On the Harmonic Origins of the World

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.

Le Menec Alignments indicate a profound astronomical work in the new stone age by 5000-4000 BC. Composite mash up by David Blake using Blender, Google Earth elevation and imagery plus Alexander Thom geometry and digitized stone locations.

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 world of 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).

Figure 1 The collision with Theia with the proto-Earth leading to the creation of our Moon. [NASA/JPL-Caltech]

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[1] of Jupiter, a diatonic semitone (16/15) to the synod of Saturn and a chromatic semitone (25/24) to the synod of Uranus.

Figure 2 The synods of the outer planets based upon the earth’s orbit make it possible, numerically, for the lunar year to evoke three of the most significant musical intervals. Earth’s orbit and the Sun’s illumination of the Moon have achieved the required lunar year length of 120, where twelve is the number of semitones in an octave, and notes on a keyboard.

For the ratios of these outer planets to relate to the lunar year requires the ratios of their sidereal periods to already have the possibility of 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 The harmonic ratios between the nearest three outer planets and the lunar year. The four-square rectangle with long side equal to the lunar year gives, geometrically, the solar year as its diagonal length. The outer planetary synods are longer since the planets have moved ahead of their last opposition to the sun, at which time they appear to perform a loop amongst the stars

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:

CyclePowers of 2× powers of 3× powers of 5Total
Lunar Year835120
Saturn128  128
Jupiter 275135

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.

Figure 4 Adam becomes 1440 and shows where the outer planets are, harmonically. Such mountains were used to tell a story that maintained the harmonic doctrine whilst providing cultural and religious stories. (http://harmonicexplorer.org#1440)

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

The Harmonic 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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[1] 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

Jupiter’s gravitational and numerical influence

This post begins a Theme relating to the Trigon event occurring on 21st December 2020, when Jupiter and Saturn are conjunct at dusk in the sky. This touches upon what such synchronicities mean for other long term periods seen from Earth, such as the Moon’s nodal period of 6800 days and even the Precession of the Equinoxes over 25,800 ± 120 years.

Jupiter is the second largest body in the solar system next to the sun itself. In fact, Jupiter is not far short of being a sun itself and, being the closest giant planet to the Earth, our planet is strongly influenced by Jupiter’s gravity which, unlike the Sun’s continuous pull to maintain Earth’s orbit around it, Jupiter pulls upon the Earth and the Moon on an episodic basis when the Earth is passing between the Sun and Jupiter.

The Trigon Period of Jupiter and Saturn

Being a dark, planetary body, the episodic pull of Jupiter follows a different pattern to each of the inner, terrestrial planets; Mercury, Venus, Earth and Mars, since each has a different orbital period which, combined with Jupiter’s orbit, brings each under Jupiter’s influence or absence. The combined episodic pull of Jupiter and Saturn, is visually seen in their conjuction every 20 years, which occurs just over a third of the Zodiac onwards, thus giving a cosmic significance to the equilateral triangle as a sacred geometry.

Figure 1 The series of Trigon conjunctions of Jupiter and Saturn, as will be the case on 21st December 2020

Only Earth’s large moon stops the axial tilt of the Earth from varying significantly, then causing large changes in climate which would have restricted the development of the relatively stable habitats and biomes we enjoy.

361 days: Jupiter and the Zodiac

The combination of Jupiter’s orbital period (of 4332 days) and Earth’s (of 365.2422 days) generates an interesting set of numerical facts since Jupiter passes through each of the twelve signs of the Zodiac in 361 days. This number is 19 times 19 days so that 12 times 361 days equals 4332 days. But these numbers are a product of the solar year of 365.2422 days, since the day length on Earth is 1 year divided by the 365.2422 days due to its rotation. If the day length were less or more then Jupiter’s complete orbit would still be as long but the numbers from Earth would not.

This is a major aspect of what the megalithic astronomy had to learn, that the relative time lengths of the many cosmic periods, counted in days, could be numerically interrelated when quantified. The situation of the earth orbit and its rotation would present Jupiter as a bright moving star which completed its journey through the stars in 12 times 361 days. Jupiter and the Zodiac of 12 constellations would inevitably become fused as seen in the story of Zeus, the Greek god name for Jupiter whose symbol is the twelve-fold circle. The pre-Classical Greeks were matriarchal, following the lunar month of twelve whole lunar months within the solar year and, the solar year only arose as the patriarchal northern tribes occupied Greece after the Bronze Age collapse. The name Zeus is therefore not matriarchal since the Greeks had no “Z”. Zeus arrived in ancient Greece with the tribes displaced from the North escaping the worsening climate at higher latitudes. And, whilst 12-foldness is associated with the Sun being in one of the 12 zodiacal constellations, Jupiter defines these through passing through each sign (on average) in 361 days.

399 days: Jupiter’s synodic period

Twelve-ness is a massively widespread tradition (see John Michell – Twelve-fold Tribes for instance) and the brightest celestial body next to the Sun is the Moon which expresses twelve whole lunar months a year (plus 7/19 of a lunar month). The common lunar year was therefore twelve months long, taking 354.367 days to complete, this countable between thirteen full moons. It is no accident that the 12-ness of the lunar year is connected with Jupiter’s 12-ness of its 361 day years, since the Jupiter synod has a strong grip on our moon: the synod is 9/8 lunar years long – a musical whole tone. And Saturn also has a similar grip, its synod of 378 days being 16/15 lunar years long.

