Gann gave much attention to grain markets, and in particular Wheat, Corn and Soybeans. Gann had a Wheat chart back to 65 BC, which Baumring took back to 1200 BC.
Long historical data made Wheat a premier market to study long term cycles, and grain markets depend on weather, a secondary phenomenon which Gann also studied and analyzed.
Hasbrouck Space and Time
With rare research from the 1920’s through the 1970’s, the Hasbrouck Space-Time Archives studied market influence based on Solar Field Force.
Muriel Hasbrouck, aided by her husband Louis, researched solar phenomena, space weather and earthquakes in relation to market forecasting, producing a well-received forecasting letter for 30 years.
A quick insight into general conditions of the market can be had by synthesizing combinations of data as simple indicators giving an overview.
Such indicators are often based on diverse data, from astrological signals, like Scott's Astronomical Market Barometer or Bradley’s Siderograph, to whether a specific market is overbought or oversold.
The origin of modern chemistry goes back to the mysterious science of Alchemy, which originated in Ancient Egypt, know to the Arabs as Kemi, the Black Lands.
Alchemical experiments with chemicals and compounds led to the modern science of chemistry, although Alchemy incorporates spiritual and esoteric elements missing from chemistry.
Leonardo Fibonacci is often cited as the discoverer of the Golden Ratio or Phi, but he was not the first, The Ancients called this the Divine Proportion and used it in their art and architecture.
The Golden Ratio is the governing principle of most natural forms, and the Divine Proportion is the most dominant mathematical form in the natural universe.
Harmonics and Music
The science of harmonics is one of the most important subjects in the esoteric and scientific traditions, positing that harmonic relationships of vibration govern the structure of the universe.
W.D. Gann called his system of market order the "Law of Vibration", and used principles of harmonics and vibration to predict trends in the financial markets.
Esoteric and Pythagorean sciences love to play with the value and meaning of numbers, from the complex mathematical theories of the Platonists, via Fibonacci’s ideas, to number progressions, ratios, proportions, sequences, and chaos theory.
We specialize in the overlap of numerical and esoteric systems positing a more integrated cosmology.
W.D. Gann Works
We stock the complete collection of the works of W.D. Gann.
His private courses represent the most important of his writings, going into much greater detail than the public book series. Our 6 Volume set of Gann’s Collected Writings includes supplementary rare source materials, and is the most reliable compliation of Gann’s unadulterated vital work.
Dr. Jerome Baumring
The work of Dr. Baumring is the core inspiration upon which this entire website is based. Baumring is the only known modern person to have cracked the code behind WD Gann’s system of trading and market order.
Baumring found and elaborated the system of scientific cosmology at the root of Gann’s Law of Vibration.
There is no other Gann teaching that gets close to the depth of Baumring’s work.
Hans Kayser's Textbook of Harmonics - Excerpts §54. Harmonic Cosmogony
A Translation Society Edition
By Hans Kayser
§54.1. Preliminary Note
The reader who has followed the investigations in this book closely up to this point, thought over their content, and above all experienced them, will wish to see in this closing chapter a certain summation of what has been achieved thus far. Admittedly, only an attempt can be made at this, in which both reader and author will do well to retain that kind of reserve that is inevitably necessary in such attempts: the general caveat of the insufficiency of human endeavors at understanding. The apparent apodictic quality of the following conclusions should therefore be understood only in the sense of a formulation appearing as correct to the author at the time.
As an interpretation concept, we choose “cosmogony” and use as its basis the systematic embodiment of akróasis, the “P”. “Cosmogony” means the study of the emergence of worlds; a significant, indeed enormous, frightening term, if we grasp it in its full breadth and depth. We will see whether and how we can treat it fairly. The accusation of inappropriately introducing and modifying the word and concept of cosmogony (and cosmology), used commonly in earlier times, can be dealt with simply by a reference to the Kosmogonie of Christian Von Ehrenfels (Jena, Diederichs, 1916), the modern founder of gestalt research. Here the concept of cosmology was awakened once again in its original meaning, under which we also have taken it up, whereas for example the cosmogony of Kant and Laplace was marked by a purely astronomical and natural-scientific attitude.
Regarding the “P” partial-tone coordinates, the reader will have been persuaded by studying §53 that it does not represent a simple intellectual scheme, but instead that both its entire form and its “selections” contain forms in themselves, which are expressively, constructively, and creatively active in nature and in our psyche. These akróatic forms thus have a reality character that is not regulative or analogizing, but instead constitutive, and as such they are indicators for us of realities in the highest sense. But the same goes for this as for all “realities”: they have their own voice, their own language, and each new language needs not only to be learned but also to be understood in its innermost nature, regardless of the individual character of those who speak the language. At this point there will always be a source of misunderstanding with regard to interpretation, and therefore one would do well to accept these “sources of error” as inevitable, not least as regards the harmonic diagram.
In what follows, we will proceed in each case by first indicating the harmonic phenomenon—which can be done very briefly since it has mostly already been discussed—then draw the cosmogonic conclusion, add a commentary to it, and finally examine what history has to say to us about our conclusions. As in all our “ektypic” examples, the following can give only a small limited selection.
Our analyses will use the 1/4 PE in its familiar modifications, and will use the polar depiction of the “P” in only one case, where it is shown to be appropriate. First of all, we use as a basis the 1/4 PE9 in the location and “variation” shown in Fig. 471: here, the tone d is set as the generator-tone. This is firstly to show how it also “works” with other tones—the logarithms naturally remain the same, i.e. 1/1 also has the log 0.000 here, 3/1 has log 1.585, etc.—and also because in this case the signs and are symmetrical to d on both sides, as we already see from the circle of fifths:
In addition, most of the scales derived from 1/1 d have a C-major character (analogous to 1/1 c = B-major), so that in the choice of this generator-tone, the “Dorian” background becomes especially conspicuous.
We did not arrive at this highest of all harmonic concepts of the 0/0 deductively, setting it at the beginning of the “P”, but instead inductively, following the generator-tone line and the equal-tone lines back beyond 1/1. This is exceptionally important for harmonic deduction, because it is precisely through this induction that we are forcibly led to this concept; so here we believed ourselves to be justified in speaking of a “harmonic proof of God,” i.e. the factual existence of an ultimate spiritual reference-point. Admittedly, our statements about this concept can only cling to words, such as totality, everything, groundlessness, eternal rest, etc., which attempt to express something for which there is no adequate term in any language, and for which 0/0 is simply the most accurate symbol. Mathematically, 0/0 can be every number, thus the totality of all numbers; therefore it meets with our definition, which indeed includes not only numbers but all being-values. Since the doubled zero is not arbitrary as a quotient (0/0), but instead is forced upon us in the mathematical-symbolic sense, we will henceforth pay special attention to precisely this expression, and draw our conclusions from it.
In §25, we already indicated those concepts of God, or better, Deity, that are to be identified with the 0/0. They are the “impersonal” concepts of God, concepts of a totality of all beings, all substances, the “Brahma” of the Indians, the “Nirvana” of Buddhism, the “Tao” of the Chinese, the “Ensoph” of the Kabbalah, the “groundlessness” of Jakob Böhme, the “absolute being” of Hegel, and finally the “unknown God” of modern Europe.
Opinions are divided regarding the ancient Judaic concept of God. In any case, the precise translation of the beginning of the Bible reads: “In the beginning, Elohim newly created heaven and earth.” The words “In the beginning” (bereshith) would be better translated “in principle”; bara means not only “to create,” but also “to create anew,” and—this is especially interesting—“Elohim” is known to be a plural, thus corresponding to our harmonic symbol 0/0, which then created, or created anew, “heaven and earth,” i.e. the polar principles 1/∞ and ∞/1. This “new” creation, however, assumes worldly conditions already gone by, and is not a creation from the Nothing, but at least a creation from existing possibilities. The metamorphosis of the “Elohim” into the later “Jehovah” or “Yahweh” then corresponds to the step from the 0/0 to the 1/1.
In the esoteric Indian teachings of the Upanishads, it is said, with an astonishing degree of philosophical wisdom for those ancient times, that the primal condition of things, the primal-being, i.e. the Brahman in the later sense, was “na a sad, na u sad” = “not being, but yet also being” (Deussen: Allgemeine Geschichte der Philosophie, vol. I, 1894, part 2, p. 117). A direct description of our harmonic symbol 0/0 can be found in a stanza of the later Upanishad: “Two things are latently contained in the eternal, endless highest Brahma: knowledge and ignorance. Ignorance is fleeting, knowledge is eternal, yet he who ordains them as Lord is the Other.” (Deussen, ibid., p .120)
“Knowledge” and “ignorance,” however, are both merely synonyms for things that are finally inexpressible, indefinable. “The Being that is Brahman should not be understood as the kind of being that we know through experience, and is, as we have seen, much more a non-being in the empirical sense. The depictions of the Brahman as the perceiving subject in us are accompanied, as a rule, by the assurance that this perceiving subject, the ‘perceiver of perception’ will remain eternally unknowable in itself, and merely indicate that the Brahman is devoid of any objective being” (Deussen, ibid., p. 133). Friedrich Schlegel (Über die Sprache und Weisheit der Inder, Heidelberg 1808, p. 247 ff.) translates the following passage from the very ancient Laws of Manu:
It is said:
Once all this was darkness, unknown, and unspecified, Unrevealed, unknowable, as if completely sunken in sleep, It was the blessed self-subsistent, discoverer of the undiscovered, The beginning of being, that steadily grows, that powerfully destroys the night, That which is never to be grasped through sense, invisible, ever-inconceivable, Which meditating, wanting to create many beings from its own body, First created water, then the light of the sun was engendered. The sun was like a shining gold egg. In it lived Brahma, lord of the universe, through his own power. In the egg this deity then sat idly for a year, Then he himself divided the egg in two by his thought, From the blessed pieces he then created Earth and Heaven…
Regarding the above lines, and many other obviously number-harmonic passages in ancient Indian wisdom, an admonition in the Upanishads (Ramap. 84) is very noteworthy: “Do not give the diagram to the common people!” (Deussen, ibid., pp. 13 and 68). One may well conclude that even then, the initiates taught their students by means of symbolic geometrical figures, in a similar way to the Pythagoreans.
The Buddhist concept of “Nirvana” is outlined in the following manner in the Udana, section 8, Ch. I: “There is, O monks, this domain where there is no earth, no water, no fire, no air, not the domain of the infinity of consciousness, not the domain of nothingness, not the domain of neither-perception-nor-non-perception, not this world, nor that world, nor both, nor sun and moon. That, truly, monks, I call not-coming, not-going, not-remaining, not-vanishing, not emerging. Not fixed, not movable, without support. It is the end of suffering [Nirvana]” (Paul Dahlke: Buddhismus als Religion und Moral, Munich 1914, p. 171). Also, Theodor Stcherbatsky states the following among a few orthodox statements regarding Buddha: “The true being (Nirvana) is not knowable. It can only be defined from the negative side, insofar as it is opposed to the entire knowable world of appearances” (Erkenntnistheorie und Logik nach der Lehre der Späteren Buddhisten, tr. O. Strauß, Munich 1924, p. 82). Here the agreement with the harmonic symbol of the 0/0 is evident.
