Appendix

The Appendix which I promised above in the index to the chapters of Book V is not the one which the reader should expect here:

They start to make a wine jar, but as the wheel turns a water pot emerges. 185

I was about to navigate a great and overflowing river. Suddenly, the waters subsided into a thin stream. A ford appeared for me to cross on foot, leaving my ship at her mooring.

I have in Greek in manuscript:

• the 3 books of Ptolemy’s Harmony
• the commentaries of Porphyry, a very profound philosopher

From the beginning Book 2 Chapter 7 is supposed to be published complete in Greek and Latin.

This is why 10 years ago I began to translate them into Latin.

That translation progressed as far as the middle of the manuscript of Porphyry. I was prevented from making further progress by my change of abode, combined with a great many troubles, and, after I came to Linz, a new start on my astronomical studies.

However, when in fact I had proposed a year earlier to issue my five books on Harmony, I saw vast weight placed on the comparison of my work with Ptolemy’s, particularly of my Book 5 with the last chapters of Ptolemy’s Book III, the last three of which contain nothing but lemmas or headings from Ptolemy.

Thus against my inclination I proposed to extract, from a work which was in itself mutilated, only a single part, which was most relevant to my material.

To that end I both translated Book III of Ptolemy from Chapter III to the end;’^® and attached to the last three meaningless lemmas their own texts, fitted to them as adroitly as possible according to the basic principles of Ptolemaic astronomy and the intention of their author; and lastly appended commentaries or notes, by which the missing part of the Porphyrian commentary, which breaks off at Chapter VII of Book II, is supplied in this third book, and the Ptolemaic discoveries are compared with my own, and the difference is shown between the symbolism of Ptolemy and my own legitimate demonstrations.’”^

Hence the weakness and imperfection of his symbolism are shown, and the chief cause of them, that is the falsity of the basic principles of Ptolemaic astronomy, is made clear. Therefore, this appendix alone was going to occupy up to 30 pages of the book;

Behold! meanwhile the neighboring Bohemian war broke out, through which not only were the roads blocked but also many of the workmen are enlisting as soldiers.

Thus first paper, and then labor which could be used in the war failed us, and finally the time was excessively protracted by the most disagreeable delays. Roused by these obstacles, eventually I took little thought for myself and did away with what I had begun, so that not only did I not bring out the book of that excellent author Ptolemy and his commentator Porphyry, in a mutilated edition of a fragment, but I destroyed it altogether. Moreover, I hesitated over the remaining half of the work in my translation of Porphyry’s exposition. Should I write notes on the remaining chapters of Books II and III, and combine them with Porphry’s and with those which I already have, written on almost the whole of Book III, so as to complete the work in that way and issue it in Greek and Latin as far as it exists?

For that publication, another time and another place are required, and a suitable printer.

However, so that nothing whatever of the things I promised above could be missed by the reader, or so that even in this last part nothing should be lacking for the completeness or for the easier understand­ ing of my work on Harmony, come, I shall write out the headings of the chapters of Ptolemy’s Book III, and compare them with the corre­ sponding points in my own work; and I shall write in summary fashion what is in my notes.

First, what Ptolemy reported in Books I, II, and the beginning of III on the discipline of harmony, I have encompassed in my Book III by another method which is considerably different. However, whereas Ptolemy looks for the basic principles of the harmonies in abstract numbers, along with the ancients, I on the other hand say that there is no force in the numbers as counting numbers, and in their place establish as the basic principles of the harmonies the counted numbers,’”” that is, the things themselves which are subject to the numbers, in other words the plane regular figures and the divisions of the circle which are to be controlled by them; and so I necessarily set Books 1 and 2 on the harmonic figures before my Book 3.

Now Ptolemy has written at the top of Book 3, Chapter 3, of his work the title Under what class of things the nature or force of harmony is to be placed, and the knowledge of it, showing that there is some principle, causal, formal, mental, or even divine, which links harmonies with things.

