The Distinction is Between the Harmoniesby Johannes Kepler
There is a fivefold distinction between the harmonies studied in Books 3 and 4.
One is the actual matter of the harmony itself, with respect to its amplitude.
The second is in its sensible terms; the third is in the cause which links the harmony with its essence; the fourth is in the means by which it is in it;
The fifth is in the arrangement of the causes which shape the terms of the harmonic proportion.
I. As far as the thing itself is concerned which is called a harmonic proportion, they first arose in the third Book from the divisions of a circle by the regular plane constructible figures.
They were then transferred to straight lines, and when contrasted and combined with each other begot a not inconsiderable amount of harmonic parts (such as the harmonic divisions, tones, kinds, modes, systems, and so forth), and a wonderful commonwealth, so to speak, among them; and almost the whole of that apparatus, extensive as it is, will also be scrutinised and applied in Book V below. Now, however, in this fourth Book, although we have started from the same divisions of the circle indeed, yet we are not going to proceed to straight lines; but we shall confine the whole range of the discussion within the bounds of the circle.
The reason has been stated in the previous Chapter, and will be stated at greater length below in Chapter VI where we shall deal further with their kinship and with the result of this distinction.-^® The harmonies more restricted in this Book.
II. As far as the terms of those harmonies or their sensible subject are concerned, in Book 3 that was the sounds which differ in height or depth of pitch; and so they were included in the class of motion, and were in a sense shaped motions. On the other hand in this fourth Book it is not notes, as was stated in the preamble, not motions of some kind, between which harmonies are to be recognized; but they are in the angles which pairs of planets, when they give off bright rays, form at the Earth, insofar as such an angle can be compared with four right angles surrounding a single meeting point. Now here the reader needs some excellent advice. For I can indeed explain these terms more clearly for purposes of perception, but I cannot do so without danger of confusion in good philosophical practice, unless I carefully forearm the philosophical reader.
For the terms of a proportion must differ in quantity; but quantity in angles, that is their measure, is an arc of a circle drawn from a point where angles meet, as we are taught in geometry.
So in the whole space of the world in fact, which is from here on Earth to the limits of things, we cannot ever draw, or perceive with our senses when drawn, a circle which is more suitable for measuring the angles of rays except that actual sensible circle at the height of the aether, represented by the very numerous fixed stars, from which, when they are assembled into the shapes of particular animals, it has taken the name of zodiac. Moreover, it is under that actual circle that the planets are always found, and it is that location alone which individually they seem to hide from us by the interposition of their bodies;
It is at its center that the Earth our home, not only in its own center, which is a point, but in the bulk of its whole body, over the surface of which we men have been distributed, seems to have been secluded.
Nothing, then, is easier to perceive than if we say, as in the previous Chapter, that the harmonic proportions, with which we are going to deal in this Book, are between the whole circle of the zodiac and an arc of it which two planets seem to mark out, bound or cut off by that visible interposition of their bodies.
Although this has been so derived, and very well postulated from geometrical and astronomical arguments, yet the philosophical reader must take the greatest possible care against presuming in his mind that this harmony (the subject matter indeed of the fourth Book) exists in the actual heaven, and in the zodiac circle, or even in the planets.
Not the least bit; for this harmony is in the parts of the zodiac not on their own account, as the radiating planets stand at an immense distance below this circle, but on account of their measuring the angles of the rays which meet at the Earth; or rather, on account of their not actually measuring it themselves, but in place of them the exact image of the heavenly zodiac in the sublunar soul undertakes this duty of measuring.
It is in the rays of the planets not inasmuch as they individually either descend from their planet or are the offspring of light (though they do not exist without it, but inasmuch as the two rays of two planetsjoined together form some definite harmonic angle here on the Earth.
Under both headings this subject of harmony is terrestrial (formally, and insofar as the rays become terms of a harmonic proportion), but in no way celestial except only in a material sense, and in respect of their own essence, without considering harmonies, that is to say insofar as the angles which are made at the Earth, that is the proper subject of this harmony, are formed by bright rays, something which must originate in the heaven, but has now descended to Earth.
However, we shall deliberately deal with the truly celestial harmonies in Book V. In brief, the terms of the harmonies in Book 3 were the work of Man or of art; in this Book IV they will be the work of Nature. Finally, in Book V they will be the work of God the Creator.