The concept of the “Tao,” for which there is no adequate expression in European languages, was not invented by Lao Tzu, who presents himself often enough as merely a preserver of ancient traditions. In the investigation of the relationship between the 0/0 and the 1/1, we will delve more deeply into the origins of the highest concepts of ancient Chinese wisdom. In the treatise Das Geheimnis der goldenen Blüte (Munich 1929, p. 11, tr. R. Wilhelm, introduction by C.G. Jung), which is based on earlier traditions of Taoism, the beginning reads: “The Master Lu Tzu said: That which exists through itself is the Tao. The Tao has neither name nor form. It is the One Being, the One primal spirit.” In complete opposition to the non-speculative tendencies of Confucianism, predominantly directed towards the practical, a metaphysically oriented movement appeared within it. “A unique speculative life was awakened in this school in the 12th century through the great sage Chu Hsi (1129-1200), who wrote about every course of life and assigned a place in the system to everyone, thereby solidifying the Chinese world of thought for many centuries. He went considerably further than Confucius with the natural-philosophical observations in his Sing-li (= natural law), in which, schematizing and developing the metaphysical views of the Ching, he arrived at an impersonal primal being, which reveals itself as eternal order” (Brockhaus).
The highest Egyptian deity is Atum-Re. “I am Atum, who was alone in Nun (chaos); I am Re with his shining, as he began to rule what he had created,” reads the Book of the Dead (F. Roeder: Urkunden zur Religion der alten Ägypter, Jena 1915, p. 239), corresponding perfectly to 0/0 → 1/1 in harmonic symbolism. “I am Re, the lord of the light-rays” (ibid. p. 266)—we need only remember our concept of the “equal-tone lines” radiating out from the 0/0 in order to obtain an even closer harmonic parallel.
The Babylonian poem of the creation of the world begins with these lines:
When the sky above was not yet named, The earth below did not yet have a name, When Apsu, the primal beginning, creator of all, Mummu, Tiamat, the mother of all, Blended into one with their waters, When there was neither dry land nor marshland, When of all the gods not a single one lived, Nothing was known, no fate defined, Then the gods were created in their midst; Lachmu and Lachamu were called into being.
(A. Ungnad: Die Religion der Babylonier und Assyrer, Jena 1921, p. 27.)
Here, as in almost all Babylonian legends of the creation of the world, a kind of chaos is assumed, a primal condition (= 0/0) from which the two principles of male and female emerge. Diodorus Siculus (II, 30) writes: “The Chaldaeans claim that the world is in its nature eternal, it has never had a beginning and can also never end; but through a divine authority all is arranged and cultivated, and also all changes in the heavens are neither effects of coincidence, nor inner laws (!), but instead a definite and unchangeably valid decision of the gods”—or, as we would say harmonically: the norms.
Kabbalistic speculation, as it is concentrated in the Zohar, says the following about the absolute primal origin, the “En-soph”: “Before the ancient of the ancients, the hidden of hiddens [revealed itself], there was neither beginning nor end ... in the Book of Secrets it is imparted: the ancient of ancients, the hidden of hiddens, has a certain form and thus far [up to a certain point] can be known. But it is once again unknowable, because it cannot be sufficiently grasped [by our thoughts]. Thus it has a certain form, but does not let itself be known [in its most innate Being], because it is the ancient of ancients [= the absolute primal origin]” (Zohar III, 128a, Idra Rabba. From Erich Bischoff: Die Elemente der Kabbalah, vol. I, Berlin 1913, p. 93). One should meditate upon this passage from the viewpoint of our symbol 0/0! Yet more interesting, in the sense of akróasis and for the meaning of the auditory (voice, word) in Judaic thought, is the following passage from the Zohar I, 246b (from E. Bischoff, ibid., p. 90): “Come and see! Thought is the origin of all that is. But it is unknowable from the beginning and closed within itself. When it begins to develop, it comes to a point where it becomes spirit. It is then called understanding and is no longer closed within itself. The spirit develops itself again in the midst of the secrets that still surround it, and the voice arises that is the epitome of all heavenly choirs. This forms itself by virtue of its spiritual origin to articulate sounds and certain words. In this, with close observation, one notices that thought, spirit, understanding, voice, and word are a single thing, and that thought is the origin of all that exists, and that no interruption is present for it.” The harmonic symbol 0/0, as a reference point of all equal-tone rays, stands as an expressive term behind the following passage from the Zohar (ibid. p. 96): “When the hidden wished to reveal himself, he began to bring forth a shining point. Before this illuminating point had broken through and become visible, the unending (En-soph) was completely hidden and spread no light.” The “mathematical” 0/0 is defined quite modernly in the Tikkunei Zohar with these words: “You are One but not in the number, thought grasps absolutely nothing of you. In you there is nothing imaginable, no form and no being” (Molitor: Philosophie der Geschichte, II, 1834, p. 247).
Jacob Böhme (Sex Puncta Theosophica, I, 7) sets the “groundlessness” as the highest principle: “Thus, the first will is a groundlessness, to be regarded as an eternal Nothing, and so we perceive it just like a mirror in which one sees one’s own image, just like a life, and yet it is not a life, but instead a figure of life and of the image of life.” Here, also, we need only imagine ourselves as a tone-point, i.e. as a being-value, and look to the 0/0 along the “direction” of the equal-tone line (“mirror”), and then we have a precise harmonic correspondence. In more recent philosophy, Böhme’s concept of “will” has been equated with that of modern philosophy (Schopenhauer etc.), and taken as anticipated by Böhme. But Böhme’s “eternal will” is not merely to be grasped voluntarily. Böhme writes (I, 13): “So the mirror of the eternal eye appears in the will, and generates another eternal basis of itself in itself: this is its center or heart, from which the sight of eternity always arises, and through this the will becomes astir and active, namely of that which generates the center.” Harmonically, we interpret this passage thus: only when the “mirror of the eternal eye” 0/0 “generates another eternal basis of itself in itself,” i.e. looks at itself, becomes conscious, which we can express with the term 0 ↔ 0, only then does the will become “astir,” i.e. becomes our modern active concept of will, and appears in the 1/1, i.e. in the first conceivable “vibration,” the actual Being, the creator-word “Let it be” (= Fiat).
As a conclusion to this historical excursion, we share yet another definition of the “nature of God” from the Catholic Kirchliches Handlexikon by M. Buchberger (article: “Gott”):
God is really and substantially different from the world and inexpressibly elevated above all that is outside of Him and that can be thought (Vatic.). As the self-existent and necessary Being, God stands so far above the world of created and contingent being that He does not connect with it, even in the highest sense. Through this, in contrast to pantheism and monism, every possibility of mixing and combining with the substance of the world is excluded, as is every relationship of substance to the worldly manifestation as though to modi and accidents of the one Divinity. God cannot be ‘seen’ (1. Timothy 6:16), but only perceived through the ‘intellect’ (Romans 1:20), he is ‘spirit’ (John 4:24), ‘one singular, completely simple and unchanging spiritual substance’ (Vatic.), thus a personality above the world.
How a “personality” should suddenly spring from this absolute transcendence of the divine—that is precisely the problem that the “intellect” wishes to investigate, and that is the path of our following steps in harmonic cosmology.
The reader interested in the history of religion will easily find a far greater number of related examples in ancient myths, religions, and scholarship; but merely from the few things imparted here, he will share the author’s deep wonder and inner awe at the remarkable convergences, all meeting together as if at a focal point in the harmonic symbol 0/0.
§54.3. The Act of Creation
Definition: The unity. “Let it be!” (= Fiat). Origo. Revealed God. Demiurge. Birth of space and time (wavelength and frequency). Uppermost being-value.
We obtained the symbol for the deity 0/0 a posteriori, since the 0/0 concept gives us no possibility of hearing, measuring, and building a system from things such as frequencies or string lengths. It is different with the unity 1/1. Here we must always begin with a phenomenal investigation, and initially a systematization. The question immediately arises: what concrete relationship does 0/0 have to 1/1?
Here we must traverse the two ways, the ̔οδόν κάτω and the ̔οδόν ̔άνω (upwards and downwards). “Upwards” (i.e. retrospective), as we saw, necessarily yields 0/0 from the results of the main “intentions” of the “P”, e.g. the generator-tone line:
0/0 ↑ 1/1 2/2 3/3 : n/n : ∞/∞
In a certain sense, the progress from 1/1 to 0/0 is psychophysically demanded and required. The case is completely different, however, for the “downwards,” i.e. when we think cosmologically. Here 0/0 signifies the primal beginning, the highest peak of the system of the world, and how should we imagine 1/1 emerging from this imaginary “groundlessness”? It is indubitable that a monstrous chasm exists between these two symbols; if it is bridged, then everything else follows legitimately and arises of itself.
Harmonically, we have two possibilities of bridging this metaphysical hiatus. First we observe once again that this double zero is necessarily yielded as a quotient from the interpolation of the “P”. We can now imagine that the symbol 0/0 becomes conscious of itself, perceives a “will” in itself, looks at itself, and this we can notate as above, thus:
0 ↔ 0
In this instant, the “all,” i.e. the fundamentally inexpressible, transmutes into a metaphysical polarity of two entities, and thereby pushes the unity 0/0 → 1/1 out of itself. This is the great act of the deity becoming conscious of itself, and simultaneously the emergence of the first “number,” i.e. vibration or wavelength (time or space), and of the first “tone,” i.e. psychical value. But we can also imagine that the 0/0 symbol potentiates itself, likewise grasping a will to become conscious of itself, to reveal itself, and we notate it as:
Here, one zero-value is set as a power of the other, and thus it thrusts the 1/1 out from itself, from its endless abundance (indeed, speaking mathematically, 0/0 can also mean “all,” every number, just like 0°). Here there is doubtless a discrepancy between the mathematical and harmonic interpretation.
0/0, just like 0°, has no definite meaning mathematically, i.e. it can mean everything.
One can think of 0/0 as appearing from 01–1 = 0°, or vice versa, but both symbols can mean every number according to the mathematical interpretation. It is different in harmonics. In the symbol 0° we see, at the least, a self-aspectation (0 ↔ 0) or self-potentiation of the zero, and at this moment the quotient 0/0 becomes an entity of a different type, namely something perceiving itself unitarily: i.e. as the unity itself. Harmonically, the passage or emanation of the 1/1 from the 0/0 signifies a transformation in the sense of becoming conscious of the self, a direction of the will, an expression out of the unity of the actual, the real. We will see in the following that harmonics, in contrast to mathematics, has definitions that are not possible in pure mathematical terms, or that no longer make sense in mathematics, especially regarding the symbols of zero and infinity (0 ∞). In the unity 1/1 we see the highest instance of all that is factual and real, and thus the realization of the first being-value itself. Through the birth of this first “generator-tone,” the unity-tone is also attached to the unity 1/1, i.e. the material (number) is placed next to the psychical (tone), or joined with it a priori, like body and soul. Since this first being-value (1/1 + generator-tone) stems directly from the 0/0—as every being-value does in later evolution via equal-tone lines—and is aspected and pervaded by the being of this ultimate spiritual court of appeal, body, soul, and spirit are unified here in every harmonic “field,” and typified in 1/1. The following section will explain why we use the ancient Chinese inverse symbol as a Psymbol for the unity (and later in Table 472 for the entire “world-axis”).
Since every being-value “is” and “tones,” and this can only occur on the basis of the temporal-spatial reciprocity of frequency and wavelength, time and space are also born with the unity 1/1, and therefore the framework for the factual existence of all being-values.