When the Earth passes by Jupiter, the latter goes retrograde or backwards relative to the stars, meaning it appears to travel east night-by-night, rather than the norm for all planets (and the sun and moon) of slowly travelling west in our skies, as they orbit. During this retrograde period, the planet describes a loop in the sky relative to the stellar background, before returning to where it should be in the stars. Between the loops of Jupiter’s synodic period the 398.88 days could be counted in days. This can only mean that over millennia, the Moon became synchronised by the regular proximity of Jupiter to our moon.

Our months today have divided the solar year into twelve months of 30 or 31 days, to resemble Jupiter’s 12-fold zodiac and 12-month lunar year, the Roman emperors vying to lengthen a month and name it after themselves (examples being October after Octavius, September after Septimius and August after Augustus). And since a zodiacal sign is traversed after 361 days by its definer, it is inevitable that there are not 12 solar years in a Jupiter orbit but just less (11.86 years). However, the fact that 4332 days is not 12 times 365.2422 days accesses, through its deficit, more subtle possibilities hidden in a numerical world of differences.

Differences between periodicities, especially involving the moon that rotates the Earth, define those periods through the fact that they endlessly repeat so that differences accumulate over longer periods and when these differences are divided into the periods, a new set of numbers are generated. One could call orbital systems differential calculators and modern math would describe them as potentially discrete systems, which form due to gravitational recurrence. This idea that the planetary and lunar systems generate numbers is somewhat hidden by our modern description of such systems as subject to gravitational dynamics. The numbers allowed the ancient astronomers to discover a static numerical view of planetary astronomy through counting days. In contrast, modern astronomy calculates the location of celestial bodies from first principles; especially when trying to visit planetary bodies in spacecraft.

pdf: Counting lunar eclipses using the Phaistos Disk

This paper* concerns itself with a unique fired-clay disk, found by Luigi Pernier in 1908 within the Minoan “palace” of Phaistos (aka Faistos), on the Greek island of Crete. Called the Phaistos Disk, its purpose or meaning has been interpreted many times, largely seen as either (a) a double-sided text in the repeated form of a spiral and outer circle written using an unknown pictographic language stamped in the clay or (b) as an astronomical device, record or handy reference. We provide a calendric interpretation based on the simplest lunar calendars known to apply in Minoan times, finding the Disk to be (a) an elegant solution to predicting repeated eclipses within the Saros period and (b) an observation that the Metonic is just one lunar year longer, and true to the context of the Minoan culture of that period.

*First Published on 26 May 2017
web page version

Cretan Calendar Disks

I have interpreted two objects from Phaistos (Faistos), both in the Heraklion Museum. Both would work well as calendar objects.

One would allow the prediction of eclipses:

The other for tracking eclipse seasons using the 16/15 relationship of the synod of Saturn (Chronos) and the Lunar Year:

God of Harmony Osiris in Egyptian Mice Tomb

Recently an “early Ptolomaic” tomb was discovered similar in themes to the famous Egyptian Books of the Dead (Middle Kingdom). Normally written on papyrus, they feature multiple tableau of Osiris judging the dead and other scenes. Osiris is a long lasting and perhaps supreme god whose cult was present throughout 3000 years of Dynastic history. I have previously interpreted his throne through drawings but, in the new tomb, he is painted on the walls at least twice and the design of his throne looks like layers of “eggs”. Below is one of the press pictures taken from the Guardian, and the headline is Mummified mice found in ‘beautiful, colourful’ Egyptian tomb.

Osiris could have been seen as a/the god of Harmony and below I explain why harmony may have been thought technically significant at the dawn of our earliest texts, then found in Sumeria 900 miles to the East. The reason I believe musical ratios were significant at the dawn of history because they had naturally emerged from measuring the lunar and solar year and comparing these with the time between loops of the outer planets Jupiter and Saturn.

Wallis Budge drawing in Osiris Judge of the Dead. We can see the lines but no detail and the bottom right is a vertical root 2 rectangle rather than a near square.
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Gurdjieff’s Diagram of Everything Living

first created: 28 October 2017

Gurdjieff first presented his ideas to groups in pre-revolutionary Russia. Amongst his carefully chosen students it was the habit to reconstruct talks and diagrams as much as possible, an endeavour that gave us a textbook of Gurdjieff’s ideas called In Search of the Miraculous (P.D. Ouspensky, 1950). This early form of the teaching was radically revised and extended by Gurdjieff, now as an author, during the 1920s, producing All and Everything whose part one was Beelzebub’sTales to his Grandson (G.I. Gurdjieff, 1950). Prior to drawing this diagram just after February 1917, Gurdjieff had been presenting ideas about transformation of energies, human and cosmic, using the musical theory surrounding the octave of eight notes. The Diagram of Everything Living was “still another system of classification… in an altogether different ratio of octaves… [that] leads us beyond the limits of what we call ‘living beings’ both higher [and lower] than living beings. It deals not with individuals but with classes in a very wide sense.”


Figure 1 The Diagram of Everything Living
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