emusonacid! legacy

i was messing around today with my test tone samples. i found that if you take a sine at 440 hz, and make the loop size 50 instead of 100, you will actualy create a "sawtooth" at 880hz. the wave looks like a saw, but it isn't like a real saw. it doesn't have the really straight lines the a real one does. what the wave basicaly looks like is half a sine looping. it seems the missed loop points created overtones.

now it gets strange here.

i know that if you filter out a square, triangle, or sawtooth with a lowpass filter you will essencially be left with a sine wave. but i didn't expect this to happen, when i filterd the sine sawtooth. i found that the sample actually reformed to an exact sine wave again. it was like the missed start and stop points on the loop disappeared. i compared the lp version with a real version and found the only difference between the waves was the lp was a bit louder. and the two waves were bascially in tune.

can anyone explain why low pass filtering that sine sawtooth would create and end result of a sine again? i would have thought that since i missed the loop points and the fact that the sine is a pure tone that i would pretty much end up with a click or something. or a wave that didn't change at all. of course you could only hear the wave below 57 hz or so do to the roll off of the 6 pole lpf. so then, if i wanted to, i could resample the wave at say c2 and set a loop and i would have a sine again.

just wondering if anyone can explain how this might work. kind of makes me wonder that if someone is having difficulties setting a loop point, one could filter the sample just a little to get rid of the overtones that are created and have a "perfect" loop...

just thought this was kind of strange.