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The stock and commodity markets have a history stretching over millennia, from the Bible to the present day, furnishing data on sun spots, planetary changes, weather cycles, volcanoes, earthquakes, solar variances, and other influences on financial markets.
Gann charted Wheat back to 65 BC and Baumring took this back to 1200 BC.
A fundamental principle of Cosmological Economics is the interconnection between galaxies, solar systems, stars, and planets, along with their interactive influences.
For example, the rotation of our galaxy is responsible for temperature fluctuations on Earth as a result of cosmic ray variations as we rotate through the spiral arms.
Celestial Mechanics deals particularly with the motion of celestial bodies, especially the solar system, but also wider regions of cosmic space.
The subject explores the relationships and processes of heavenly bodies, examining cycles of time, motions of celestial bodies, and the influences between cosmic and local forces.
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.
A branch of Chaos Theory, fractals are beautiful self-similar patterns mathematically generated from non-linear equations.
Fractals apply directly to financial market phenomena, and time-periodic market charts show that similar patterns permeate each time level.
Gann and Baumring saw common patterns foreshadowing coming events within consistent structure.
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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 Gannís system of trading and market order.
Baumring found and elaborated the system of scientific cosmology at the root of Gannís Law of Vibration.
There is no other Gann teaching that gets close to the depth of Baumringís work.
Harmonics In The Ancient World From The Textbook Of Harmonics
A Translation Society Edition
By Hans Kayser
In Genesis, the acts of creation out of the tohuwabohu of the primordial waters begin with the words: “And God said: Let there be light ... And God said: Let there be a firmament in the midst of the waters ... And God said: Let the waters under the heavens be gathered together into one place, and let the dry land appear ... And God said: Let there be lights in the firmament of the heavens ... And God said: Let the waters bring forth swarms of living creatures, and let birds fly above the earth ... And God said: Let the earth bring forth living creatures ... And God said: Let us make man in our image ...” And it was so! Thus the act of creation, the work of six days, is accomplished in succinct beats, through the medium of speech, the word, and therefore through the medium of tone.
Psalm 19 begins with the verses: “The heavens are telling the glory of God; and the firmament proclaims his handiwork. Day to day pours forth speech, and night to night declares knowledge. There is no speech, nor are there words; their voice is not heard; yet their voice goes out through all the earth, and their words to the end of the world.” To tell, say, inform, sound, speak—all these acoustic things, psychically intensified through the antitheses “without speech, without words, with an inaudible voice,” through this secret ̔αρμονία ̕αφαρής, the inaudible harmony of the Pythagoreans: who could overlook the acoustic-harmonic influence that pervades the entire Old Testament, just like an “inaudible voice”? The Judaic philosophy of religion is also full conscious of this. Ben Joseph writes: “Judaic logic is acoustic, not intuitive. Judaic thought is predominantly an inner speech, words in the heart, Debarim sche be leb, which consciousness perceives and judges. In the language of the Bible, instead of ‘I think, I have thought,’ it reads: ‘I speak, I have spoken in my heart.’” Singing, here as in all ancient religions until Christianity, has not only coincidental but substantial significance in the sense of a strong emotion, an aspiration of the soul towards God. In the Zohar, the main book of the Kabbalah, which still preserves ancient traditions of Judaic mysticism, there is a wonderful passage about “the hymns of the angels”:“Now at sunset, the cherubim who stood at that place and had their domain in the ‘sign,’ beat their wings and spread them, and the music of their wings was heard above. Then those angels who sang hymns in the night began to sing, so that the glorification of the all-holy rose up from below … And at the second vigil, these cherubim again beat their wings upwards, so that the music of their wings was heard. Then those angels who held the second vigil began to sing … And at the third vigil, the cherubim again beat their wings, and the angels sang: Hallelujah, sing praises, ye servants of Jehovah, praise the name of Jehovah … thus sang all the angels who held the third vigil, and all the planets and constellations in the heavens began to sing.” The origin of this “singing” is in acoustic articulation, which is correspondingly pervaded by consciousness. The same Zohar reads: “‘Those using consciousness will illuminate’—i.e. consonants and vowels, ‘like the light’—i.e. the melody; ‘of the firmament’—i.e. the expansion of the melody: the way the notes spread out and flow along in the melody. ‘And give justice to the multitudes’: i.e. the pauses of the tones in their continuation, through which the word is heard.”
