Plato proposed a World Soul that took the form of a musical octave—having been given that form by the Demiurge, a creator god—bringing harmony to the earth’s surroundings. The octave is so named because in modal music there are only eight tones, and the beginning and ending tones differ in frequency by a factor of exactly 2. In the act of creation there were two further tones within the octave—mirror images of each other. This mirroring, called symmetry, is crucial within all created octaves as tones arise that are reciprocal to each other and to both ends of the octave, like twins. To see the octave’s true form, one must visually mimic the ear’s ability to see all identical intervals as equal, and to use the eye to see all octaves as circles going clockwise from top (= 1) until the top is reached again. At the bottom of the circle lies a possible tone that is equidistant from the top, traveling either clockwise or counterclockwise. Since each path is equal, the value of this tone must be the square root of 2, whose square would then be the multiplication by 2 involved in doubling. The Demiurge must decide on what is going to be doubled in size to form the octave, in the context of what is going to populate this tone circle.
Plato’s World Soul coalesced into this harmonic pattern about 200,000 years ago, a time frame parallel to the evolution of modern man. It therefore appears Plato’s Demiurge referenced a lost body of knowledge that understood that the major planets were in harmonic relationship to our moon.
Humans of the Neolithic period built a large number of megalithic monuments. A representative number of these have survived the eroding effects of natural and human forces, which has allowed the design of these megalithic monuments to be assessed by some, including myself, as demonstrating a very sophisticated and advanced understanding of astronomical time periods. But such interpretations are effectively ignored by academic archaeology since they imply the existence of exact sciences and numeracy in the Neolithic, which is only thought of as innovating agrarian lifestyles; while there is some consensus that monuments had some astronomical uses: for example, tracking the seasonal motion of the sunrise (or sunset) to form a solar calendar, or tracking lunar phases using daily horizon events. But evidence supporting an exact and unique form of megalithic astronomy is resisted because counting time periods and constructing numerate monuments requires some form of mathematics.
The natural unit of time on Earth is the day, and the counting of days would lead one to see that there are 59 days between three full moons. But this generates a problem when we ask whether the number 59 could have had any meaning in a pre-arithmetic society, which the Neolithic appears to have been. Marks on bones from the Stone Age suggest that counting occurred but without thought for number as an abstract or an externalized entity. Instead, the number of day marks probably led to the notion of numbers as equal to a length containing “that many,” as a number.
The sun offers a more direct form of calendar than the moon, corresponding to the new needs of seasonal farmers in the Neolithic and hence the agricultural context within which megalithic monuments were being built, in some regions. The sun appears to move north (in the Northern Hemisphere) toward summer and south toward winter. Looking south, the noonday sun gets higher in the summer and lower in the winter and, as a rule of thumb, this is what makes summer hotter than winter. Summer moves the location of sunrise and sunset toward the northeast and northwest, respectively, and by the same amount per day. At the spring and autumn equinox, sunrise and sunset are exactly due east and west in most latitudes, and in winter they move south so as to be (equally) southeast and southwest. Their furthest positions are the solstices of summer and winter, after which they head back to their equinoctial locations, east and west.
This movement of the sun to north and south therefore causes sunrises and sunsets from the center of any megalithic site to move along the horizon between two extreme positions during the year—the summer and winter solstice—and thus, the horizon to east or west of a megalithic site formed a natural solar calendar. At megalithic sites one often finds that some key points on the horizon coincide with sunrise or sunset for a solstice or the equinox, which means that the site was likely selected to have that characteristic—namely, that the view from a fixed observation point at the site naturally aligned to the sun on the horizon at a moment significant to a megalithic solar calendar. This alignment to the natural landscape could then be extended by providing man-made features, typically standing stones, which could then be viewed from the megalithic site’s observation point to indicate where the sun would stand at another point of the solar year. Between the solstice “extremes,” each such marker to the horizon in fact marks two days in the year, since the sun travels both north and south during the year and will stand above that marker twice in the year, during the waxing and waning of the sun’s influence.
