Author: Richard Heath

Distribution of Prime Numbers in the Tone Circle

first published 13 February 2018

The ancient notion of tuning matrices, intuited by Ernest G. McClain in the 1970s, was based on the cross-multiples of the powers of prime numbers three and five, placed in an table where the two primes define two dimensions, where the powers are ordinal (0,1,2,3,4, etc…) and the dimension for prime number 5, an upward diagonal over a horizontal extent of the powers of prime number 3. Whilst harmonic numbers have been found in the ancient world as cuneiform lists (e.g. the Nippur List circa 2,200 BCE), these “regular” numbers would have been known to only have factors of the first three prime numbers 2, 3 and 5 (amenable to their base-60 arithmetic). Furthermore, the prime number two would have been seen as not instrumental in placing where, on such harmonic matrices, each harmonic number can be seen on a harmonic matrix (in religious terms perhaps a holy mountain), as

  • “right” according to its powers of 3.
  • “above” according to its powers of 5.

The role of odd primes within octaves

An inherent duality of perspective was established, between seeing each regular number as a whole integer number and seeing it as made up of powers of the two odd two prime numbers, their harmonic composition of the powers of 3 and 5 (see figure 1). It was obvious then as now that regular numbers were the product of three different prime numbers, each raised to different powers of itself, and that the primes 3 and 5 had the special power of both (a) creating musical intervals within octaves between numerical tones and (b) uniquely locating each numerical tone upon a mountain of numerical powers of 3 and 5.


Figure 1 Viewing the harmonic primes 3 and 5 as a mountain of their products, seen as integer numers or as to these harmonic primes
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Erdeven Alignment’s counting of Metonic and Saros Periods

first published in March 2018

The word Alignment is used in France to describe its stone rows. Their interpretation has been various, from being an army turned to stone (a local myth) to their use, like graph paper, for extrapolation of values (Thom). That stone rows were alignments to horizon events gives a partial but useful explanation, since menhirs (or standing stones) do form a web of horizon alignments to solstice sun and to the moon’s extreme rising and setting event, at maximum and minimum standstill. At Carnac the solstice sun was aligned to the diagonal of the 4 by 3 rectangle and maximum and minimum standstill moon aligned to the diagonal of a single or double square, respectively.

It seems quite clear today that stone rows at least represented the counting of important astronomical time periods. We have seen at Crocuno that eclipse periods, exceeding the solar year, are accompanied by some rectalinear structures (Le Manio, Crucuno, Kerzerho) which embody counting in miniature, as if to record it, and it has been observed that cromlechs (or large stone kerb monuments) were built at the ends of the long stone rows of Carnac and Erdeven. Sometimes, a cromlech initiated a longer count,with or without stone rows, that ended with a rectangle (Crucuno). The focus on counting time naturally reveals a vernacular quite unique to this region and epoch. We have seen that the Kerzerho alignments were at least a 4 by 3 rectangle which recorded the 235 lunar months in feet along its diagonal to midsummer solstice sunset. After that rectangle there follows a massive Alignment of stone rows to the east,ending after 2.3 km having gradually changed their bearing to 15 degrees south of east. Just above the alignments lies a hillock with multiple dolmens and a north-south stone row (Mané Braz) whilst below its eastern extremity lies the tumulus and dolmen,”T-shaped passage-grave” (Burl. Megalithic Brittany. 196) called Mané Groh.


Figure 1 The intermittent extent of the Erdevan Alignments, and associated dolmens
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Kerherzo Rectangle near Erdeven & Crucuno

first published in March 2018

In 1973, Alexander Thom found the Crucuno rectangle to have been “accurately placed east and west” by its megalithic builders, and “built round a rectangle 30 MY [megalithic yards] by 40 MY” and that “only at the latitude of Crucuno could the diagonals of a 3, 4, 5 rectangle indicate at both solstices the azimuth of the sun rising and setting when it appears to rest on the horizon.” In a recent article I found metrology was used between the Crucuno dolmen (within Crucuno) and the rectangle in the east to count 47 lunar months, since this closely approximates 4 eclipse years (of 346.62 days) which is the shortest eclipse prediction period available to early astronomers.


