The anniversary of the Octon (4 eclipse years in 47 lunar months) did not provide similar eclipses and so, by counting more than four, the other motions of the Moon could also form part of that anniversary. This is especially true of the anomalistic month, which changes the changes the apparent size of the Moon within its phase cycle, recreate the same type of lunar eclipse after nineteen eclipse years. This 18 year and 11 day period is now taken as the prime periodicity for understanding eclipse cycles, called the SarosThe dominant eclipse period of 223 lunar months after which a near identical lunar or solar eclipse will occur. period – known to the Babylonian . The earliest discovered historical record of what is known as the saros is by Chaldean (neo-Babylonian) astronomers in the last several centuries BC.
The number of full moons between lunar eclipses must be an integer number, and in 19 eclipse years there are a more accurate 223 lunar months than with the 47 of the Octon. This adds up to 6585.3 days but the counting of full moon’s is obviously ideal as yielding near-integer numbers of months.
We noted in a past post that the anomalistic month (or AM), regulating the moon’s size at full moon, has a geometrical relationship with eclipse yearthe time taken (346.62 days) for the sun to again sit on the same lunar node, which is when an eclipse can happen. (or EY) in that: 4 AM x pior π: The constant ratio of a circle's circumference to its diameter, approximately equal to 3.14159, in ancient times approximated by rational approximations such as 22/7. (of 3.1448) equals the 346.62 days of the eclipse year as the circumference. Therefore, in 19 EY the diameter of a circle of circumference 19 x 346.62 days must be 4 x 19 AM so that , 76 AM x pi equals 223 lunar months, while the number of AM in 223 lunar months must be 239; both 223 and 239 being prime numbers.
The lunar month then relates to the AM as 15/14 since 239/223 equals 15/14 to one part in 3345, so that in 14 lunar months there are 15 AM. This causes the nearness of the moon, and its greatest size, to recur over a period of 14 lunar months; a largeness visible to the long term naked-eye observer.
As we saw in the last post, 239 is the number of squares that generates the angle that corrects two stacked {5 12 13} triangles (or two stacked {5 12} rectangles.
It is as if the pattern of eclipse time periods reflects an angular world defined by low integer triangular and rectangular geometry and that, in order to achieve this in this case, a correction must be applied, as one expects in the numerical turning theory of music.