The study of ancient monuments from the megalithic world and the pyramids, reveals a profound connection between time, space, and the cosmos, that stretches across millennia. Perhaps these ancient designs encoded a vast body of knowledge, about the the earth and the motions of the heavenly bodies, about geometry, and more besides. Whether in the megalithic sites of Europe or the pyramids of Egypt, these measures offer us insights into how ancient civilisations understood and mapped time through the stars, the solar year, and lunar cycles. The proportions of structures like Stonehenge and the Great Pyramid are not arbitrary. They reflect an understanding of the perceived cosmic order.
Though they are not contemporary with the building of many of the megalithic monuments and pyramids, texts from ancient Greece, such as Plato’s, and ancient India, such as the Vedas, present a focus on harmony, proportion, number, cycles and astronomy. This approach to an understanding of the world can help to make sense of the dimensions and proportions of certain ancient monuments, and through a reading of these dimensions and proportions, we might be able to guess, tentatively, at the manner in which geometry and number were seen to illustrate, or even perhaps explain, the workings of the cosmos.
In particular here, we will look at a particular ratio that becomes apparent when the cycles of the sidereal year, sidereal month, the traditional "planets", axial precession, the Metonic cycle, and the geometry of the circle (pi) are combined.
The sidereal year, sidereal month, the traditional "planets", axial precession, the Metonic cycle, and pi
The values of these cycles are:
Metonic cycle: 19 years
Axial precession: 25 920 years (traditional value)
Mercury 0.24 years
Venus 0.615 years
Mars 1.88 years
Jupiter 11.86 years
Saturn 29.46 years
Of the seven traditional 'planets', the sun's apparent cycle as seen from earth, and the moon's cycle, are included in the Metonic cycle. This important cycle is a period of almost exactly 19 years after which the lunar phases recur at the same time of the year.
2π / 3 x 19 x 25 920 x 29.46 x 11.86 x 1.88 x 0.615 x 0.24 / 10⁸ = 1.00002038
Or 19 x 25 920 x 29.46 x 11.86 x 1.88 x 0.615 x 0.24 / 10⁸ x π = 3 / 2
Which is equivalent to:
Metonic x precession x Saturn x Jupiter x Mars x Venus x Mercury / 10⁸ x π = 3 / 2
This could be understood as the diameter of a circle equal to all these cycles multiplied (Metonic cycle, axial precession and six of the seven ‘planets’), producing a circumference equal to 100 000 000 x 3 / 2.
This is, incredibly, almost exact, using the value for pi given by the calculator and the values for the cycles given by Wikipedia, except for the cycle of precession, for which the traditional value was used.
In music, the 3/2 ratio is called a perfect fifth. The ratio 3 / 2 is a perfect fifth, the musical interval between the first to the last of the first five consecutive notes, in diatonic scale. Is this heavenly body equation part of the idea of the music of the spheres?
It is plausible to conclude that ancient astronomers regarded certain rations such as 3/2 as highly important, not because they were purely symbolic, but because they actually described aspects of the world. In this case, 3/2 describes the combined motions of various key cycles of time: the Metonic cycle, which brings together the cycles of the earth, sun and moon, and precession, which is the apparent motion of the stars over a 25 920 year period, and the planets, Mercury, Venus, Mars, Jupiter and Saturn.
A 3 / 2 connection to Robin Heath's Lunation Triangle
This equation is already a very impressive natural coincidence, but if we remember that the 2 / 3 ratio is present in the Robin Heath Lunation triangle, it is even more so. Did the architects of the time then also encode their knowledge of geometry and time in physical structures?
This Pythagorean 5:12:13 triangle representing the number of lunations per year, a line drawn from the tip of the triangle linking the ‘12’ and ‘13’ sides to the 3:2 point of ‘5’ side is 12.369 units long.
Robin Heath discovered a remarkable geometrical feature at Stonehenge: the 5:12:13 Pythagorean triangle, which made up half of the Station Stone Rectangle, could be interpreted as reflecting the relationship between the solar year and the lunar cycle (2). The synodic lunar month (lunation) averages 12.368266 per year, making 12 and 13 key numbers in the solar-lunar relationship. Interestingly, a rectangle with sides of 12 and 3 has a diagonal approximating this value. The diagonal (12.3693168) is also the square root of 153, a number rich with symbolic meaning. The number 153 is significant in biblical texts, as in John 21:11, where Simon Peter catches 153 fish. As John Michell observed, 153 is closely related to 17 (as the sum of integers from 1 to 17) and 1224 (8 x 153), a number representing both "the net" (το διχτυον) and "fishes" (ιχθυες) in Greek gematria. Such numerical connections suggest a symbolic link between geometry and cultural mythologies, which may have inspired the use of these proportions in ancient monument design. The square root of 153 can be rounded to 12.369, and 369 is a number associated with the moon, in the lunar magic square, in which all rows, columns and diagonals have a sum of 369, and is composed of 9 smaller magic squares which also reference 369.
