Sorry that I keep resurrecting old threads. I guess it’s because I am very late to the Model:Samples game?
What I wanted to point out for others who may eventually be searching for this: The site mentioned above recommends (among other things) 734 samples for a single-cycle wave and I’ve found today (after writing some Python code that generates single-cycle waves) that indeed the reproduction on the Model:Samples is most accurate (i.e. 0 cents difference from normal) for that number of samples.
At first I tried 183 samples because, you know, 48000/261.63 is roughly 183.465 but that (as well as 182, 184, or 185 samples) always diverged by at last 5 cents from normal. Alas, rendering the same wave 4 times out to 734 samples actually gets to the “correct” reproduction. I am not 100% sure why that is but I guess at 4 waves the floating point inaccuracies “cancel out enough” in terms of integers for things to sound “perfect” as it were. If anyone has deeper insight on this, please feel free to educate me. Otherwise, to anyone else playing with single-cycle waves on the M:S, I recommend going for 734 samples.
Oh, and here’s an archived copy of that site, apparently it went away sometime after 2021: How to convert wavetables for Elektron Machines - KIMURA TARO
EDIT: I should have said “… if you’re going for C4 pitch that is …” because that’s where the 261.63 Hz comes from after all. If you are interested in another pitch the math is presumably different and I have not yet done the experiment to find the best sample length. But I probably will do that eventually and I wouldn’t be surprised if again “four waves” does the trick. We’ll see. Or maybe someone else beats me to it?