In §25a, we introduced various examples from history regarding both the eidetic God-concept of the 0/0 and the Origo 1/1, and a few of the highest philosophical system-concepts, which we broadened in the previous historical review with regard to the Eidos. There we observed that between these two different viewpoints, the Eidos (0/0) and the Origo (1/1), one can perform a certain classification of these highest concepts, and subsequently of the various religions and wisdom-teachings, which can also be important for the inner characteristics of the studies in question. Here we want to take the reverse path and allow ourselves a possible overview, admittedly also very limited, of whether religious studies and philosophical or cosmological systems exist that combine the two elements, Eidos and Origo. As a result, we can say here, without being able to prove it due to the restricted space, that although there are doctrines which in their collective character outspokenly tend toward one pole or another (0/0 or 1/1), both elements are found in almost all of them, albeit in more or less strong “potency.”
This time we shall begin with the Christian concept of the “personal” God, whose origin is in the Judaic concept of Yahweh, and who definitely exhibits a stark Origo (1/1) character: But even with such an explicitly concrete and unity-affirming God-concept, we find some philosophizing over the “nature of God” on the orthodox side (as we saw from the above quote from Bucher’s Kirchliches Lexicon) that has hardly anything to do with a “personal creator God.” On the other hand, besides the almost materialistically emphasized concept of Yahweh in the Old Testament, there is the En-Soph of Judaic mysticism and tradition, about which any adequate statement is explicitly denied. Obviously there are eidetic elements here.
If we understand the above concept of God in terms of his inner nature in the sense of the harmonic 1/1, and less in terms of the actual genealogy in the relevant pantheons (since these are by no means unified, much less complete, especially in Babylon and Egypt, and even less so in India), then we can introduce something like the following entities: Marduk (Babylon), Yahweh (Bible), God the Father (New Testament), Zarathustra (Persia), Osiris (Egypt), Mithras (Iran), Zeus (Hellas), Jupiter (Rome), Buddha (India), the Monas (Gnostics, Neopythagoreans, and Neoplatonists), the “One” (Plato), the Demiurge (Greek philosophy), the Monad (Leibniz), and indeed all “monistic” systems.
As one can already see in the mythological and religious entities that have the character of the Origo, the idea of the redeemer or mediator is bound up with most of them, for example when Christ is different from God the Father, he is still “consubstantial” with him. In our following cosmogonic steps, we will also see a precise harmonic correspondence.
A. von Thimus, who gives an exhaustive analysis of some inscriptions at the Temple of Karnak in the 15th section of his Harmonikale Symbolik, writes the following (II, 339), based upon Lepsius and other sources about the Egyptian god Nubti: “Also in his earth-born form, he is one with the permeating divine spirit that vivifies the material creation; the figure of this god symbolizes both the creative artificer of the All, and also the world of elementary created things, fertilized by the life-breath of the divine spirit. But he is also symbolically the bearer of the secret thoughts that lead to a future spiritualization and transfiguration of the ensouled human creature, summoned to union with the divine nature and to unification with its creator.” The inner identification of this Nubti with the 1/1 and his “mission” as concentration towards progress (or regress) to the 0/0 should not be misunderstood. Thimus shares a wonderful passage from the unfortunately much misunderstood Iamblichus (De mysteriis sections 8.1 and 2) on the ancient Egyptian doctrine of the first cause (ibid. II, 453-355):
Before any true being, and before the beginnings of all things, is the One God, predominant over the first God and King, staying immovable in the oneness of his unified Being. For neither the intellectual nor anything else is mixed into his Being. He is set up as the primal concept of the truly good God, who is father and creator of himself and the sole father. He is greater and first, and source of all things, and the primary form of the first archetypes of Intellect and Being. From this One, the self-sufficient God has created himself, radiating in his brilliance, thus both sufficient to himself and father of himself. For this God of Gods is the beginning, and the Monas proceeding from the One, and the pre-substantial = primary origin of all that is. From him proceeds Existence and likewise Being, due to which he is also called the Father of Being; because he himself is the Being above all being, the beginning of intellectual things, and for this reason he is also called the beginner of the Intellectual.
Thus Thimus quotes Iamblichus. The words “and the Monas proceeding from the One” show clearly that this entire passage is about the attempt to build the demiurgic Origo concept of God together with that of the eidetic deity (0/0), or through words and concepts (where the sign of the “One” is obviously used for the 0/0 concept!) to somehow clarify the relationship between Eidos and Origo.
F. Cumont (Die Mysterien des Mithra, Leipzig 1911, p. 125) writes: “Mithra the creator is, to use the philosophical language of that time, the Logos emanating from God, who partakes in God’s omnipotence, and after he, as demiurge, has formed the world, he watches over it. The initial overthrow of Ahriman, however, has not condemned him to impotence. The struggle between good and evil continues on earth between the envoys of the Olympian ruler and those of the prince of demons; he reveals himself in the heavenly spheres in the opposition of the propitious and unpropitious stars, and reflects himself in the heart of man, the microcosm.”
Here, then, as with the Logos concept of St. John, the Logos is considered as emanating from God (0/0), i.e. as the Origo (1/1).
Proclus (in Timaeus 155) mentions a beautiful legend: According to Pherecydes, the teacher of Pythagoras, Zeus (1/1) changed himself into Eros after he had decided to create the world from opposites, and to bring things into friendly symmetry and to agreeable unity with themselves. The speculations of Plato and the Neoplatonists (Plotinus, Proclus) about the “One” are so well known that here we can be satisfied with this simple reference. Through harmonic analysis, Plato’s Parmenides (The Ideas and the One) in particular, and his supposedly last dialog, the Philebus, might receive a whole new illumination, just as all of the Platonic “dieresis” of ideas and concepts can be derived straight from the “law of harmonic quantization” as our “P” embodies it. (For background, Stenzel’s Zahl und Gestalt bei Plato und Aristoteles, Leipzig 1924, is best.)
Ancient Chinese speculation places the Tai-ki (1/1) under the Tao (0/0) as a demiurgic principle; Windischmann writes on this in his excellent Philosophie im Fortgang der Weltgeschichte (vol. I on China, Bonn 1827, p. 142 ff.), a book which has hardly been equaled even today, though some of his understanding of details has been superseded (especially regarding music and the study of numbers, for which he refers to the French Abbé Roussier, Amiot, and others):
The ancients knew well that over this natural principle (Tai-ki) another ruled, ... and Shi-tsen, an ancient writer from the Chou dynasty, says expressly that Tai-ki has a lord over it ... further it reads: The Tao goes before the beginning of things. Tai-ki is thus, in the sense of the ancients, simply the terminus a quo of all creatural existence. But since this terminus is simultaneously regarded as a beginning that proceeds from eternal wisdom or, as we would say, as the basis for the world, as its firm coherence, thus it is also the axis around which everything moves, including the main girder that unites the whole building, as the sensory image of the spiritual Tai-ki, which is the same as Tai-i (the unity). It is also called axle-tree, root, and peak of the tree, foundation, axis, column. It is taught that it is not to be confused with the doctrines of the disciples of Fo (the Buddhists) or with the Nothing of the Tao-sse. It is the (positive) beginning that has been before all things, but in reality is difficult to differentiate from them; because all things are Tai-ki according to their type. In this sense it is also called the axis of the world, that reaches from one pole to another and around which everything changeable moves. Human understanding is incapable of grasping this beginning, an unapproachable power, spiritual and inexpressible. The elements came forth from it, and from them both the heavenly and the earthly. Obviously the Tai-ki, since it starts from Tao, also translates as supremum principium, as far as it makes itself the foundation of the world!
then everything is immediately clear; but one also sees how hard it is for speculation, with simple words and concepts, to bring into our waking consciousness that which lies in us unconsciously as a psychical form. Moreover, it appears not impossible to me that ancient Chinese number harmonics arrived very early at a system analogous to our “P”. The material that Windischmann gives based on French scholars such as Roussier etc. (whom I have not yet been able to study) and which, after over a hundred years, still remains completely untapped, especially in the Mémoires concernant les Chinois, must be newly approached from harmonic viewpoints. The volume Chinesische Musik, published by R. Wilhelm at the China-Institut (Frankfurt a. M. 1927) is very beautiful with regard to the general attitude of the Chinese philosophers, but is more than lacking with regard to fundamental number-harmonic problems.
The reader might be satisfied with these few examples, which offer historical ektypics about the relationship of the Eidos to the Origo; it will be easy for him to complete the material.
§54.4. The Creation Triad
Expression: 0/0 1/1 d 1/2 d, 2/1 d¢
Definition: In the beginning of the creation process, three entities form themselves, equal in value and different in nature. In and through this ternary, the entire form of further evolution is given.
Commentary: Just as we no longer indicate the Eidos with a single 0 but instead with a doubled 0/0, we indicate the Origo not with a single 1, but with a doubled 1/1. The duplicate form of these terms is, as we saw, not arbitrary, but is yielded through strict induction from the structure of the “P” itself. Mathematically, the two series are naturally identical:
2 3 ...
g,, d, d d′ a′
Harmonically, not at all; because here another element of symmetry of the intervals is expressed, which is missing from the mathematical series; besides, through the double-signature 1/1 we first obtain the possibility of clarifying evolution from the Monas.
This twofold setting of the One as the simplest proportion 1 : 1 or 1/1 involves the Two a priori, since two unities are placed in relation to one another. With this, therefore, the two is born, namely in doubled form: two units as plain 2 (two), and each individual unit as 1/2 (the half) of the whole signature 1/1—where naturally it is not the sum or the half of 1 that is understood, but simply the possibility of arriving at the forms of the 2 and the 1/2 from the double-concept of the 1/1. This purely spiritual deduction of 2 and 1/2 from 1/1 now allows us, however, to set it out factually, and thereupon the ternary 1/2 1/1 2/1 is obtained as the first stage of development. Now we also understand why we use the ancient Chinese sign for Tai-ki
... 1/3 1/2 1/1 2/1 3/1 ...
The fact that one half of the sign is shaded is connected with the “earthly” character of the series 0 = 1/∞ 1/3 1/2 ← 1/1 and the “heavenly” character of the series 1/1 → 2/1 3/1 ∞/1 = ∞, which we will discuss later. We see on this occasion that the Tai-ki symbol emerges as a very precise designation of one of the highest harmonic conditions, and thus as an archetypal form anchored deeply in our psyche.
As for the triad:
appearing right at the beginning of the creation process, here we have harmonically three different (here = d-) values, which are inwardly equal and yet different in nature (in their location and pitch). Since we can not only judge the three octave-tones d, d d¢ intellectually and physically (number-measure) but also evaluate them psychically, and since they are at the pinnacle of the “P”, this is probably the single instance, in the history of ideas, of a psychophysical explanation for the “mystery” of the Trinity. Compare to this our statements in §30 of this text.
There is so much literature on the trinity problem in mythology, the history of religion, and the history of philosophy (three-step dialectics), that we cannot discuss it further here, and must refer the reader to the few bits of information about it given in §30a and §50.5. Anyone who seeks to obtain any degree of historic insight can only conclude that ever since humans have thought, they must have held the form of this ternary as one of the most important psychic prototypes in the subconscious, a form of entirely characteristic quality which strives again and again in the most varied domains, above all those of religion and mythology, toward some symbolic realization. And the phenomenon of the dialectic, with its logical triad of thesis, antithesis, and synthesis, shows that the ternary rules the form of our thought itself. Harmonics, however, simultaneously shows that the ternary (as a cadence : crystal surfaces!) also inhabits nature as a form-potency; through this it is raised above its merely “anthropomorphic” meaning and obtains a universal character—which once again explains and makes comprehensible such a far-reaching significance in the most varied human spiritual domains.