Chapter IV: That the force of harmonic combination belongs to all things whose natures stand at a higher degree of perfection; and that that is chiefly apparent in human minds and in the heavenly revolutions. There you see the division of what remained for Ptolemy to say: that is, first, on the harmonies which exist in minds, second, on the harmonies in the motions of the heaven. And on the first there follow in fact three chapters; on the second the remaining nine. Chapter V com ­ pares individual consonances with individual faculties of the rational soul, and does that concisely, by the subdivisions of each of the things compared. Chapter VI compares individual kinds of harmonies with individual kinds or classes of virtues. Chapter VII compares modu­ lations of tones with the modulations of public feeling as times change, and thus with sudden modulations of emotions in minds. In this part I disagree with Ptolemy on many points, arguing of course that the symbolic associations are for the most part not nec­ essary, or causal, or natural, but rather poetic and rhetorical. For those special faculties and virtues which belong to minds are not allotted either their Idea or the numbers representing their constitution by reason of harmonies, as if from an archetype, but have other admitted and evident causes. Indeed they do not even correspond numerically, but by a far-fetched or overstrained effort an appearance of division into an equal number of parts is imposed on them; many which are surplus, or on the other hand shortages, are disguised; and some which are less appropriate are dragged in by the short hairs. Last, those which do correspond best and most neatly are nevertheless not included on account of some proportion between quantities of the same kind, though harmonies can only subsist in comparisons of quantities. Yet I showed the comparison between musical tones and public emotions and behavior to be extremely natural, and to be related to their cause, when prompted by the text of Ptolemy I adduced the opin­ ions of various philosophers on the affinity of minds, numbers, and harmonies with each other, to which I also attached the Epilogue to my Book V. Also as far as the specific effects of the tones in moving minds in various ways are concerned, I embraced that matter in par­ ticular in Chapter XV of my Book III. Similarly as far as Justice of exchange and of distribution, and friendship, and economics and poli­ tics are concerned, I made a digression at the end of my Book III on the subject of how far musical proportions are significant for them. Last, I embraced the subject matter of Chapter III and IV, which had already been set out in advance, and the points in Chapters V, VI, and VII in general which could be said to be true, in the first three Chap­ ters and again in Chapter VII of my Book IV. There, after explaining the nature of minds, I showed that since a circle divided geometrically by inscribing the plane figures defines the harmonic proportions truly and appropriately, by comparison of the parts with the whole, there­ fore, by a particular line of essential reasoning the circle must exist in minds, formally and in the abstract, not only in respect of matter, but also in a way in respect of actual quantity, materially considered. Hence as well as the circle the harmonies also exist in minds, and this is the reason why minds are moved by harmonies. But all this was only in a general way, and no plea followed for the division of the mind into special faculties. Such, therefore, is the position in regard to hu­ man minds.

As far as celestial motions are concerned, Ptolemy compares the zodiac with a musical system or scale in Chapter VIII of his Book III, and the actual consonances with the aspects of the planets in Book 9.

Here I have shown the particulars in which the theory of aspects in Ptolemy is defective, and how by reestablishing the number of the aspects on one hand and of the consonances on the other there eventually appears a natural and causal connection between the two.

However, this is the true subject matter of my Book IV, especially of Chapters IV, V, and VI. In Chapter X Ptolemy produces a sort of melody from the motion of a planet from east to west; in Chapter XI he produces the kinds of music from the true motion of the planets upwards and downwards;**® in Chapter XII he produces the variety of the musical tones from their motion from side to side of the equator;

In Chapter 13, he produces the different tetrachords of the system from the various configurations of the planets with the Sun.

I have shown that in these four chapters Ptolemy runs riot in using poetic or rhetorical comparisons, since what he compares are not real objects in the heaven, with the exception of a small part of Chapter 11 which I wish to be consigned to the last three chapters on account of the affinity of their subject matter.

I have also shown that here there is partly a comparison between things which are incompatible, as the nature of what is compared proclaims, and partly things which cor­ respond in all their branches do so merely accidentally, but do not agree by the necessity of any cause.

So far, therefore, there is nothing or very little which agrees with my celestial harmonies. However, Ptolemy’s following Chapter 14, raises the question in terms of what primary numbers can the sounds of the musical system or scale be compared with the primary spheres in the planetary system.

