Harmonic errors in acoustic instruments If a note has a fundamental frequency of 100Hz, then its second harmonic is located at 200Hz and its tenth harmonic is located at 1000Hz. But for acoustic instruments, the harmonics will not occur at exact multiples of the fundamental. My question is, how much error is typical and what is the relationship between the degree of error and the harmonic number. So for example, is it common for the error in the tenth harmonic to be as much as, say, 50Hz. 1050Hz in other words. That's a 5% error. But would a 5% error be just as likely for the second harmonic?
A few things:


Not all instruments have partials neatly defined by the $h_n = nf$. Kettle drums would be an obvious example, but bells are another. In this case, you will be way off looking in the "usual places" +/- 5%.
Many instruments have only even or odd harmonics. Others are designed to omit some harmonics. The piano, for example, is designed to have almost no 7th harmonic. This may not matter to you, but it's worth pointing out in case it does.
It is common for higher harmonics to be "out of tune", that is, not in the "usual places". An engineer who once worked as a piano tuner once admonished me for using harmonics to tune my upright bass (a technique that works well for lighter-stringed instruments), because, he said, the partials are more out of tune with heavier stringed instruments. He said it's especially true told of higher harmonics, explaining that the math that gives you the simple formula for partials assumes that strings have no mass. 5% strikes me as a little much (almost a semi-tone!), but I don't think it's out of the question.
Many instruments have vibrato. This throws all your harmonics out of wack: