Harmonic Origins of the World inserted the astronomical observations of my previous books into an ancient harmonic matrix, alluded to through the harmonic numbers found in many religious stories, and also through the cryptic works of Plato. Around 355 BC, Plato’s dialogues probably preserved what Pythagoras had learnt from ancient mystery centers of his day, circa. 600 BC.
According to the late Ernest G. McClain*, Plato’s harmonic matrices had been widely practiced by initiates of the Ancient Near East so that, to the general population, they were entertaining and uplifting stories set within eternity while, to the initiated, the stories were a textbook in harmonic tuning. The reason harmonic tuning theory should have infiltrated cosmological or theological ideas was the fact that, the planets surrounding Earth express the most fundamental musical ratios, the tones and semitones found within octave scales.
* American musicologist and writer, in the 1970s, of The Pythagorean Plato and The Myth of Invariance.
Ancient prose narratives and poetic allusions were often conserving ancient knowledge of this planetary harmony; significant because these ratios connect human existence to the world of Eternity. In this sense the myths of gods, heros and mortals had been a natural reflection of harmonic worlds in heaven, into the life of the people.
In the Greece before the invention of phonetic writing, oral or spoken stories such as those attributed to Homer and Hesiod were performed in public venues giving rise to the amphitheaters and stepped agoras of Greek towns. Special performers or rhapsodes animated epic stories of all sorts and some have survived through their being written down.
At the same time, alongside this journey towards genuine literacy, new types of sacred buildings and spaces emerged, these also carrying the sacred numbers and measures of the megalithic to Classical Greece, Rome, Byzantium and elsewhere, including India and China.
Work towards a fuller harmonic matrix for the planets
In my first book, called Matrix of Creation, I had not yet assimilated McClain’s books, but had identified the musical intervals between the lunar year and the geocentric periodicities of the outer planets. To understand what was behind the multiple numerical relationships within the geocentric world of time, I started drawing out networks of those periods and, as I looked at all the relationships (or interval ratios) between them, I could see common denominators and multiples linking the celestial time periods through small intermediary and whole numbers: numbers which became sacred for later civilizations. For example, the 9/8 relationship between the Jupiter synod and the lunar year could be more easily grasped in a diagram revealing a larger structural network, visualized as a “matrix diagram” (see figure 1).
One can see the common unit of 1.5 lunar months, at the base of the diagram, and a symmetrical period at the apex lasting 108 lunar months or 9 lunar years (referencing the Maya supplemental glyphs). In due course, I re-discovered the use of the Lambda diagram of Plato (figure 8.7), and even stumbled upon the higher register of five tones (figure 2) belonging to the Mexican flying serpent, Quetzalcoatl (as figure 8.1), made up of [Mercury, the eclipse year, the Tzolkin, Mars and Venus], Venus also being called Quetzalcoatl.
These periodicities are of adjacent musical fifths (ratio 3/2), which would eventually be shown as connected to the corresponding register of the outer planets, using McClain’s harmonic technology in my 5th book Harmonic Origins of the World (see figure 3).
Probably called the flying serpent by dynastic Egypt, Quetzalcoatl’s set of musical fifths was part of the Mexican mysteries of the Olmec and Maya civilizations (1500 BC to 800 AD). This serpent flies 125/128 above the inner planets – for example, the eclipse season is 125/128 above the lunar year: 354.367 days × 125/128 = 346 days, requiring I integrate the two serpents within McClain’s harmonic matrices in Harmonic Origins of the World (as figure 9.3).
Uranus is above Saturn
The eclipse year is above the lunar year
the Tzolkin of 260 days is above the 9 lunar months of Adam
By my 6th book, Sacred Geometry: Language of the Angels, I had realized that the numerical design within which our “living planet” sits is a secondary creation – created after the solar system, yet it was discovered before the heliocentric creation of the solar system, exactly because the megalithic observed the planets from the Earth. Instead of proposing the existence of a progenitor civilization with high knowledge** I instead proposed, as more likely, that the megalithic was the source of the ancient mysteries. Such mysteries then only seem mysterious because; a kind of geocentric science before our own heliocentric one seems anachronistic.