Before the actual acts of creation at the beginning of Genesis, introduced by the repeated phrase “and God said,” it reads:“And the breath (ruach) of God moved upon the waters.” Luther translates ruach as “spirit.” In the Zohar, however, there is the following commentary: “‘But ‘Ruach’ is the great voice, which rules over the Bohu and grasps it and leads it to where it is needed. This secret is spoken in the words: ‘The voice of Jehovah is above the waters,’ in the same sense as in the sentence: ‘The spirit of God moves upon the waters.’” Furthermore: “The world was made at once through the word and through the breath. As it reads: ‘The heavens were made from the word of Jehovah, from the breath of His mouth all its multitudes.’” It is well known that the meaning of the “word” at the beginning of the Gospel of St. John is related to the concept of the “Logos,” in which “word” is unified with “spirit,” i.e. the acoustic with the metaphysical principle, whereby the Logos is identified with Christ.
In Babylonian mythology there is an ancient Sumerian hymn, a lament to the destroyer-god Ellil, reminiscent of the “curse songs” that endured into the Middle Ages. Bruno Meißner introduces this hymn as follows: “Remarkably enough, the means by which Ellil brings forth all these disastrous effects is above all his word. Ellil’s word is omnipotent here, similarly to the Logos in Judaic-Alexandrian philosophy. Later, other gods also stepped up to this position, especially Marduk, as in the following song, whose surviving form is recent but whose later interpolations can mostly be easily removed: ‘The word, above / makes the heavens tremble; the word, below / makes the earth waver; the word that makes the Annunaki / nothing. His word has no seer / has no indicator; his word is a rising tidal wave / that has no opponent. His word makes the heavens tremble / makes the earth waver; his word wipes away mother and daughter / as one wipes off a rush mat.’ These hymns were accompanied by temple music, performed elaborately. As we already saw, two choirs usually stood across from one another, alternating their voices in antiphony.” Of course, these choirs did not only sing curse songs like the one above, but also mainly hymns of praise and thanks to the gods.
In the ancient Persian rites of the Avesta, the meaning of the “word” often changes into the more concrete meaning of the “name.” Zarathustra asks the creator Ahura-mazda in the Khorda-Avesta: “What is ... the most triumphant, the most powerful, the most majestic ..., what of the whole world, endowed with bodies, is that which purifies the inside the most? To this answered Ahura-mazda: Our names ... O holy Zarathustra ... the most powerful, most triumphant, etc.” And to Zarathustra’s further question—what are these names—Ahura-mazda refers to twenty qualities, such as purity, understanding, wisdom, etc., and calls on him to “retain and utter these names, day and night, sitting and standing.” In another passage, Ormuzd says to Zarathustra: “You should return me, proclaiming the word, to my initial condition, which was all light...” “Speak, O Zoroaster, my pure word, when language deserts you and you are without hope. Whoever speaks the pure word in my domain, the world, and sings it in proper form with the high voice of harmony, his soul shall soar freely into the heavenly realms; I, Ormuzd, will make the bridge three times wider for him; he will be heavenly, celestially pure, and will shine.”
A great, nearly forgotten scholar of this ancient mythology writes: “Zoroaster thinks of the act of creation as mediated not simply through the speech of the great deity, as occurs in other sensorily perceiving religions, although this speech with his idea of the great deity as a great space is wondrous enough; instead he thinks of the enunciated creating word as an independent, spiritual, divine being, just like the other primordial elements, which is an even stranger idea. This creator-word, Honover, appears often in Zend writings, and is also applied to other divine beings. According to the Yacna, it existed before all other created beings: ‘The pure, holy, speedily working word (honover), O Zoroaster, was before the heavens, before the water, before the earth, before the hearths, before the trees, before the fire [!], Ormuzd’s son, before the pure people, before the Devs [demons], before the entire existing world, before all that is good, all pure seeds made by Ormuzd.’ Like the primal lights, it is ‘existing for itself, independently created’ and has, like Ormuzd, a spirit and a light-radiating body.” Surely this idea, considering the Avesta as a religion of light (fire cult, etc.) is “wondrous” and “strange” enough, as E. Röth writes. But if we can grasp the real depth of this “word” as a concept central to akróasis, then we know that the “sound of the world” is expressed in this acousticon, as in all ancient religions and mythologies. Likewise, the Biblical “word of God” must also be understood not literally, but in the sense of a pervading akróasis.
