Here's something else to consider.
If you play a note... say 440 (A) .... unless it is a pure sine wave (and very few sounds we use are pure sines) you will have harmonics above and below that note. There are the dominate ones and the less dominate ones. (440x2, x3, x4, x5,x6 and so on and on the other lower end 440x.5, x.25, and so on. the harmonics below the primary note are generally very weak) Even and odd order harmonics will be generated from the primary note. How loud each harmonic is determines much of the character and color of a given note. It is these very harmonics, especially the even order ones that guitarists love. We call it "tone"....
While this is sometimes hard to hear since we hear the primary the loudest, it is easy to see on an oscilloscope.
But it gets better. As you add other notes, these notes are also doing the same thing but with one more interesting factor. You now get the two or more notes interacting with each other. It's called "beat frequency" and other harmonics are generated as a result. These harmonics can be much higher in the frequency band above the original notes, but they are there and they can often cause havoc in frequency bands we think are totally unrelated to where the primary is located. Some extend well past 10k, and they are shaping the color of that note that is down around 440. that's the "air" frequencies Danny ( I believe) mentioned above.
I don't try to figure things out scientifically when I'm mixing and adjusting the EQ on something. I listen to the mix and try to determine what the issue is, what's causing it, and then what steps or adjustments are needed to fix it. The stuff above about harmonics and beat freqs is nice to know, but mix by using your ears. So yes, it is totally within the realm of possibility that you need to adjust the EQ well above the primary instrument or voice to solve an EQ issue.