Could also be the deflection yoke. Usually, these are composed of two windings on a two-piece ferrite core.
You can also get a whine from a corona leak. With the lights in the room out and the face of the CRT masked so that no light gets out, you can sometimes see a faint purple glow either in the flyback transformer or the anode lead that comes off of it where the leak is occurring. A blob of corona "dope" can clear the right up.
If the CRT has any sort of a shield around it, check that for noise also. Sometimes these whines can be hard to track down. On the other hand, if you wait until your 80th birthday, your high-frequency hearing will deteriorated sufficiently that you won't hear it. So, as a last resort, you can put the monitor into storage for a few years....