>Thus we have a single strong Mathieu modulation term along with a pair of weaker Hill terms operating on different scales (1) a strong biannual modulation (2) a weak 12 year modulation and (3) and even weaker 50 year modulation.

Paul your QBO modulation looks impressive, even if I don't understand how you arrived at it. That in particular I think you have now a different model than before, because I don't
think that introducing an extra term into Hills equation is the same as letting the solution depend on an oscillatory extra term that would probably be big news if this were the case.

Anyways I give up trying to understand your calculations. It would though be interesting for me to hear your opinion about that blog posts QBO data you linked to. That is your QBO data, although
it is hard to see, seems to look quite differently from that.