§54.5. The Creation-Polarity
Definition: The creation triad requires creation-polarity. Infinity (∞) and Nothing (0) emerge, as well as the median line (1/12/23/3 ...) = Origo-axis.
In the progression from the Eidos 0/0 to the Origo 1/1 we see, harmonically, the actual process of the world’s becoming. We can easily go on to describe the further evolution from the 1/1, indeed we must follow a “before” and “after” here, or some kind of progression. But this is only required by our method of expression; because fundamentally, with the birth of the Origo 1/1 the immediate emergence of the entire cosmos is given in its ideal form. Its temporal developments are only evolutions of the system of the “P”. We could thus just as well have put the polarity before the triad and discussed the subsequent creation steps in any order, since they spontaneously emerged, as great cosmological prototypes, with the creation of the Origo, comparable with the sudden crystallization of a substance, the completion of a chemical process, the “brainwave” of a thought, an idea—these examples taken admittedly only as completely insufficient comparisons. The reader should turn his attention more to the types in themselves than to the series-progression.
The creation-polarity, and the Origo-axis (generator-tone line) which it necessitates, bring into the world the concept of the Infinite (∞),the concept of the Nothing (0), and the concept of constancy, perseverance (1/1 2/2 up to ∞/∞).
All three of these concepts have vectorial, direction-giving, “intentional” character. Whereas the vectors 0 and ∞ go out from, or back to, the origin 1/1, the vector ∞/∞ (origo-line) takes its origin from the highest harmonic value 0/0. Cosmologically, these expressions and definitions are of great significance.
From this, we see firstly that the Infinite requires the concept, indeed the actuality, of the Nothing, and vice versa. Both concepts, and not only the one “or” the other, are intentionally posited for the reality of the creation. These two are primal principles of the limitless (̔άπειρον) and of the limiting (περαίνοντα) of the Pythagorean-Platonic philosophy, and furthermore the prototypes of all dualistic systems, be it in mythology, religion, or science. But we see further that these two principles have no direct participation in the deity 0/0 as vectors or intentions, but are instead “origo-nally” required, i.e. are a direct emission of the Monas 1/1, the concrete act of creation. Thus in harmonics, the two directions that embrace the Monas 1/1, the Nothing (0 = physically the “empty” universe, philosophically the absolute privation, ethically the complete want) and the Infinite ∞ = of the unending universe, the concept of endlessness, (the infinite plenitude), stand in opposition to the symbol of eternal rest, the deity (0/0), or simply eternity. We will soon speak in more detail of the inner psychophysical content of these vectors.
These two principles are now brought into a sensible relationship through the Origo-axis (1/1 2/2 3/3 ...), which we can also call the unity-line of the world; indeed without this they are entirely unthinkable. This unity-line, however, goes as a vector back to the 0/0 and thus symbolizes its direct origination from the deity. Precisely this fact allows deep speculations (Plato, Plotinus, etc.) to conceptualize about the “unity,” while the epistemological deliberations and analyses of the concept of the “Nothing” and the “Infinite”—if I may express myself in the mode of the ancients—never participate in “the gods” and remain as they have remained, more or less domiciled in purely logical spheres.
An ektypic evaluation of the two vectors 0 ← 1/1 → ∞ was already attempted in §19a ad 1 and §50.5, especially with regard to the Pythagorean concepts of the unlimited (∞) and the limiting (0). We will add a few more examples here. If one sees in the Origo-axis 1/1 2/2 3/3 ... the single, cohesive element of the 0 ← 1/1 and 1/1 → ∞ vector, then one can understand the dark declaration of Heraclitus’s riddle: “The way up and down is one and the same” (Diels: Fragmente der Vorsokratiker, Heraclitus fragment, 60).
Robert Eisler writes, in his Weltenmantel und Himmelszelt (Munich 1910, pp. 558-559):
When Pherecydes was the first to teach that souls were “eternal,” i.e. not merely immortal, as Homer said they were, but instead beginningless and endless, and that birth and death mean only a changing of place in the universe, this agrees very well with the striving for reunification with the two eternal and beginningless principles ̕Aιθήρ (ether) and Γη̃ (earth). But of course, it can just as well be said that body and soul, spirit and matter are imperishable and without origin. There can be no doubt that this dualistic anthropology under Pherecydes had an ethical goal, if one remembers that the primal origin of one element of man, Zeus-Ether, is called the ‘perfect good,’ whereas Chthonie Ge appears throughout as mother of the riotous ... foes of the gods ..., the source of everything evil and of that in man which opposes the will of gods.
Harmonically, we understand souls as “eternal” when we assume the reference-direction of all being-values as being toward 0/0. If it is true that Pherecydes explained souls as “eternal” and “not immortal,” then this expresses that wonderful impression that the Pythagorean-harmonic symbol of the Eidos (0/0) allegorizes so beautifully—and realizes. The idea of immortality, to which something more or less material always clings, is stripped of all materiality through transformation into the “eternal,” and transposed to the highest reality of the Eidos (0/0).
The equating of the 1/1 → ∞ pole with “good” and the other 0 ← 1/1 with “evil” once again reveals the replacement of outline and possibility with fact and reality, typical of the ancients; compare this to the following step.
The Orphic expressions ΑΙΩΝ ΑΠΕΙΡΟΣ (unending duration = 1/1 → ∞) and NYΞ ΑΠΕΙΡΟΣ (unending night = 0 ← 1/1) are very remarkable; they doubtless correspond to the inner psychical configuration of our two harmonic series-pairs. If one applies the ancient procedure of “psephoi” (gematria), as mentioned with similar examples in §17b, substituting the corresponding number of the alphabet for every letter, then for both double names one obtains the sum 128 = 27, the seventh octave-power!
The two polarities Yin and Yang (– – and —) which proceed from the Tai-ki of ancient Chinese wisdom, on which not only the I-Ching but all of Chinese philosophy is based, are the exact counterparts of our harmonic series-pairs 0 ← 1/1 → ∞, and their definitions as darkness and light, no and yes, female and male, etc., show just how purely Chinese thought grasped and manipulated a prototypical psychic form—remember what was said in §50.8 regarding the I-Ching diagram.
A related symbol comes to mind here, upon which Egyptological research has continually foundered, despite its known content, namely the so-called “Ankh,” . This hieroglyph, signifying the symbol of divine life, is known to appear even in the earliest monuments and inscriptions, and not only in Egypt, but also on Etruscan, Sicilian, Persian, Babylonian, and Chaldaean images, gems, coins, etc. (Thimus II, 111 ff. with ill.). One should read Thimus on the contrast of this hieroglyph with the sign of the cross and his deep speculations about it. Unfortunately, Thimus, whom I so much admire, either completely missed the simplest derivation of this Ankh, or else did not think about it at all, since it seemed self-evident to him. Namely, if one draws the “P” with basal series not bent at a right angle but lying along a line, with the 0/0 point as a circle above and the generator-tone axis directly below, then the result is Fig. 471a.
One must admit that for the most important laws of the “P”—Eidos, Origo with its three “directions”—no better graphic image-concept could be found. This same symbol, so widely used in Egyptian hieroglyphics and on Egyptian reliefs, allows one to assume with the highest probability that the system of the “P” established on the basis of the monochord was known in the secret schools of Egypt, and that Pythagoras brought the system from there to Greece.
The ancient Babylonian doctrine, still echoing in the cosmogony of Berossus, of the emergence of the world of the senses from the unification of a creating male and receiving female, birthing, primal force (corresponding to the Chinese Yin-Yang principle) is recorded in the Origenian Philosophumenis. This “Origenes of the Heathens and Neoplatonists”—not to be confused with the church father of the same name!—next to Plotinus the most significant scholar of Ammonius Saccas, declares (according to Friedrich Münter: Religion der Babylonier, Copenhagen 1827, p. 46): “Diodorus the Eritrean and the musician Aristoxenus say that Charatas the Chaldaean taught Pythagoras this: two are the principles of all things from the beginning; a paternal and a maternal. One is light, the other dark. Qualities of the light are warmth, dryness, lightness, swiftness; to the darkness belong the cold, damp, heavy, and sluggish. And from all these, along with man and woman, emerges the world, and there is a musical harmony.”
The Neopythagorean Numenius of Apamea (2nd century a.d.), forerunner and influencer of Plotinus, “founder of the doctrine of the three deities following one another in rank: the highest principle νου̃ς, the demiurge, and the world” (Überweg, Geschichte der Philosophie, vol. I, 1926, p. 514), assumes a principle (0/0) that is timeless, eternal, always the same as itself, spatially unmovable, unchanging, simply being. But since the world cannot be identical with this absolute, a second principle must mediate: the demiurge (1/1).
Numenius differentiates first the world-maker (δημιουργός) from the highest god as a second god. The first god is good in and through himself; he is pure thought-activity (νου̃ς) and principle of being (ο̕υσίας ̕αρχή) and as King (βασιλεύς), free from all labor. The second god (demiurge) is good through participation in the nature of the first; he looks at the supernatural primal images, works with matter, and thus sculpts the world, in that he is the principle of becoming. The world, the product of the demiurge, is the third god. The basis for this doctrine was first supplied by the demiurge and the divine world of the Platonic Timaeus. But the overseer (demiurge), to whom the same original ideas apply, cannot be the highest court of appeal in the longing for absolute divine transcendence. Thus a higher god prevailed over him, to whose designation the Platonic ideal of the good and the Aristotelian placement of the deity as the basis of the pure νου̃ς offered a footing, perhaps with a contribution from the character of the βασιλικη επιστήμη (royal knowledge) from Plato’s Politicus, 305d. Also Plato’s Sixth Letter comes into consideration.
(Überweg, ibid. p. 521)
Now, when Numenius, as Proclus tells us (in Timaeus III), “traced the soul back to numeric relationships,” and, according to Eusebius XI, 22, commends penetration of the numeric secrets as the way to knowledge—just as for the Pythagoreans, the source of all Platonism (Eusebius IX, 7 and XIV, 5)—then the presumption is allowed that Numenius probably used direct Pythagorean traditions as a basis, and knew of the Pythagorean “P” system in some form. When he designates his three deities (besides the titles Nous and Demiurge) expressly with πατήρ (father), ποιητής (overseer, demiurge) and ποίημα (the created, the world), the harmonic succession 0/0 → 1/1 → “P” is so obvious that no doubt can remain that he was a true and not merely “syncretistic” Pythagorean.