**such as Atlantis as per Plato’s Timaeus: an island destroyed by vulcanism, Atlantis and similar solutions have simply “kicked the can down the road” into an as-yet-poorly-charted prehistory before 5000 BC, for which less evidence exists because there never was any. In contrast, the sky astronomy and earth measures of the megalithic are to be found referenced in later monuments and ancient textual references. That is, megalithic monuments recorded an understanding of the cosmos then found in the ancient mysteries. A geocentric world view was a naturally result of the megalithic, achieved using the numbers they found through geocentric observations, counting lengths of time, using horizon events and the mathematical properties of simple geometries.
Geo-centrism was the current world view until superseded by the Copernican heliocentric view. This new solar system was soon found by 1680 to be held together by natural gravitational forces between large planetary masses, forces discovered by Sir Isaac Newton. The subsequent primacy of heliocentrism, which started 500 years ago, caused humanity to lose contact with the geocentric model of the world: though figure 4 has the planets in the correct order for the the two serpents, of inner and outer planets, this is also (largely) the heliocentric order, if one but swaps the sun and the moon-earth system.
All references to an older and original form of astronomy, based upon numerical time and forged by the megalithic, was thus dislocated and obscured by our heliocentric physical science and astronomy of the modern day – which still knows nothing of the geocentric order that surrounds us.
The geocentric model entered Greek astronomy and philosophy at an early point; it can be found in pre-Socratic philosophy … In the 4th century BC, two influential Greek philosophers, Plato and his student Aristotle, wrote works based on the geocentric model. According to Plato, the Earth was a sphere, stationary at the center of the universe.
Those new to Ernest McClain and his The Myth of Invariance, should know this book was a seminal work for anyone in my generation, that opened up a Pythagorean vision; of how number operates in the domain of harmony. This world of harmony can be numerically defined in a quite extraordinary and specific way and we, as human beings, can receive it through our mind whilst also through the senses. This relates to the unusual fact that, whilst all notes can be doubled in frequency through the number two, with a perfect consonance, a new population of notes is then opened up, within an octave, of intervals that are also harmonious, through the use the two next prime numbers: three and five. Thus music, so effective upon the human heart, can build a world of meaning, sometimes referenced in myths as sacred numbers, written through understanding harmony as fundamentally generated through numeric transitions within music.
In 2008 I prepared a summary of Ernest McClain’s statements about Agni because, in the midst of the perfect symmetry of musical harmony lies something new, born to the world opposite its beginnings and endings. I originally made the pdf below for my friend Anthony Blake, part of our attempt to study the origin of creativity within the existing world. It appears that something important comes into being at the centre of this issue of octaval harmony, just as we ourselves come into existence in the middle of the universe, as conscious beings, conscious then of our incompletion.
It occured to me to include this in an email to Ernest and, all in, he said in reply “I can’t imagine anyone improving on your few pages” and “Put it out now on your own website stamped with my approval”. Please enjoy this transmission from the centre of the octave:
What Ernest McClain says about Agni in The Myth of Invariance:
After the ice receded, late Stone Age people developed the farming crucial to the development of cities in the Ancient Near East (ANE). On the Atlantic coast of Europe, they also developed a now-unfamiliar science involving horizon astronomy. Megalithic monuments were the tools they used for this, some still seen in the coastal regions of present day Spain, France, Britain and Ireland. Megalithic astronomy was an exact science and this conflicts with our main myth about our science: that ours is the only true science, founded through many historical prerequisites such as arithmetic and writing in the ancient near east (3000- 1200 BC) and theory-based reasoning in Classical Greece (circa 400-250 BC), to name but two. Unbeknownst to us, the first “historical period” in the near east was seeded by the exact sciences of the megalithic, such as the accurate measurement of counted lengths of time, developed by the prehistoric astronomers. With the megalithic methods came knowledge and discoveries, and one discovery was of the harmonic ratios between the planets and the Moon.