As far as the rational cause is concerned, which procures for harmonies their essence, there is no distinction between Books III and IV in general, but only in particular. For in Book III the harmonies flowed into the senses by reason of their material subject (the sounds) and were received and judged by reason of their formal essence, by which they are harmonies (that is they were shaped) by instinct which is created along with the mind, and participates in the reason without contemplation.
And to that extent they were considered as harmonies only in themselves.
Next, however, by a hidden but avowed traffic with the faculties of the soul, the harmonies were received within and transfused into the varying emotions of the heart, by certain likenesses or images of themselves; and they were also transfused into the locomotive faculty, so that Man might express the representation of harmony which he had conceived in his mind not only with his voice but might also imitate it with the motion of his body. Thus the harmonies underwent the vicissitudes of one cause or another.
Similarly in this case also it is necessary to suppose that the soul, which has had by instinct right from the creation of things this “test” of harmonic proportions and which on its own account estimates the angle between two radiant stars, however it is received within it (whether that comes about by something analogous to the senses, or by a property of its essence in virtue of which it is soul — on which there was a statement in the previous Chapter, and more will be stated in the following ones), compares it with four right angles, discriminates the harmonic from that which is not harmonic, and thus gains its own intellectual essence of harmony, which these angles did not yet have outside the doors of the mind.
These harmonies But if the question is asked, what manner of thing is this soul, shine out: where or in what body is it located, I reply first that the minds of Man. of all men are such. But in Book III there was a faculty which controls the hearing, and so the senses: here it is not a case of a sensitive faculty.
For the eyes, the subject of which is light, and shining rays, do not have a suitable indication of the harmonic radiations of pairs of planets.
Nor is it a case of a reasoning faculty: for although reason does find and compute, from astronomical observations which have to be man aged through the eyes, what the aspects are at any given time, yet it does not do that by nature, seeing that it is not in the power of all men indiscriminately, but by the exercise of will, within the power of a few singularly dedicated astronomers. But human souls are the subject of those harmonies, first by reason of their natural instinct, insofar as souls are copies of the Creator, as was stated in Chapter 2; second by reason of their faculties, vital and natural, and of vital and natural motions, or in the Platonic style,’^^ of the lustful and irascible parts —by reason of the former, indeed, insofar as they are harmonies, and by reason of the latter insofar as the representations of the harmonies are imprinted on those faculties, and are causes of the works of Nature, both in the mind and in the body, as instigators and stimulants.
2 . in sublunary Next, the chief soul into which these harmonies of the radiations Nature or called by the philosophers sublunary Nature, diffused the Earth, through the whole body of the Earth, our nurse, and rooted in some particular part of it exactly as the human soul is in the heart.
From it as if from a hearth, fount, or inner sanctum it emerges by its emanation into the ocean which surrounds the lands and the air which is over both.
Now a man who is listening to the agreeable song of a good singer bears witness by the delight in his expression, by his voice, and by the clapping of his hands and feet, in time to the rhythm of the melody, that he perceives and approves the harmonic content of the melody.
In exactly the same way sublunary Nature, by a remarkable and obvious commotion of the bowels of the Earth, particularly on those days on which the wandering stars are in a harmonic configuration with their rays at the Earth, bears witness to what we have already said by way of preface, that is to say that it has just as much power of perceiving the harmonic proportions of the angles by a kind of natural instinct as it has of heating and agitating the body of the Earth and the underground workshops in its mountainous regions at certain times of harmony by a natural faculty similar to our natural faculty, so that they exhale a great amount of vapor and clouds, from which, through reciprocal production of cold on high, all kinds of occurrences in the sky are shaped.
Eor this soul must be placed in the body of the Earth, as the harmonic angles of the rays exist in no other part of the world but on the Earth, and the works of Nature which follow upon the configurations of the rays take their origin from the bowels of the Earth and the caverns of the mountains. See chapter vii.
The fourth distinction consists in the ways in which the various harmonies are present in their subjects.
For in Book 3 where they were in music they were in the whole The concealment of it, that is to say in the whole of the time for which the music lasted. And though the intervals between the notes, as they all participate harmonies in quantity, admit of continuous division, yet in that case the music in continuity, did not have a transition from the lower sound through an infinity of intermediate stages up to the one which was consonant or melodic with the first, but crossed over all the intermediate stages at a leap and in silence, so that the voice dwelt only on sounds which were melodic with each other.
In the same way in part singing, although there are infinite intervals between the diapason and the dihex, yet the application of the voices was not continuous through all the intermediate stages, until the sixth emerged from the diapason, but the voices were carried with a leap from the pure diapason to the pure sixth, passing over all the intermediate stages in silence.