In the Indian esoteric doctrine, the Upanishads, and related writings, there is a metaphysical acousticon related to the Persian “honover”: the holy syllable “Om.” Here Prajapati, creator-god of the Brahmanas, instructs the other gods regarding Atman and the Om-sound: “The gods spoke to Prajapati: Instruct us, O exalted one, about this Atman as the Om-sound! [Prajapati answers:] This universe never even exists, only the Atman resting in its own majesty, unlimited, unique, self-observing, self-illuminating. You yourselves are it [Atman], I say. If you saw it, you would not recognize the Atman, because it is the self, not the other. The Atman is without worldly adherence. So you are it yourselves, and the light with which you illuminate is your own ... Thus although you do not see the Atman, you should observe it [i.e. hear inwardly] through the word Om. This is the truth, the Atman, the Brahman, because the Brahman is the Atman. Yes, it is not to be doubted: Om is the reality; it is what the sages see. Yes, this toneless, feelingless, formless, etc. ... is what the Upanishads teach as nobly illuminating, glowing in unity, nobly enlightening this whole world, timeless, see, I am it, and it is I!” And at another passage (op. cit., fol. 226) it reads:
Know the holy call [Om] as God, Enthroned in all hearts; The wise one, who knows the Om-sound As all-pervading, will not be sad. Of infinite divisions and undivided, It is the blissful repose of duality; He who knows the Om-sound as such Is a Muni [silent observer], and no other.
It is also highly remarkable that here, in a clearly optical context of observing, self-illuminating, glowing, looking, the acousticon of the Om-sound suddenly appears as something that bypasses all other discursive and meditative means of perception as a direct way to the Atman (Brahman), and indeed is explained simply as “reality.” In akróasis, however, we understand this holy syllable Om (actually AUM) as the highest concentration and abstraction of spoken enunciation; in murmuring it, he who prays and meditates senses the sound of the world, just as the Parsee does in the calling and honoring of the “creator word.”
In Egyptian mythology, the first creator Kneph—the original, immortal god, the spiritual principle corresponding to the Greek Zeus, according to Plutarch—breathes the cosmic egg from his mouth, from which Ptah, the second creator, emerges: the orderer, the artful. “He [Ptah] created all gods, Atum, and his divinity—truly, every divine word emerges from the thought of the heart and the mandate of the tongue ... He became the tongue, and he became the heart as part of Atum.” The highest spiritual principle, Kneph, breathes the cosmic egg from his mouth; Ptah, the demiurge, emerges from it, the actual former and arranger whose tongue speaks the divine word; and thus the world is first articulated!
The akróatic element is present to a far wider degree in the legend of Memnon. Admittedly, it overlaps strongly with Greek mythology; the Egyptian mythological sources are sparse here, but are concentrated in the Colossi of Memnon, still surviving, around which grew the well-known legends of a mysterious connection between tone and light. This is inferred more precisely from Greek sources, which refer specifically to Egyptian origins. All of the Near East had so-called Memnonia—Memnon shrines. Of two it is reported: “And in Meroë and Memphis, the Egyptians and Ethiopians make sacrifices to him (Memnon) when the sun sends forth its first rays, when the statue lets a voice sound to greet its worshippers.” Today in Thebes, the so-called “Columns of Memnon,” the two weathered colossi of Amenhotep III (1400 B.C.), still guard his mortuary temple (now entirely vanished), one of the greatest and noblest works of art ever created in Egypt. They were originally over 20 meters high and (as shown by the graffiti on their bases) were visited around the time of Christ by many Greek and Roman travelers who wanted to hear the wonderful voice, which one of these colossi in particular gave forth every morning at sunrise. Physically, this is explained by the fact that the monoliths, made of a hard conglomerate of pebbles, acquired cracks through sudden changes in temperature, and this gave rise to a sound—a phenomenon that was lost through later restoration.
The spiritual akróatic content of the Memnon legend is more important for us than this deliberate or fortuitous sensory acousticon of a monument. The elements of this myth are light and color, tone and song, water-stream and time-flow, auspicy and plumage, celebration of joy and sorrow, and tombs built on the banks of the rivers. All these elements are harmonic through and through. Light and color blend into a unified concept in the “harmony of the spheres”; tone and song are added to this when the priests sing of the planetary gods, and Memnon, the spirit of light, is greeted with psalms at sunrise. Water-stream and time-flow refer to the eternal melody of events; in auspicy and plumage we remember the beating of the wings of the singing angels in the Zohar, the personification of the toning spheres through the Sirens, the mythos of the singing swan; the expressive basis of the celebration of joy and sorrow lies in the two prototypes of major and minor, whose chords could be played on any ancient Egyptian harp, and the tombs on the banks of the rivers indicate a connection between the Memnon legend and the flowing of rhythmical waves. All these typical harmonic indicators gather in the rich mythology of Memnon like points on the circumference around the center, the form of Memnon himself. “And as Titan rose up, forging through the ether with his white horses, and as he reached his eventide goal of the Hours, Memnon, touched by the rays, opened his clear-toning voice” — thus wrote a poet of his impression of image and legend in the hard stone of the Memnon column.