The moon’s behavior on the horizon is a more complex phenomenon, so it is easier to track over a smaller time frame using its waxing and waning phases, these defining the synodic lunar month and the moon’s changing illumination by the sun. The full moon and the different moon halves are particularly distinct phases, the growing half waxing and the diminishing half waning.
Thus, the fundamental observing framework for the sun was the horizon, while for the moon, the phases of the lunar month were easier to observe. Such observations provide no real explanation for the building of complex megalithic monuments. If only such basic observational astronomy was involved, what drove the complex design of monuments? Two types of explanations arose in the twentieth century, once the sites started to be accurately surveyed and dated.
The first type of explanation suggests that an already existing cultural framework that some would call religious, or at least involving death and the dead drove the building of monuments. It gave significance to dates within the solar year, or parts of the lunar month, within which commemorative rites were practiced or celebrated at the monuments. Such proposed explanations therefore saw megalithic monuments as symptomatic of preexisting religious frameworks tied to celestial events.
The second type of explanation was that the monument builders were an intellectual elite of their day who achieved significant feats of astronomical understanding, self-evident in the forms that the monuments took. Prominent was a proposed explanation, based upon factual evidence, that the monuments embodied a metrological and geometric competence enabling a pre-arithmetic Neolithic Age to solve arithmetical problems and resolve astronomical facts not thought knowable to Stone Age people but easily graspable using our own scientific methods.
The first explanation, that monuments were venues involving proto-religious calendric events, surprisingly accepted by today’s specialists, lacks concrete evidence that would prove such a usage as having been primary for megalithic monuments. In other words: to accept time-factored ritual as the raison d’être for megalith-ism in general is a leap of faith that can neither be proven nor refuted. This interpretation therefore forms a cul-de-sac for rational thought and prevents the search for why complex megalithic monuments were built.
Contrast that with the second explanation that the monuments involved a sophisticated combination of astronomy, geometry, and metrology, which has been criticized as being far too precise and the result of overenthusiasm by individuals predisposed to find their own meanings in these monuments, meanings they are therefore “selecting for” and thus rendering them not objective. However, unlike the ritual explanations for which there is no concrete evidence, the metrological explanation can be tested through measuring the sites and so may be refuted, in the Popperian sense, as to its validity. The problem lies in cultural resistance to revising the standard model of history. Those proposing a ritual explanation are deselecting explanations that the megalithic was an advanced and highly numerate culture because modern numeracy first developed in the ancient Near East, before the development of our geometrical methods for solving astronomical problems.
This unfortunate rejection is fortunately irrelevant to our concerns here. What follows is an abbreviated account of how the megalithic builders, having conquered the challenge of gaining accurate knowledge of celestial time periods, were thus led to the discovery of musical harmony between planetary periods. Musical harmony is based on the three earliest prime numbers: 2, 3, and 5. The discovery of celestial harmonies may have ended the megalithic project and initiated the new religious, literate, and mathematical civilizations in the Near and Far East that, through their written and other records, gave us our earliest histories.
The geometrical comparison of lengths of time can only have arisen through the adoption of a standard length for counting, where one day was counted a standard unit of length such as, for example, the inch. Robin Heath and I found, within Carnac’s Le Manio quadrilateral, a monument in which a special trigonometric triangle had been defined. Its base is four units and its shortest side one unit: that is, it is a triangle based upon a four-by-one rectangle, where the triangle’s longest side is the rectangle’s diagonal. The two longer sides of this triangle were “day-inch” counts for three lunar years (the base) and for three solar years (the hypotenuse), so that the unit sides of the squares in the foursquare rectangle (and the short side of the triangle) were nine lunar months long, in day-inches. If instead one built a four-square rectangle with a unit side one rather than three lunar months long, the base and diagonal would be the day-inch counts for a single lunar and a single solar year. Once this geometry had been found, it could be reproduced like a calendar.
