Harmonic Division CanonIntroduction from the Book

Introduction by Hans Kayser

Harmony: a word almost forgotten in the current apocalyptic collapse of European culture, amidst the hecatombs of blood, the destruction of cities, the torture of human souls, and all the endless suffering connected with these things: the now almost unendurable martyrdom of those who have been forced through the merciless grinder of almost six years of war! But when we speak the word “harmony,” when we allow its sound to play gently through our souls like a long-forgotten melody, then perhaps it will appear to us that a new hope is resonating along with it; that amidst the demonic noise of these dark times, a spark of tranquility, rest, and inner peace may be glimmering, a “song that is the lingering sound of the melody of the eternal spheres” for which the human soul has forever yearned, and yearns still.

This yearning, keenly present in all races and peoples, but especially to us today, caught in this storm of ghastly experiences, may well be the reason why the human capacity for thought has grown since the early ages of the harmony concept, and has developed it into a discipline whose name bespeaks its origins: harmonics.

In classical and pre-classical thought, and in the traditions of peoples outside of Europe, there is a relatively well-defined domain that has been almost completely neglected by historical studies: that of number harmonics and harmonic symbolism. Viewed outwardly, it appears to deal with connections between numbers, stars, notes, and mythological symbols in relation to the harmony of the spheres—but viewed inwardly, it deals with the great question of the relationship between nature and the soul, the influence of the psychical over the natural, and transmutation from the psychical into original, prototypical image-concepts. The approach behind this kind of thought is consciously or unconsciously “harmonic,” meaning that behind these image-concepts, there are forms that are either directly derived from tone-number relationships, or else correspond to psychical elements equivalent to these relationships. In the ancient Chinese political science of Li-Gi, harmonic thought was promoted to the level of political wisdom: “Music brings about unification, conventions bring about separation. In unification people love one another, in separation they are wary of one another.” This synthesis of tone-values and analysis of tone-numbers (in the harmonic manner of speaking), or the world of values (prototype: “music”) and the world of knowledge (prototype: “convention”), is summarized in the following words: “Music has its creative origin in heaven, conventions are formed on earth. If the formations are too many, there is confusion; if the creations are too many, there is violence.” With these simple maxims, the Chinese people preserved their culture for 3,000 years. Lao Tzu’s 42nd chapter—“The Tao gave birth to the One, the One gave birth to the Two, the Two gave birth to the Three, the Three gave birth to all creations, all creations leave the darkness behind them and embrace the light”—can be connected directly with the fundamental harmonic diagram. These two examples will suffice, though there are many more from the mythology and wisdom of the East, for which harmonic analysis often offers surprising insights.

In Pythagoreanism, harmonic thought often manifests as an independent science. According to legend, Pythagoras, shortly before his death, asked his favorite pupil to strike the monochord, the one-string, for one last time, thereby indicating that the highest thing in music was not of sensory nature, but instead related to intelligible observation. The monochord was the Pythagoreans’ experimental instrument. The system of tone-numbers they discovered through monochord experiments was the mathematical tool with which they analyzed the cosmos and the psyche. Today it is assumed that European science holds the birthright to the knowledge of the dependency of interval on string length and the numeric establishment of this relationship (Windelband: Lehrbuch der Geschichte der Philosophie, ed. Heimsoeth, 1935, p. 326).

In this way the qualitative (tone) is precisely connected to the quantitative (wavelength). But here, people forget that for the Pythagoreans, the converse was at least equally meaningful: the quantitative, the material, and things calculable by means of number thus gained psychical form and value, since the number ratios could be heard! This was the “formidable experience” of which the ancients spoke, and on the basis of this experience of toning numbers, the world began to resonate. Matter gained psychical tectonics, and spiritual things, the realm of ideas, obtained a concrete rooting in harmonic forms and elements. This last aspect of harmonics was almost completely lost, with only a few exceptions, and the task of modern harmonics is to reintroduce it into the scientific way of thinking as equal to what it was in ancient times. Unfortunately, none of the main harmonic works of ancient times have been preserved, and we can only reassemble some parts of the outline of ancient harmonics through the indirect analysis and reconstruction of various theorems and fragments (Philolaus, Archytas, the Timaeus scale, the ancient harmony of the spheres, the dieresis in Plato’s later works, and so forth). However, the way of thinking itself, and presumably a few handed-down items, were passed on from Ptolemy to the Renaissance (Alberti, like Vitruvius, uses harmonic proportions for architecture), as far as Kepler and his Harmonice mundi. In this latter work, Kepler’s famous Third Law of planetary motion was derived by means of a systematic harmonic technique, namely tone-number operations. And the last great harmonist, Albert von Thimus, in his little-known late 19th century work Harmonikale Symbolik, offers a historically oriented overview of the number-harmonic relics of Eastern and Western antiquity, as well as many symbolic analyses and syntheses.

Almost 3,000 years of tradition stand behind harmonics. And yet, in modern reference books, one will search in vain for any mention of it as a world view, much less as a science. How is this possible?