In the 3rd century B.C., a wealthy Chinese businessman and patron called Lü Buwei commissioned from savants an encyclopedia of the knowledge of his time: Spring and Autumn of Lü Buwei. In this oldest extant Chinese work, which contains a music theory strongly pervaded by number-harmonic elements, it reads: “The origins of music go a long way back. Music emerges from measure and is rooted in the great One. The great One generates the two poles [1/n ← 1/1 → n/1]; the two poles generate the power of darkness and light. The power of the dark and the light changes; one rises up high, the other sinks down low; they unite and form bodies, surging and undulating. If they are separated, they unite again; if they are united, they separate again. That is the eternal progression of the heavens. Heaven and earth are held in a cycle ... the origin of all beings is the great One; they build and perfect themselves through the duality of darkness and light. As soon as the seeds begin to sprout, they develop into a form. The bodily form is within the world of space, and all spatial things have a sound. Harmony emerges from their concord. Harmony and concord are the roots from which the music appeared which was written down by the ancient kings. When the world is at peace, when all things are at rest, all following their superiors in their changes, then music will perfect itself. Perfect music has its effects. When desires and passions do not follow false paths, then music is perfected. Perfect music has its origins. It emerges from equilibrium. Equilibrium emerges from the right, the right emerges from the meaning of the universe (Tao). Thus one can only talk about music with someone who has known the meaning of the universe. True, fallen nations and people ripe for decline do not dispense with music, but their music is not serene ... great music is something in which prince and official, father and son, old and young, delight. Joy comes from inner equilibrium; inner equilibrium comes from meaning (Tao). What one calls ‘meaning’ (Tao) is something one looks at without seeing it, listens to without hearing it; one cannot perceive it physically. Whoever sees the incommunicable, hears the inaudible, knows the form of the formless, he approaches true knowledge.” In the speeches and parables of the Taoists Chuang Tzu and Lie Zi, there are wonderful allegories and myths about the universal meaning of “music,” which in the sense of akróasis are some of the deepest and most beautiful writings about this art—and no less than two and a half millennia ago!
Our short summary of non-European peoples and their attitude toward the acoustic and tonal in a broad sense would be incomplete were we not to consider a race whose entire feeling and thought is directly pervaded by the akróatic way of thinking: the Polynesians. We have E. Reche’s book, Tangaloa, to thank for an elucidation of this. Reche, apparently a Marine officer, was able to study the thoughts and psyches of the natives at a time when the plague of European colonization had not yet destroyed everything. The entire psychic life of these people is based on two concepts of image and hearing: “Moana,” the blue without surface, the infinitude without reality, the sea—and “Langi,” singing, creation, the ungraspable stream of eternity. Reche writes: “But is there then a seeing, which is nothing other than time? His [the ‘Tangata’s’] color-eye leaves him here, he turns to the ear—talinga (the answering, that which answers to the vibration of the world). There the waves roar, the winds sigh, the storm sings its wild song, and then again in the later silence of the sea, the entire world is silent around him ... Music is the world—it is singing—langi—singing, creation, cosmos. There he has the word. The all, the heavens are langi and the earth is laloangi, the singing below ... but then does the whole world sing, do all things sing? Is the world also silent? Is there a song to be heard, then, in the stillness of the sea and the silence of the forest? ‘Yes,’ says the Tangata, ‘every silence also has its world of tones—but you cannot listen in casually (fa alongo = to hear, literally: to make an answer), you must listen keenly with your innermost ear’ (fa alolongo = doubled hearing = silence). ‘Then, Tangata,’ I say, ‘sing me a song in harmony with the tones that you take from the foaming of the waves, the thunder of the surf, the rustling of the leaves—but also sing me a song on the accompanying harp of silence! Then I will know whether you really hear something.’ And a flower-decked host of girls stand on the beach before the fuming surf of the lagoon reef, and I ask them, who are always happy to sing, to sing me a song. The song begins—every throat instantly has exactly the same tone. Where did they find it, where did they grasp the beat? And how wonderful this song is! What is its charm? I still feel it now: It is the harmony of the environment, the voice of the surf, over which the tones of the song glide. And I wander further along the shore, and again I meet a group of Samoan girls. ‘E fua, langi ia le pese lelei o le na ou fa alongo anamuna!’ (Hey! Flowers! [young girls are addressed thus] Sing me the most beautiful song that I have ever heard) I call to them. They all laugh, and one walks forward, shakes her flower-bedecked head and says: ‘E lemafafali i matou’ (we can’t do that). And now I learn that they all know the song very well, but do not want to sing it at this place, no, they claim, they can’t sing it. And finally I find out that at this point on the coast the surf roars differently and crashes upon the reef with different intervals. The accompaniment is not in tune with the song—and disharmony is a moral offense ... and love? When the hearts of a boy and girl find each other, they both know it well, but the boy may not ask. One day the girl says to him, at a holy hour: ‘Ua se langi i lou loto’ (there is a song in me). Then he knows that he is the song in her heart.”
