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Modes due to lunar and solar periods

Some cycles with lunar and solar periods are known in astronomy and history: For these cycles it has been calculated when the lunar/solar month/year period fit best on a certain Date (unsing the FDM). Comparable studies can be done for other cycles (if you want a cycle to be covered, let me know).

I have kept the durations of all periods te same, although they slowly change over time: the durations of period , which I used in the below evaluation, changes only some 0.000007% over the 410 years.

Metonic cycle

The following method has been used for the Metonic cycle: The following graph is obtained for the Metonic cycle; every symbol is a point where the difference (with regard to a precise fit) was smaller than 1 day:
What can be seen in the above  graph:

Metonic cycle incl. sidereal months

The following method has been used for the Metonic cycle incl. sidereal months: The following graph is obtained for the Metonic cycle incl. sidereal months; every symbol is a point where the difference (with regard to a precise fit) was smaller than 1 day:
What can be seen in the above  graph:

Saros cycle

The following method has been used for the Saros cycle: The following graph is obtained for the Saros cycle; every symbol is a point where the difference (with regard to a precise fit) was smaller than 1 day:

What can be seen in the above graph:

General remarks

The above graphs provides some insight what and how people in former times could have measured/experienced similar occurrences, if they would have historic tables/tallies of information. In my opinion, they should at least have this information for several occurrences, say 50-100 years, otherwise accuracy could be too low.

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Last major content related changes: May 5, 2001