Finally, I will give a few more interesting related Kabbalistic passages from the strange work already mentioned above. Anonymously published in his own time, Molitor’s Philosophie der Geschichte, oder über die Tradition (Münster, 4 vols., 1834 ff.) treats “the tradition in the old covenant and its relation to the church of the new covenant, with especial reference to the Kabbalah” in a most thorough and profound manner, and should have been republished long ago as one of the most important spiritual products of the Schelling-Baader era. In the appendix to vol. II of his work, Molitor offers a few passages from Kabbalistic writings (Zohar etc.) in Hebrew and German, from which I choose the following:
Of the Ain-soph, it is said: “Before the world was created, He, the [Most Blessed] and His name were one.” “He created the tangible from the void and made its nothing into something.” “Even in the minerals, like dust and stone, there is necessarily life and spirit, and a star or watchman over it.” “Ain-soph is separate and removed from all imaginable. It comes before all emanations and creations, and in it is no time.” The Kabbalists distinguish the Being from the Light within the Ain-soph, and say that the world was created from the light. Etz ha Chaiim tells us, in the passage: From Ain-soph came out a straight, fine line in the manner of a canal: “Only the illumination of Ain-soph, but not its Being. This is what the doctrines say: it is the place of the world; but the world is not its place. For its Being does not extend itself, but its light does.” Here think of the equal-tone rays from the harmonic symbol 0/0!
§54.6. The Creation of Paradise and the Spiritual World
Expression: (Fig. 472)
The first senary evolution cycle of the “P” creates a world of pure major and minor chords, mutually pervading each other, a pure “paradisiacal” world that ends in the seventh ratio-series as a closed index, repeating itself again in several “senary” series-groups and series-pairs, but these become ever rarer in the course of further differentiation. Thus we can with good reason conceive of the closed complex PE6 (as well as PE8) as a world of pure chords reposing in themselves, as a domain of pure harmonic conditions, which is unique in its type and represents the first cycle of harmonic cosmogonic evolution.
If one now builds a pure spiritual world behind the 0/0, on the model of the imaginary basal series 0/∞ ← 0/1 0/0 1/0 → ∞/0, which can happen purely constructively and is shown in the upper sector of Fig. 472, then we see in this imaginary “P” domain to a certain extent the spiritual prototype for the “real” “P” realized in the lower sector. The reader is asked to inwardly grasp the illustration of Fig. 472, i.e. the “above,” “below,” as well as the variation and combination of the “P” given there, in terms to its form; of course, we can also lay it on its side, place one of the two imaginary basal series upon the other, choose the hexagonal form of the illustration, etc. This imaginary, purely spiritual world has a much simpler structure compared to the real “P”. Its axis is the 0/0-axis, that of the Eidos. At the left we see only vertical 0-series of identical spiritual values; to the right we see only vertical series of the spiritual “whole numbers”; we can no longer logically or material-mathematically grasp the terms of 0/3 and 3/0, for example, as quantities, but instead as purely spiritual values. A spiritual zero-world appears in this upper sector left of the 0/0 line: to the right, the metaphysical “birth” of the whole numbers. We have not reached this arbitrarily, but through retrograde interpolation of the “P” in a strictly legitimate way, similarly to how we arrived at the elicitation of 0/0.
The reader has been carefully instructed in previous chapters regarding the “senarius” and its closed core in index 6 of the “P”, as well as regarding the “ekmelic” character of the seventh-series, being the first beyond the senary. In Fig. 472, we attempt to show the corresponding difference between the “spiritual,” “emmelic” (senary), and “ekmelic” (outer senary) central ratio-builders of the vertical middle axis by leaving the ancient Chinese Yin-Yang symbol “empty” in the first case, half-shaded in the second case, and filled out in black in the third case. Through this, we obtain a clear optical image of the conditions in question.
It is now the time to discuss summarily the problem of the transcendent signs, becoming especially important in Fig. 472, 0, ∞, 0/∞, ∞/0, ∞/∞, etc. For the mathematician, 0 and ∞ are still unequivocally ratio-based concepts: “zero” and “infinity.” The definition of 0/0, which can mean “all,” i.e. every number, is more difficult for him, and the terms 0/∞, ∞/0, ∞/∞, ∞, ∞/n, have hardly any meaning for him.
Let us look at what harmonics says to this (see Fig. 472). Let us begin with the perpendicular middle axis. In the upper domain, up to the middle field, which belongs to both sectors, it has the value 0/0. The mathematical conclusion “everything” agrees with the harmonic one here, even if this naturally also attains the greater amplitude, since the harmonic concept of 0/0 designates the highest concept of the Eidos reachable in us. In the lower domain we find the value 1/1, generally speaking n/n, which is mathematically equal to 1. Harmonically, however, it is evident that besides the unity (Monas), the situs, the place, i.e. the location in the field, also plays a role. Thus the 1/1 is different from 2/2, 3/3, etc. in its position, since it must obviously be ascribed an exceptional rank in contrast with the other units. The units 2/2 ... 6/6 are once again different from units such as 7/7, 11/11, 13/13 etc., since these units represent intersection points of ekmelic series-pairs. Here, therefore, we have three different characters of units, whose being-values are the same but whose field-value within the “cosmological” succession is different. This difference applies only in the topological sense, not in the ontological, and can be taken into consideration only in judgments of location, not in terms of being. It is interesting that the vector of all these units 1/1 2/2 3/3 ... ∞/∞ leads to a doubled infinity ratio, which we must view harmonically as the maximal Being, and cosmologically as the end of the development of the world. If this point is reached, then ∞/∞ ignites itself upon 0/0 and the entire world-system is cleansed again in an enormous melting process. As for the imaginary basal series that belong to both sectors:
0 = 0/∞ ... 0/2 0/1 ← 0/0 → 1/0 2/0 ... ∞/0 = ∞
with regard to the symbol ∞ = infinite, we are still in agreement with mathematics, though harmonically we grasp the concept of infinity not only in terms of size, but as the infinity of the being-values. The term 0 = zero, on the other hand, can mean the mathematical Nothing or a limiting value (limes), while harmonically, we grasp it more in the sense of an absolute lack (ethically), a thickest concentration (materially), and simply a limit (in the sense of not being able to go any farther). It is these two imaginary series, coupled in the 0/0 value, that represent the communication between the “lower” real world and the “upper” spiritual world. Parallel to them, in the lower (material) sector, run only series of the limited form 1/∞ 2/∞ 3/∞ ... or ∞/1 ∞/2 ∞/3 ... which, taken themselves again as vectors, tend in both cases toward the maximal being-value ∞/∞. The corresponding parallel lines in the upper (spiritual) sector, on the other hand, always collectively observed from the 0/0 line, have the limited form 0/∞ 0/∞ 0/∞ ... or ∞/0 ∞/0 ∞/0 ..., and do not construct any recognizable vector tendency, whereas the not yet limited parallel lines, for example 0/5 0/4 0/3 0/2 0/1 0/0 or 5/0 4/0 3/0 2/0 1/0 0/0, all turn themselves from the imaginary basal series toward the highest 0/0 value. Whereas all concrete partial-tone series of the lower sector still express, in their limiting values, what I might call a “concrete” infinity (1/∞ 2/∞ 3/∞ ... or ∞/1 ∞/2 ∞/3 ...), all the analogous series of the spiritual sector, turning away from the 0/0 axis, point to the two completely transcendent concepts, 0/∞ and ∞/0, and, turning toward the middle axis, to the highest transcendent concept of 0/0.
The collective impression of the spiritual sector is one of absolute repose, symbolized by the three great harmonic-metaphysical principles of the 0, the ∞, and the 0/0, and characterized by the majesty of the spiritual being-values1° 2° 3° ... and the connected transcendent emergence of the whole numbers, adjoined to which we must imagine toning spiritual media, for whose description every term fails us.
The collective impression of the lower “material” sector is one of a temporal-spatial and psychophysical agitation, a world of reality, into which the reflected splendor of the repose of the spiritual sector radiates (which is especially symbolized by the middle axis 0/0 1/1 2/2 ... and the pencil of rays of the equal-tone lines radiating out from the 0/0), but which soon proceeds according to its own laws, and above all in periods of certain cycles, at the beginning of which is the “paradisiacal” cycle.
For review, I shall compile the symbols discussed above once more:
1/1 Origo Self-awareness of the Eidos. Logos. Creative principle. Highest being-value.
n/∞ Relative nothing Concrete final conditions of the individual being-directions. System of natural conditions.
∞/n Relative infinity Concrete infinitude concepts of the individual being-directions. System of natural laws.
∞/∞ Being Maximal Origo-value. Final state of the world.
The reader should not stumble over the term “paradise.” I have used it for the first cycle of the pure harmonies appearing in the harmonic system, to refer simultaneously to the doctrine, appearing in all religions and mythologies since ancient times, of an original perfect, “paradisiacal” condition of nature and the human race, a condition of harmonic polarities, a “golden age,” in short an ideal wish-fulfillment, which, regardless of whether we consider it to have ever been reality or to be pure illusion, still belongs de facto among the most ancient ideas of humanity. And this is precisely our concern here: to make conceivable and evident how one should imagine this condition, which is certainly strange in itself. If we assume the construction of the harmonic forms, as it is symbolized by the “P”, as a psychophysical reality, i.e. as a prototypical form inherent to both our psyche and to nature, then we have the explanation and interpretation in the first senary-closed sector of the “P”, which consists merely of interpenetrating pure major and minor chords.
The terms “paradise” and “golden age” may suffice for the reader in lieu of further historical evidence, which anyone who is interested can easily obtain from the literature. In philosophical terms, as far as I know, Jakob Böhme and Franz Baader were the last and only ones who supposed a condition of “eternal nature” on purely speculative and epistemological grounds, a configuration of being-values originally emanating purely from the act of creation, in which as yet no Luciferian disruption had a part. These studies of Böhme and Baader are interesting and important, and it is impossible to discuss them with any thoroughness within the framework of this text.
The idea of the correspondence of “below” and “above” is also ancient, and has taken form in countless mythological emblems and religious, as well as philosophical dogmas. “The whole lower world is made according to the model of the upper world. All that exists in the upper world only appears to us here below as in an image, and yet both are the same” (Zohar II, 20a, from E. Bischoff, ibid., II, p. 99). From the point of view of Fig. 472 and its upper and lower sectors, perhaps the following mysterious passage from the Zohar (III, 292a, b, ibid., p. 102) becomes understandable: “There have been old worlds that were destroyed again immediately after their emergence, worlds without form, which are called sparks, just like sparks that the smith lets fly in every direction when forging the iron, and which die out immediately. These sparks are the original kings of the ancient worlds. They were destroyed and could not exist, because the Old One, blessed be his name [0/0], had not yet taken his form [1/1], a form that represented itself in the male and female, because the two light-faces, revealing themselves in nobility and justice, did not yet look each other in the face [i.e. because the condition of the becoming conscious of the Eidos 0 ↔ 0 had not yet entered!] and the overseer [1/1] was not yet at his work.” Consider, furthermore, the concept of the “angel” and “blessed spirit,” Plato’s Allegory of the Cave, and all the alchemical ideas (going back to ancient Hermetic writings) of the correspondence of an upper spiritual and lower material sphere, ideas that again have their origin in the notion, common to all the idealistic philosophies since ancient times, of a pure world of thought, toward which the Being of nature and humans directs itself. In the upper sector of Fig. 472, we have obtained an image-concept of this “angelic” world, namely in the same way as in all our harmonic diagrams: not arbitrarily, but through strictly legitimate interpolation of the “P” itself.
