Wavetables and Partials
Harmonic partials have frequencies $f_i=if_1$, $i=2,3\ldots,$ where $f_1$ is the fundamental frequency. So the frequencies are not doubled, but they are integer multiples of the fundamental frequency. But if you talk about periods, then you have $T_i=1/f_i$, i.e. $T_i=T_1/i$, $i=2,3,\ldots$. So the period of the $i^{th}$ harmonic partial is the fundamental period divided by $i$.