In 17 patients with rapid cycling bipolar disorder, time-series analyses detected synchronies between mood cycles and three lunar cycles that modulate the amplitude of the moon's semi-diurnal gravimetric tides: the 14.8-day spring-neap cycle, the 13.7-day declination cycle and the 206-day cycle of perigee-syzygies ('supermoons'). The analyses also revealed shifts among 1:2, 1:3, 2:3 and other modes of coupling of mood cycles to the two bi-weekly lunar cycles. These shifts appear to be responses to the conflicting demands of the mood cycles' being entrained simultaneously to two different bi-weekly lunar cycles with slightly different periods. Measurements of circadian rhythms in body temperature suggest a biological mechanism through which transits of one of the moon's semi-diurnal gravimetric tides might have driven the patients' bipolar cycles, by periodically entraining the circadian pacemaker to its 24.84-h rhythm and altering the pacemaker's phase-relationship to sleep in a manner that is known to cause switches from depression to mania.