## Harmonic Numbers of the Earth: Circumferences

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The ancient world had unreasonably accurate knowledge of the size of the earth and its shape: Analysis of ancient monuments reveals an exact estimate for the circumference of the mean Earth, a spherical version of the Earth, were it not deformed by its spinning once a day.

* Figure 1 The Earth as a circular Equator and a spherical Mean Earth, whose half circumference approximates the non-circular distance between north and south poles**The Size of the Earth*

Half of this circumference forms a north-south meridian, known to be 12960 miles (of 5000 geographical Greek feet of 1.01376 ft), a number which (in those Greek units) is then 60^5 = 777,600,000 geographical Greek inches. One has to ask: how are such numbers to be found very accurately, within a planet formed accidentally during the early solar system?

In the addendum of his booklet on Jerusalem, John Michell found the walls of the Temple Mount, extended for the rebuilding of the Temple of Solomon, were a scaled down model of the mean-earth Meridian in its length. These walls are still 5068.8 feet long, which is the length of a Greek geographical mile. This unit of measure divides the meridian into 12960 parts, each a geographical Greek mile.

**12960** - the Greek miles between poles

This is a harmonic number made up only of harmonic prime number factors; 2, 3 and 5. The mean-earth circumference is therefore twice this, or 25920 Greek miles and therefore equal in year-miles to the ancient duration of the ancient estimate of 25920 years for the Precession of the Equinoxes.

777,600,000 - the geographical inches between the poles

## Double Resonances within Three Lunar Years

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Readers of my article Lunar Counting from Crucuno Dolmen to its Rectangle will be familiar with the finding that in 32 lunar months there are almost exactly 945 days, leading to the incredibly accurate approximation (one part in 45000!) for the lunar month of 945/32 = 29.53125 days. In the previous article on Seascale I noticed that 36 lunar months (three solar years) divided by 32 lunar months is the Pythagorean tone of 9/8. This leads to some important thoughts regarding the tuning matrix of the Moon within the periods of the three outer planets, since the synod of Jupiter divided by the lunar year of 12 lunar months is the tone 9/8, the same tone that on "holy mountains" of Ernest G. McClain's ancient tuning theory, are only found between two tonal numbers separated horizontally by two perfect fifths of 3/2, since 3/2 x 3/2 = 2.25 which, normalised to the octave of 1 to 2, is 1.125 or 9/8.

If the matrix unit is one tenth of the lunar month, then three lunar years become 360 units which, taken to be do^{2} = D'' = the harmonic limiting number, which presents the matrix in figure 1.

*Figure 1 The Harmonic Matrix for 360 = 36 months, showing that the 32 lunar month period of 945 days starts the second row as harmonic number 320. Screen grabbed from my online app Harmonic Explorer for Ernest McClain's tuning mountains*

This matrix, being two dimensional, has to be read in one dimensional ways:

- The number 320 in the matrix is the 32 lunar month period whilst in between lies two lunar years as G=240.
- To the right of D = 360 lies 270 which is two Jupiter synods taking 27 lunar months.
- Saturn is the bottom left "cornerstone" of a-flat = 256: again lasting for two of it's synods of 12.8 lunar months.
- On top of the matrix is a periodicity of 25 lunar months during which exactly two synods of Uranus equal to 12.5 lunar months, complete.

## Harmonic Astronomy within Seascale Flattened Circle

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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).

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.

### The first steps taken by Megalithic Astronomy

Read more: Harmonic Astronomy within Seascale Flattened Circle

## Harmonic Metrology: the Moon and Outer Planets

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The moon has enabled the semi-harmonic orbits of the outer planets (Jupiter, Saturn and Uranus) to become fully harmonic, expressing two of the three intervals necessary for the type of *modal* music found in the earliest civilization of the Sumerians. Harmonic Origins of the World plots how the ancient world from then on interpreted musical harmony as a cosmic principle, in which the harmonic planets were gods. This connection, between harmony, planets, and a divine world can only have emerged from the greatest astronomical culture in prehistory, responsible for building megalithic buildings and earthworks in many regions of the Earth, over the last seven thousand years.

