A language model developer is adapting a model originally trained with a maximum sequence length of 4096 tokens to now work with a maximum sequence length of only 2048 tokens. They use the standard period scaling formula for position interpolation: $T'_k = \frac{m}{m_l} \cdot T_k$, where $m$ is the new sequence length and $m_l$ is the original maximum length. Analyze the effect of this change on the periods of the positional encoding functions. Will the periods increase or decrease, and by what factor? Explain your reasoning based on the formula.