One of the portals through which the akróatic way of thinking entered European culture—if we do not assume an autochthonous emergence—is the form and myth of Orpheus. According to Greek legend, Orpheus, the son of Apollo and the Muse Calliope, could tame the wildest animals and even affect trees and stones with the power of his singing and playing. After his beloved wife Eurydice died, he descended to the underworld and charmed its dark ruler with his music. Hades gave Eurydice back to him, on condition that Orpheus would not look back until they had both reentered the upper world. But Orpheus disobeyed, and lost his wife forever. Later, putting himself in opposition to the wild orgiastic cult of Dionysus, he was torn apart by enraged Maenads. This legend reveals deep insight: the bearer of measure and harmony, who charms the world with song and tone, meets his end through unfettered chthonic forces. The legend also tells that Orpheus accompanied the Argonauts on their voyage. In a poem, Orpheus the Argonaut, appearing later but faithfully preserving ancient traditions, we find the lovely passage:
But when I, like those others, took up the lyre, From my throat then melodious song came forth. The dark song first, about the early chaos Lost in natures, closed in by bounding heaven; The wide world’s birth, the deepness of the sea; The highest, wisest, self-perfecting Eros, How what he generates then separates; And Chronos the destroyer, thundering Zeus Who gained the power of immortal gods. Then of the birth of younger gods I sang; Then Brimos, the giants, and Bacchus’ gruesome deeds; Of dynasties of powerless men destroyed I told; through narrow crevices my voice rang, As the hollow lyre sweetly whispered. The song flew to mountain peaks, and wooded valleys Of Pelion, and through the high oak branches, And oaks uprooted marched for the cave’s mouth, Where the melody cracked rocks, and drove beasts wild, Remaining shyly charmed before the cavern; And birds of prey circled Cheiron’s horse stalls With neglectful wings, forgetting their own nests.
This is the legendary Orpheus. Much more important, however, is Orphism as a mythos and religious disposition. The myth of the cosmic egg mentioned above plays an important role in the cosmogony of Orpheus. Both in this and in many other myths of Orphic cosmogony, there are close connections to concrete harmonic theorems; and it is assumed that shortly after the influx of Orphic ideas into Greek culture, Pythagoras and his followers adhered very strongly to Orphism. Indeed, most traditional “Orphica,” especially the fragments of the great didactic poem, the “Holy Legend,” are attributed to Pythagoras or his school, though they contain many ancient elements from long before Pythagoras (stanzas from this follow directly).
The Orphic sects, especially in Attica and lower Italy, were fundamentally opposed to the pleasure-loving Greek culture. They practiced abstemiousness in various ways, and taught that there was a world of evil beside a world of good, but that after many rebirths, the human soul would finally purify itself to enlightened immortality. These concepts of an abysmal entanglement in earthly things, and the immortal soul, make Orphism the complete opposite of the Homeric circle of ideas.[
I will now give a few examples from Orphic tradition, collected and translated with great diligence and effort by Eduard Röth. Röth gave the fragments the title Heilige Sage (“Orpheus, as he sang the true Holy Legend—̔ιερός λόγος,” wrote Clement of Alexandria in Protreptic Ch. VII, in the course of a longer quotation); he comments on them extensively, and holds the opinion that the poem of Pythagoras was based on Egyptian sources:
Youths, listen in awe to all that follows. I shall now sing to the sanctified. Close the doors to the profane! Hear us, exalted number, Who begets gods and men! Son of Leto, O Lord, whose rays reach strong and far, All-seeing sentinel, ruling gods and men, Helios, gliding exalted on golden wings: I heard thy proclamation descending from heaven, And I heard thy utterance, Of this I call thee, Lord, to witness!
There is one power, one God, great origin of all; He is One, his own source. From the One comes all that is created. Therein he appears; For there is no mortals strong enough To look upon him; In darkness he is hidden And we mortals have merely foolish mortal eyes, Too weak to see him, The God who governs all. For on the high vaults of heaven he has set His golden throne And the earth lies at his feet.
Unerring and exalted spirit, the everlasting ether. Ether and the gaping void, on all sides infinite, Through all of which he hears and understands; Because there is no speech, there is no tone, No noise, there is no whisper even, That escapes the ears of Zeus.