The line which represents the average number of lunations per year so precisely bissects the '5' side of the Pythagorean 5:12:13 triangle at the 3:2 point. This creates a new geometric figure, with its own importance and associations: the quadruple square. Four squares side to side are part of the astronomical geometry at Le Manio, as discovered by Robin Heath and Richard Heath (3). The triangle found at Le Manio, in France, having proportions of 1:4:√17, can be found at Stonehenge also. The lower half of the Pythagorean 5:12:13 triangle, created by removing the 3:12:12.3693169 triangle, is precisely the Le Manio triangle, though on a different scale
At Stonehenge, the 5:12:13 Pythagorean triangle is half of the rectangle made up by the Station Stones, which are numbered 91, 92, 93 and 94. It is well known that at Stonehenge the midsummer sunrise can be seen to appear just over the Heel Stone for a person standing in the centre of the Sarsen circle. The Station Stone Rectangle is another important part of the astronomical geometry at Stonehenge. The diagonal (stones 93 to 91) “indicates sunrise on two of the Quarter Days of the prehistoric solar calendar at the beginning of February and the beginning of November, respectively. The opposite direction marks sunset on the other two Quarter Days, at the beginning of May and of August. At the latitude of Stonehenge, a natural coincidence means that the rising and setting sun can be seen on the horizon at key times of the year in such a way as to form a rectangle." (4)
The 3/2 ratio is an important aspect of this astronomical geometry.
Plato
In Timaeus (35b-36d), Plato recounts the creation of the cosmos by the Demiurge.
[35b] And when with the aid of Being He had mixed them, and had made of them one out of three, straightway He began to distribute the whole thereof into so many portions as was meet; and each portion was a mixture of the Same, of the Other, and of Being. And He began making the division thus: First He took one portion from the whole; then He took a portion double of this; then a third portion, half as much again as the second portion, that is, three times as much as the first; he fourth portion He took was twice as much as the second; the fifth three times as much as the third; [35c] the sixth eight times as much as the first; and the seventh twenty-seven times as much as the first. [36a] After that He went on to fill up the intervals in the series of the powers of 2 and the intervals in the series of powers of 3 in the following manner: He cut off yet further portions from the original mixture, and set them in between the portions above rehearsed, so as to place two Means in each interval, —one a Mean which exceeded its Extremes and was by them exceeded by the same proportional part or fraction of each of the Extremes respectively; the other a Mean which exceeded one Extreme by the same number or integer as it was exceeded by its other Extreme. And whereas the insertion of these links formed fresh intervals in the former intervals, that is to say, intervals of 3:2 and 4:3 and 9:8, He went on to fill up the 4:3 intervals with 9:8 intervals. (1) [italics added]
Here, the 3:2 ratio (the perfect fifth) appears as one of the primary divisions used to construct the intervals within the World Soul. These intervals are the foundation for the harmonic structure of the universe. The ratios Plato mentions are: 1:2 (octave), 3:2 (perfect fifth), and 4:3 (perfect fourth), and these are fundamental in Pythagorean harmonic theory and are seen as organising both music and celestial movements.
Plato explains how the heavens are divided into intervals that correspond to musical harmonies. The planetary orbits and motions are not arbitrary but reflect proportional relationships that are harmonious:
The movements of these circles of the heavens follow the proportions of the harmonious intervals: the fastest to the slowest move in the ratio of 2:1, 3:2, or 4:3, creating a symphony in their revolutions.
The 3:2 ratio is directly tied to the musical structure of the cosmos. While Plato doesn’t elaborate further here, this reflects the Pythagorean idea that celestial bodies create a "music of the spheres" based on harmonic intervals. The idea is developed also in the Myth of Er (Republic 616b-617d), in which Plato describes the turning of the cosmos on the spindle of Necessity, accompanied by the harmonious sounds of the spheres:
The whorl spins with a single note, harmonious with the intervals of the heavens. Each orbit is a proportion of the others, echoing the harmony of the universe. (5)
Though 3:2 is not explicitly stated, the concept of harmonic intervals influencing celestial motion is consistent with the Timaeus. In the Republic, Plato emphasises the importance of musical training in the education of the guardians.
Conclusion
The interplay between ancient metrology, geometry, music and cosmology reveals a profound unity in the way early civilisations understood the universe. Whether encoded in the proportions of Stonehenge or the Great Pyramid, these measurements reflect a sophisticated grasp of celestial cycles and mathematical principles. The 3/2 ratio, a cornerstone of musical harmony, appears across these systems, echoing the ancient belief in a "music of the spheres" where planetary motions resonate with cosmic order.
Plato’s writings, particularly in the Timaeus, provide a philosophical lens through which we can interpret these ideas. His descriptions of harmonic intervals as the structure of the World Soul align with the recurring appearance of ratios like 3:2 in metrological and astronomical contexts. Similarly, the Pythagorean fascination with numbers as the essence of reality finds resonance in the precise alignments and proportions of ancient monuments.
As we uncover these connections, it becomes clear that the ancients saw geometry, music, and astronomy not as isolated disciplines but as facets of a unified cosmic vision. By retracing their steps, we can glimpse a worldview where harmony pervades both the heavens and the Earth, a perspective as inspiring today as it was millennia ago.
Notes
Plato, Timaeus, 35b, in Plato. Plato in Twelve Volumes, Vol. 9 translated by W.R.M. Lamb. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1925. https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0180%3Atext%3DTim.%3Asection%3D35b
Heath Robin & Michell, John, The Lost Science of Measuring the Earth, Adventures Unlimited Press
"The Origins of Megalithic Astronomy as found at Le Manio", by Richard D Heath and Robin Heath, 2010
https://www.academia.edu/5384545/The_Origins_of_Megalithic_Astronomy_as_found_at_Le_Manio
“A new look at the astronomy and geometry of Stonehenge”, by Euan MacKie, https://www.academia.edu/10789056/A_new_look_at_the_astronomy_and_geometry_of_Stonehenge
Plato, Republic (616b-617d): trans. Allan Bloom
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