The Universal Harmonies of all the Six Planets, as if in Common Counterpoint, Occur in Four Parts

Now there is need, Urania,*”” of a grander sound, while I ascend by the harmonic stair of the celestial motions to higher things, where the true archetype of the fabric of the world is laid up and preserved.

Follow me, modern musicians, and attribute it to your arts, unknown to antiquity: in these last centuries, Nature, always prodigal of herself, has at last brought forth, after an incubation of twice a thousand years, you, the first true offprints of the universal whole.*

By your harmonizing of various voices, and through your ears, she has whispered of herself, as she is in her innermost bosom, to the human mind, most beloved daughter of God the Creator.

What harmonic proportions the pairs of neighboring planets embraced at the extremities of their motions has Shall 1 be committing a crime if I demand some been expounded above. However, it happens very ingenious motet from individual composers of this age for this declaration?

The royal psalter"’rarely that the two, especially the slowest, reach and the other sacred books will be able to supply their extreme intervals at the same time. For ex­ a suitable text for it. Yet take note that no more than six parts are in harmony in the heaven." ample, the apsides of Saturn and Jupiter are For the Moon warbles her solo independently, about 81 degrees apart. Therefore, during the attending the Earth as at a cradle. Compare the symbols; in making the book, I promise to be a time in which this separation between them, in zealous overseer of the six parts.

If anyone particular leaps of twenty years, measures out expresses more closely the heavenly music de­ the whole Zodiac, eight hundred years slip scribed in this work, to him Clio pledges a wreath, Urania pledges Venus as his bride. by.**® Yet the leap which concludes the eighth