In the case of organs indeed there was a leap from one pipe to another; in the case of stringed instruments, as on an instrument like a harp, from one string to another; or if strings giving many notes were taken, as on a clavichord, pandora, lute, zither, from one fret, or in the case of wind instruments, from one aperture, to another; and in the human throat, from one circle of the rough windpipe to another.
It is not so in Book 4.
For the harmonies which we shall consider, as I began to say in the previous Chapter, do not always exist between the angle formed by pairs of radiant planets, and four right angles. On the contrary there occurs a continuous separation of planets, and their passage under the zodiac circle is through all the “unharmonious” intervals to the harmonious ones, among which is the extreme, two right324
They are momentary.
Yet their effect is not momentary.
They are mixed with incongruent ones having no influence. B ook I V angles, a semicircle, or opposition, and from there in reverse order again through all the unmelodic and dissonant intervals as far as conjunction.
In this case there is no leap from one harmonic angle to another, for example from the trine to the quartile; but the transition from the former to the latter is continuous, through all the intermediate stages. For that reason the whole time of the heavenly motions is taken up by unmelodic configurations of rays, but they are marked off only at particular moments by harmonic configurations of 2, or sometimes three, or even four, while the rest proceed to incongruence, as if seven organ pipes gave out the same number of dissonant sounds with a continuous variation in the tuning, and it came about by a mutual coincidence of the tunings that sometimes two or three were in consonance, with the rest in dissonance.
Thus to speak truly and properly, the actual harmonic configurations are not in time, but are produced at indivisible moments.
Yet it is equally true also that the commotions which are due to these harmonies in souls are not momentary; for the harmonic configurations excite them, as long as they are in the process of becoming, and at the moment at which they become complete their stimulus relaxes again.
However, the operations of Nature which are stirred up through these stimuli now take the measures of their time from the conditions of matter, and often last far beyond the moment at which the radiation is finished.
Thus when a bronze cannon is fired, it is inflamed by the force of the burning fiery powder, and does not immediately relax its heat when the material of the fire is used up. Thus the body of an animal, to use a more appropriate example, which is tossed by a paroxysm of fever, even though the faculty of the vital soul, the author of the inflammation, relaxes from its effort, seeing that its function has been performed, and the feverish matter has either been dissolved or ejected from its innermost dwellings to the outside, is not, however, immediately freed from all heat. For the heat adheres to the matter of the body, the flesh, bones, and sinews, for a long time, until with the passing of time it perishes itself.
Therefore, these harmonies are from among the number of those which as we have stated in Chapter II are not under the sway of free providence, but by the necessity of motions are mixed with an infinity of incongruent ones of their kind, for which God has ordained minds to recognize the harmonies when they meet them.
Yet sublunary Nature is far more fortunate in recognizing them than the ears are in the case of music.
or the hearing is not greatly delighted by the harmony of two notes, if five other dissonant ones shout against it; but sublunary Nature, accustomed to perpetual incongruent configurations, does not take them into account because it notices nothing new.
In fact it concentrates on the harmonic angle as if it was the only one. Similarly if some prediction goes wrong a thousand times, that is nevertheless disregarded; but if it once hits the mark, that is deemed worth remembering, that is acknowledged in everybody’s conversation.
Distinction between the H armonies
From this, then, we may understand that the harmonies in the case of music indeed are placed under the judgment and decision of the singer; whereas in the case of angles between rays they emerge not by any decision of sublunary Nature, but by the pure geometrical necessity of the motions. For because two planets have to be separated by the length of a whole semicircle or 180°, it must be the case that at specific moments they are also distant by harmonic parts of it, that is 30°, 60°, 90°, 120°, and so on. Thus the harmonies of music are sought within by the singer; the harmonies of the rays are looked for outside by sublunary Nature, are observed when met, are discriminated from those which are not harmonic (and thus take from it their essence), are selected, and are applied. In brief, the configurations sing the leading part; sublunary Nature dances to the laws of this song.
V. The fifth distinction must in a way be linked with the first.
For the harmonies of this and the preceding Book do not differ only in breadth, but also in the order of the features by which the geometrical figures beget the two kinds of harmonic proportions.
For in Book III the feature of knowability was the more important, in this Book IV that of congruence will be the more important.
But we shall now deal with this fifth distinction specifically in Chapter V, while expounding the axioms.