The idea here is to link up different lunar periods in a schematic intended to show how they integrate into a ‘bigger picture’, for lack of a better phrase.
This chart of selected lunar data is based on the numbers from this blog post comment:
The top line of the chart contains original data. The rest shows the differences between the original figures (e.g. 2079 – 1973 = 106) in a structured format. By using periods where there’s a good match with whole numbers, the patterns of the relationships can perhaps more readily be identified in diagrammatic form.
One point to note is that one more tropical year would give 1974 = 329 x 6 (also 987 x 2).
The figures at the bottom of each chart are validation only.
Now a chart using the same method, based on exactly seven times the period of the first chart:
This chart is a period of exactly 766 Saros cycles:
‘The saros is a period of 223 synodic months (approximately 6585.3211 days, or 18 years and 11+1/3rd days), that can be used to predict eclipses of the Sun and Moon. One saros period after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, a near straight line, and a nearly identical eclipse will occur’ – Wikipedia
Note here that one more draconic year would be 14554 = 766 x 19.
Also that six more full moon cycles would be 12256 = 766 x 16.
These differences (as -6 and -1) are reflected in the top line of chart 2.
Compare with the Wikipedia notes:
‘The saros is an eclipse cycle of 223 synodic months = 239 anomalistic months = 242 draconic months. This is also equal to 16 full moon cycles.’
(239 – 223 = 16, 242 – 223 = 19)
Talkshop contributor Paul Vaughan quoted these figures from JPL data in another thread:
apse cycle – 6798.38 days
nodal cycle – 3231.5 days
Results from these charts (against tropical years):
apse cycle – 6798.329 days [using ‘APC’ in chart 1]
nodal cycle – 3231.4925 days [using ‘LP’ in chart 1]
The conclusion is that the charts closely follow lunar periods, so the relationships shown should be reasonably accurate over the long term.
The basic period appears to be 1973 tropical years, which is 987 x 2, – 1 (see chart 1). 987 is a Fibonacci number.
The difference between the number of draconic years and full moon cycles in chart 1 is 329 (as shown), which is 987/3.
(The second chart is just a factor of 7 greater than the first one so the same comments apply).