to celestial blue.’

“He takes great care to strengthen these beautiful discoveries with the testimony of Aristotle. That’s all that Father Kircher, otherwise one of the greatest mathematicians and most learned men of his time, teaches us; and that’s how, more or less, all those who were not learned reasoned at the time. Let’s see how Newton reasoned.

“There are, as you know, in a single ray of light, seven main rays which each have their own refrangibility: each of these rays has its sine; each of these sines has its proportion with the common sine of incidence; observe what happens in these seven primordial traits, which escape by spreading out in the air.

“It is not a question here of considering that in this very glass all these traits are separated, and that each of these traits takes on a different sine: we must consider this collection of rays in the glass as a single ray, which has only this common sine A B; but at the emergence from this crystal, each of these traits, spreading out noticeably, takes on its own different sine; that of red (the least refrangible ray) is this line C B, that of violet (the most refrangible ray) is this line C B D (figure 44).

“With these proportions established, let’s see what this relationship, as exact as it is singular, is between colors and music. Let the sine of incidence of the white beam of rays be to the sine of emergence of the red ray, as this line A B is to the line A B C.

Given sine in the glass A B.

Given sine in the air A B C.

“Let this same sine A B of common incidence be to the sine of refraction of the violet ratio as the line A B is to the line A B C D. A B A B C D

“You see that point C is the term of the smallest refrangibility, and D the term of the greatest: the small line C D therefore contains all the degrees of refrangibility of the seven rays. Now double C D above, so that I becomes the middle, as below:

A I C H G F E B D.

“Then the length from A to C makes red: the length from A to H makes orange; from A to G, yellow; from A to F, green; from A to E, blue; from A to B, purple; from A to D, violet. Now, these spaces are such that each ray can indeed be refracted, a little more or less, in each of these spaces, but it will never leave this space that is prescribed for it; the violet ray will always play between B and D; the red ray, between C and I; and so on, all in such a proportion that if you divided this length from I to D into three hundred and sixty parts, each ray will have for itself the dimensions you see in the large figure attached hereto [See at the end of the note.]

“These proportions are precisely the same as those of musical tones: the length of the string which, when plucked, will produce C, is to the string which will give the octave of C, as the line A I, which will give red at I, is to the line A D, which gives violet at D; thus the spaces that mark the colors, in this figure, also mark the musical tones.

“The greatest refrangibility of violet corresponds to D; the greatest refrangibility of purple corresponds to E; that of blue corresponds to F; that of green, to G; that of yellow, to A; that of orange, to B; that of red, to C; and finally the smallest refrangibility of red relates to D, which is the higher octave. The lowest tone thus corresponds to violet, and the highest tone corresponds to red. A complete idea of all these properties can be formed by looking at the table that I have drawn up, and which you must find next to it.

“There is still another relationship between sounds and colors: it is that the most distant rays (violets and reds) come to our eyes at the same time, and that the most distant sounds (the lowest and the highest) also come to our ears at the same time. This does not mean that we see and hear at the same time at the same distance: for light is perceived at least six hundred thousand times faster than sound; but this means that blue rays, for example, do not come from the sun to our eyes any sooner than red rays, just as the sound of the note B does not come to our ears any sooner than the sound of the note D.

“This secret analogy between light and sound gives rise to the suspicion that all things in nature have hidden relationships, which perhaps will be discovered one day. It is already certain that there is a relationship between touch and sight, since colors depend on the configuration of the parts; it is even claimed that there have been people born blind who distinguished the difference between black, white, and some other colors by touch.

“An ingenious philosopher wanted to push this relationship of the senses and light perhaps further than it seems permissible for men to go. He imagined an ocular harpsichord, which must successively make harmonic colors appear, just as our harpsichords make us hear sounds: he worked on it with his own hands; he claims, in short, that one could play tunes to the eyes. One can only thank a man who seeks to give others new arts and new pleasures. There have been countries where the public would have rewarded him. It is undoubtedly to be wished that this invention is not, like so many others, an ingenious and useless effort: this rapid passage of several colors before the eyes perhaps seems likely to astonish, dazzle, and fatigue the sight: our eyes perhaps want rest to enjoy the pleasantness of colors. It is not enough to propose a pleasure to us, nature must have made us capable of receiving this pleasure; it is up to experience alone to justify this invention. In the meantime, it seems to me that any fair-minded person can only praise the effort and genius of whoever seeks to enlarge the career of the arts and nature.”

In the 1741 edition, the end of this last paragraph was abbreviated. After the words new arts and new pleasures, one read only: “For the rest, this idea has not yet been executed, and the author did not follow Newton’s discoveries. In the meantime, it seems to me that any fair-minded person can only praise the effort and genius of whoever seeks to enlarge the career of the arts and nature.” Table of colors and musical tones.

In the 1738 editions, as in that of 1741, after these last words, were the last three paragraphs of chapter xiii. This arrangement is in the 1748 edition.

It is Father Castel whom Voltaire designates here by the words ingenious philosopher, and whom he calls Euclid-Castel in his letter to Thieriot, of November 18, 1736. But in the letter of March 22, 1738, it is Zoile-Castel; in that to Rameau, of March 1738, it is the Don Quixote of mathematics;

In the letter to Maupertuis, of June 15, 1738, he disavows the praise he had given to Father Castel, and which he nevertheless still allowed to remain in 1741. (B.)