with periods that are twice the main-band values. Light curves that fall in the long period sequence for $N = 2$ and $N = 3$ show multiple minima in a cycle when phased at the long period. Changing the number of harmonics in the fit can select different harmonics of the true period. Light curves with multiple, unequal, minima in a cycle or light curves that are not perfectly periodic (e.g. due to spot evolution, or uncorrected systematic errors in the photometry) are particularly susceptible to choosing an incorrect harmonic of the true period. For the remainder of the paper it is important to have a sample of stars with unambiguous periods. We therefore select a clean sample of 372 stars for which periods determined with $N=1,2$ and $3$ do not differ by more than $10\%$. For this sample we adopt the $N=2$ periods. As seen in figure \[fig:BVPeriod\_multiharm\] and \[fig:AverPeriod\_multiharm\], the half-period harmonic sequence is removed from the clean sample. We note that a handful of long-period variables remain in the clean sample, we discuss these further in §9. Tables \[tab:M37\_rotation1\] and \[tab:M37\_rotation2\] include the full sample of stars, the $N = 1$, $2$ and $3$ periods are provided 