  We present evidence that $>25$ MeV solar proton events show a clustering in
time at intervals of $\approx$ six months that persisted during the rising and
peak phases of Solar Cycle 24. This phenomenon is most clearly demonstrated by
considering events originating in the northern or southern solar hemispheres
separately. We examine how these variations in the solar energetic particle
(SEP) event rate are related to other phenomena, such as hemispheric sunspot
numbers and areas, rates of coronal mass ejections, and the mean solar magnetic
field. Most obviously, the SEP event rate closely follows the sunspot number
and area in the same hemisphere. The $\approx$ six-month variations are
associated with features in many of the other parameters we examine, indicating
that they are just one signature of the episodic development of Cycle 24. They
may be related to the "$\approx$150~day" periodicities reported in various
solar and interplanetary phenomena during previous solar cycles. The clear
presence of $\approx$six-month periodicities in Cycle 24 that evolve
independently in each hemisphere conflicts with a scenario suggested by
McIntosh et al. (2015, Nature Com. 6, 6491) for the variational time scales of
solar magnetism.