The world of the gods has always been inherent to human thought and perception: it is an image of higher beings, gods, saints, concretizing in the human type of the genius and sublimating philosophically in a world of values. We can identify this harmonically with the first great senary interval-forms (octave, fifth, fourth, thirds, and whole-tones), which appear again and again and “reincarnate” in the different P-cycles as meaningful value-concentrations. We can extract these great forms from the “P” system as “interval-power diagrams” (see the fifth-diagram, the fifth-third diagram, etc.) and will find exceptionally important conclusions about certain problems from the isolation or “rendering independent” of these primary interval forms. In the following section, the fifth-diagram will give us such information.
In the above, we have attempted to describe the first harmonic evolution cycle, which we have closed with index 6, and constructed the “spiritual mirror,” an imaginary world which is only approximately signifiable with familiar mathematical symbols, but which we are forced to accept from the “retrograde” interpolation of the “P”. Now we will leave this imaginary world, whose further progress is indeed unequivocal, to itself, and in the last section observe our harmonic cosmogony of the entire “P” system of index ∞.
§54.7. The Creation System and the Earthly World
Expression: The entire “P” system.
Every cosmogonic development has a beginning and thus also an end, even when we set the “limit” to ∞ = infinite. Since we can well imagine such harmonic diagrams, but can only produce them graphically up to certain indexes, the reader must use his powers of imagination to help here, and check the following statements on previous diagrams.
Now we shall try to describe the further “progression” of harmonic cosmogony—which we can only ever illustrate successively, although in principle it is realized simultaneously with the 1/1—in its further important great forms; and to attempt an interpretation of these forms.
With the Six as the ratio-builder, the core of the mutually consonant pure chords is closed, and with the Seven, a foreign element intrudes for the first time. These heterogeneous steps then repeat themselves in ever-increasing sequences:
so that the entire “P” system is obviously underlain by an ever-increasing differentiation, whereby the possibility of consonance becomes ever more rare and difficult. On the other side, however, the senary steps “reincarnate” again and again, only they “become isolated” at increasing indexes, and finally almost disappear in the mass of non-senary material; but they have such great significance precisely because of their value-weight. One can imagine that the differentiation leads to confusion at a certain point, and regeneration can occur only through a self-metamorphosis of being-values or through a return to an earlier, simpler index, in which the ratios are still simple and comprehensible. The self-recollection, the “monastic” or “ascetic” way, is symbolized by a kind of “potentiation” that we can notate harmonically on some ratio, such as 22/34 or in general x/y, thus:
22°/34° or x°/y° = 1
i.e. self-potentiation by means of the doubled zero-symbol 0/0 leads every being-value back to the 1/1 and thus back to the Origo. The individuality is extinguished here, and changes itself back again in the act of creation. The second way of “regeneration,” i.e. the withdrawal to simpler conditions, is only imaginable collectively. History provides countless examples for the two possibilities. It is easy to see one of the origins of worldly evil in this ever-widening differentiation and complication, which must finally lead to lack of orientation. And from here it appears—we have already discussed this—that only on the basis of certain normative selections within the “P” system can a means of healing against this excessive splintering be created and found, which has happened de facto for a long time in the arts, through ethical principles, social regulations, etc., and which symbolizes our above mentioned “regeneration” only singularly or collectively. Another “concrete” condition of the worldly evil can be seen in the sudden appearance of the first “ekmelic” seventh periods and the things that follow it. In the sense of harmonic consonance, i.e. of the possibility of a real and not only “statistical” world harmony, these ekmelic ratios are actually elements of disturbance, while in contrast the great harmonic senary steps try again and again to substitute themselves, not only “psychologically” but cosmically, as Kepler’s investigations and our own contributions prove. This entire Textbook attests to this in our ektypic excursions. The most visible harmonic evidence for a domain of “light” and “darkness” appears, however, to be the dualism already immanent in the very peak of the Origo, which takes effect in a thoroughly polar manner in the > 1 and < 1 sectors of the “P”-development, and which we find expressed symbolically in the most varied ancient mythologies and wisdom-teachings. But precisely this interpretation, i.e. the anchoring of worldly evil in dualism and the reflection of good-evil in an original polarity, already appears untenable to me, because we find this dualism in the purely senary domain of the PE6 and cannot possibly include the “thorn of evil” in the pure major and minor chords appearing here. In this supreme dualism, i.e. in the Origo itself, a deeper, meditative contemplation can certainly see the possibility and the anchoring upon which the world-catastrophe must occur, with the index raised to the maximum, i.e. at the highest tension between vast concentration 1/∞ = 0 and vast expansion ∞/1 = ∞, together making ∞/∞; and from this tension inherent to every index of the system an original transcendence of evil in “eternal nature” may be derived—as was done by Jakob Böhme and, in more primitive form, by the ancient dualistic systems and religions. But important and interesting as these designations of the “possibility” are, our interpretative consciousness seeks more “real” reasons, at least an explanation for how dualism hardened and isolated itself in contrast with the highest instance 0/0 and its deputy 1/1.
Here, in our harmonic selective diagram, we have sharply indicative evidence that is just as remarkable as the problem itself, namely in the so-called “fifth-diagram,” i.e. the interval-power diagram of the fifth, which we technically discussed in §39.2e and §39.3b. This fifth-diagram, built on only one ratio—namely the three with its powers and reciprocals, thus the first and most important interval after the octave—has a thoroughly hierarchical structure in contrast with the overtone diagram (from which it indeed represents a selection), and because of its interval (the “dominant”), it embodies, in a certain sense, a “divine world”: a world that does not yet partake of the major-minor dualism and is genderless, appearing to express purely linear principles (identical tone-lines, whole-tone scales, material for diatonic, chromatic, and finally enharmonic scales) in unapproachable perfection.
We already noticed, in §39.3b, that there is a strange tendency in this diagram to “manage without” the generator-tone. Indeed, not only that. The inclusion of the generator-tone line somehow “disturbs” the construction of the scales, which can be derived without it and without “hiatus” in the right and left sectors (see Fig. 473) by means of the “substitute generator-tones” his and deses.
This “adversarial” relationship between the two sectors becomes completely clear if we draw all ratios of this fifth-diagram including the generator-tone in a polar projection (Fig. 474).
For comparison, the 12 tempered semitones are drawn in dotted lines (30° 60° 90° etc.). Here we see plainly how the two “adversarial” camps have their own succession in their (1/n)n and (n/1)n powers, and neither needs the generator-tone at all. If we write out the 1/n and n/1 series separately:
95 75 95 75 95 75 75 95 75 95 75 75 95
(5 × 95); (7 × 75)
75 75 95 75 95 75 75 95 75 95 75 95 75
(5 × 95); (7 × 75)
then here we have two very regular chromatic scales with 5 × 95 and 7 × 75 logarithmic semitones, which appear to have nothing to do with one another. In every case they obviously defer to the generator-tone, the “demiurge” = creator-god, the value to which they owe their existence, and it is precisely here that we must direct our utmost attention. For it means simply that within the entire “P” system, the most important interval configuration (after the octave) of the fifth expresses tendencies that press on the one hand towards a self-isolation and emancipation from the 1/1 (Origo), and on the other hand sharpen this isolation further with an adversarial dualism.
Here, therefore, we have an exact psychophysical proof of an ancient mythological and religious theorem: a fraction or dispute already entered into the “divine world,” as well as an associated turning away from God (Origo = 1/1).
The only “synthetic” element of the fifth-diagram, with the exception of the “evacuated” generator-tone line and the rigid egocentric equal-tone parallels, is the “whole-tone scale.” But precisely this, which appears to our perception as something completely “unnatural,” demonstrates the inner psychical tension of the diagram.
If we now return to the complete diagram of the familiar “P”, we find, as one of the further cosmological archetypes, the generator-tone line 1/1 2/2 3/3 ∞/∞ ..., running through the middle of the entire system, which we can also call the Origo-line or Origo-axis. It symbolizes the ever-present creative primal force that gives stability to the system and, as the deputy of the Eidos 0/0, the actual “mediating principle” of harmonic cosmogony. Because every being-value x/y, born of the two “intentions” 1/1 → n/1 → ∞/1 = ∞ and 0 = 1/∞ ← 1/n ← 1/1, as the intersection point of an undertone and overtone series, must pass the Origo line in one of its “ancestral series,” this mediating principle is inherent a priori in every being-value. Besides, as we saw above, every being-value is able to identify itself with this mediating principle through self-potentiation with the Eidos (x°/y°)° – 1, to return to it, through which the naturally necessary presence of the Origo changes itself into a self-willed “unio katholica” (καθολικός = affecting the whole; here the Monas 1/1, which rules and expresses the entire “P”). In terms of religious cosmology, harmonics sees the Origo axis as the symbol for the idea of a redeemer pervading all the thought and feeling (belief) of humanity, and in the relation of every being-value to the Origo, the symbol for the belief in a “personal” God.
As a final great cosmogonic form, we see the pencil of rays of the equal-tone lines, reaching out from the Eidos 0/0, illuminating the whole system, and imbuing every being-value. Since here every being-value has its own unique ray, by means of which it is in direct relation to the deity (0/0) without any other mediation—i.e. it receives its spiritual existence from the deity—harmonics sees therein an emblem of the direct relationship to the deity, a symbol for the “unio mystica,” a religious attitude that was the goal of the mystics of all times and peoples.
If we want an idea of how to imagine the emergence of the three kingdoms of nature from the “P” system, we can say the following (cf. ill. Harmonia Plantarum, p. 288):
In the crystal, the prototype of “matter” in its macroscopic appearance, the “P” realize themselves precisely according to the group-theoretical arrangements out of and around the generator-tone center 1/1. Here the index plays no role as yet, as opposed to the generator, i.e. the inner choice principle of favored ratios and certain arrangements. In plants, the “P” system splits into n/1 and 1/n sectors; the resulting polarity between light and darkness roots the plant in the earth and leads to the emergence of life as a primal inner polar tension. The index is added here to the generative selection as form-limitation, due to which the plant, after completion of its individual life-indexes, “dies.” In animals, the polarity receives an augmentation through the conjunction (combination) of two independent “P” systems, which are coupled in 1/1. As the geotropic 1/n-n/1 relationship of plants disappears, the possibility of movement enters in. Furthermore, the appearance of circular scale-structures rounds off the animal body, forming both outer and inner “organs” and, psychically, the ability to “hear” and to “speak”—this is admittedly meant only as an initial rudimentary expression of a conscious manifestation of will (scale phenomenon). The next higher kingdom of nature always absorbs the last norm-step reached by the previous one. Thus one can say that the law of the crystallographic surface differentiation, which is common to all classes of crystals, harmonically connects directly with the laws of ramification, and that the norms attained in the plant blossoms are taken up directly by the lowest representatives of the animal kingdom—clearly shown by sea lilies, jellyfish, sea anemones, starfish, etc., whose form-harmonics are in such striking concordance with the blossom-harmonics of plants. In humans, the harmonic dichotomy then potentiates itself to the highest harmony, and we become conscious of the sense of our form as a synthesis of the forms of the three kingdoms of nature. We are able, by means of akróasis, to spiritually objectify the sense of this, our own form-synthesis, by means of the “P” system, thus creating a valuable means of understanding our own Being and the Being of the world.
Our harmonic cosmogony has been supported until now upon the scheme of the quadratic 1/4 PE, which indeed forms the foundation and starting point of all harmonic systems. If we now convert this system into polar coordinates, then we obtain an image that simultaneously illustrates ancient astronomical cosmological ideas and seems to do justice to the latest concepts of the presumed form of the universe. According to §33.3, we can reduce the polar coordinates of the “P” to the simple scheme of Fig. 476.
