This book offers a short and understandable survey of the theory of harmonics, a field of investigation which is new and at the same time very old. And, wherever possible, without tables, numbers, and diagrams within the text. This is roughly comparable to a survey of the problems of mathematics or of relativity made without the help of mathematical formulae or diagrams. The danger of such an undertaking is obvious.
Over the years I have been asked many times to write such a survey, but only now, when I can look back on my harmonical work completed in the meantime, may I begin it. My books were designed to show harmonics from different points of view, thus giving a foundation for this new theory. Now it is possible to refer to the appropriate passage in those books; there is no need to project assertions in a vacuum. Thus the text remains free of numbers ,Ind formulae. Technical terms and those of foreign derivation are explained in parentheses. Footnotes for the most part refer to those passages in my own works and to those of others where the related problems are dealt with at length. A few pages in this book deal intentionally with certain problems in a more technical way, partly to give the scientist more precise material, and partly to offer the lay reader some important harmonic theorems that he may test by examples.
The title Akroasis ( from the Greek ακροασις, hearing; in contrast to aesthesis, αισθεσις, seeing or perceiving) should not be understood as an attempt to introduce a new concept in philosophical or scientific terminology. For practical reasons it was thought best to choose a simple, concrete expression for a subject still strange to many people. Thus homage was paid to the spirit of the ancient Greeks by choosing the word akroasis. But there was yet another reason for deciding on the new expression. The term "harmonics" is familiar as a classical concept of Pythagoras, which was revived by Kepler in his Harmonice mundi. It should not be confused with the familiar term "harmonics" as used in music where it means chords, or as it refers to fingering technique in string playing.
Our harmonics is, in contrast to the term used in music, of a more universal kind. It tells of the old, yet always new, theory of the "Harmony of the Spheres", an attitude of the spirit which Dante touches upon in Purgatorio, XXX. v.92:
"The song of the angels, which is only the echo Of the song of the eternal spheres,"
and which Shakespeare, in The Merchant of Venice, puts in the mouth of Lorenzo:
"Look how the floor of heaven
Is thick inlaid with patines of bright gold;
There's not the smallest orb which thou behold'st
But in his motion like an angel sings,
Still glaring to the young ey'd cherubims:
Such harmony is in immortal souls;
But, whilst this muddy vesture of decay
Doll, grossly close it in, see cannot hear it."
Hans Kayser
Hans Kayser, rediscoverer of the ancient discipline of harmonics, died April 15, 1964. With his incessant and original work extending over decades, he was the sole representative in his time of this many-branched science.
Kayser grew out of no existing school, no circle of like-minded colleagues. His immediate predecessors and teachers--Albert von Thimus and Johannes Kepler (not to 'nem ion the Neo-Platonists and the Pythagoreans) had lived and worked decades, even centuries, before him. He will go down in the spiritual history of our century as a highly gifted, unique individual, a pioneer and a discoverer, for whom the spiritual attitude was as important a. the scientific. He was a man who never lost sight of the whole for the sake of the particular.
Akroasis deals on every page with the meaning and nature of harmonics. Any further word here concerning its teaching and world-concept would be bringing water to the brook. Instead, let me in the next few pages sketch the course of the author's life, and mention briefly the works published since 1946, thus bringing up to date Kayser's own listing (p. 170).
Hans Kayser was born April 21, 1891, in Buchan (Upper Danube Valley), the son of an apothecary. How significant his father's example was for his life and work is to be gathered from this excerpt from the dedication to his deceased father in the If Harmonia Plantarum:
"Music and plants appeared to you the two gates through which the divine light shines in our souls, the former as the proclaimer of eternal laws, the latter as the manifester of the unchangeable laws of the beginnings of life. Tone and form were proof to you that to be a citizen of this earth had a meaning, and that our yearning to belong is fulfilled through hearing.
How often you took me with you in search of plants, even while I was still a small boy. Hardly a valley, hill or rock in the Alb region, florally perhaps the richest in German terrain, was safe from us. Yet only occasionally, and in small amounts, did we bring home any plunder. The real plunder we kept in our minds, and the sight of countless stands of rare and beautiful flowers, shrubs and bushes is guarded unforgettably in my thoughts even today, like precious old pictures . . And often, when we came back to the house tired, and you had shut up shop, another realm awaited us, an inner one, music. When you were forty years old, in that little town far away from any music center. you learned to play the viola and you had me, at the age of ten, begin playing the cello. Together with other enthusiasts we played Haydn quartets, for better or for worse, and ended up playing Beethoven and Schubert. The old stone figure standing by the splashing fountain in the market place in front of our house must have felt a strange sensation in its breast from our heart-rending tones. It seemed beautiful to us then, and still seems so today."