He [Zeus] surrounds the Universe with unending ether And places the heavens in its midst In it the mighty Earth With the sea and all the wonders That the heavens enclose; Thus he surrounds the All with an indissoluble bond And he ordains the golden chain of ether; So that everything exists as one, And yet separate. The great and sacred number [Tetraktys] goes Out from the depths of unity, the unadulterated, Until it arrives at the sacred four.
The actual harmonic content of this lavishly poetic Orphic fragment, of which only the beginning is quoted here, will become clear to the reader in the course of this book—for example, the emphasis on the “One who is hidden in darkness” (0/0 or 1/1) as the “mighty origin of the universe”; the “great and sacred number,” the Tetraktys 6-8-9-12, in which the three proportions (arithmetic, harmonic, and geometric) are concealed, and from which (from the Pythagorean viewpoint) the construction of the world and its forms emerge; and the “golden chain,” which we identify with the “generator-tone line”: “so that everything exists as one, and yet separate.” I thought it necessary to offer a sample of this controversial Orphica, in order to give the reader an idea of the peculiarly archaic timbre and impressive formation of this poetry. In conclusion, we quote the following passage from the same Orphic fragments, as applicable in its deep pessimism to our times as to 2,500 years ago:
Truly, there are races of men loaded with curses, Burdens of the earth, embodied specters, in utter blindness Living, and just as incapable of seeing evil Approaching, and of repelling misfortune in a timely manner, As of turning the existing good toward themselves and correctly Using it; relying on good luck, unconscious and without foresight.
Here, we can marvel all the more at Orphism, still striving for the good, for salvation and immortality; and also at the adoption of the Orphic concept of the cosmos by the Pythagoreans, who supported the entire theory “scientifically” by means of tone and number, building it into a unified doctrine.
We shall discuss Pythagoras in section III, as far as the space of this Introduction permits. For now, we shall seek further akróatica within Greek culture.
Next, we find the nine Muses. They are the sisters of Apollo, nine beautiful maidens of whom little more is known than that they change everything they know into music. Thus they are a kind of sensory abstract embodiment of the “sound of the world.” André Bonnard described them, faithfully to the sources, with incomparable charm: “Clio sings of the past, of life, of the glory of cities and peoples that no longer exist. She is history. Euterpe, the double flute at her lips, charms shepherds, flocks, and wild beasts. She roves about with satyrs and sometimes leaves Apollo to follow Bacchus and the Maenads. Polyhymnia knows the oldest hymns, sung at the altars to honor the gods and memorized by the priests. She also knows the elegies taught to youths, praising past heroes. Melpomene has a solemn countenance. She tells of sorrow and death, the fate assigned to guilty and innocent alike. But from all the misery that affects mankind, she produces a noble song in the theater, to which people listen enchanted. She is the liberating beauty of poetry. She is the desire for the tragic. Terpsichore has the dance-devil in her belly. Erato knows the joys, games, and pain of the living. Calliope adjusts her steps to the rhythm of human speech. She walks in step with Homer’s verses, beats the rhythm to the sentences of Demosthenes. Harmony blooms on her lips. Urania has eyes like the sky and stars. She sings the paths of the constellations. She is the harmony of the spheres. Thalia, the last, is the most beautiful and the most mischievous; she is so amusing that one must laugh for sheer delight. The wine of banquets goes to her head. She sings mocking songs about important personages and takes various liberties on the comic stage against established order, decorum, and state.”
Interestingly, the passionate Virgil does not call on these sound-skilled beings for help with poetry, but instead to impart knowledge of cosmic laws:
But receive me, friendly ones; I bear the sign Of your holy service, filled with fervent love, Muses, teach me of the planets’ paths, Of eclipses, and the changing labors of the moon, And why the earth quakes, and the open sea Flows over shores and then sinks back again, Or why the sun sinks fast on winter’s days Into the ocean, which holds back hesitant night. But should a cold, hard nature of the heart Never grant me such secrets of sense and knowledge, In your woods and pastures, traversed by clear streams, I will gladly live, happy and inglorious! ... Happy is he who can know the world’s origins. ...
The Muses are the sisters of Apollo, the god of music and the arts, of measure and harmony. Around Apollo and the Muses another series of mythological figures is grouped, which in fact can only be sensibly categorized within the framework of universal akróasis: the Sirens, the singing swan, the winged beings (angels), and the dolphin.