In modern times this triangle, base 12 lunar months (the lunar year) and short side 3 lunar months, was first established as having been a useful geometry by my brother around 1990. By noting that the Station Stone rectangle at Stonehenge was 12 units by 5 units, a division of the 5 units into 3 units and 2 units allowed an intermediate hypotenuse to be formed that, compared to the base of 12 units, would then be 12.368 units long. This hypotenuse generated the number of lunar months within a solar year (12.368 months), so the triangle geometrically represents the relationship between the lunar year and solar year, in lunar months. This triangle was therefore called the lunation triangle, since its formation appears to represent how the megalithic astronomers had resolved the great challenge of forming a simple sun-moon calendar, successfully integrating lunar months within the solar year as a quantifiable though endlessly slipping ratio, as one might find between two gears of a car.
At Stonehenge the lunation geometry can only be inferred as a potential meaning for the rectangular dimensions 12 by 5. The metrology of the Station Stone rectangle’s longest side is 8 × 12 megalithic yards, numerically correct for the 12 side of the lunation triangle. If used as a calendar (where one “counts” outside of the present moment) the monument could (a) be counting in months rather than days over (b) the eight-year periodicity for a first good solar return on the horizon (where the sun rises in exactly the same place on the horizon, on the same day of the year it had in a previous year), and its units are 8 megalithic yards.
Le Manio preceded the Station Stone rectangle by at least five hundred years, so its quadrilateral could be closer to the moment at which astronomers discovered the foursquare geometry of the sun and moon (this construction being the best and easiest way to reproduce the lunation triangle). Another key discovery at Le Manio appeared as the difference in counted length between the solar and lunar years, over three years; in day-inches it is the megalithic yard of 32.625 inches, a result that probably reveals the origin of the megalithic yard as a measure then used throughout the megalithic period to count lengths, within monuments such as the Station Stone rectangle, in months. It is also true that, by using a slightly smaller megalithic yard of 19/7 feet to count lunar months, the fractional part of the lunation triangle’s hypotenuse (the lunar months in a solar year) of 12.368 megalithic yards could be made a rational fraction since 0.368 = 7/19 (lunar month). Further details about the Manio quadrilateral and the lunation triangle can be found in Richard and Robin Heath’s, The Origins of Megalithic Astronomy as Found at Le Manio.
A key feature of the lunation triangle calibrated in megalithic yards is that, over a single year, another key unit of length emerges: the English foot of twelve inches, as the difference between the solar and lunar years. It also generates the royal cubit, of 12/7 feet, as the difference between the lunar and eclipse years, which added to one foot equals 19/7, the astronomical megalithic yard. It appears that, in the move to counting lunar months in megalithic yards rather than day-inches, the metrology of the late megalithic and of later ancient buildings became founded upon the English foot and fractional variations of it, such as 12/7 feet; 3 that is, all ancient measures are related to the foot through one or more rational fractional conversions. If the megalithic yard was the measure first derived from the difference between the solar and lunar years, then it follows that only the megalithic astronomers could have given birth to such a science of measure and geometry that reduced the complexities of horizon astronomy to the kind of predictive certainty seen in the Antikythera mechanism (using gears by the time of classical Greece) or the Mayan calendar (using a long count by the time of the Olmec in Mesoamerica). Such anachronisms should be pondered further as being due to megalithic science.
CAPTIONS: Le Manio Quadrilateral
Diagram from The Harmonic Origins of the World by Richard Heath (Inner Traditions, 2017)
The above is an edited excerpt from the book Harmonic Origins of the World, by Richard Heath, which explores the author’s insights into the simple numerical ratios underlying the solar system, its musical harmony, and the earliest religious beliefs (Inner Traditions, 2017). This excerpt is reprinted by permission from the publisher. The book is available for purchase from the Atlantis Rising store: shop.atlantisrising.com.