Chapter 3

The Types of “The Harmonized” Sensible or Immaterial Things

by Johannes Kepler Icon

What are the types of the harmonized sensible or immaterial things and how are they expressed?

How do the harmonies exist as agent, shaper, or creator? The previous chapters answer this.

How do they exist as the creation which is shaped? This chapter will answer this.

All things are either immaterial or material.

The soul is immaterial (in relation to the body).

In relation to its essence, it has wholly been designed by God in the harmonic proportions.

those which were previously in the Mind as their creator, that is inasmuch as it is an activity, are now in the Mind because it is a creation of God.

Now what participates in matter also at the same time participates in number and magnitude. But a consequence of magnitude is a position in space.

Finally, local motion is attributed to them. Therefore, number is something prior by nature to harmony, because the terms of each harmony must be more than one in number.

However, the number of the primary bodies of the world also has its causes in geometry, which I repeat below in Book V from my Mysterium Cosmographicum {The Secret of the Universe).

A consequence of quantity is shape, its individual property; and why a global shape was necessary for the stars, and so for the world itself, that is as a result of the archetype of the spherical, is generally explained at various points elsewhere.

An immediate consequence of the shape of different bodies is a definite proportion, and that in three ways: one in their diameters, another in their surfaces, and the third in their volume or bodies.

Therefore, if no other causes for these proportions were forthcoming, we should probably be able to affirm that they had been taken from the harmonies.

Yet whatever they are, the celestial globes preserve them without any change, seeing that they do not become larger or smaller by any motion or lapse of time.

It is otherwise in the case of those proportions which belong to bodies on account of their position and because of their local motions.

For they retain the character of the motion itself; and as it is in a state of continual BECOMING, and is never occupied in BEING, similarly the proportions of motions are not constant and are different at different times. It is indeed true that if the motion of the celestial

bodies did not produce variations in their distances from their common starting line or the original state of the world, that is they had no motions upwards or downwards, but it was all in a pure concentric circle, in that case not only would the proportion of the distances have been constant, but it would also have been purely harmonic, if no other causes had been forthcoming.

The same has to be said of the motion, the cause of their essence, that is the cause of their true speed through the ether.

If it were constant and perpetual in individual cases, there is no doubt that these speeds, or slownesses, of the various bodies would have been attuned to harmonic laws. Lastly the same has also to be said of the same motion on account of the enclosed space which is apparent beneath the zodiac.

For if it had been necessary for all the planets to proceed with the same apparent motion under the zodiac, and never be further separated one from another, there is no doubt that God would from the beginning have established their position relatively to each other under the zodiac (if in fact His disposition of them had been unrestricted and not linked to other laws of necessity) in a way that would split up the zodiac in harmonic ratios.

In fact, it is generally agreed that that was the case at the start of the motions (since the start of time is considered without reference to time), so that from their common position and harmonic configuration (as it could have appeared either from the Earth, or rather from the Sun), as if from starting gates, each departed into their own spaces or paths.

But because the planets move upwards and downwards, changing the distances between their positions; and because as well as this motion it follows by physical necessity that there is also a real intention and remission^2 of their motions, on account of their speed.

Lastly, because through the unequal apparent speeds of the different planets the area of the zodiac which they seem to traverse is divided differently at different times —for these three reasons, the same thing happens both to their positions and to their motions, through time, as to the actual quantities without reference to time.

For just as the terms or markers of the harmonic ratios are not on the whole circle, or on a straight line and all its points, but in fact on certain of them, so also in this case the harmonies cannot exist in the whole time of the motion, nor in the distances, nor in the speed of the motions, nor in the areas of the zodiac intercepted between the planets.

However, they can exist completely at certain moments of time, and they can do that without any further operation by God, once the motion has been started. For if He has prescribed the extremes for the motions, and has granted them the favor of changing from one extreme to another, He has also bestowed on them all the intermediate points, both the incongruent ones, which are infinite, and the ones which are congruent and harmonious, interspersed in a definite number between the incongruent.

For God has not left them changeable without any care for the display of harmony. Rather, He has reduced some of them (such as the proper motions of the planets) to harmonic order by prescribing their extremes, which will be the subject matter of Book 5.

