The idea of this post is to try and show that the lunar apsidal and nodal cycles contain similar frequencies, one with the full moon cycle and the other with the quasi-biennial oscillation.
There are four periods in the diagram, one in each corner of the rectangle. For this model their values will be:
FMC = 411.78443 days
LAC = 3231.5 days
LNC = 6798.38 days
QBO = 866 days (derived from 2 Chandler wobbles @ 433 days each)
The QBO period is an assumption (see Footnote below) but the others can be calculated.
The letters in the rectangle represent ratios of the periods on that side i.e.:
A = FMC:LAC = 1 : 7.8475526
B = QBO:LNC = 1 : 7.8503233
C = FMC:QBO = 1 : 2.1030421
D = LAC:LNC = 1 : 2.1037846
Obviously A and B are nearly the same, as are C and D (99.964% match, both pairs).
Hence the rectangle in the diagram.
The A (and B) numbers are also tropical years (TY):
7.8475526 FMC = 8.8475526 TY = 1 LAC (TY minus FMC = 1)
8.8475526 x 365.24219 days (1 TY) = 3231.5 days = 1 LAC
7.8475526 / 3 = 2.6158508 x 3
7.8503233 / 3 = 2.6167744 x 3
Phi² = 2.618034
So the two ratios are very close to 1 : 3 x Phi² (better than 99.9%).
– – –
Footnote – re the QBO period:
In Talkshop Suggestions 18 there are various references in the comments to a period of 2.369718 TY or 865.521 days.
If we use that instead of 866 days the ratio to LNC is 1:7.854668
7.854668 / 3 = 2.6182226 = > 99.992% match to Phi².