zero yields the same signal as using the correct period and setting the amplitude of the fundamental to one and all harmonics to zero). Because we limit the period search to 20 days, periods longer than 10 days cannot be recovered at twice the period or three times the period, and periods longer than 7 days cannot be recovered at three times the period. As a result the recovery fraction for long periods using the multi-harmonic AoV selection is close to the recovery fraction when the AoV selection is not used. For more realistic spot models the degeneracy between choosing the fundamental mode with the true period or either of the harmonics with a longer period is broken, so applying the multi-harmonic AoV selection does not have as significant an effect on the recovery fraction. In this case the recovery fraction is reduced by $\sim 20\%$ independent of period. Based on the results for the spot model signals we conclude that the rotation period-color diagram may be biased toward brighter stars, but at fixed magnitude, it is not strongly biased in period due to incompleteness.

Field Contamination
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In addition to incompleteness, the presence of field stars may also bias 