For a long time the versatile youth was undecided whether or not to develop his talent for painting. But the hearing man in him finally gained the upper hand. At twenty Kayser studied music and natural science in Berlin, and after many stimulating experiences and profound study, he took his doctor's degree in History, Philosophy, and the History of Art at the University of Erlangen. He first made a name for himself as editor of the series Dom—Bucher deutscher Mystik (Cathedral Series—Books of German Mysticism), published by Insel-Verlag, a commission which concurred with his innermost bent for the philosophy of nature and for mysticism. In this series, he reserved the volumes on Paracelsus and Böhme for himself.
In 1920, after studying Kepler's Harmonice mundi and Albert von Thimus' Harmonikale Symbolik des .Altertums (Harmonical Symbolism of Antiquity), he turned to harmonics, a turn which was to prove decisive in his later life. In Pythagoras' basic esoteric diagram, known as the Lambdoma, he gained possession of the key which for the first time opened the door to an understanding of the mysteries of minerals and plants, their proportions and the rhythms of their growth, by means of the musical number. Von Thimus had approached the Lambdoma chiefly in retrospect as a philologist and antiquarian, using it as a cultural symbol. Kayser extended it beyond the bare framework outlined by Iamblichus and made it into a tool for his new harmonical investigations in natural science.
The first work along this line, Orpheus, a bibliophile edition in folio (Potsdam 1924), was issued in just two hundred copies and today has great value as a rare edition. Fight years later Der hörende Mensch (The Hearing Man) followed, whose profound Introduction assails in particular the one-sidedness of the haptical, quantifying tendency of modern science and philosophy, thus postulating as well as justifying philosophically a new world-concept founded on the higher senses of seeing and hearing.
Kayser married Clara Ruda in Berlin before the First World War. This happy marriage produced three children: Clara was an understanding and true helpmeet to the end of Dr. Kayser's life. Hitler's assumption of power moved Kayser to accept, in 1933, an invitation from friends in Bern. In Switzerland he subsequently not only gained further adherents and assistants, but also had the rare good fortune to find people who through their readiness to make sacrifices, enabled him and his family to settle and live permanently in Switzerland. Thus freed from the cares of earning a livelihood, he thereafter devoted all his powers to his research activity as an independent scholar. In the little house in Ostermundigen-Bern which friends placed at his disposal, and in the more spacious and beautifully situated country house built by himself in 1952 in Bolligen, all his later works were written.
He considered himself unsuited to lecturing, and only reluctantly consented to do so, "after hard inner wrestling". A lecture cycle from his early years in Bern ( winter of 1935-36) however was the occasion for the beautiful book, Yom Many der Welt (The Sound of the World), which perhaps leads more immediately and easily into the facts and particular problems of harmonics than most of his other writings. Later, after an interval of nearly twenty years, I twice succeeded in bringing Kayser to the lectern at conferences on symbolism in Basel (1955 and 1957). The gratifying reception which he found there encouraged him later to give a course in harmonics at the Academy of Music in Basel (1956-57), also to deliver two lectures at the Academy of Music in Vienna (1959). He also took an active part in an Eranos conference in 1958.
This aversion to public lecturing, which Kayser never fully overcame, resulted in his not having pupils in the full meaning of the word? although individual researchers—among them myself—took over from him the fundamental symbols and concepts of harmonics and worked with them in their own way.
If I have spoken of rare good fortune, of self-sacrificing friends and similar matters, it must not be supposed that Kayser enjoyed a fully assured, carefree existence. Not at all. He had to experience the inconsistency of fortune speedily and bitterly. Sponsors upon whom his living depended died suddenly overnight, and despite his natural warmth he, proud and sensitive, withdrew from others. More than once he found himself without financial means.
"Worries, worries, worries! The whole of life is nothing but one worry, and becomes more questionable any way one looks, the older one grows. Only the spiritual world resounds and glows in primeval and eternal splendor." (From a letter, April 5, 1955.)