Here the Origo 1/1 stands in the middle as the circle of unity; from it, all < 1 ratios go inwards and all > 1 ratios go outwards. Every ratio (= being-value) has its own sphere (circle) and its angle (= direction = vector) within the circle periphery, which we identify with the octave. Thus we have a domain of contraction, gravity, concentration, attraction (within the 1/1 circle), and a domain of unfolding, evaporation, expansion (outside the 1/1 circle). These domains obey the symbols:
0 ← 1/1 → ∞
We will soon see that with this harmonic prototype, we come very close to the real story of the emergence of the planetary bodies and their gravitational relationships. I demonstrated in my “Tonspektren” (Abhandlungen) that various atomic laws and primal ideas can be derived from it, and the fact that it corresponds precisely to the image of the Pythagorean cosmos will be briefly intimated near the end of this chapter.
Regarding this polar representation of the “P”, it is interesting that here the 0/0 (Eidos) disappears along with its “envoys,” the equal-tone lines. This is a pointer for the fact that the harmonic polar coordinates are more signatures for aspects of the cosmos realizing itself in forms, while the familiar “P” not only gives us information about material elements and backgrounds, but also about the spiritual ones.
As a conclusion to the didactic part of our textbook, we turn once again to our venerable experimental instrument, the monochord. It will give us information about a theorem which, although very insignificant in itself, opens up problems of very far-reaching perspectives, and is of exceptional interest in various regards.
Namely, the theorem of the “metaphysical remainder.”
The Metaphysical Remainder
By “remainder,” we mean that part of the string that remains left over, in all monochord experiments, from a fixed bridge point x/y to the 0/0 0/1 0/2 ... 0/∞ line. In general it does not matter whether, with the bridge point at 2/5 e¢ (for 1/1 = c), I pluck and sound the segment 2/5 e¢ or the segment 3/5 a. In the first case the remainder is 3/5, in the second it is 2/5. But in a particular case we will have to hold to one or the other arrangement.
Now when we “realize” the “P” system in its wavelengths (string-length ratios) using the monochord, we can only ever set the monochord up so that the string is bounded on one side by the 0/0 0/1 0/2 line, on the other side by the 0/0 1/1 2/2 ... line. If we now draw the equal-tone lines, through which every ratio on the monochord realizes its tone-number and tone-value, then we will observe that above, at the “head” of the monochord, i.e. where it touches the 0/0 0/1 0/2 line, there is always an empty space left over, a remainder, regardless of how large the index is set. For when I draw the equal-tone lines out from the 0/0 through all ratios of the uppermost row 1/1 1/2 1/3 ..., this remainder remains always the same, and is never exceeded, with constant size of the field 0/0 0/1 1/1 1/0. With this type of illustration (see Fig. 477) one can also speak of a “constant.” This remainder, tangent to the “metaphysical” domain of the 0/0 series and surrounded by the two transcendent vectors 0/∞ and ∞/0, is only relative in its “size,” as images 1-6 in Fig. 477 immediately show. The relationship to the string unity diminishes rapidly as the index increases, proportionally to the index in question. If I fix the unit instead of the remainder, as Fig. 478 shows, then this remainder, i.e. the fundamental length of the monochord 1/1, always remains of the same size, but the “metaphysical remainder” quickly becomes smaller with an increasing index. Here one can no longer speak of a “constant” remainder, but only of an ever-diminishing one. In both cases, the result is that this remainder diminishes more and more with increasing indexes in relation to the monochord unit, up to index ∞ where it ...?
The mathematician would say here: “... disappears.” And it is evident that at index ∞ the remainder becomes so minimal, falls so far short of every “size,” that we can “neglect” it both practically and ideally. On the other hand, there is the indubitable fact, visible in Figures 477 and 478, that this remainder must and will endure in some size identical to 0/0 → 1/1, even at index ∞, and that for this reason, we cannot eliminate it.
Every mathematician will immediately know that this is related to the ancient problem or controversy of the “differential quotients,” and that this dilemma retains the same antinomic poignancy in the axiomatics of modern infinitesimal calculus as it did at the time of its discovery by Newton and Leibniz.
The harmonic approach to it should then interest us all the more.
In the harmonic way of thinking, the monochord represents the realization of the being-values in time (frequency), space (wavelength), and number (causality). This “realization” naturally resides in the diagram itself, and thus far the monochord is more the visual display of the “P”, and above all the practical possibility of direct sensory realization through the ear. This monochord is limited on the one side by the unit, and on the other side it touches a line whose vector we designate with the symbol 0/∞ (not arbitrarily, but legitimately yielded from the “P” system!) and which we designated above as “Nothing = absolute limit, maximal concentration” etc., in short with a purely abstract, metaphysical expression. But only the monochord pushes forward up to this metaphysical limit 0/∞; the equal-tone lines of the individual being-values reach only up to the line of the “relative nothing” 1/∞ (n/∞), and it is precisely this “metaphysical remainder” between the vectors n/∞ and 1/∞ (n/∞) that obtain a new, or a first, interpretation through harmonics. This is no longer about a negligible or non-negligible “quantity” dx, but instead this infinitely small but enormously important step from the relative into the absolute “Nothing” of the entire cosmological configuration. To this is added, on the other side of the system, the polar correspondence of the two vectors ∞/0 (= infinite, absolute expansion) and ∞/1 (∞/n) (= relatively infinite, concrete infinity concepts), which our monochord does not touch, but which sets the entire “P” system at index ∞ in this enormous tension, precisely due to its polar correspondence to 0/∞ and 1/∞, which we believed we could propose as the origin for a future world-renewing process. The very visual and symbolically instructive illustration of Figures 477 and 478 shows the deeper background of this tension, which we may safely call “epistemological.” The greater the indexes of the “P” become, the more the unit of the monochord “fills out” with ratios, i.e. the more restlessly the system of matter operates, the smaller the “metaphysical remainder” becomes—in this case the metaphysical “substance”—until it is finally “pressed to the wall” so much that in terms of matter, it becomes almost nothing!
For a deeper meditative observation, however, it is precisely this “metaphysical remainder,” i.e. what still remains of a metaphysical “remnant,” albeit minimal, that is the key to the solution of the whole cosmological puzzle, and if we observe its purely mathematical formulation in the symbol dx, then we can say without going too far that the differential quotient contains a metaphysical problem of the first and foremost order, and that its harmonic “formulation” gives it a deepening and amplitude, which the mathematical symbol, together with its merely logical concept construction, does not attain.
On “self-awareness” and “regeneration.”
The self-potentiation of every being-value by 0/2, i.e. by the doubled Nothing that is simultaneously everything, changes it into the Origo 1/1 and can be understood in its most extreme sense as the monastic, ascetic way, but in general as tending toward the concentration of the highest creative-value of every being-realization. In contrast—here we anticipate—the recollection of the being-value by means of its “equal-tone line” to the Eidos 0/0 no longer actually signifies a self-awareness, but an identification of the “self” with the deity. Here monasticism and asceticism lose their meaning, due to which all mystics who take this “direct” path regard the substantiality of their Being, the “potentiation” of their being-value in the personal God-concept of the Origo 1/1 and thus all monastic and ascetic isolation, as secondary if not absolutely nothing, and direct their entire inner thought and aspiration toward the “vision” of the Eidos 0/0.
That which we named “regeneration,” the liquidation of collective conditions that have become unstoppable and caught in insoluble tangles, and the going back (which admittedly is often viewed as “going forward” in the sense of some kind of modernism!) to newly visible, simpler situations, has always been connected with the concept and the fact of “revolution,” a “renewing,” reformation (renaissance, rebirth), which, as the last words express, not only represents a reversal of the existing, but also a return to simpler norms, inherent a priori in humanity. Now whether we observe this regeneration harmonically as a reemphasis of normative selective elements or as a renaissance of simpler cycles, it will always be connected with a rectification of the “correct,” the “in tune,” in short, of the harmonic, and an abolition or at least an attempted disarming of the dissonant. Should such a revolution be contrived, however, by purely negative powers and sink into evil, it leads either to the catastrophe of entire cultures or to a gigantic struggle between positive and negative principles. Then at the end of the struggle, if the good wins, a new cultural epoch begins.
This struggle, which the individual must continually endure with himself and humans amongst themselves, since life is not in a simple condition of equilibrium like inorganic nature, but instead in an inner polar tension in the direction of the divine, is, as we saw, represented prototypically in various ways in the “P” system. As for the “war of the gods,” as so wonderfully symbolized by the inner content of the fifth-diagram (§54.7), the various mythologies and religions have always known of it.
Ancient times they were There Ymir dwelled There was no sand nor sea Nor salt waves No earth below Nor heavens above Bottomless gaping But nowhere grass.
Thus reads the third stanza of the famous ancient Germanic poem of world creation, Der Seherin Gedicht (Edda II in Thule, tr. by F. Genzmer, vol. II, 1920, p. 35). Hardly was this great giant Ymir slain by the divine race of the Asen, led by Odin, than the latter fell into a struggle with the second race of gods, the Wanen. Stanza 13 of the above poem reads:
Odin threw the spear Into the opponent; The first war Came into the world; It broke the border-wall The fortress of the Asen, The Wanen stomped Eager for fighting on the ground.
The Babylonian creation epic expresses similarly grandiose and dark ideas. Here, Ymir’s place is taken by the “Chaos Mother Tiamat.” The 2nd tablet of this epic (A. Ungnad: Die Religion der Babylonier und Assyreer, Jena 1921, p. 31 ff.) reads:
When Tiamat had thus completed her work, Then she strode to the battle with the divine children.
She brings a division of the gods to her side, who:
Striding to Tiamat’s side Blustering, planning, restless day and night Armed for the struggle, raging , raving, Banded together to wage the fight.
Only with difficulty can Marduk, the god of light, put a stop to the gruesome deeds of Tiamat, catch her in a “net,” and then destroy her:
After he struck Tiamat, Broke her forces, the hordes, the gods, who went to her side to help, bowed trembling, turning back. They sought to flee to save their lives: They were captured and flight was impossible: then he bound them all, destroyed their weapons, They sat in the snare, trapped in the net. The spheres resounded, filled with moaning...
In Persian tradition (Schahrastani tr. Haarbrücker I, 278, from Eisler, ibid., pp. 529-530) it reads: “A few Zervanists believe that ... Ahriman ... found himself in a place separated from heaven, but hatched his plots so long that he tore apart the heavens and climbed upon them. Others say that he is in heaven and the earth is free from him, but he hatched his plots so long that he tore apart the heavens and with all of his beings climbed down to earth. The light with his angels fled, Satan pursued him until he shut him in his garden [= paradise] and fought with him for 3000 years.” Further on it reads: “God created this world as a net for Ahriman, into which he has fallen and in which he is held.”
The image-concept of the “net” (already appearing in the Babylonian Epos)—to which Eisler also dedicates almost all the content of his work Weltenmantel uns Himmelszelt (Munich, 1910), supporting it with countless examples—is especially important conceptually in analogy to, and as a background for, our prototypical idea of the tone-mesh of the “P”; but we must forgo examples and refer the reader to Eisler’s work.