Originally, the Sirens were not the temptresses we know from the Odyssey. Maidens of wondrous beauty, gifted with great voices, they were cursed by Ceres because as playmates of Persephone, they had allowed her to be abducted without hurrying to her aid. Now they lie in wait on beaches for passing ships, to deceive and destroy them. Only Orpheus the Argonaut was able to redeem them; his song charmed them so that they jumped into the waters and turned to stones:
And so I played my tune; and from the snowy rocks The Sirens appeared stunned, forgetting their own song. Some threw their flutes away, and others tossed their lyres; They then sighed heavily; because their grim fate came, And brought sure death to them; and from the jagged cliff They leapt into the depths of the salt-eddying sea. And there in fearful form, they now appeared as rocks.
I interpret this myth as the struggle between the divine world of sound (Orpheus) and the sensory earthly world (Sirens), and as the conquering of the latter by the former.
The Singing Swan
For Homer, the Sirens were beautifully singing birds with the faces and upper bodies of women. The element of feathers and wings reminds us of the actual “harmonic” magic bird—the singing swan—and indeed of the entire mythology of the winged gods, who accompany their wing-beats with singing and hymns. Swans are consecrated to Apollo. In Birds, Aristophanes writes:
And swans voiced Songs together and rejoiced loudly, Beating with their wings to praise Apollo, Resting on the banks, all along the flowing Hebros; And their song floated up to the ether above: Beasts of the forest listened and halted, Mirror-bright the waves rested flattened – All of Olympus resounded, Astonishment gripped the throne The Gods, the Graces, and the Muses Harmonized in jubilation!
The remarkable “singing” of swans is, of course, legitimized through their being Apollo’s birds. But this interpretation appears to me secondary compared to a much more deeply rooted harmonic interpretation, referring to the Orphic world-egg and the birds that hatch it in various mythologies (phoenix, roc, griffin, etc.). The winged Pegasus, on which Apollo, god of the musical arts, flies into the sky, also belongs in this category, as does the strange legend of the music-loving dolphin.
The quickly hurrying sea-dogs, tone-loving dolphins...” Hölderlin translates a verse from Pindar about the dolphin, “who in the waveless depths of the sea, moved by flutes, adores song,” and makes the following insightful comment: “The song of nature, in the weather of the Muses, when the clouds hang like flocks over the blossoms, and over the melting of golden flowers. At this time every being gives forth its tone, its devotion, the way by which one holds itself together. Only the difference of species, then, makes the separation in nature, so that song and pure voice is all the more the accent of necessity or, on the other hand, speech. It is the waveless sea where the moving fish feel the pipe of Triton, the echo of growth in the coarse water-plants.
The Harmony of the Spheres
The concept and worldview of the harmony of the spheres is common to almost all classical and pre-classical peoples. But in it we find not only the “cosmic” content of akróasis, expressed in myths and legends and interwoven in numerous forms, but even more, we find that specialized harmonic research since the earliest antiquity repeatedly sought concrete connections between the stars and the laws of tones, until Kepler and modern harmonics proved these connections. I will give a few examples so that a few of these mythological forms of the celestial world can be “heard.” Lucian writes: “Thus the lyre served Orpheus, its inventor, as the noblest instrument of his clandestine religion; but this lyre, which had seven strings, was to him a symbol indicating the harmonies of the planets. It was with this secret science that he charmed and mastered all: his concern was not the lyre he had made himself, nor what one generally thinks of as music.” In the Orphic hymns, Helios Apollo is entreated: “You who with golden lyre guide the harmonic progression of all”; Pan is addressed as “under the stars playing / the harmonies of the world on a jesting flute”; and Apollo is sung to thus: “With your bright playing you guide / the whole pole; now changing to the lowest string / now to the highest, and now, in the Dorian mode / completely harmonizing the pole”—the celestial pole, of course. Franz Cumont found depictions of the Muses on seven Roman sarcophagi from the 1st to the 4th centuries, and comments on them as follows: “The sister goddesses who oversee the harmony of the spheres awaken in people’s hearts, through music, the passionate longing for those divine harmonies and the yearning toward the heavens. At the same time the daughters of Mnemosyne recall to consciousness the memory of the truths she knew in an earlier life. They share their wisdom with her, the pledge of immortality. Thanks to them, thought rises up to the ether, is initiated into the secrets of nature, and reaches the circle of the choir of the stars. It is relieved of the worries of this world, is transported to the world of ideas and of beauty, and cleansed of material passions. And after death the heavenly maidens summon the soul they have consecrated in their service to the celestial sphere, and allow it to take part in the blissful life of the immortals.” Of the eight heavenly spheres, Plato writes that on each circle sits “a siren, who goes round with them, hymning a single tone or note. The eight together form one harmony; and round about, at equal intervals, there is another band, three in number, each sitting upon her throne: these are the Fates, daughters of Necessity, who are clothed in white robes and have chaplets upon their heads, Lachesis and Clotho and Atropos, who accompany with their voices the harmony of the sirens—Lachesis singing of the past, Clotho of the present, Atropos of the future.”
