As a nonlinear dynamical system with limit cycles but subject to periodic forcings associated with the seasonal cycle, the quasi-biennial oscillation (QBO) displays seasonal modulation such that phase transitions are more likely to occur in certain months than in others. Modulation is distinct from seasonal synchronization, defined as quantized QBO periods and identical cycles. Instead, nearly identical QBO cycles can be identified in the data having similar period, internal structure, and (optionally) timing with respect to the calendar year. Four such categories are found using a spectral phase method based on the 2-D phase space of the leading rotated principal components (RPCs) of near-equatorial monthly mean zonal wind in the layer 70-10 hPa. The most prominent category, containing as many as 15 cycles of the 28 observed thus far, is "nearly biennial" with period slightly greater than 24 months. All results, prior to the recent QBO anomaly in Cycle 28, are demonstrated to be statistically stationary in the sense that the RPCs are temporally invariant and insensitive to the inclusion of data to 100 hPa and with higher vertical resolution. Inclusion of Cycle 28 has no effect on the rotated empirical orthogonal functions but a microscopic change in the long-term average, since strong easterlies are missing in the anomalous cycle. For objective definition of QBO cycles in physical space-time, westerly onsets in the 40-53 hPa layer are least likely to stall and provide unambiguous starting times. Half of these onsets cluster in April-May, consistent with the seasonal modulation obtained with the spectral phase method.