Also in classical Greek mythology, much closer to us in its “human-like” figures, there is a great battle of the gods at the very beginning, concentrated in the archetypes of Gaea, Uranus, and Chronos. Chaos, incited through Eros (Love), generates the dark heavy depths of Tartarus. From this originates Gaea, the Earth, and Uranus, the Heavens (female and male principle), which generate the Titans as the primal substance of formed life. But these Titans, including Chronos, moaning muffled from the depths, shake the heart of their mother Gaea, who then incites the youngest of her children, Chronos, against his own father Uranus. Chronos castrates Uranus, the terrible deed disturbs the peace, rips evil and good away from one another, and war follows. Uranus’s member, thrown in the sea, gives rise to the “foam-born Venus,” the symbol of earthly love. True, this somewhat alleviates the terrible tragedy, but still it allows full play to the thoughts and original feeling of a dissension reaching into the deepest foundations of the world and of consciousness.
When we called the generator-tone line 0/0 1/1 2/2 3/3 ... ∞/∞ the “mediator line,” it was not only because of its outer position in the diagram, but above all because of its inner relationship to all ratios in the diagram. If we grasp this line prototypically as a unity of the creative force, forever passing through the entire spatial-temporal cosmos, always present and ever repeating, then it symbolizes a principle common to all religions and most mythologies: the redeemer principle, or the mediator principle, i.e. a force that releases the being-value from its spatial-temporal entanglement, and through assimilation to unity leads it back into the deity. The 1/1 emanating from the Eidos 0/0, the concept of a personal God, requires an enduring, ever-repeating self-realization, a “proxy” in the domain of historical reality. Only the Origo as a continuously repeating existential fact holds the “P” system in psychophysical equilibrium, and right from the basis, our religious conduct is required to manifest this prototype, unconsciously present in us from the beginning, again and again in image-concepts and religious psychical forms.
Instead of giving examples of this idea of a savior and its various manifestations, I refer to the excellent work of Alfred Jeremias: Die außerbiblische Erlösererwartung (Berlin, 1927), in which the reader is presented with comprehensive material, discussed with thorough responsibility and strong spiritualization. In the introduction to his work, Jeremias writes: “The most important theorems which this book will prove, on the basis of the sources and their spiritual-historic interpretation, are these: Human culture is a unified whole, and at its core is religion. Human religion is a unified whole, and at its core is the expectation of a savior. The individual religions of the world are to each other as sects are to one religion, or as dialects of a spiritual language. And the original Christianity is the fulfillment of religion.”
Our above mentioned view (based on the limes ∞/∞ of the Origo line) of a limit of the universe reached with this limes, and thus a necessary world-collapse, is likewise a most ancient idea of the religions, mythologies, and wisdom. In the above mentioned ancient Germanic poem of the creation of the world, stanza 44 reads:
The sun goes out The land sinks into the sea From heaven fall The holy stars. Smoke and fire Roar below High heat Climbs skywards
One need only speak the word “apocalypse” to know and understand that this important harmonic prototype also tended toward corresponding ektypic image-concepts among early people who were as yet unspoiled, and still possessed an inner magical vision.
The destruction and recreation happens according to Indian wisdom through the world-burning. The seeds of all things are thrown into the womb of Bhavani, whose image is the lotus, and thus a new world can exist once again. This dogma of world-fire (̕εκπύρωσις) is specifically designated as Orphic by many authorities. Refer merely to Plutarch (De defectu oraculorum), Proclus (on Plato’s Timaeus II, p. 99), Clement of Alexandria (Stromata, V). Commonly this doctrine is also called Heraclitean, and there can be no doubt that in the system of Heraclitus it was very highly developed; which, incidentally, also speaks for the relatively early knowledge of it on the part of the Greeks. An agreement with the Indian type of idea appears immediately in the Heraclitean fragments, in the approach of the fire-wind [the Blitz!] (πρηστήρ) that sets the world on fire. The world-fire was also a main theme in the Stoic system. According to this, after the universal destruction, Zeus alone remains, who takes everything into himself and preserves it. If the Orphic schools followed oriental sources, as they doubtless did, they presumably taught, like their sources, of the persistence of the world-substance during the burning of the individual things. This is also suggested by the teachings of Proclus (in Timaeus ibid.) on the re-gathering of things into God as an Orphic doctrine.
(F. Creutzer: Symbolik und Mythologie, 2nd ed., vol. 3, 1821, p. 317.)
Finally, we shall give one more historical example for an application of the polar “P” (“P” as polar coordinates). Fragment 7 of Philolaus (Diels: Fragmente der Vorsokratiker, 3rd ed., vol. I, 1912, p. 312) proclaims: “The first composite, the One at the center of the Sphere, is called the Hearth.” Fragment 17 (ibid. pp. 316-317) proclaims: “The universe is one, and it began to come into being from the center, and from the center upwards at the same intervals as those below. For the parts above from the center are in inverse relationship to those below; for the center is to what is below as it is to what is above, and so with all the rest; for both stand in the same relationship to the center, except insofar as their positions are reversed.”
The reader, at this point, should once more observe Fig. 476, or any of our polar depictions of the “P”. Here the Philolaic or Pythagorean cosmos is revealed in a completely unconstrained manner, whereby one should consider that this kind of tone-number illustration or conversion was certainly known to Philolaus, an outspoken Pythagorean. “The One at the center of the Sphere = hearth” is the circle of the unity 1/1. If the world order appeared “from the center, in the same intervals upwards as downwards,” and “what lies above the center [outside the 1/1 circle] is in inverse relationship to what is below [within the 1/1 circle]”—then this is also a precise description of Fig. 476; because the octaves (as framework for the sequence of ratios) go out from the 1/1 circle in opposite directions. And when it finally reads: “for both directions are the same in their relationship to the center [i.e. the 0-point], except they are reversed,” this is once again a precise description of the “equal” line (vector) of the c-tone with its octaves; they simply turn around on the periphery of the 1/1 circle, i.e. one is directed outwards, the other inwards. In all the literature on Pythagoras, I have found not even a slightly satisfactory solution for this theorem. I offer it here yet again, even though I have already published it in my “Pythagorasaufsatz” (Abhandlungen 1938) with many other interpretations of Pythagorean fragments regarding which philology has hitherto been more or less helpless.
A. von Thimus, in his Harmonikale Symbolik (vol. I, pp. 265 and 339 ff.), mentions the Celtic bards (“those Pythagoreans of the North”) and Druidism, which finally died out in the old Irish and English monastery-schools, although its peculiarities still endured well into the Middle Ages. He quotes, from Ferdinand Walters’ Das alte Wales (Bonn, 1859), a few remarkable statements from the “Trioedd Barddas” (Theological Triads), of which one is repeated here, since its conceptual image has an astonishing similarity to the above Pythagorean idea: “There are three circles (or conditions) of being: the circle of infinity, where nothing exists, living or dead, except for God, and only God can traverse it; the circle of the beginning, where all natural things rise up out of death, and which humans must traverse; and the circle of happiness, where all things spring from life; humans will traverse this circle in heaven.” If we use the concept of “condition” here instead of “circle,” then we can equate the first circle to the outermost condition n/1, the second with the condition 1/1, and the third (the center, where humans and all other things emanate, i.e. become conscious of themselves in highest concentration) with the condition 1/n.
§54.8. Results of Harmonic Cosmogony
According to akróasis, the world emerged from a depth (Eidos 0/0) that cannot be explored, and can only be insufficiently described with words, by virtue of an act of self-examination and self-beholding. Harmonics thus proposes an act of creation at the “Beginning” of the world, but not a creation from the Nothing (0), but instead a creation from the All (0/0). The sinking back or rising up into the All (0/0) that is necessary with the end of the world (∞/∞) thus means not absolute annihilation, but instead the possibility of a total renewal. In the act of creation (Origo 1/1), the first being-value is realized. The “being” is in reciprocity of frequency and wavelength, with which time, space, and causality (number), as well as inversion to itself, is born. The “value” sounds and produces the word, the Logos. The temporal element of the being-value (frequency) symbolizes the will; it evolves a long series of forms (history), at the end of which is love. The spatial element of the being-value (wavelength) simply symbolizes the (material) “gestalt”; it evolves a long series of spatial forms, at whose end stands the order of the cosmos and whose concentration is the human form. The tonal element of the being-value (tone, sound) symbolizes the “word” in general; it evolves a long series of forms, at the end of which is the psychical and spiritual expression of man. Harmonics summarizes the synthesis of all these elements in the concept of “akróasis.” In the first evolution of the unity (Origo), the Trinity is born, and with it the interval of the octave (the octave of Pythagoras), the framework-interval, within which the entire subsequent development at last becomes possible and obtains its stepwise significance. In principle, with this creation-triad the creation polarity is also given, which is already based in nuce on the inversion in the Origo. The concepts and conditions of the Nothing (0) and the Unending (∞) emerge, as well as the unending plethora of being ∞/∞, first as directions, vectors—then limited in the relevant symbols themselves. The world shows itself spread within this polarity in the three principles of the limiting (1/∞) (atom, darkness, inhaling, female, passive, attraction, etc.), the unlimited (∞/1) (universe, light, exhalation, male, active, repulsion, etc.), and the equal (n/n, ∞/∞) (equilibrium, balance, mediating principle). Within these principles, all the development of nature unfolds. The first “senary” cycle, the appearance of the “foreign” seven-series, the analysis of the fifth-diagram, etc., show that there are disturbance factors inherent a priori in the harmonic cosmology, which can only be overcome, or built in, rebuilt, through human “retrospection,” be it upon the Eidos, the Origo (middle line), or upon simpler selective norms. Only within these selections do we step outside the simple necessity of nature, only here can we “express” ourselves and create a realm of human freedom in the direction of the Beautiful and the Good.
This is the great framework of harmonic cosmogony. All chapters of this book will be useful for completing it in detail.
One might say that this “result” offers little that is new, and has already been realized in its characteristic features in some way in the religion, philosophy, and art of all times and peoples—which indeed our ektypic examples prove. This is undoubtedly correct. But beside the fact that there will hardly ever be a doctrine that is able to unify in itself such a great number of heterogeneous things, and to bring them into a sensible relationship with one another, harmonics is still about something more than a simple intellectual synthesis. All harmonic forms and entities are not only intelligible products of logical deliberations, but are also anchored in nature and in our psyche, and precisely this double foundation secures them a substantially persuasive epistemological weight. In harmonics we are no longer directed only to belief, to factual knowledge, or to logical conclusions, which often enough can be brought into contact with each other with difficulty or not at all. By virtue of its approach to the primal phenomenon of tone-number, akróasis takes its soundings a priori in nature and in our psyche, and this very fact makes its results compelling in a completely different way. What is important is not the simple connecting and systematizing from some ”holistic” or other viewpoint—although this can and must be so under certain conditions—but the leading back to a common root which we can physically and psychically control. And this is precisely what our harmonic studies are about. I have emphasized continually, in all my writings, the fact that this also represents only a single “road to Rome,” and have checked myself against a hypertrophy of harmonic ambitions. But finally, it is important to “get to Rome” one way or another; the fact that there may be more or less difficult ways there, straight ways and roundabout ways, is secondary.
For 2 and 3, see §25 of this book. For 4, see §30. For 5, see §23. For 6, see §26. For 7, see §13-§16, and §24 (equal-tone lines). Furthermore: H. Kayser: Akróasis, last section.
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