Would a string vibrating in an atmosphere that is different from Earth's have a different overtone series? The overtone series is defined as a set of characteristic harmonic oscillations of a vibrating string. It is a core concept of Western music theory.
Are these characteristics a result of the string interacting with the medium it exists in (i.e. would the same string in a different medium display a fundamentally different overtone series)?
 A: No.  To a very good approximation, the frequencies of the vibration of the string are determined solely by three things:


*

*the tension in the string, which determines how fast the string "snaps back" when it is disturbed;  

*the mass of the string, which determines how quickly the string responds to these tension forces; 

*and the length of the string, which determines the specific conditions under which a standing wave can form.  


Under these assumptions, you obtain the standard overtone series for the vibrations of a string;  the medium in which the string moves doesn't enter into these calculations.
The air in which the string moves probably does have some small effect, shifting the "canonical" overtone frequencies ever so slightly.  However, many other effects could also shift the frequencies by comparable amounts:  the endpoints not being perfectly rigid, the string not being perfectly flexible, the fact that the tension will change slightly in the string due to Hooke's Law, unevenness in the mass distribution of the string, and so forth.  To actually try to calculate the degree to which the air affects the frequencies while ignoring all these other factors might be an interesting exercise, but in practical terms it wouldn't be a terribly useful result.
A: No interaction with an external environment is assumed when deriving the allowed frequencies for a string. The basic assumptions are that tension is the same at every point on the string, and that there are no other forces acting on it (gravity, air resistance, etc). Thus the overtone series will remain the same if the string length, density and tension are the same.
However, changing the medium may or may not change the frequency of the sound wave such a vibrating string generates, I do not know about the acoustics of a vibrating string.