In other cases, where the extremes are not laid down, but the quantity of the motion in a circle is interrelated with itself, the Creator deemed it sufficient to shape souls, which control earthly creatures, in such a way that they expected and observed and noticed the harmonies, all round the circle, as they occurred at their own moments over time, and fitted their own doings to the prescription of the harmonies.

That is the case with the apparent motions of the planets beneath the zodiac, as seen from the Earth,*^^ the proper subject matter of this Book 4.

With the works of God known to us, then, it is as follows. If we now compare with them the works which men ordain in accordance with harmonic laws, we shall have to say that they are partly the same and partly different.

First, though in song continuous increase and decrease in quantity are possible no less than in the heaven, yet in the motions of the heaven it is necessary by definite laws of nature, but in the human voice it is neither necessary nor even easy.

For the throat is made to produce identifiable notes by various sizes of circle. We pass more easily from high to low, and the other way round, by leaping, so to speak, over intervals, and separate sounds, than if we were instructed to use continuous intention.

Therefore, it is nothing surprising if in the celestial motions, with actual continuous increase and decrease, which could not be avoided, there also remained unmelodic intervals mixed with melodic and consonant ones; whereas in human music, all the unmelodic intervals are eliminated and only melodic and consonant ones are admitted.

Yet that gives no reason for exalting music above the celestial motions. For those are charged with another duty to perform: harmonic tuning is for them only ancillary.

Music has nothing but the harmonies to keep in view, and seeks for nothing beyond it: it is directed to the sole aim of giving delight.

There are also other human activities into which the mind introduces harmonic proportions, though more obscurely and ignobly, as when music is formed not only by the quality of high or low pitch, but in addition by the rhythmic measure as well, participating in double and triple proportion, and again in the movement of bodies, when dances are performed, first in the proportion of equality, and after that in double proportion. Poets also imitate the same thing, by making melodic feet from long and short syllables, the former being taken as double the latter.

Thus the iamb - - , the trochee - - , or dact yl ——- anapaest - - - , the tribrachys—- is to the spondee - or amphibrachys or proceleusmaticus as 3 to 4; to the bacchii - — , —– -, the cre tic—— , and peons - as 3 to 5, to the molossus——, choriamb ionics and their compounds as I to 2.

To the same feet the spondee, dactyl, and those which take the same time as them are as 2 to 3; and the same are to the peons as 4 to 5, whereas the peons are to the choriambs and their kin as 5 to 6.

Poets and grammarians also delight in the names of the proportions, with a peculiar usage, calling feet of four syllables by one short name, epitrites, that is four thirds.

For as in the proportion 4 to 3 as expressed by parallel lines the first three units are in fact represented by a double line, and the fourth only by a single additional line, so in the foot there are three syllables of two units of time and a fourth of only one.

And as the name “feet” itself alludes to dances, a part of comedies and tragedies, the actors also by the motion of their feet seem to have expressed all those proportions, no less than the double and triple proportions are expressed today.

In architecture whatever proportions of length to breadth or thickness are most approved,even by observers who are not mathematical, are found to be as close as possible to harmonic. In fact the reason why the proportions of sounds are more exact than all of those, and the nature of man delights in their more eager expression, is that every living thing has sounds most of all in its power, seeing that they are shaped within it, emitted by its very midriff, and most obedient to every whim of its mind, every movement of its heart, and that, as has been stated before, it has been allotted the most suitable instrument, the throat stretched at full length, like a string or rather a pipe, and the voice roves up and down with the least impediment along the straight line of its length.

However, in general in everything in which quantity, and harmonies in accordance with it, can be sought, their presence is much more obvious through motion than without motion. For although in any given straight line there are its half, third, quarter, fifth, sixth, and their multiples, yet they are lurking among other parts which are incommensurable with the whole, in one and the same confusion with the whole, concealed in such a way that if in particular a second line equal to one of the aliquot parts is placed next to the whole —for example a lintel beam of three feet next to a doorpost of five —yet its proportion to the whole will not be as easily apparent as if some motion distinguishes and establishes and determines the comparable lengths. The reason is this, that where there is a quantity without a

motion in accordance with it, in that case everything which is present in quantity is present together at the same time, that is all the proportions of all its parts to the whole. However, if some quantity is traversed by a certain motion, then (as is the essence of motion) those proportions which have been traversed are not present any more than those which have not been traversed, and do not yet even exist; and any one proportion is the only one present when the motion reaches its location.

