One can define nodetides for the lunar year of 12 months, using the same two formulae.
For an eclipse cycle of M months and E eclipse seasons, setting M = 12*Y in the second formula gives:
N = E - M/6
The shorter year makes a longer nodetide and this lunar nodetide is equal to exactly six eclimpiads and so consists of a number of six-month eclipse season intervals and six five-month eclipse season intervals (Pentalunex). This comes out at about 21.7 years (22.4 lunar years) on average.
Lunar year: 1 year, 0 nodetides
Unidos: 67 years, 3 nodetides
Trihex: 201 years, 9 nodetides (3 Unidos)
Unnamed (327): 337 years, 15 nodetides
Hexodeka: 402 years, 18 nodetides (6 Unidos)
Grattan-Guinness: 403 years, 18 nodetides
Basic Period: 537 years, 24 nodetides
Tetradia: 604 years, 27 nodetides
Hyper Exeligmos: 939 years, 42 nodetides.
In all these examples, the number of lunar nodetides is divisible by 3. The longest cycle listed of a whole number of lunar years (Immobilis) has 84 lunar nodetides also divisible by 3. I expect a longer cycle will have a number of lunar nodetides not divisible by 3.
The number of lunar nodetides in a cycle of A Inex cycles and B Saros cycle is equal to
(4/3)*A + (5/6)*B.
From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Helios
Sent: 27 October 2016 08:43
To: [hidden email] Subject: Nodetides
Dear Calendar People,
There's a basic period between when a node alignment and the solar year
nearly coincide. This period averages about 9.3 years. I call this a
mean nodetide = 1/[ ( y/e ] - 2 )
Should we subtract from the year two eclipse seasons, the remaining 19 days
is the portion of the year within which we can expect a node alignment to
occur every nodetide.
A luni-solar eclipse cycle will always contain a whole number of nodetides.
For a luni-solar eclipse cycle, we can subtract from the eclipse seasons the
number of years doubled to find the number of nodetides in the cycle.
N = E - 2*Y
Beginning from a node alignment at a certain time in year 0, we can predict
the following nodetide years. I'm satisfied with the following accumulator