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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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.

Figure 1 The metamorphosis of loop shape when Jupiter is in different signs of the Zodiac
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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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