The singing swan also reaches the stars. Virgil tells of the legend:
For it is told that Cygnus [the swan], mourning for beloved Phaeton, Under budding poplar branches and the shadows of the sisters, As he sought to ease the sorrow of his love by singing songs, Old age hastened in upon him, silver-gray with tender down, And flying up from earth, he pursued the stars with chanting.
There are many more examples of ancient poetry and speculation relating to the harmony of the spheres. We will mention only a few others.
Pindar, a contemporary of Pythagoras (6th century B.C.), sang:
Golden lyre, Apollo plays you above in heaven, and you rule the dance and song of the violet-ringlet Muses. Below on Earth the choirmasters hear these sounds, and the singers follow the directions when you strike up the prelude giving beat and tone to the song.
Willamowitz-Moellendorf, from whom this translation is quoted, recognizes in this poem a poetic veiling of the harmony of the spheres. The dance, so closely bound up with music for the Greeks, is a symbol of the heavenly dance of the stars: “For what is this round dance of the stars, this regular interwoven movement of the planets in relation to the fixed stars, and the rhythmical unification and beautiful harmony of their movements, if not proof of a great primal dance?” writes Lucian. Cicero moves entirely in the akróatic realm of ideas when he writes of soul, tone, and cosmos: “Indeed, Socrates asks Xenophon from whence we have conceived the soul, if there is none in the world. And I ask, whence speech, whence the regular harmony of speech, whence song? We would have to assume that the sun converses with the moon when they approach each other, or that the world sings in harmony, as Pythagoras says. These are works of nature, Balbus, not of an artificially intrusive nature, as Zeno expresses it, but one that stimulates and drives everything through its own motions and changes.
We will remark only in passing that the ancients closely studied the analogies of the elements of speech, of vowels and consonants to the tones of the planets and celestial spheres, through which they regained a connection to the most ancient cosmic meaning of sound and of the word itself; we will return to this later. But the reader will agree with me that a name, indeed an entire realm of concepts, can now no longer be avoided: Pythagoras.
 “Die Struktur der jüd. Religionsphilosophie” as an introduction: “Geist und Struktur der jüdischen acoustischen Logik” from his greater Hebraic work: “Die Stimme der Prophetie und der Geist der Musik,” published in Jüd. Jahrbuch für die Schweiz, Basel 1919-1920.
 Der Zohar in selection, translated by E. Müller, Vienna 1932, pp. 71-72.
 Eusebius, Praeparatio Evangelica, III, from Porphyry. See E. Röth, op. cit. I, pp. 138 and 60, and F. Creutzer, Symbolik und Mythologie, 2nd ed., 1821, vol. 3, p. 313 etc. In a study of my own that has yet to be published, I was able to prove that a certain diagram of the “audition visuelle” contains a concrete harmonic prototype for the cosmic egg present in many ancient mythologies.
 G. Roeder: Urkunden z. Religion des alten Ägypten, Jena 1915, pp. 166-167.
 I infer the following mainly from Creutzer, op. cit., I (1819), p. 450 ff., where the ancient references and later writings on Memnon are named.
 Tr. by R. Wilhelm, Jena Diederichs 1928—I quote from pp. 56-57.
 Recently, for example, the article “Orpheus” in Religion in Geschichte und Gegenwart, 2nd ed., 1930, vol. 4, one once again inclines us to locate the center of Orphic theogony in the 6th and 7th centuries B.C.
 Flöten = flutes, not Fluten (=floods, streams) as was erroneously printed in the source.
 Lucian, Sämtliche Werke, tr. by Wieland, Propyläen-Verlag, Berlin 1922, vol. 4, pp. 328-329.
 Die Hymnen des Orpheus, tr. by Dietsch, 1822, pp. 23, 33, 86-87.
 In his last master-work, Recherches sur le symbolisme funéraire des romains, Paris 1942—quoted from the translation by E.R. Curtius in europ. Literatur und lateinisches Mittelalter, Bern 1948, p. 239.
 Republic X, 617, tr. by Benjamin Jowett, New York: P.F. Collier, 1901.
 Aeneid, X, 198, from Voß: Mythologische Briefe, vol. 2 (1794), pp. 98-99.
 Die Harmonie der Sphären, Berlin 1915, p. 130.
 Von der Tanzkunst, op. cit., vol. 4, pp. 89-90.
 De Natura Deorum, tr. by Kühner 1862, Book 3, Ch. 11.
 See, among others, Franz Dornseiff: Das Alphabet in Mystik und Magie, 1922, p. 82 ff.
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