The following wavelet transform of the SOI (since 1960) clearly shows two periods that are part of the 31-year Perigean New/Full Moon tidal cycle. These periods are the 18.03 year Saros Cycle and the 12.97 years ~ 13.0-year lunar pseudo cycle, such that:
31 years = 18 years + 13.0 years
If the ENSO cycle (i.e. La Ninas and El Ninos) is caused by a combination of the 31.0-year Perigean New/Full Moon lunar tidal cycles and the 11.2-year solar sunspot cycle, then you might expect to see a periodic peak at the mean of the 13.0-year lunar pseudo cycle and the 11.2 solar sunspot cycle i.e.
(13.0 + 11.2)/2 = 12.1 years.
Close inspection of the following figure shows that this appears to be the case.
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