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Author Topic:   The Science of Harmonics
AbsintheDragonfly
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Posts: 147
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posted April 28, 2010 11:48 PM     Click Here to See the Profile for AbsintheDragonfly     Edit/Delete Message
Really Fascinating reading!

http://hanskayser.com/EZ/kayser2/kayser2/index.php

Judaea

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 ...”1 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 voice2 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:3 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 Joseph4 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”:5 “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 Zohar6 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:7 “And the breath (ruach) of God moved upon the waters.” Luther translates ruach as “spirit.” In the Zohar,8 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:9 “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.'”10 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.

Babylon

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.11 Bruno Meißner12 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.
Persia

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:13 “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...”14 “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.”15

A great, nearly forgotten scholar of this ancient mythology16 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.

India

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:17 “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.18 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.”

Egypt

In Egyptian mythology, the first creator Kneph-the original, immortal god, the spiritual principle corresponding to the Greek Zeus, according to Plutarch19-breathes the cosmic egg from his mouth, from which Ptah, the second creator, emerges: the orderer, the artful.20 “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.”21 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.22 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.


China

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.23 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,24 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!

Polynesia

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,25 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.”26

Plato's and Aristotle's position on akróasis

The position on akróasis of the two great ancient philosophers, Plato and Aristotle, is interesting to us. Today it is agreed that for the ancient Greeks, “music” (understanding this concept in its broadest meaning, i.e. “akróasis”), like poetry (which is also perceived through the medium of the ear), was not merely an art, but that they sensed the singing and the order of the cosmos in the phenomenon of tone.27 Physiologically, the eye was more spiritual for Plato; for Aristotle, the ear.28 Plato29 gives the eye the predicate “sun-like,” and speaks30 of an “eye of the spirit.” Aristotle31 was of the opinion that the ear is the most spiritual organ of the human senses (!). For both however, Plato and Aristotle, the high value of “music” and the musical in educational and ethical terms is self-evident. The two thinkers only differ regarding their physiological priorities in that Aristotle, especially in his Metaphysics, argues against the Pythagorean speculations numbers. The examples he gives show clearly, for those who have worked over the actual Pythagorean tone-number system and analyzed its forms, that Aristotle did not know the concrete basis of Pythagorean harmonics, and therefore did not understand many of the traditional Pythagorica. Plato, on the other hand, only objects fundamentally to the “haptification” of those Pythagoreans who treated tone-number like “hair splitting,” and seeks, in the acoustic phenomena in question, an ascent to the spiritual, to the Idea. In the Philebus, Plato introduces the arrangement of the sound system in speech with these words: “Some god or divine man observed that the voice [phonè] was infinite...” In his later works, he returns openly to Pythagoreanism, presumably as a result of personal contact with Pythagoreans in Sicily and southern Italy. His harmonic derivation of the soul of the world in the Timaeus is both famous and infamous. Since Plato was avowedly an initiate (see his Seventh Letter), he gave this derivation only in veiled language. However, for those who know, there is no doubt that the two series given by Plato, 1 2 4 8 and 1 3 9 27, joined in the correct way,32 produce what is still the only correct formula for the diatonic scale, and therefore a law on which not only all practical music is based, but also, for the ancients, the music of the cosmos; which is exactly what Plato wished to show. Plato's thoughts are even closer to Pythagoreanism in his enigmatic posthumous work, the Epinomis. This has long been assumed to be the work of his student Philippos of Opus, but arguments are now being made for its authenticity.33 It is possibly a transcription of one of Plato's later lectures. “If the Epinomis is authentic, then its special significance lies in the fact that it represents Plato's closest approach to Pythagoreanism.”34 The subject of the Epinomis is the question: what must mortal men learn in order to be wise? The individual observations of this work continually lead back to number. Everything unintelligent, incalculable, unordered, non-rhythmical, and inharmonic is lacking in number-ratio. Number is the gift of the divine universe. The harmonic idea of unity rules the forms of the upper and the lower world, and also determines that in which man is absent: at death the multitude of sensory perceptions are extinguished, the dying go from the condition of multiplicity to that of unity and thus attain perfect wisdom and happiness.35 Looking at the “Lambdoma”36 or simply at the “partial-tone coordinates,” one can see the tendency of all tone-values to return to the unity of the generator-tone line, and from there to achieve the “perfect wisdom and happiness” of the 0/0. In the series of mathematical sciences, from arithmetic to geometry and stereometry to the harmonic intervals, the Epinomis gives special attention to the arithmetic, geometric, and harmonic proportions. I suggest that the reader look at Fig. 179 in this book. These three proportion types were therefore present in the original Pythagorean diagram, which may serve as further proof of the connection between Plato's later works and Pythagoreanism.37

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We cannot seek or attain health, wealth, learning, justice or kindness in general. Action is always specific, concrete, individualized, unique. --Benjamin Jowett


It is in giving that we receive. --Saint Francis of Assisi

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Glaucus
Knowflake

Posts: 3289
From: Sacramento,California
Registered: Apr 2009

posted April 29, 2010 02:14 AM     Click Here to See the Profile for Glaucus     Edit/Delete Message

Very interesting stuff

Astrological aspects are based on harmonics too.

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Raymond

Supporting the Neurodiversity Movement

A Different Mind Is Not A Deficient Mind.

http://people.tribe.net/4b0cf8c4-1fc3-4171-92d3-b0915985bf95/blog

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AbsintheDragonfly
Knowflake

Posts: 147
From:
Registered: Apr 2010

posted April 29, 2010 08:00 AM     Click Here to See the Profile for AbsintheDragonfly     Edit/Delete Message
I know! And Music Theory too, and Geometry
http://www.youtube.com/watch?v=kkGeOWYOFoA

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We cannot seek or attain health, wealth, learning, justice or kindness in general. Action is always specific, concrete, individualized, unique. --Benjamin Jowett


It is in giving that we receive. --Saint Francis of Assisi

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