Here I have shown that for Ptolemy and the Pythagoreans the comparison was impossible in their conventional astronomy, though I have attempted to devise something which agrees with the Ptolemaic principles, so that in this way a suggestion of their coherence might be supplied by the bare title.

I have also shown that, since the primary spheres depend on their quantities, no less than strings on their lengths, the comparison should have been instituted in accordance with the quantities, even though the proportion of the spheres is extremely repugnant to the proportion of the consonant strings. However, at the beginning of my Book V I have also renewed from my Mysterium Cosmographicum in corrected form the causal or archetypal link between the spheres of the world and the five regular solids.

Ptolemy’s Chapter XV asks how the proportions of the planets’ own motions can be derived through numbers, but the text is missing. I have, therefore, shown the same as in the preceding chapter. As to the rest, I have presented for consideration the fact that here, 1500 years ago, Ptolemy would have set about handling the subject matter belonging to my Book V, if he had been able to through his own astronomy.

Thus I, in the corrected astronomy, which keeps the true and simple motions of the planets, eliminating apparent motions, which depend on optical illusions, have shown that in the heaven according to true and genuine quantitative reasoning, and based on measurement, but not by mere trivial interpretation of symbols, there are all the harmonic proportions, the kinds of harmonies, the musical system or scale, and most of its keys, the varieties of tones, planets which emulate the figured music of voices, and finally the universal counterpoints of the six pri­ mary planets, varying both in kinds and in tones. In Chapter XVI which is his last, Ptolemy promises that he intends to investigate on what basis the family relationships of the wandering stars can be compared with the family relationships of sounds. That is to say, he has busied himself in deriving the basic principles of astrology, on benign and malignant planets, and those which are friendly or inimical to each other, through the celestial harmonies. And because the text is missing for this chapter also, I have supplied it as far as I could, especially from Macrobius;*®® but at the same time I have shown in the notes what this business lacks for success according to the ancient astronomy.

However, in my work I have no section corresponding with Chapter XVI, except for a few lines in the Epilogue to Book V. For astrology deals with the effects of the stars on the Earth; whereas my celestial harmonies are formed by rays, not at the Earth but at the Sun.

This is the end of Ptolemy’s work.

Along with it I should also bring to a close the appendix promised at the entry to Book V, if the affinity of the subjects did not incite me also to give a satisfaction to those who have been in contention with me, such as Mr. Robert Fludd, the Oxford physician. He filled his book on the Microcosm and the Macrocosm,® published a year ago, with reflections on harmony, so that I should not omit to mention

