Category: Planetary Harmony

Celestial time periods forming musical intervals

The Geocentric Planetary Matrix

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.

The Heraion of Samos, late 8th century BC. [figure 5.9 of Sacred Geometry: Language of the Angels.]

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).

Figure 1 Matrix Diagram of Jupiter and the Moon. figure 9.5 of Matrix of Creation, p117.

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.

Figure 2 My near discovery of Quetzalcoatl, in fig. 8.1 of Matrix of Creation

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
Figure 3 The two harmonic serpents of “Heaven” and “Earth”

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.

Figure 4 The Geocentric Model by 1660

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.

Wikipedia: “Geocentric model”

The Richard Syrett Interviews on Sacred Geometry: Language of the Angels

I recently recorded a podcast with Richard Syrett and will be talking with him again today (January 2nd) on Coast to Coast, starting 10pm Pacific time. In the UK, this is tomorrow (Sunday the 3rd) at 6am GMT. Both these interviews are in response to my new book Sacred Geometry: Language of the Angels, which goes on release Monday 4th of January 2021.

Ways of Purchasing: This large-format book, richly illustrated in color throughout, can be seen in the sidebar (on mobiles, below the tag cloud) or visit Inner Traditions.

from Book 5: Harmonic Origins of the World

Intelligent Star Systems

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

Astronomy 3: Understanding Time Cycles

above: a 21-petal object in the Heraklion Museum which could represent the 21 seven-day weeks in the 399 days of the Jupiter synod. [2004, Richard Heath]

One of the unfortunate aspects of adopting the number 360 for calibrating the Ecliptic in degrees is that the megalithic counted time in days and instead saw the ecliptic as divided by the 365¼ days. In transferring to the number 360, with all of its easy factors, 8 x 9 x 5, moderns cannot exploit a key advantage of 365¼ days.

If the lunar orbit takes 27.32166 days then each day the moon moves by 1/27.32166 of the ecliptic every day. For this reason, after 27.32166 days the orbit completes because the Moon’s “year” then equals one as the angular motion has been 27.32166/ 27.32166 = 1.

The same is true of the lunar nodes, which retrograde to the east along the ecliptic in 18.618 years. For this reason one can say, the lunar nodes move by 1/18.618 DAYS (in angle) every day and to travel one DAY in angle, the nodes take 18.618 DAYS per day (needing the new term “node day” equal the 18.618 days.*** A solar year takes 19.618 node days (since 365¼ equals 18.618 x 19.618) and an eclipse year takes 18.618 x 18.618 – 346.62 days

*** These are average figures since the moon comes under variable gravitational influences that are episodic.

A general rule emerges in which the larger, whole cycles, lead to reciprocals which can be numerically characterized by knowing the number of the days in the larger period.

For instance, Jupiter has a synodic excess over the solar year of 398.88 days and this means its angular motion is 1/ 398.88 DAYS per day while Saturn’s synod is 378.09 days and its angular motion is 1/ 378.09 DAYS per day. These synods are, by definition, differential to the Sun at 1/ 365.2422 DAYS per day.

Without seeing astronomy as calibrated to day and year cycles, one is robbed of much chance to appreciate the megalithic view of time and the time-factored buildings that came to be built in pursuit of quite advanced knowledge.

Looking from the relatively large cycles to the extremely small, daily angular changes of celestial bodies seen from Earth, reveals a further obscuration created, in this case, by the heliocentric view of the solar system, rather than the geocentric view which is obviously founded on days and years seen from the surface of the planet.

The largest cycle the megalithic could see using their techniques, reverses the direction from large-to-small to small-to-large since the precessional cycle (of the equinoctal nodes of the earth’s obliquity) is around 25,800 ± 100 years long. A star or constellation on the ecliptic appears to move east, like the lunar nodes, and using the angular measure of DAYS, it is possible to estimate that the equinoctal points move by a single DAY, in a given epoch, something like 71 years. The precessional cycle is therefore 71 years multiplied by the 365.2422 DAYS of the whole ecliptic.

The most important benefit of using DAY angles is that knowledge of a few celestial periods opens up a realm in which different scales of time can be derived from first principles. And added to that, the celestial periods appear related to one another so that so-called sacred numbers emerge such as the seven day week which divides into both the Saturn synod (54 weeks), Jupiter synod (57 weeks), the 364 day saturnian year (52 weeks) and others.

