Digital Rhythm?

[KirkP]

The first time a singer uses in-ear monitors for stage performance they often express this same problem, and typically complain that what they are hearing is "not clear" or that they are having trouble "hearing themselves". What's happening is that their perceived singing pitch is not aligning to the acoustic pitch of the rest of the band.

It seems more likely to me that the problem is a phase shift between the signal coming through the headphones and the band. This would result in reenforcement and cancellation effects that vary with frequency. As I mentioned in another post, I doubt there is perceived pitch shift. I won’t say it’s impossible, but I need scientific evidence to be convinced.
Edit - I’ve found some references to effects on perceived pitch by varying volume levels. So perhaps my experiment would have resulted in an effect if I played the music much louder. That’s not a proximity effect though, except in the sense that sound gets louder as it gets closer to your ear. In free space the power increases by square of the distance, so putting on headphones would have a great effect on volume.
Another possible effect: The human auditory system is able to perceive pitch of a complex signal from the harmonics even when the fundamental frequency itself is suppressed. When you remove headphones, the bass frequencies drop out, so pitch perception probably relies more heavily on this effect than when the headphones are on. I’ll speculate that the perceived pitch based on this reconstruction from harmonics might be less accurate than if the fundamental were present. If that error is biased toward the flat side when the fundamental is missing that might explain the perception of being perceived as flat when headphones are removed. Even if that is true, I wouldn’t describe it as a proximity effect.
I think the unpleasantness of singing with headphones has more to do with how the headphones change the acoustic properties of your head and the transmission of your voice to the ear. Try singing a capella with closed back headphones (turned off) or your hands over your ears. Your voice is mostly received through bone and tissue rather than the air, and it sounds horrible.

[M-ster]

... Your voice is mostly received through bone and tissue rather than the air, and it sounds horrible.

Apparently you've heard me singing.

[fep]

Try singing a capella with closed back headphones (turned off) or your hands over your ears. Your voice is mostly received through bone and tissue rather than the air, and it sounds horrible.

Funny I've said before, when I record my voice my goal is for it to be "not horrible".