him in my book but should briefly show the reader the subjects on which there is agreement between him and myself, and those on the other hand on which we differ. That author, then, has promised two volumes, one of which, writ­ ten on the Macrocosm, has already seen the light, while the second, on the Microcosm, is still awaited. The former volume embraced two treatises, and also brought them out at different times. For I saw the first treatise, on the threefold cosmos, after the autumn Frankfurt Fair of the year 1617, and the second on the Arts, which he calls the apes of cosmic nature, at the Easter Fair of the following year, 1618. In the second treatise, then, he has placed music among the arts, embracing up to a point the subject matter of my Book III. However, in the earlier treatise, which is contained in seven books, he has allotted the third book to cosmic music, taking the same title as I put at the head of my entire work. However, he has taken on the subject matter of my Book IV and Book V. Therefore, we shall start with his artificial music. He tells us of that in seven books, in the first of which he reviews the authorities, the nomenclature, and the force exerted on the minds of men. On the authorities, or the history of the discovery, I have said nothing, or little, inasmuch as my intention is to reveal the causes of things which are natural. The necessary nomenclature I have embraced in my definitions throughout; the superfluous I have omitted. I deal with the force of music in minds in Chapter XV of Book III and through­ out Book IV. In the second book the author attacks the actual subject matter, which he speaks of as intervals and times. Again, I have said absolutely nothing about times, or the length or brevity of sounds; for they are arbitrary, and do not need inquiry into causes. He calls certain intervals simple which for me are the smallest melodic disso­ nances, the major and minor tone, the semitone, and the diesis. He considers the others, which I call consonances, as compounds of these. But I have expressly refuted this opinion of the ancients, that the con­ sonances are composed of smaller intervals which are, so to speak, prior by nature, in Chapter IV of my Book III, showing that the smaller intervals on the contrary arise from the consonant intervals which are larger than themselves. In his third book he expounds the musical system or scale, which is a main part of my Book III from Chapter IV to Chapter IX. The author’s remaining four books are on the prac- tical side, which I do not even touch. For in Book IV he gives advice on the measure of the beat, and on its various modes, and on the value of the notes in them, on which I have a very few points in Chapter XV of Book III and in Chapter III of Book IV. In V he has advice on the composition of figured melody, an art which I do not profess. In VI he also digresses to various musical instruments, to which I had not even given thought. Last, in VII he reveals a new instrument him­ self. In these last four chapters he differs from me in the way in which a practitioner does from a theorist. For where he writes on instru­ ments, I enquire into the causes of things, or of consonances; and where he gives instruction on composing a tune for several voices, I provide mathematical derivations of many features which occur naturally both in choral and in figured melody. Consequently, there are also many pictures in his work; in mine, mathematical diagrams organized with letters. Notice also that he takes great delight in topics which are hid­ den in the darkness of riddles, whereas I strive to bring topics which are wrapped in obscurity out into the light of understanding. The former is familiar to chemists, Hermeticists, and Paracelsians; the latter is con­ sidered their own by mathematicians. Furthermore, indeed, in Books II and III, where he is dealing with the same subject matter as myself, this is the difference between us; what he takes over from the ancients, I draw out from the nature of things and establish from the very foundations. He applies what he has got in a confused (on account of the varying opinions of his sources) and uncorrected form: I proceed in the natural order, so that every­ thing is set right according to the laws of nature, and confusion is avoided; so much so that I do not even relate what has been established to the opinions of the ancients, except where no confusion follows. Thus at the point where I expressly refute the ancients’ treatment of the causes of consonance, he follows the ancients, without the hazard of hesitation; he does not even give a thought to the truer causes. In a word, in the discipline of harmony, one plays the part of a vocal and instrumental musician, the other of a philosopher and mathematician. Let us now pass on to another passage of the author’s, in which he introduces music into the cosmos. Here the difference between us is of immense size. First, what he endeavors to teach us as harmonies are mere symbolism. O f them I say what I said of Ptolemy’s symbolism, that they are poetic or rhetorical rather than philosophical or mathe­ matical. This is the spirit of the whole of this work, as is evident even from the title of Macrocosm and Microcosm. For in the second vol­ ume he will undoubtedly endeavor to demonstrate this noble thesis.

that the ideas of the whole great cosmos, and of all its parts, are found in man. This same spirit is also that of the first volume, as he divides the whole cosmos into three regions; and there in accordance with the most celebrated axiom of Hermes he makes the higher things simi­ lar or analogous to the lower. However, for this analogy to succeed in all cases, the points of comparison on either side often have to be dragged in by the short hairs. My opinion of analogies is clear from the digression at the foot of my Book III: in other words, although the analogy of proportions in geometry is something formal, in re­ spect of the actual quantitative matter, which is indefinite and un­ determined, yet in respect of harmonic proportions it can be considered rather as a material property of the harmonic proportions. For since the harmonic proportions define a certain quantity, analogies on the other hand are apt to extend themselves to infinity, and thus counter­ feit the material property of infinity. However, I also deal with some points similar to what he says on the Microcosm in my work, such as what I say in Book IV. I make the Earth a living creature: but that is for quite different reasons. For I do not contend that there is a pure analogy between the Earth and living things, and neither do I mean that the archetype of a living thing has been taken from the Earth itself; but the proposition which I mean to demonstrate is simply that those works which are seen on the Earth’s globe cannot come about from the motions of the elements, or from the properties of matter on their own, but bear witness of the presence of a soul. In that case for my arguments to be understood it was necessary to adduce the various functions of the soul in the body of a living creature. Let us now come closer to the foundations on which Robert Fludd erects his cosmic music. First, he takes pos­ session of the whole cosmos and all its three parts, empyrean, celes­ tial, and elementary: I, of the celestial alone, and not the whole of it, but only of the motions of the planets, so to speak, against the zodiac. He trusts the ancients, who believed that the force of the harmonies comes from abstract numbers, and considers it sufficient if he demon­ strates that there is consonance between any of the parts, in whatever way he expresses them in numbers, not caring what sort of units are combined together in that number: I teach that harmonies should never be sought when the things between which the harmonies are cannot be measured by the same quantitative measure, in such a way that with respect to quantity the proportion between them is the same as there is with respect to length between two strings at the same tuning. Consequently, he divides the whole cosmos into three equal parts by means of a radius, taking it as sufficiently well known that they are far from equal, but for the sole reason that the first unit is the ele­ mentary world, the second the aethereal world, and the third the empyrean. And in fact the units cannot be depicted otherwise than by equality of lines.