Neither unsocial nor uncommunicative—for all his reluctance for public life—Kayser nonetheless considered it his primary task to influence his contemporaries, and those who would come after him, through the medium of the printed word. His substantial books have accomplished that task with ever-growing success. Their influence has proved more decisive, the inspiration which comes from his fresh insights reaches considerably further, than was heretofore known or surmised! And yet this is likely to be but a beginning. That which characterizes our century, that tendency to shatter and destroy all traditional forms and orders—in political and social life, in religion, poetry, the arts and music--becomes more and more shallow and meaningless, and is running towards a desolate void and thus to its inglorious end. Sooner or later the pendulum of our western cultural development must swing back in the opposite direction. Kayser believed this to the very end, and his conviction that, according to inner law, the perverse and absurd which offended his eye, ear and feeling, would die of its own accord, held him back from stigmatizing it openly. In harmonics, this universal and timeless teaching of order, would one day assume a decisive role in the task of reconstruction and thus become a leading power as a philosophy in which measure, value and quality would once again be honored.
Of the works of Kayser which were in preparation when .Throasis was published, the two harmonic studies, Der harmonikale Teilungskanon (The Harmonic Canon of Division) and Die Form der Geige (The Shape of the Violin) appeared in 1946 and 1947, The Lehrbuch der Harmonik (Fundamentals of Harmonics), monumental in every respect, was published at the end of 1950. For the scientifically working harmonicist it will always remain the indispensable, fundamental work of Kayser.
Meanwhile the plan for a new comprehensive work, the Hatmonikalen Symbolik (Harmonical Symbolism), intended to be in three parts with the overall title Orpheus, had matured. In seven years (1949-1956) Kayser was able to finish the first third, Die Welt der Götter (The World of the Gods), and get it ready for the press in a setting of about seven hundred and twenty pages in his own handwriting.' It is to be hoped that this work, which is complete in itself, can be made public in the next few years. The material had exceeded all the author's expectations as he worked on it, so he decided, after the completion of Part I, not to publish it immediately, but first to publish as an independent work some thing that originally was but a digression, namely, a study on Paestum and the harmonics of its Doric temples. The beautiful book Paestum, completed at the end of 1954, was published in Heidelberg in 1958. Kayser called it "in a certain sense a counterpart to the Harmonia Plantarum, As in the sphere of the plant kingdom, so here in the sphere of architecture, it is shown how to apply harmonical investigation and analysis concretely". Paestum was the last of his books which Kayser lived to see in print. Whether and to what extent he had added to his Orphikon ( which no doubt occupied his thoughts constantly), remains an open question, as it has not yet been possible to make a complete survey of his spiritual legacy. It is certain however that apparently in the last year of his life he began to make another copy by hand of the already finished part of the Orphikon: a truly splendid copy. When I saw it, I couldn't help but think of the pious labor of medieval monks who gave months and years of their lives to copying a precious manuscript.
And I asked myself if such a document really could have been intended as copy for the typesetter. Did Kayser have in mind to dedicate it to someone? Or was it begun solely for the joy and edification of the author, already in the shadow of death, who had always loved a generous format. handsome paper, broad margins, a well-proportioned page design, and a beautiful type face or handwriting? According to Dr. Hermann Augustin of Basel, a friend of Kayser who visited him a few weeks before his death in Bolligen, Kayser had not at that time considered a printed edition of the manuscript in the near future and had begun the copy so painstakingly to facilitate its distribution through microfilm. However that may be, Kayser was far from completing the copy. It includes only a fifth of the original manuscript and breaks off with the prophetic words:
"This world is no vale of tears, but is filled with fearful dangers and lordly beauties at the some time. Each of as steers his little ship of life between a Scylla and Charybdis existing both within and outside ourselves. But if we hold to our course, perform our mission from on high to the best of our strength, the sky is blue above as and the goal of our homeland beckons nonetheless. And should misfortune come upon us, we know that in another existence there is compensation. And when we take the path leading to that door through which each one of us must someday pass, we shall enter into the eternal where, in the great repose of the Source, we shall find shelter and peace, freed from earthly limitation. There we shall entrust ourselves to the great mystery, the endless good, the light and the harmony of eternity".
Julius Schwabe
Basel, September 1964