The idea that the planets were gods had been born before the ancient world, through the data of megalithic astronomy and this megalithic idea was the basis for the religious ideas of the East. Megalithic astronomy and Near Eastern religious and harmonic ideas have both been written out of our history of civilization, leaving us with enigmatic monuments and ill-defined religious mysteries. How this slighting of our real history happened is perhaps less important than our discovering again the purpose of the megalithic monuments and of those religious ideas that sprang from the discovery that the planets were harmonically related to life on Earth.
Is human history lacking something fundamental?
The Harmonic Origins of the World first explores this alternative late stone age, the megalithic, as more culturally significant than the advent of Neolithic farming. But ironically, the megalithic culture has been eclipsed by the history-building developments of the middle-eastern civilisations, all because intellectual histories could only start when written records began within the civilizations. Writing did not make people literate and they still relied on an oral tradition of story-telling which had descended from the stone age. But writing did record the oral stories which became our texts.
Subsequent civilisations changed the civilized soul, through contact with the material cultures necessary to support urbanisation: written records, accountancy, religious ideas, reason and most recently our own science and technology. To get closer to the meaning of the megalithic enterprise, one must recognise that its primary cultural norm was astronomical. Numbers were sublimated as counted lengths, these representing the duration of celestial cycles where days were counted using small standardised units such as a digit or inch. This counting of time, to form a length where numbers were then implicit, enabled the geometry of the right triangle to also sublimate the multiplicative and trigonometrical functions used, in our mathematics, to calculate. Today’s methods for studying astronomy are therefore completely different to those of the megalithic: we don’t look to the horizon, count lengths or use geometry to compare. Therefore 20th century science has vastly underestimated the scope, sophistication and significance of megalithic astronomical knowledge.
Why was Religion astronomical?
The religious thoughts that subsequently emerged in the ANE were mainly based upon the celestial heavens; where the planets, sun and moon were gods responsible for the creation of the world. Our word religion expresses the notion of a human effort to reconnect with a cosmic world above our heads. Ancient religion had a sacred basis that was kept secret from the ordinary man and this established the division between the secular and the sacred which still exists today. The most direct way of explaining why ancient religions sought to connect with gods, literally in heaven, is to see in it the product of a prior age in which the heavenly world was intensively studied so as to understand the behaviour of the celestial bodies within a heavenly worldof time, as where something divine is happening. This work must have predated the earliest historical civilisations. No written record of megalithic astronomy has ever been found so that only the monuments can speak of it, if we understand their astronomical language of number and proportion.
By 3000 BC, the Sumerians had inherited fully developed astronomically-based religious ideas in their oral traditions (such as Gilgamesh, then fortunately written down on cuneiform tablets.) Thus, whilst the megalithic was reaching a zenith in Europe, the great historical civilisations recorded beliefs that could only have evolved from their concrete astronomical knowledge of the heavens, an activity brought uniquely to a high level of sophistication by the builders of the megaliths. But why were astronomical truths used as a basis for religious thought? To understand this requires we re-interpret the megalithic record, a record largely concerned with discovering the time-patterns of the sun and moon.
Astronomical Ratios are the Matrix of Creation
The pattern of time formed by planets can be found within the stories and symbols of the historic period, but the techniques for finding this pattern only existed in the megalithic period as it must have been based upon measuring ratios between time periods. Planetary time ratios naturally lead to a pantheistic insight; that the planets are gods, instrumental in the creation and maintenance of the world.
The megalithic established the ratio (between counted lengths) of the lunar to solar years, as the basis of their astronomy, and this approach was then crucial to understanding the musical pattern of time formed by the planets to the moon (as per figure 3).
The moon was formed after the collision of a proto-earth with a smaller Mars-like planet, as the inner solar system was coalescing its solid matter into the present inner planets: Mercury, Venus, Earth and Mars. Billions of years later, the moon achieved an orbital distance from the earth that made the lunar year (of twelve lunar months) musically resonant with the three outer planets. The lunar year formed a tone (9/8) to the synod of Jupiter, a diatonic semitone (16/15) to the synod of Saturn and a chromatic semitone (25/24) to the synod of Uranus.
