In this short paper, we look at two-scale limits of sequences with varying homogenization periods, each period being a multiple of the previous one. We establish that, up to a measure preserving rearrangement, these two-scale limits form a martingale which is bounded: the rearranged two-scale limits themselves converge both strongly in $\mathrm{L}^2$ and almost everywhere when the period tends to $+\infty$. This limit, called the two-scale shuffle limit, contains all the information present in all the two-scale limits in the sequence.