This website uses the basic techniques of these early astronomers,

- alignment to horizon events, exactly counted time periods using fixed measures (
**metrology**), - triangular, square, rectangular and circular
**geometries**to enable comparison, calculation and simulation

to interpret their surviving monuments as to their purpose and thus learn from them what their astronomy might have revealed.

*Figure 1 New Dawn No. 168 for May-June, 56-60.*

Here I present how our historical metrology, which the Neolithic astronomers evolved, comes to have the metrological ratios that enable a single length to have modelled the synodic periods of the Moon (lunar year), Jupiter, Saturn (and Uranus). My recent article for New Dawn (issue 168) progresses, in one graphic, the ratios between the planetary synods and how these are transformed by the lunar year in its present length of 354.367 days. Probability not 100% proof can be offered; instead perhaps joy that such an ancient and important intellectual tradition should have come down to us in recognisable form, without writing.

## Enigmatic Earthworks of the Cursus Culture

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The megalithic was the most visible of several phases of building types, only recently identified as the actual built heritage of the British "neolithic" period; that is, between the widespread building of long and round barrows and the last stone circles in Britain. Avebury and Stonehenge were just starting to be built as stone circles towards the end of the main** Cursus-building period**, dated as between 3600 and 2800 BC.

*Figure 1 The Stonehenge Cursus*

## The Samian Foot (of Samos), Saturn and the Moon

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Herodotus, the great 5th century BC historian, mentions that the key south-facing "datum" edge of the Great Pyramid was 800 feet long whilst in English feet, the best survey found it was 756 feet long. Dividing 800 by 756 gives a foot length of 0.945 feet (fractionally 189/200 ft). John Neal has called this foot the Samian foot, since Herodotus lived as a young body on the island of Samos, as did Pythagoras. Neal found another historical reference to the same ("Samian") module in the pre-metrification city standards of at least seven German cities; in Danzig the variation was the Root value for the module (33/35 ft), in Bremen the Root Canonical (x 176/175), in three others the Standard microvariation (i.e. x 441/440) and two more the Root (33/35).

The Samian module is therefore quite well attested by Neal as a historical measure, but my own work finds a new significance in it. Neal's Standard Canonical is a foot 0.945 feet long, where 1000 such feet are 945 English feet which, divided by 32, equals 29.53125 feet, the number of days in a lunar month. At Le Manio Quadrilateral, the 32nd stone from the "sun gate" origin of day-inch counting appears to signify 945 day-*inches* from which I discovered this relationship between 32 lunar months and 945 days of day counting, in any unit. Could the Samian foot (then using feet to count days) have used one thousand such feet to conveniently arrive at 32 lunar months? I will return to this, but also need to point to the apparent coding of 27 feet to represent months at the Crucuno complex. This led to finding that this same 27 regular feet is 29.53125 Iberian feet (each 32/35 feet), allowing days to be counted within a lunar month counted in units of 27 feet! One must also recognise that 27 feet is ten steps (viz. megalithic yards) of the Druzian foot from which the astronomical megalithic yard is derived as 176/175 of 2.7 feet.

## Placing "Stonehenge" within the Aubrey Holes

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*Sarsen Circle (blue) within the preexisting outer circle of Stonehenge*

It is important to see the practical problems faced by the builders of megalithic monuments. By 3000 BC, Stonehenge was the ring now called the the Aubrey Circle, a set of postholes now thought sockets for bluestones brought from the Preseli hills in Wales. Other rings of postholes were dug in the centuries following, the Z and Y-rings, these perhaps containing 30 and 29 sockets for bluestones but not properly concentric with the Aubrey Circle or evenly spaced. Around 2500 BC, a new and complex design was carefully and concentrically placed within the area within the Y-ring. It has been suggested its design was influenced by the dynastic cultures of Egypt which had their own megalithism of pyramids and obelisks, employing faced masonry and stone joints but now in the British idiom of stone circles natural to higher latitudes. The Aubrey Circle came to be just as dynastic Egypt began whilst the Sarsen Circle was built in the middle of the second dynasty (Old Kingdom) (2625-2510).

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