For the ratios of these outer planets to relate to the lunar year requires the ratios of their sidereal periods to already havethe possibilityof achieving this musical resonance, when viewed from Earth’s orbital year. Figure 2 shows the situation within which the synods of the outer planets are themselves expressing lesser-known musical intervals between each other. Saturn is the common factor of 128 units of time in length to Jupiter’s 135 units and to Uranus’s 125 units. It is these numbers in ratio that enable the lunar year to achieve a duration of 120 units and, since the lunar year is made up of 12 lunar months, these units of time are one tenth of a lunar month long or 2.953 days.
Forming the Cosmic Octave
The optical discovery of Uranus in ancient times is dubious, but we can assume that the synods of Jupiter and Saturn became known to a megalithic astronomy which, as already stated, specialised in measuring time periods and in comparing these to other time periods, using trigonometrical triangles.
Figure 3 shows how megalithic use of triangular comparison would have revealed the common factor, of 1/10th of a lunar orbit, between the outer planets, namely the Jupiter synod is 13.5 lunar months, that of Saturn is 12.8 lunar months (and that of Uranus is 12.5 lunar months.)
The Gods of the Ancient World
This was the principle discovery on which ancient speculation, that the planets were gods, was based. These same lords of time were celebrated in the New World, after the Bronze Age collapse of 1200 BC in the Old World, firstly with the Olmec and subsequently the Maya and Aztec religions of Mesoamerica. Passed on from the Ancient Near East, Olmec religious ideas contained elements soon suppressed in the Old World. Numerical tuning theory was closer to its astronomical origins before 1200 BC so that, the fantastic information placed into mythic stories could still be read with regard to the harmonic numbers referred to in stories. These numbers could be abnormally long ages or reigns, the numbers of things, the number of syllables or stanzas, and so on. Ancient myths hold many astronomical and harmonic allusions which have long puzzled scholars unable to find the missing link in the megalithic.
A couple of seminal books on this subject emerged simultaneously with similarly challenging proposals. In Hamlet’s Mill (1969) the Precession of the Equinoxes (and of the earth’s Poles) was shown to be a common theme within myths and; in The Myth of Invariance (1976), Plato’s tuning theory was shown to be “the tip of an iceberg” of ancient harmonic allegory: both books implied there had been a near world-wide oral tradition that had incorporated such matters in their epic works.
For example, the Bible has a flood hero called Noah, reused from those of Marduk in Babylon and Indra in the Rig Veda. Precession was considered the creator of world ages, that is, of History itself; and the great numbers of India expressed time as a harmonic ceiling for an octave, such as 8,640,000,000 – a number which turns up in many traditions, for example the Edda’s final battle of the gods, and the design of Angkor Wat. The Bible significantly starts with a smaller number, the first man is called Adam, whose name in letter-number equivalence is 1 + 4 + 40 = 45 when added whilst in place notation he is 1,440, which is 32 x 45. This takes us back to the Moon.
Music from the Moon
If one wants to generate a harmonic ceiling for the lunar year and outer planets, whose numbers are 120, 128 and 135, Adam as 45 must be doubled twice to 180, the age at which Isaac, son of patriarch Abraham, dies. This implies that the lunar year lies within a harmonic system of 18 lunar months, which is exactly the time period of the Olmec and Maya Supplemental Glyphs, sometimes added to their Long Count marking upon stela (engraved standing stones) as if these cultures had derived from the megalithic. The Olmec appear to carry forth parts of the intellectual life of megalithic times otherwise lost to the historic record. The Bible writers were evidently privy to this harmonic tradition which seems to have travelled alongside an oral tradition, lost though cryptically recorded by the genuine literacy of Plato’s age, in texts and secret Pythagorean groups.