century does not come precisely to the actual apsides; and if it should be a little further out of place, another eight hundred years must be awaited, to make it reasonably possible to look for a leap which will be more fortunate than the former one, and that must be repeated as often as the measure of the error is contained within the extent of half a single leap. The other individual pairs also produce such periods, though not so extensive. In the meantime, however, other har­ monies of pairs of planets occur, which are not between motions which are both extreme; but with an intermediate motion, either one or both, and those at different tunings, so to speak. For as Saturn is extended from G to and a little further, and Jupiter from io d and beyond, therefore, the following harmonies at a diapason above can occur be­ tween Saturn and Jupiter; either of the thirds, and a diatessaron."’* Of the thirds indeed, either one can occur through a tuning which covers the extent of the other; whereas the diatessaron can occur over the extent of a major tone."^ For there will be a diatessaron not only from the G of Saturn to the cc of Jupiter but also from the A of Saturn to the dd of Jupiter, and over all the intermediate notes from the G and A of the former to the cc and dd of the latter.“® However, the diapason and diapente occur only at the apsidal points. However, Mars which takes a larger interval of its own has acquired the feature that it also makes a diapason with the superior planets, by a certain lati­ tude of tuning."’ Mercury has occupied an interval o f a size such that it generally sets up all harmonies with all planets, within one of its own periods, which is not more extensive than the space of three months. The Earth, on the contrary, and Venus much more, on account of the narrowness of their own intervals, restrict their harmonies not only with the other planets, but most of all their mutual harmonies with each other, to a remarkably small number. But if three planets must combine together into a single harmony, many alternations must be awaited. However, there are many harmonies, so that they occur all the more easily, when all the nearest planets catch their neighbors; and triple harmonies between Mars, the Earth and Mercury seem to occur rather often. However, harmonies of four planets now begin to be scattered over centuries, and those of five planets over myriads of years. However, an agreement together of all six is hedged about by very long gaps of ages; and I do not know whether it is altogether impossible for it to occur twice, by a precise rotation, and it rather Character of the demonstrates that there was some beginning of time, from which every •>‘8’”"’’^ age of the world has descended."* But if there could occur one single sixfold harmony, or one out­ standing one among several, that undoubtedly could be taken as char­ acterizing the Creation. We must therefore enquire whether and in how many patterns altogether the motions of all the six planets are combined into one common harmony? The method of enquiry is to begin from the Earth and Venus, as these two do not make more than two consonances, and those (which contains the cause of this phenomenon) through very brief coincidences of the motions. Come, therefore, let us first set up two, so to speak, skeletons of the harmonies, individually bounded by the pairs of extreme num­ bers (by which the terms of the tunings are represented), and let us set out to find what agrees with them out of the variety of motions permitted to each planet. Let the first skeleton have as the proportion between the Earth and Venus 3:5, and at the lowest tuning the daily motion of the Earth at aphelion, 57 minutes 3 seconds, at the highest tuning the motion of Venus at perihelion, 97 minutes 37 seconds."^ Therefore, the rest will be as follows. [See page 444.] Therefore, the second skeleton will be one in which between the Earth and Venus there is another possible harmony, 5:8. In this case of the daily motion of Venus at aphelion, 94 minutes 50 seconds, one eighth part, 11 minutes 51 seconds + , taken five times, matches the motion of the Earth, 59 minutes 16 seconds, and a similar fraction of the motion of Venus at perihelion, 97 minutes 37 seconds, matches the motion of the Earth, 61 minutes 1 second. Therefore, the rest of the planets are in harmony with the following daily motions. [See page 445.] Therefore, the experience of astronomy bears witness that univer­ sal harmonies of all the motions can occur, and both kinds, hard and soft; and in each kind in twofold shape or (if the term is permissible) tone; and in any one of four situations, with some latitude of tuning, and also with some variety in the particular harmonies of Saturn, Mars, and Mercury, each with the rest. Nor is it evinced only in the inter­ mediate motions, but in absolutely all the extreme motions, except for those of Mars at aphelion and of Jupiter at perihelion; for since the former occupies/g and the latter d, Venus which perpetually oc­ cupies the intermediate dQ or e does not allow those dissonant neigh­ bors in the universal harmony, which it would do if it had been granted room to go beyond e or dg. This is the impediment which the mar­ riage of the Earth and Venus has, as male and female, and they are the two planets which distinguish the kinds of harmonies, that is to say into hard and masculine, and soft and feminine. It is as if one of the spouses has done a favor to the other, that is to say the Earth is either at his aphelion, preserving, so to speak, his marital authority, and pressing on with tasks which are worthy of a man, pushing aside and banishing Venus to her perihelion as if to her distaff; or he has courteously allowed her to ascend towards her aphelion, or the Earth himself has descended towards his perihelion in the direction of Venus, and of her embraces, so to speak, so as to make love, laying aside for a little while his shield and arms, and those tasks which are proper for a man; for then the harmony is soft. But if we command this antagonistic lady, Venus, to be silent, that is, if we consider what harmonies there can be, not of all the planets, but at least of the remaining five, excluding the motion of Venus, the Earth indeed is still astray on his note g, and does not ascend more than a semitone from it. Therefore, b, !^, c, d, dg, and e can still agree with g, in which case Jupiter, as you see, representing the note d by its motion at perihelion, is admitted. The difficulty of the motion of Mars at aphelion therefore remains. For the motion of the Earth at aphelion, which occupies^, does not allow Mars on fg , whereas at peri­ helion, as has been stated above in Chapter V, it shrinks from agree­ ment with the motion of Mars at aphelion by about half a diesis. [See page 447.] However, there can also be the following harmony of the four planets Saturn, Jupiter, Mars, and Mercury, which would also include the mo­ tion of Mars at aphelion; but it has no latitude of tuning.’^s [See chart, page 448.] Therefore, the motions of the heavens are nothing but a kind of perennial harmony (in thought not in sound’^^) through dissonant tunings, like certain syncopations or cadences (by which men imitate those natural dissonances), and tending towards definite and prescribed resolutions, individual to the six terms (as with vocal parts) and mark­ ing and distinguishing by those notes the immensity of time. Thus it is no longer surprising that Man, aping his Creator, has at last found

a method of singing in harmony which was unknown to the ancients, so that he might play, that is to say, the perpetuity of the whole of cosmic time in some brief fraction of an hour, by the artificial concert of several voices, and taste up to a point the satisfaction of God his Maker in His works by a most delightful sense of pleasure felt in this imitator of God, Music.