But I, unless astronomy bears witness that the units share the same quantitative measure, do not in any way employ them as units for numbering the harmonic proportions. He, however, standing on his principles, and erecting a pyramid on the great circle of the Earth as base, sets its vertex at the very apex of the empyrean heaven; and dividing its height into three equal sections (just as if he had in absolute truth had equal units), he counts how many parts belong to the empyrean, how many to the celestial, how many to the elementary. For the top of the elementary region on this showing is twice as far away from the top of the celestial region as from the top of the empyrean; and in the division of the pyramid, with respect indeed to the axis, three equal sections belong to the three regions, but with respect to the triangle on the axis, one unit belongs to the empyrean, three units to the celestial, and five to the elementary. Finally, with respect to volume or fatness of shape, one unit belongs to the empyrean, seven units to the celestial, and nineteen to the elementary.

Now what shall I say about the other, contrary pyramid of light, of which he makes the worshipful Trinity itself the base, at the topmost apex of the empyrean heaven, and places the vertex on the very Earth? Since he mingles these two pyramids with each other, and elicits musical pro­ portions from the mixture, he is attempting something entirely differ­ ent from the intention of my work.

For he compares light (which bestows form and spirit) and matter, two things which are completely different from each other, and to which quantities do not in any way belong in the same respect; but I admit, as terms in forming harmonic proportion in the universe, only those things which admit quantities in the same respect, for instance the motion of Mars and the motion of Jupiter, both diurnal.

The difference between us consists equally of this fact also, that he ascribes to the elementary region four degrees of obscurity and darkness, because, he says, everything has four quarters, certainly no less than three thirds or five fifths; and in fact all four belong to the Earth, three to water (and therefore, it is in fact trans­ parent), two to air, and one to fire. Again elsewhere he subdivides every region, belonging either to an element or to a heaven, into three spaces, top, middle, and bottom, which the agreement of the senses does not follow in every case.

You see that his units are again arbitrary. However, he proceeds on that account to establish a diatessaron between Earth and water, and to relate its three intervals, a tone, a tone and a semitone, to the three spaces, top, middle, and bottom, since the former have definite quantities arising from their causes, the latter not even boundaries from nature, but measures which are plainly in­ determinate drawn from these very general principles; and so on. But I have set out units which are natural, that is to say the two extreme motions of each planet (whether diurnal or hourly makes no differ­ ence), expressed by their nature in their definite quantities, in which to seek harmonies. He seeks harmonic proportions in degrees of dark­ ness and light, without respect to any motion:

I seek harmonies only in motions. He plucks out a few trivial consonances, and elicits them from the mixture of his pyramids, from which he conjures up the cosmos privately depicted in his mind, or deems them to be represented by it. I have demonstrated that the whole body of harmonic combina­ tions, with all its parts, is found in the planets’ own extreme motions, according to measures which are certain and derived from astronomy.

Thus for him his conception of the cosmos, for me the cosmos itself, or the real motions of the planets in it, are the basis of the cosmic harmony.

From this short discussion I think it is established that, although knowledge of the harmonic proportions is absolutely necessary for understanding the crowded secrets of the deepest philosophy, of which Robert tells, yet even if he has thoroughly learnt the whole of my work, he will still be considerably further from those most intricate secrets; and the proportions have departed from the totally accurate certainty of mathematical derivations. And now let this also be the end of the Appendix.