If one factorises the numbers 120, 128 and 135, one can place them according to the presence of prime numbers 2, 3 and 5, since it is these primes which form the musical intervals between tones:
Powers of 2
× powers of 3
× powers of 5
One can see that the lunar year and Jupiter synod both have the factor 5 whilst they differ in two ways; by 9 (3 x 3) and by 8, hence the interval 9/8 between them. Saturn differs in three ways from the lunar year; by 16 (128/8), and by both 3 and 5, hence the interval 16/15 between them.
The writers of the Bible raised Isaac up from 180 through reproductive doubling to 360 (x 2), then 720 (x 4) to reach the fullest extent of Adam’s name, namely 1440 (x 8), meaning we must multiply these planetary numbers by 8 to become 960, 1024 and 1080 – numbers which have rich meaning in ancient number symbolism. They can be viewed on a mountain made of increasing powers of 2, 3 and 5 under the 1440 limit (figure 4) and this mountain uses units one 80th instead of one 10th of a lunar month.
One 80th of the lunar month of 29.53 days is 0.369 days, which times 1000 is the synod of Uranus (starts 4th row), the air god Enlil, who launched floods to cleanse the earth of human wickedness. The Bible replaced him with YHWH and the seven planetary gods were removed from the week, numbering weekdays rather than deifying them as of the god, as per; “Thou shalt have no other gods before me”. And yet, the harmonic doctrine still lay behind the outer biblical narrative, secretly informing it.
This situation is repeated in many ancient texts and in many different ways. The widespread insertion of harmonic numbers within literary texts gives three rows of darker notes around D a special capacity to form musical scales. In this case the gematria limit for Adam of 1440, gives him the ability to play five modal scales, some of the notes having these planetary numbers.
This type of work was originally deduced from some of Plato’s dialogues, seen as a codification of the ancient methods by Ernest G McClain, who wrote The Myth of Invariance to illustrate its widespread use in the ancient world. I have continued in this rich vein whilst connecting McClain’s work with my own work: on megalithic astronomy and discovery (in 2000) of the musical intervals between the lunar year and the outer planets.
Bringing it all together
TheHarmonic Origins of the World is the latest exploration of this domain, revealing some famous figures in ancient myth, through visualising their “holy” mountains whilst introducing how practical musical scales work on these mountains. The significance of McClain’s work is deepened through the restoration of an important missing history which can explain why our oldest texts, often religious, are peppered with harmonic numbers. And part of that missing history is that harmony between the lunar year and outer planets has arisen relatively recently, alongside the modern humans of the last 200,000 years.
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 Synodic periods are the time taken for the Earth to again stand between that outer planet and the Sun, longer than a year because the planets are slowly moving during the solar year. These synods therefore only apply to those living on the surface of the Earth. The synods are: lunar month 29.53059 days; lunar year 354.367 days; Jupiter synod 398.88 days; Saturn synod 378.09 days; Uranus synod 369.66 days
The harmony of the spheres can only be found in our world of time, where it is a strong and compelling phenomenon. Such a harmony was no prescientific fantasy. Pythagoras, who coined the term, probably did so based on the geocentric time world, a view lost to history apart from cryptic references that can no longer be interpreted.
In our age of system science, musical harmony is not thought relevant to the design of dynamic systems such as the planets, yet they appear adapted to just intonation seen from the exclusive perspective of our planet. Why should our planet have a harmonious view of time, and what difference does time’s harmoniousness make to life on Earth? Is there some other purpose to this harmony or none at all? To answer such questions one has to recognize just intonation as being a holistic system that demands human insight into the nature of whole phenomena (a so-called gestalt). Such gestalts flow from the need to see higher-level relationships rather than the raw complexity of their parts. All higher structures of meaning subsume lower levels of meaning. For example, microclimates are a structuring of meaning higher than trees, water, weather, and topography, usefully integrating these parts within a newly perceived whole. Such insights reveal a higher idea that indicates new potentials within a system. The new level of conceptual order has not changed in the phenomenon but how we relate to it. This profound faculty is the basis of what we call understanding rather than knowing, and it enlarges our “world.” The world is already structured, and a sensory insight re-creates that structure as a simplifying aspect, already present, to expand the intelligibility of the sensory world and with it, our present moment. Insight and the world’s creation were considered similar acts within ancient cosmologies, in that an insight about the world resembles the structure of the world as it would be conceived by any god in the act of creating it. Such a vision involves a special effort but provides a creative view of the world, in which simplicity and relatedness replace functional complexity with a new appreciation of the sensory world. The celestial behavior in Earth’s skies is a prime example of such an action: the rotation of Earth, its orbit around the sun, the moon’s orbit, and its illumination by the sun complicate the observed orbital periods of the other planets and yet, that added complexity has produced harmonic simplicity between synodic periods!
