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The Tetraktys as plan of planetary harmony and the four Elements

In "Planetary Resonances with the Moon" I explored the astronomical matrix presented in The Harmonic Origins of the World with a view to reducing the harmonic between outer planets and the lunar year to a single harmonic register of Pythagorean fifths. This became possible when the 32 lunar month period was realized to be exactly 945 days but then that this, by the nature of Ernest McClain’s harmonic mountains (figure 1) must be 5/4 of two Saturn synods.

Figure 1 The elimination of 5 as a factor in the harmonic mountain for 36 lunar years, resolved using matrix units of one tenth of a month and the limit 360 units.

Using the lowest limit of 18 lunar months, the commensurability of the lunar year (12) with Saturn (12.8) and Jupiter (13.5) was “cleared” using tenths of a month, revealing Plato’s World Soul register of 6:8::9:12 but shifted just a fifth to 9:12::13.5:18, perhaps revealing why the Olmec and later Maya employed an 18 month “supplementary” calendar after some of their long counts.

By doubling the limit from 18 to three lunar years (36) the 13.5 is cleared to the 27 lunar months of two Jupiter synods, the lunar year must be doubled (24) and the 32 lunar month period is naturally within the register of figure 1 whilst 5/2 Saturn synods (2.5) must also complete in that period of 32 lunar months.

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Kaaba’s Numerical Picture of Harmonic Origins

A recent plan of the Kaaba[1] indicates that its walls, by their odd-number proportionality, symbolised the numerical origins of musical harmony through the first six numbers, 1, 2, 3, 4, 5 & 6, sometimes called the Senarius meaning “existence out of six”.

According to Plato, the world was created using the rules of musical harmony in a scheme involving perfect fifths of 3/2, fourths of 4/3 and tones of 9/8, leaving “leftover” semitones of 256/243: a rudimentary musical scale. This only used prime numbers 2 and 3 and multiplications with themselves and each other; a system called Pythagorean tuning. The Kaaba incorporates another prime number 5, called the human number, this enabling two more large intervals called thirds, the major third of 5/4 and minor third of 6/5. Using 5 enables more and better scales to be formed and fills in the gap between 4 and 6 to show all the large intervals in the first six numbers, 1:2:3:4:5:6. This fuller tuning system has been found in the ancient Near East as long ago as the Sumerians, in their tuning texts on cuneiform (c. 3000 BC onwards).

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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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Musical Tones of the Outer Planets

My crucial entré to planetary harmony came when I noticed musical ratios in the synodic time periods of Jupiter and Saturn relative to the lunar year. This approach differs from the norm for “harmonies of the spheres” (a.k.a. Musica Universalis which are geometrical and spatial, rather than temporally harmonic.

The planetary harmony I found within synodic periods became the subject of my new book The Harmonic Origins of the World (pub. 2018). These synodic ratios have been parts of my work from c. 2000, then expressed as “matrix diagrams” (Matrix of Creation, figure 2 below). In my new book, I show how ancient tuning theory seems to have presented the same information, in a different type of matrix (see figure 4).

Below I connect the outer planets using two additional (and useful) kinds of diagram, the right-angled triangle (figure 1) and the Pentad (figure 5), the latter developed in the 20th century within a discipline called Systematics.

*Figure 1 The harmonic ratios between the nearest two outer planets and the lunar year. The four square rectangle with side length of four, when equal to the lunar year gives, geometrically, the* solar year as its diagonal length. The outer planetary synods are longer than the solar year as the planets have moved ahead of their last opposition to the sun. Such oppositions are marked by an outer planet appearing to travel in a loop, amongst the stars

The Cult of Seven Days

Published in Nexus Magazine in 2004

When understanding the origins of human knowledge, we tend not to look into the everyday aspects of life such as the calendar, our numbering systems and how these could have developed. However, these components of everyday life hold surprising clues to the past.

An example is the seven day week which we all slavishly follow today. It has been said that seven makes a good number of days for a week and this convenience argument often given for the existence of weeks.

Having a week allows one to know what day of the week it is for the purposes of markets and religious observances. It is an informal method of counting based on names rather than numbers. Beyond this however, a useful week length should fit well with the organisation of the year (i.e. the Sun), or the month (i.e. the Moon) or other significant celestial or seasonal cycle. But the seven day week does not fit in with the Sun and the Moon.

The Week and the Year

Megalithic Measurement of Jupiter’s Synodic Period

Though megalithic astronomers could look at the sky, their measurement methods were only accurate using horizon events. Horizon observations of solstice sunrise/set each year, lunar extreme moonrises or settings (over 18.6 years) allowed them to establish the geometrical ratios between these and other time periods, including the eclipse cycles. In contrast, the synod of Jupiter is measured between its loops in the sky, upon the backdrop of stars, in which Jupiter heads backwards each year as the earth passes between itself and the Sun. That is, Jupiter goes retrograde relative to general planetary direction towards the east. Since such retrograde movement occurs over 120 days, Jupiter will set 120 times whilst moving retrograde. This allowed megalithic astronomy to study the retrograde Jupiter, but only when the moon is conjunct with Jupiter in the night sky and hence will set with Jupiter at its own setting.