Figure 1 Two key features of Crucuno’s Rectangle

About 1.22 miles northwest lie the alignments sometimes called Erdeven, on the present D781 before the hamlet Kerzerho – after which hamlet they were named by Archaeology. These stone rows are a major complex monument but here we consider only the section beside the road to the east. Unlike the Le Manec Kermario and Kerlestan alignments which start north of Carnac, Erdevan’s alignments are, like the Crucuno rectangle accurately placed east and west. 


Figure 2 Two stones, angled to the diagonal of a 3-4-5 triangle 235 feet from north west stone and setting sun at summer solstice
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Harmonic Astronomy within Seascale Flattened Circle

first published in July 2018

Only two type-D stone circles (see figure 3) are known to exist, called Roughtor (in Cornwall) and Seascale (in Cumbria). Seascale is assessed below, for the potential this type of flattened circle had to provide megalithic astronomers with a calendrical observatory. Seascale could also have modelled the harmonic ratios of the visible outer planets relative to the lunar year. Flattened to the north, Seascale now faces Sellafield nuclear reprocessing plant (figure 1).


Figure 1 Seascale type-D flattened circle and neighbouring nuclear facility.
photo: Barry Teague

Stone Age astronomical monuments went through a series of evolutionary phases: in Britain c. 3000 BC, stone circles became widespread until the Late Bronze Age c. 1500 BC. These stone circles manifest aspects of Late Stone Age art (10,000 – 4500 BC) seen in some of its geometrical and symbolic forms, in particular as calendrical day tallies scored on bones. In pre-literate societies, visual art takes on an objective technical function, especially when focussed upon time and the cyclic phenomena observed within time. The precedent for Britain’s stone circle culture is that of Brittany, around Carnac in the south, from where Megalithic Ireland, England and Wales probably got their own megalithic culture.

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Number Symbolism at Table des Marchands

Table des Marchands, a dolmen at Lochmariaquer, can explain how the Megalithic came to factorise 945 days as 32 lunar months by looking at the properties of the numbers three, four and five. At that latitude, the solstice angle of the sun on the horizon shone along the 5-side of a 3-4-5 triangle to east and west, seen clearly at the Crucuno Rectangle [post2post id=”237″].

Before numbers were individually notated (as with our 3, 4 and 5 rather than |||, |||| and |||||) and given positional notation (like our decimal seen in 945 and 27), numbers were lengths or marks and, when marks are compared to accurately measured lengths measured out in inches, feet, yards, etc. then each vertical mark would naturally have represented a single unit of length. This has not been appreciated as having been behind marks like the cuneiform for ONE; that it probably meant “one unit of length”.


Figure 1 The end and cap stone inside the dolmen Table des Marchands in which the elementary numbers in columns and rows perhaps inspired its attribution to the accounts of merchants
Locmariaquer (Morbihan, Bretagne, France) : la Table des Marchand, interieur.
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Megalithic application of numeric time differences

Natural time periods between celestial phenomena hold powerful insights into the numerical structure of time, insights which enabled the megalith builders to access an explanation of the world unlike our own. When looking at two similarly-long time-periods, the megalithic focussed on the difference between them, these causing the two periods to slide in and out of phase, generating a longer period in which the two celestial bodies exhibit a complete ensemble of variation, in their relationship to each other. This slippage of phase between celestial periods holds a pattern purely based upon number, hidden from the casual observer who does not study them in this way. Such numerical patterns are only fully revealed through counting time and analysing the difference between periods numerically.

For example, the solar year is longer than the lunar year by 10 and 7/8 days (10.875 days) and three solar years are longer than three lunar years by three times 10.875 days, that is by 32 and 5/8th days (32.625 days), which is 32/29 of a single lunar month of 29.53 days.

The earliest and only explicit evidence for such a three year count has been found at Le Manio’s Quadrilateral near Carnac (circa 4,000 BCE in Brittany, France) used the inches we still use to count days, a “day-inch” unit then widespread throughout later megalithic monuments and still our inch, 1/12 of the foot [Heath & Heath. 2011]. The solar-lunar difference found there over three years was 32.625 day-inches, is probably the origin of the unit we call the megalithic yard and the megalith builders appear to have adopted this differential length, between a day-inch count over three lunar and solar years, in building many later monuments.


Figure 1 (in plan above) The monumentalising of a three-year day inch count at Le Manio as a right triangle based upon its southern kerb (in profile below), automatically generating the megalithic yard.
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