To understand the full scope of megalithic astronomy requires a geocentric calibration of the ecliptic as having 365¼ angular DAYS.

Geometry 6: the Geometrical AMY

By 2016 it was already obvious that the lunar month (in days) and the PMY, AMY and yard (in inches) had peculiar relationships involving the ratio 32/29, shown above. This can now be explained as a manifestation of day-inch counting and the unusual numerical properties of the solar and lunar year, when seen using day-inch counting.

It is hard to imagine that the English foot arose from any other process than day-inch counting; to resolve the excess of the solar year over the lunar year, in three years – the near-anniversary of sun and moon. This created the Proto Megalithic Yard (PMY) of 32.625 day-inches as the difference.

Figure 1 The three solar year count’s geometrical demonstration of the excess in length of 3 solar years over 3 lunar years as the 32.625 day-inch PMY.

A strange property of N:N+1 right triangles can then transform this PMY into the English foot, when counting over a single lunar and solar year using the PMY to count months.

The metrological explanation

If one divides the three-year excess (here, the PMY) into the base then N, the normalized base of the N:N+1 triangle. In the case of the sun and moon, N is very nearly 32.625, so that the lunar to solar years are closely in the ratio 32.625:33.625. Because of this, if one counts 

  • months instead of days,
  • using the three-year excess (i.e. the PMY) to stand for the lunar month,
  • over a single year,

the excess becomes, quite unexpectedly, the reciprocal of the PMY;

One has effectively normalized the solar year as 12.368 PMYs long. This single year difference, of 0.368 lunar months cancels with the PMY; the 0.36827 lunar months becoming 12.0147 inches. Were the true Astronomical Megalithic Yard (AMY of 32.585 inches) used, instead of the PMY, the foot of 12 inches would result. Indeed, this is the AMYs definition, as being the N (normalizing value) of 32.585 inches long, unique to the sun-moon cycle. The AMY only becomes clear, in feet, after completion of 19 solar years. This Metonic anniversary of sun and moon over 235 lunar months, is exactly 7 lunar months larger than 19 lunar years (228 months).

But this is all seen using the arithmetical methods of ancient metrology, which did not exist in the megalithic circa 4000BC. Our numeracy can divide the 1063.1 day-inches by 32.625 day-inches, to reveal the AMY as 32.585 inches long, but the megalithic could not. Any attempt to resolve the AMY in the megalithic, using a day-inch technology***, without arithmetical processes, could not resolve the AMY over 3 years as it is a mere 40 thousandths of an inch smaller than the PMY. So arithmetic provides us with an explanation, but prevents us from explaining how the megalithic came to have a value for the AMY; only visible over long itineraries requiring awkward processes to divide using factorization. However, by exploiting the coincidences of number built in to the lunar and solar years, geometry could oblige. 

***One can safely assume the early megalithic resolved
eighths or tenths of an inch when counting day-inches.

The geometrical explanation

In proposing the AMY was properly quantified, in the similarly early megalithic cultures of Carnac in France and the Preselis in Wales, one must turn to a geometrical method

  1. One clue is that the yard of 3 feet (36 inches) is exactly 32/29ths of the PMY. This shows itself in the fact that 32 PMYs equal 29 yards.
  2. Another clue is that the lunar month had been quantified (at Le Manio) by finding 32 months equalled 945 day-inches. By inference, the lunar month is therefore 945 day-inches divided by 32 or 945/32 (29.53125) day-inches – very close to our present knowledge of 29.53059 days.

From point 1, one can geometrically express any length that is 32 relative to another of 29, using the right triangle (29,32). And from point 2, since the 945 day period is 32 lunar months, as a length it will be in the ratio 29 to 32 to a length 32 PMYs long, the triangle’s hypotenuse.

Point 1 also means that 32 PMY (of 32.625 inches) will equal 1044 inches, which must also be 29 x 36 inches, and 29 yards hence handily divides the 32 side of the {29 32} right triangle into 29 portions equal to a yard on that side. One can then “mirror the right triangle about its 29-side so as to be able to draw 29 parallel lines between the two, mirrored, 32-sides, as shown in figure 1. The 945 day-inch 29-side which already equals 32 lunar months (in day-inches), now has 29 megalithic yards in that length, which are then an AMY of 945/29 day-inches!

Figure The 29:32 relationship of the PMY to the yard as 32 PMY = 29 yards whilst 32 lunar months (945 days) is 29 AMY.