Chapter 1 showed how Late Stone Age astronomers used geometrical counts of synodic periods to discover this harmony of the spheres, which modern astronomers have not seen because scientific calculation methods deal instead with planetary dynamics modeled by equations. Simplicity has somehow adapted our solar system without breaking physical laws. At the level of gravitational dynamics, many complexities were required to achieve just intonation seen only from Earth, especially the lengthening of the lunar month as an intermediary to the planetary synods seen from Earth. Any demiurgic preference for harmony (seen from Earth) resembles the human gestalt that revealed the harmony of the spheres to human sensory intelligence in the Late Stone Age, and it must be noted, humanity has become demiurgic since the Stone Age, creating man-made worlds.
Demiurgic intelligences are probably part of each star system and, if our star has a demiurgic intelligence, this action seems to have used the moon to establish a justly intoned time world for the third planet. It adapted the unchanging orbital pitches of an n-body planetary system to present harmonic synodic systems that planetary orbital periods alone could never express. Our geocentric system is harmonically founded between 1, the zeroth power of 2 (the Saturn synod) and the fifth power of 60 (YHWH, as 365-day year), which is the smallest numerical resolution to contain just intonation of both inner and outer planets, as in the implied holy mountains of our ancient texts.
Harmonic Origins of the World Contents (272 pages, 100 b&w illustrations) Preface Introduction: The Significance of Planetary Harmony (5) PART 1: RECOVERING LOST KNOWLEDGE OF THE WORLD SOUL 1 Climbing the Harmonic Mountain (20) 2 Heroic Gods of the Tritone (19) 3 YHWH Rejects the Gods (15) 4 Plato’s Dilemma (22) PART 2: A COSMICALLY CREATIVE HARMONY 5 The Quest for Apollo’s Lyre (25) 6 Life on the Mountain (23) PART 3 THE WAR IN HEAVEN 7 Gilgamesh Kills the Stone Men (16) 8 Quetzalcoatl’s Brave New World (31) 9 YHWH’s Matrix of Creation (19) 10 The Abrahamic Incarnation (15) Postscript: Intelligent Star Systems APPENDIX 1: Astronomical Periods and Their Matrix Equivalents APPENDIX 2: Ancient Use of Tone Circles (11) Notes Bibliography Index
Ancient musical knowledge came to Just tuning long before Greek music, in Babylonia. It now seems likely that two sources of musical information, were involved in an early tradition of musical tuning by number: firstly, the early number field is the original template upon which musical harmony is based; and secondly, the prehistoric geocentric astronomy which preceded the ancient world had been comparing counted astronomical time-periods, and had discovered the rational tone and semitone intervals between the lunar year, Jupiter and Saturn . Ernest G. McClain identified a harmonic parallelism within ancient texts in which the anomalous numbers found within mythic narratives inferred a unique array (a matrix) of whole numbers, shaped like a mountain, which could explain plot elements, events and characters of the narrative, as intended parallels to such harmonic mountains. McClain’s matrices allowed the author to locate the harmonic intervals found between planetary synods as a reason why religious texts should have employed harmonic numbers, these relating to planetary time as gods alongside ancient systems of tuning. Based on a talk delivered at ICONEA2013, 5th December at Senate House, University College London.