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 I originally made the pdf below for my friend Anthony Blake, part of our attempt to study the origin of creativity within the existing world.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
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.
“We have long known, thanks to Ernest McClain, that the ancients were obsessed with harmonic numbers and that the Bible encodes these from beginning to end. Now new evidence appears, as these numbers correlate with the planetary periods, and their discovery is pushed far back into the prehistoric era. Richard Heath’s work, based not on speculation but on objective data, challenges all accepted notions of cultural evolution and religious origins.”
–JOSCELYN GODWIN, author of Harmonies of Heaven and Earth and Atlantis and the Cycles of Time
As modern humans first walked the Earth roughly 70,000 years ago, the moon’s orbit came into harmonic resonance with the outer planets of Jupiter, Saturn, and Uranus. The common denominators underlying these harmonic relationships are the earliest prime numbers of the Fibonacci series–two, three, and five–the same numbers that interact to give us the harmonic relationships of music.
Exploring the simple mathematical relationships that underlie the cycles of the solar system and the music of Earth, Richard Heath reveals how Neolithic astronomers discovered these ratios using megalithic monuments like Stonehenge and the Carnac stones, discoveries that informed later myths and stories, including the Epic of Gilgamesh, the Resurrection of Osiris, the Rg Veda, the Hebrew Bible, Homer’s epic tales, and the Return of Quetzalcoatl. He explains how this harmonic planetary knowledge formed the basis of the earliest religious systems, in which planets were seen as gods, and shows how they spread through Sumer, Egypt, and India into Babylon, Judea, Mexico, and archaic Greece. He exposes how the secret knowledge encoded within the Bible’s god YHWH was lost as Greek logic and reason steadily weakened mythological beliefs.
Revealing the mysteries of the octave and of our musical scales, Heath shows how the orbits of the outer and inner planets gave a structure to time, which our moon’s orbit could then turn into a harmonic matrix. He explains how planetary time came to function as a finely tuned musical instrument, leading to the rise of intelligent life on our planet. He demonstrates how this harmonic science of numbers can be read in the secret symbolism and sacred geometry of ancient cities such as Teotihuacan and in temples such as the Parthenon, connecting the higher worlds of planetary time and harmonics with the spiritual and physical life on Earth.
Recasting our understanding of the solar system, Heath seeks to reawaken humanity’s understanding of how sacred numbers structure reality, offering an opportunity to recover this lost harmonic doctrine and reclaim our intended role in the outer life of our planet.
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
RICHARD HEATH is a development engineer with degrees in systems science and computer-aided design. His interest in megalithic astronomy and ancient metrology has resulted in 6 books, including, in January 2021, Sacred Geometry: Language of the Angels. He lives in the Preseli hills of West Wales.
The work of the late Ernest McClain [1918-2014] was based upon a technique in which ever higher numbers appear to have been studied in antiquity as to the harmonic field of intervals possible within that integer limit. Such a single number reference can be mentioned en passant within texts like The Bible, Homer’s Illiad or the Sumerian story of Gilgamesh and be ignored today as a frivolous use of large numbers, such as great ages of the gods, the number of ships, or tithe goods and so on, when in fact the numbers were referring to a musicological field relevant to the narrative and its elements.
McClain’s work was very briefly introduced in Precessional Time and the Evolution of Consciousness(2011) in its Chapter 3 on the Age of Aries, when such calculational musicology/theology seem to have replaced the megalithic activities in Age of Taurus. After then collaborating with Ernest for a few years, after his death I attempted to make an accessible book on Ernest’ work in my 2018 book Harmonic Origins of the World.
Ernest had a fine sensibility for the Ancient Near East (or A.N.E.), its number science and symbolisms. Through many email exchanges I wanted to be able to generate his tonal diagrams for myself; to both learn more and answer specific questions. I was able to make a web page so that people like myself could more easily enter his world of tonal yantras (that look like mountains) and their corresponding tonal mandalas (the octave circle); without having to learn the method of “limiting the products of powers of three and five and then doubling all numbers to the limiting number”. This Harmonic Explorer app enables ridiculous freedom over the previously required manual calculations, including walking through limiting number space with prime factor buttons, multiplying/dividing by 2, 3, 5, 10 or 12. It can also be very useful for screen grabbing when discussing a given tuning system as in:
This paper attempts to interpret the first two books of the Bible, according to Ernest McClain’s methods. It is contended that the compositions of ancient texts, as Plato insinuated, were both inspired and used for the science of numerical harmonics.
The invariant properties of harmonic numbers, and their evolution through limiting whole numbers, offer a large variety of distinctive scenarios which can be set into compatible narrative forms such as the Seven Days of Creation, the Garden of Eden, the Flood, the Patriarchal development of the Twelve Tribes and Moses meeting with YHWH.