Comparing the two AMYs and their necessary origins

Using a modern calculator, 945 divided by the PMY actually gives 28.9655 PMY and not 29, so that 945 inches requires a unit slightly smaller than the PMY and 945/29 gives the result as 32.586 inches, which length one could call the geometrical AMY. This AMY is 30625/30624 of the AMY in ancient metrology which is arrived at as 2.7 feet times 176/175 equal to 32.585142857 inches. By implication therefore, the ancient AMY is the root Drusian step whose formula is 19.008/7 feet whilst the first AMY was resolved by the megalithic to be 945/29 inches.

This geometrical AMY (gAMY?) obviously hailed from the world of day-inch counting, which preceded the ancient arithmetical metrology which was based upon fractions of the English foot. The gAMY is 32/29 of the lunar month of 29.53125 (945/32) day-inches, since 945/32 inches × 32/29 is 945/29 inches.

Using ancient metrology to interpret the earliest megalithic monuments may be questionable in the absence of a highly civilised source which had, in an even greater antiquity, provided it; from an “Atlantis”. In contrast, the monumental record of the megalithic suggests that geometrical methods were in active development and involved less sophisticated metrology, on a step-by-step basis.  From this arose the English foot which, being twelve times larger than the inch, could provide the more versatile metrology of fractional feet, to provide a pre-arithmetical mechanism, to solve numerical problems through geometrical re-scaling. This foot based, fractional metrology then developed into the ancient metrology of Neal and Michell, which itself survived to become our historical metrology [Petrie and Berriman].

The two types of AMY, geometrical and the metrological, though not identical are practically indistinguishable; the AMY being just over one thousandths of an inch larger. The geometrical AMY (945/29 inches) is shown, by figure 2, to be geometrically resolvable, and so must have preceded the metrological AMY, itself only 40 thousandths of an inch less than the PMY.

The two AMYs, effectively identical, reveal a developmental history starting with day-inch counting, and division of 945 inches by 29 was made easy by exploiting the alternative factorisation of 32 PMV as 36 × 29 yards using geometry. The AMY of ancient metrology was the necessary rationalization of 945/29 inches into the foot- based system.

Bibliography for Ancient Metrology

  1. Berriman, A. E. Historical Metrology. London: J. M. Dent and Sons, 1953.
  2. Heath, Robin, and John Michell. Lost Science of Measuring the Earth: Discovering the Sacred Geometry of the Ancients. Kempton, Ill.: Adventures Unlimited Press, 2006. Reprint edition of The Measure of Albion.
  3. Heath, Richard. Sacred Geometry: Language of the Angels. Vermont: Inner Traditions 2022.
  4. Michell, John. Ancient Metrology. Bristol, England: Pentacle Press, 1981.
  5. Neal, John. All Done with Mirrors. London: Secret Academy, 2000.
  6. —-. Ancient Metrology. Vol. 1, A Numerical Code—Metrological Continuity in Neolithic, Bronze, and Iron Age Europe. Glastonbury, England: Squeeze, 2016 – read 1.6 Pi and the World.
  7. —-. Ancient Metrology. Vol. 2, The Geographic Correlation—Arabian, Egyptian, and Chinese Metrology. Glastonbury, England: Squeeze, 2017.
  8. —-. Ancient Metrology, Vol. 3, The Worldwide Diffusion – Ancient Egyptian, and American Metrology.  The Squeeze Press: 2024.
  9. Petri, W. M. Flinders. Inductive Metrology. 1877. Reprint, Cambridge: Cambridge University Press, 2013.

pdf: Synchronicity of Day and Year with the Lunar Orbit

This document was prepared by Richard Heath as a letter for Nature magazine and submitted on 14th April 1994 but remained unpublished. For readers of the Matrix of Creation (2nd ed, Inner Traditions Press, 2004) it marks the discovery of a unit of time proposed and named the Chronon, as being 1/10000th of the Moon’s orbit and also the difference between the sidereal and tropical day of the Earth. The paper also documents a discovery made, with Robin Heath, later to be documented in his books: that one can divide up the solar year by its excess over the eclipse year to reveal an 18.618:19.618 ratio between these years, and many other interesting numerical facts not mentioned in this place. The puzzle here is a connection between the rotation of the Earth, the solar year and the precession of the Moon’s orbit which (a) may be explainable by science (b) appears to have puzzled Megalithic astronomers and (c) should puzzle us today.