Category: Planetary Harmony

Celestial time periods forming musical intervals

The Approximation of π on Earth

π is a transcendental ratio existing between a diameter/ radius and circumference of a circle. A circle is an expression of eternity in that the circumference, if travelled upon, repeats eternally. The earths shape would be circular if the planet did not spin. Only the equator is now circular and enlarged, whilst the north and south poles have a shrunken radius and, in pre-history, the shape of the earth’s Meridian between the poles was quantified using approximations of π as was seen in the post before last. In some respects, the Earth is a designed type of planet which has to have a large moon, 3/11 of the earth’s size and a Meridian of such a size that the diverse biosphere can be created within the goldilocks region of the Sun’s radiance.

It would be impossible to quantify the earth as a physical object without the use of approximations to π, a technique seen as emerging in Crucuno between its dolmen and famous {3 4 5} Rectangle where the 32 lunar months in 945 days was used, through manipulation of proximate numbers to rationalize the lunar month to 27 feet (10 Drusian steps) within which days could be counted using one Iberian foot (of 32/35 feet) as described here and in my Sacred Geometry book.

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Book: Matrix of Creation

Sacred numbers arose from ancient man’s observation of the heavens, and represent the secrets of cosmic proportion and alignment. The ancients understood that the ripeness of the natural world is the perfection of ratio and that the planetary system–and time itself–is a creation of number. We have forgotten what our ancestors once knew: that numbers and their properties create the forms of the world.

Introduction to my book Harmonic Origins of the World

Over the last seven thousand years, hunter-gathering humans have been transformed into the “modern” norms of citizens (city dwellers) through a series of metamorphoses during which the intellect developed ever-larger descriptions of the world. Past civilizations and even some tribal groups have left wonders in their wake, a result of uncanny skills – mental and physical – which, being hard to repeat today, cannot be considered primitive. Buildings such as Stonehenge and the Great Pyramid of Giza are felt anomalous, because of the mathematics implied by their construction. Our notational mathematics only arose much later and so, a different maths must have preceded ours.

We have also inherited texts from ancient times. Spoken language evolved before there was any writing with which to create texts. Writing developed in three main ways: (1) Pictographic writing evolved into hieroglyphs, like those of Egyptian texts, carved on stone or inked onto papyrus, (2) the Sumerians used cross-hatched lines on clay tablets, to make symbols representing the syllables within speech. Cuneiform allowed the many languages of the ancient Near East to be recorded, since all spoken language is made of syllables, (3) the Phoenicians developed the alphabet, which was perfected in Iron Age Greece through identifying more phonemes, including the vowels. The Greek language enabled individual writers to think new thoughts through writing down their ideas; a new habit that competed with information passed down through the oral tradition. Ironically though, writing down oral stories allowed their survival, as the oral tradition became more-or-less extinct. And surviving oral texts give otherwise missing insights into the intellectual life behind prehistoric monuments.

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The Many Faces of Great Time

Figure 7.5 The widespread tradition of a God who changes the astrological Age, through the Precession of the Equinoxes: Top left, Mithras as Sol Invictus; top right, Mithras slaying the Age of Taurus; bottom left, Aion, God of Ages; and bottom right, Orphic God Phanes. Mithras slaying the Age of Taurus (photo by Tim Prevett courtesy of the Segontium Museum, 2005)

This article has been extracted from my 4th book Sacred Number and the Lords of Time as being a fairly self-contained read. The “great time” in the heading is the Precession of the Equinoxes or Great Year of Plato, in which god-like human figures are posited in ancient times as governing the Age named after the Zodiacal sign in which the sun sits at the spring equinox, today the age of Pisces is about to become the age of Aquarius, but the Current Era corresponds to the age of Pisces, inaugurated by the birth of Jesus, hence also called A.D. for “anno dominie” or “year of Our Lord”.


Figure 7.4. The conceptual model of Great Time as two bands at right angles, joined at the equinoctial points where the celestial meridian of the Age crosses the equator and ecliptic
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Twelve: determining Time and Space on the Earth

ABOVE: South rose window in Angers Cathedral of Saint Maurice. Stained glass by Andre Robin created after the fire of 1451. At centre, Christ of the Apocalypse, in glory (Revelation 21:5). At bottom, 12 radial windows showing 12 elders, crowned and playing musical instruments, rejoicing, indicating the remade world (the heavenly Jerusalem). At top, circular ends of 12 radial windows showing the 12 signs of the Zodiac, indicating the incarnation of Christ as a man on earth under the stars. Sequence from left to right has last 2 signs before first, i.e. Aquarius/Water-bearer (grey), Pisces/Fish (grey), Aries/Ram, Taurus/Bull (yellow), Gemini/Twins, Cancer/Crab (red), Leo/Lion (yellow), Virgo/Virgin, Libra/Scales, Scorpio/Scorpion, Sagittarius/Archer, Capricorn/He-goat (blue background)
photo: Chiswick Chap for Wikipedia Foundation.

The Moon was the means by which a 12-fold harmony became established on the Earth. This harmonization occurred through the lengthening of the lunar month until 12 months fitted, in a special way, within the solar year. The excess of the solar year over the lunar year of 12 months became 7/19 lunar months, causing seven extra whole months over 19 years. This 19-year (235 month) Metonic period was well-known to the ancient world, and it leads to the remarkably short cycle for the pattern of similar eclipses, we call the Saros period, which repeat every 18 years (235 minus 12 months = 223 months). And eclipses are highly visible because the disk of the Moon has come to be the same angular size as the disk of the Sun, causing total solar eclipses.

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Powers of the Golden Mean

Sheikh Lotfollah Mosque  is one of the masterpieces of Iranian architecture that was built during the Safavid Empire, standing on the eastern side of Naqsh-i Jahan Square, Esfahan, Iran. Construction of the mosque started in 1603 and was finished in 1619.
for Wikipedia by Phillip Maiwald

The Golden Mean (1.618034) or Phi (Greek letter) is renowned for the behavior of it’s reciprocal and square which are 0.618034 and 2.618034 respectively; that is, the fractional part stays the same. Phi is a unique singularity in number. While irrational, shown here to only 6 figures, it is its infinite fractional part which is responsible for Phi’s special properties.

The Fibonacci series: Found in sacred buildings (above), it is also present in the way living forms develop. Many other series of initial number pairs tend towards generating better and better approximations to Phi. This was most famously the Fibonacci series of 0 1 1 2 3 5 8 13 21 34 55 89 … (each right hand result is the simple sum of the two preceding numbers (0+0 = 1, 1+1=2, etc.

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