Thanks MrMark for your help. I'll test the code today. I've got only one question. Is it possible and usefull to change to constant samplefrequency that you've implemented to a higher one for the high frequencies / strings?
Edit:
So I've tested the code. The problem with my code was that I had implemented interpolation wrong, and the problem with yours was that the sample buffer was too large. I don't know why, but when I changed it to 512 samples (instead of 1024) it worked unbelievably well! With the larger amount of samples it puts out almost nothing, like you said.