Celestial time periods forming musical intervals
I have interpreted two objects from Phaistos (Faistos), both in the Heraklion Museum. Both would work well as calendar objects.
One would allow the prediction of eclipses:
The other for tracking eclipse seasons using the 16/15 relationship of the synod of Saturn (Chronos) and the Lunar Year:
The egg-shaped stone circles of the megalithic, in Brittany by c. 4000 BC and in Britain by 2500 BC, seem to express two different astronomical time lengths, beside each other as (a) a circumference and then (b) a longer, egg-shaped extension of that circle. It was Alexander Thom who analysed stone circles in the 20th century as a hobby, surveying most of the surviving stone circles in Britain and finding geometrical patterns within irregular circles. He speculated the egg-shaped and flattened circles were manipulating pi so as to equal three (not 3.1416) between an initial radius and subsequent perimeter, so making them commensurate in integer units. For example, the irregular circle would have perimeter 12 and a radius of 4 (a flattened circle).
However, when the forming circle and perimeter are compared, these can compare the two lengths of a right-triangle while adding a recurring nature: where the end is a new beginning. Each cycle is a new beginning because the whole geocentric sky is rotational and the planetary system orbital. The counting of time periods was more than symbolic since the two astronomical time periods became, by artifice, related to one another as two integer perimeters that is, commensurate to one another, as is seen at St Pierre (fig.3).
Continue reading “St Pierre 1: Jupiter and the Moon”The traditional way to express the Harmony of the Spheres is geometrically, despite the fact that geometrical knowledge of the heliocentric planetary system was not available to Pythagoras who, for the West, first established this whole idea – that the planets were part of a system expressing harmony.
The opening picture is from Kepler’s Harmonices Mundi :
from a scan made of the Smithsonian’s copy,
made available on Wikipedia as in the public domain.
In my own work, on the type of ancient astronomy based upon time and not space, I find it to be the outer planets in particular which express harmony in their geocentric synods relative to the lunar year. This applies to Jupiter, Saturn and Uranus but Neptune expresses a rational fraction of 28/27 involving prime numbers {2 3 7} whilst the other three planets only involve ratios involving primes {2 3 5}. The harmony of the outer planets has been a strong source for the sacred numbers found in ancient texts, as with Jupiter 1080 – considered a lunar number perhaps because the Moon is resonant to Jupiter – who is shown by figure 1 to be geocentrically resonant to the other planets and the Moon.
Continue reading “Further Ratios of the Outer Planets to the Lunar Year”The Fibonacci series is an ideal pattern, widely found within living systems, in which the present magnitude or location of something is the product of two previous magnitudes or locations of it. The next magnitude will again be the sum of the last two magnitudes in what is, an algorithmic pattern producing approximation to the Golden Mean (designated by the Greek letter φ,’phi’). As the series gets larger, the ratio (or proportion) between successive magnitudes will better approximate the irrational value of φ = 1.618033 … – which has an unlimited fractional part whilst the virtue of the Fibonacci numbers within the Series is that they are integers forming rational fractions.
Ad Quadratum is a convenient and profound technique in which continuous scaling of size can be given to square shapes, either from a centre or periphery. The differences in scale are multiples of the square root
of two [sqrt(2)] between two types of square: cardinal (flat) and diamond (pointed).
This was recorded before 2012 using diagrams slides and voice-over. It still introduces well how the megalithic solved astronomical problems.
