Wavetables and Partials I am reading Direct Synthesis versus Wavetable Synthesis. The quote below explains code I have read but I don't get why it's a division by the integer multiple, when multiples increase in frequency. Doesn't that mean we need more samples (higher sample rate mapping to more samples for same accuracy) to deal with the higher frequencies, resulting in a larger wavetable.? 


  If you play a loop of a wavetable that is exactly one period at the fundamental frequency then the harmonic partials will fit within that loop. That is because the period of the harmonic partials are the fundamental period divided by N.
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 $i$.