Defense of The Harmony of the World

APPENDIX TO THE HARMONICS

I seek Harmonies as they appear from the center of the sun. In this way, the motion of the apsides original: motus Augium; the movement of the points in a planet's orbit farthest from the sun is not a physical motion, but rather a difference between real motions, and an intentional moving object: the star alone is the true moving body, and it moves not with one motion, but with several, according to the diversity of the center, the axis, and the body of the star. The reader will act much more advisedly if, setting aside those things which you write here so confidently about astronomical matters and the periods of the planets, they instead consult the astronomers themselves; they will find a far different period for Mars, and other details not a little dissimilar to yours.

But you ask (and you do not wish this to be taken as a foolish remark) since the motion of the planets occurs in time, why do I refuse the variety of "times" or measures? Because not everything joined with motion contributes to the Harmonies. For the variable phases of the Moon contribute nothing to them, even though the motion of the Moon does not proceed without them. Insofar as slowness or swiftness is defined by time in different ways, the primary consideration of time is valid, and I have not refused it, as I said. But I cannot hide this from my reader: there is a more elegant distribution of the voices of polyphonic music original: Vocum Musicæ figuratæ among the planets found in my work than here in yours. For regarding the Harmonies of two planets, it matters not how many days the entire period of each consists of; what matters is how slow or fast its motion is at any given moment. In a full period, all slownesses and swiftnesses are confusedly mixed together.

I was mostly content to mark my sounds with semibreves the equivalent of a whole note in modern music, not because of an ignorance of the many variations, but so that I might leave something in your work to which I could refer the reader—you who place such great value on the science of arbitrary musical notation.

As for Oedipus, do not send him to solve this riddle of yours for me, where you command my Triangular bodies to sound in some unknown proportion. I recognize no triangular body among the celestial objects, nor do I establish actual sounds in the heavens. I do indeed place a Tetrahedron a four-faced solid made of triangles between the orbits of Jupiter and Mars; but that is for the sake of spatial size, not for sound. Other causes are added later which arrange the motions of these planets into the proportion of concordant sounds.

You assert that the study of musical notes requires a massive investigation of causes, and that it is of no small importance which notes are "perfect." Therefore, I do not hinder your arbitrary causes for this arbitrary perfection; my discussion concerns natural causes. Or rather, you tell me: what natural cause taught us to mark sounds with these specific notes and no others? Or what is the natural cause why a note with a "tail" is the shortest; one without a tail is a semibreve; and a square one is a breve? For my part, I would have thought it more correct to measure time by the length of the tail, if the matter had been up to my own choice at the beginning.

Indeed, you are quite playful to demand Pauses from me as well, since there is no Harmony in a pause (the origin of which was the subject of my dispute), nor does the heaven ever "pause." I, however, wrote for the sake of celestial Proportions.

But let this analysis end with an argument that possesses a appearance not to be despised: for if measures of time must be employed in human music, it seems to you that they cannot be absent from celestial things either. You confirm this with a divine sentiment from Iamblichus a Neoplatonist philosopher who wrote on the soul and mathematics, which I would certainly wish to see radiating and illuminating Chapters 2 and 3 of my Fourth Book like a precious gem. Although a Christian man cannot accept the descent of Souls from the "intelligible world" from a Pythagorean Philosopher in any sense other than the one I expressed on page 121: namely, insofar as the image of the Creator naturally shines back in created Minds.

But I return to the argument. It does not follow, Robert, from human Song to celestial Motions. For those things which are Harmonic in human song are not taken from a Harmonic contemplation of celestial motions; instead, both the former and the latter—even by the authority of your own Iamblichus—descend from the Ideas of the intelligible world. Just as Iamblichus introduces a diversity of Souls themselves, of which one is more and another less affected by Harmonies; so much more are there diverse subjects in which Harmonies could be represented according to "more" or "less." In the motions of the Planets, they are represented according to only one respect of time; but in Song, according to two—a distinction I diligently emphasized in Book IV, page 125. Why say more? The matter speaks for itself. The human voice traverses intervals by leaps, not by continuous tension; planetary motions change from fast to slow by a continuous tension, not by a leap. By this negation, all temporary measurement of the duration of the same speed is removed. This, this one thing, Robert, is what I wish were more deeply infused into the divine power of your intellect: you would see immediately