Thus it comes about by the succession of motions that the harmonic proportions are unwrapped from unmelodic ones, and by separation from mixture with them are established in full view, as it were, in their purity, and proffered for the senses to grasp.

In fact not even the mind itself distinguishes the harmonic proportions in a given quantity from the infinity of unmelodic ones standing before and after without some image of motion; but when (to take the example of a circle) an infinity of chords has been traversed, it operates on the chord subtended by a third or a quarter of the circle, and similar ones, and seeks for its construction.

It evinces by contemplation what the hand evinces by drawing a line, the actual separation of that one from the infinity of others which have not been contemplated and not been drawn, and the observation by the mind of its congruence or incongruence apart from the others.

The mind indeed can do that because it employs the will, and dances by its own decision on that infinite division of quantities, the whole of which is present simultaneously to the mind for contemplation.

On the other hand the sensations, and the other natural perceptions, and indeed the bodily motions by which the perceptions are assisted, are not under the control of a living creature in such a way that if infinite sounds, or the infinite angles separating a pair of planets on their way around a circle, were mixed up with each other at the same time, they can withdraw from the unacceptable ones and retreat only to those which are pleasing. They therefore need motion, and with its intervention everything which has been mixed up as far as quantity was concerned will be sorted out through the sequence of time, so that it is presented individually to the senses on its own.

But if the eyes are capable of anything like the mind, so that from a single infinite confusion of things which are present without motion they pick out the more important (as if by using the assistance of the hands they pick out from the infinite possible chords of a circle and sketch out the chord subtended by a third of it, that is the side of a triangle), that very thing should be considered as done not so much by the eyes as by the mind itself through the eyes, and this is clearly not without motion of the hands, as I have said.

Then to apply this observation to the previous pronouncements, there must, if something is to be the genuine subject of a harmonic proportion, there must, I say, be both a quantity, that is a length, in that thing, and two reference points at least, if the length is a circle, or three, if it is a straight line, of which either one or all pass over the length of the thing by some motion, and become the terminal points of the parts of its length between which there is a proportion: and that as a minimum.

That comes about in part in the configurations, which are the proper subject of this Book IV. For as will be stated in the following Chapter, the harmonies indeed in the angles which the zodiac measures out are considered without motion; but the actual angles, one giving place to another, are established by the motion of the radiating bodies through the zodiac.

However, there are more important processes which tend towards the same result, as when bodies themselves which have length are bounded by such reference points, which rove up and down, and their stumps which have been cut off by some vicissitude, move at the same time.

Thus not the bodies in this case but the actual motions of the bodies, with respect to length and breadth which is not temporal but corporeal (in fact a kind of motion placed in bodies, or bodies established in motion) are compared with each other. It is like that with sounds; for a sound is an emanation given out by a body, and in accordance with its size, and to a certain extent how it is shaped, and how it is established in motion.

For both motion and sound depend on what suits the shape. And this again is another and more obvious reason why the nature of Man is devoted most of all to harmonic proportions in sounds.

For once again this is due to the shaping of the body.

In it the throat is that body which in accordance with the tightening of the upper or lower circle of gristle in the rough windpipe is now long, now short, and which, driven by the breath expelled from the bellows of the lungs, by its concavity (in other words its shape) gives out a similar motion, the emanation of which reaches the ears, and also the sensation (of the actual windpipe, as it is established in the motion) is present to the sentient soul. Of course sensing by the common sense is to partake of the emanations of the organs of the body, as they are influenced, and, so to speak, shaped, by different motions.

Those emanations, as I have explained in the Dioptrics, a r e carried by a continuum of spirits from the organs of the body, even if they are at a distance, to the seat of the common sense. It therefore comes about that as a man by the frequent sensation of his rough windpipe established in motion absorbs a certain idea of the shaping of bodies which are in any way sounding, he recognizes all the more easily, and as it were judges, the shaping of bodies outside himself which are in motion, and emitting sounds by that motion, and examines them in comparison with each other according to the laws of harmonic proportions.

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