I believe (based on what I remember from a Physics of Music class I took back in the mid-1960s) that the overtone would be a major third, completing a major chord: root, major third, perfect fifth.

As I recall from the NPR broadcast, the female mosquito produces a note of about 400 cycles per second, which is close to an A, but somewhat flat (reckoning by the current standard of 440 cps = concert A), and the male tries to zing in on about 600 cps (also, flat compared to what it should be: 660 cps [ratio, 2 to 3 to produce a perfect 5th]). The two notes together actually mix several overtones, but the strongest one is a major third above the root of A, namely C# in this case. [Note that the female 'skeeter has a deeper voice than the male 'skeeter.]

Every note (with the possible exception of "purified" electronically produced notes) produce both the fundamental and a series of overtones. The varying strengths of the overtones of different instruments is why you can tell, say, a flute from a clarinet, even when they're both playing the same fundamental note. Some overtones reinforce each other, and this is what happens when 'skeeters--or anything for that matter--start playing duets.

. . . I think. . . .

Don Firth