The reason is simple. The original systematic harmonic works (those of Archytas, Democritus, etc.) have been lost. All that remain are certain theorems and methods, only rudimentarily applicable in their corresponding domains (the study of proportion, music, architecture, astronomy, symbolism). Just as it is impossible for an art historian to restore a temple frieze with numerous missing fragments to all its original beauty, so a purely historical reconstruction of the true ancient harmonice from the remaining fragmentary material is impossible. Here only one way remains: delving into the depths of Pythagorean thought and experimenting for oneself with the time-honored monochord in order to conjure up the voices of the ancient harmonists and open one’s spirit to them in admiration and love.

The result has been the discovery of the great phenomenon of tone-number as a synthesis of two worlds: nature and the soul. This primal phenomenon has its own norms and laws. It gives rise to “harmonic theorems,” a kind of syntax in the harmonic language. Harmonic theorems in turn form the building material for “harmonic value-forms,” a kind of psychophysical tectonics, on the basis of which harmonics as a science first becomes possible. Beside the world view (Weltanschauung, aesthesis), harmonics places an equally valid and previously unknown factor of perception: world hearing (Weltanhörung, akroasis). Since all inwardly experienced harmonic forms can be tested by our psyche according to their “correctness,” their “tuning,” the psyche is the judge, the interpreter, and the intellect, with its logical forms, is merely the intermediary. The great domain of the unconscious should not fall directly within discursive thought, but should be understood thoroughly in the forms of harmonics, which are appropriate for it, and then divided “ektypically” into various domains, i.e. examined in terms of its outward forms. In harmonics, the sense of hearing, like the intellect, plays the role of sensory mediator. This is a decisive role, for it has an advantage over all the other senses: direct a priori numeric perception. We can hear numbers as tones! Since all harmonic numbers are number ratios, i.e. proportions, and since every proportion can be illustrated visually, there is the possibility of a direct transposition of the auditory into the visual. This audition visuelle is the domain of harmonic symbolism.

It has become apparent that harmonics, newly established, has the possibility of revealing commonalities in the most varied disciplines, which we can experience as psychical certainties in ourselves. The “tone spectra” reveal harmonic structures in atoms; cadencing resonates in the indexes of crystal forms, whose typical three-step progression is also found in logical dialectic; the space-time phenomenon acquires a psychical (major-minor) aspect via harmonic analysis, as well as an interpretation surprisingly close to the modern view; quantum theory and mutation theory have their prototype in the tone-number discontinuum; the shell-like form of the inner earth reveals an obvious chord structure; the eye and the ear can be psychologically proven to be “reciprocal,” i.e. to complete one another mutually, via the application of harmonic data; a harmony of plants (Harmonia Plantarum) is entirely possible as a morphological study; historically, harmonics sheds new light on all disciplines, from Pythagorean fragments to Plato’s later philosophy, and especially in ancient Eastern mythology and symbolism; in the arts, harmonics leads to a view of aesthetics without arbitrariness as both desirable and possible; and even in religion, harmonic diagrams, admittedly sub specie aeternitatis and divinitatis, can offer modern people an ample, comforting certainty.

Two forms of protection are absolutely necessary for harmonics today: the defense of being a “discipline for everything” and protection against being cheap monism. But a discipline can be universal in the best of senses, without fancying itself to be able to solve the universe’s puzzles completely; without this belief, philosophy would be impossible. And as for the danger of wild synthesizing, against which rigorous and precise education in harmonic theorems offers protection, it is enough to point to the present situation, which certainly arises not only from a deluge of wholeness but equally from a schizophrenia of thousands of halfways and ready-mades that have nothing to do with one another.

Here, harmonics makes at least an attempt to build a two-way bridge, founded on psychical values born from truly humanitarian ideals and aspiring to the sphere of the divine. How successful it is in this attempt—that depends on the relative nature of our human abilities of perception, and can only be found through the work of the harmonic scholar.

“Harmonic studies” picks certain topics from the broad domain of harmonic application possibilities, and examines them without the usual scientific baggage, in such a practical and elementary way that anyone who takes an interest in the relevant domain can verify things first hand. As with all harmonic work, it is essential not only to read, but also to work through things in an applied manner, especially drawing and copying the relevant diagrams. One should not be intimidated by the numbers and geometric drawings; only the simplest concepts of geometry and arithmetic are necessary for understanding them, and working along with them oneself will soon give one a deeper view into the audition visuelle that provides the initial foundations and assumptions for an akroatic mentality.

For further help in expanding the knowledge acquired in individual studies, the following harmonic works are recommended:

1. Hans Kayser, Der hörende Mensch, Verlag Lambert-Schneider, Berlin, 1932.
2. Hans Kayser, Vom Klang der Welt (introductory lectures in harmonics), Verlag M. Niehans, Zurich, 1937.
3. Hans Kayser, Abhandlungen zur Ektypik harmonikaler Wertformen, Verlag M. Niehans, Zurich, 1938.
4. Hans Kayser, Grundriß eines Systems harmonikaler Wertformen, Verlag M. Niehans, Zurich, 1938.
5. Hans Kayser, Harmonia Plantarum, Verlag B. Schwabe, Basel, 1945. 6. Hans Kayser, Akroasis, Verlag B. Schwabe, Basel, 1946.

In progress

7. Harmonic Studies, Volume 2: Die Form der Geige aus dem Tongesetz konstruiert, Occident-Verlag, Zurich, 1946.
8. Lehrbuch der Harmonik, Occident-Verlag, Zurich, 1947.