Everyone who has ever messed around with a recording device–tape, digital, Dictaphone, belt, record, whatever–knows that what comes out of the speaker in no way resembles what they hear in their head. (Most of the folks I’ve asked about this say what they hear subjectively is deeper) Is there any research as to what the pitch change is? Is there a rule of thumb that lets me know what Mary and Max Macaroon think they sound like? Does the apparent pitch change make it harder for folks who are trying to do overdubbing, or are they so used to the sound of their own voices that they can just shrug off the difference?
You’re talking about the way your own voice sounds different on tape, from the way it sounds in your head? We should distinguish between “pitch” and “timbre”. The “pitch” doesn’t change, the actual “note”, between hearing it in your head, and hearing it on tape. If you tape yourself singing an A above middle C, the pitch on the tape will still be an A above middle C. What’s different is what’s called the “timbre”.
A French horn has a different “timbre” from a flute. Your voice, as heard by your middle and inner ear through the bone and muscle of your head, sounds to you as though it has a completely different timbre from your voice as reproduced by a tape recording.
I don’t know of any way offhand to reproduce on a tape how you sound to yourself in your head, other than by simply adding a lot of “fuzz” and overtones here and there, essentially at random.
I always sound louder to myself when I hear myself on tape. “Am I that loud?” I wonder. Everybody says, “Um, yeah, you are.” 
This means that the bone and muscle in my head is filtering out a lot of the “brighter” harmonics and overtones, which is part of what makes music “loud”, so I don’t sound as loud to myself.
My understanding of the way that overdubbing or “looping” works, is that either you are only singing along with the instruments, or else that you just get used to the sound of singing along with yourself. It’s not that hard to do–music kids fooling around with two cheap tape recorders do it all the time. Sing the soprano part into the tape, then play the tape on Recorder #1 and use Recorder #2 to tape yourself singing alto along with the soprano tape. It’s actually kind of a kick, to sing along with yourself.
**There is a Mary Ford vs. Karen Carpenter joke lurking here somewhere, but I’ll let it pass. Anyway, thanks for the reply!
Just a slight nitpick on DDG’s post.
To properly emulate the sound of a voice as the speaker hears it, you wouldn’t add fuzz. Fuzz is distortion and adds harmonics that were not part of the original signal. You would need to filter (i.e. eq) the sound.
I remembered this subject being research in regards to signers. I found this very short abstract on google.
There are two problems with the emulation/analysis of the change in timbre.
The first one is that, like the voice itself, it is dependant on the speaker’s physical constitution. Different people, different variation in timbre.
The second is that the variation is not uniform. If it was only caused by filtering of partials by bone and tissue, the issue would be simpler. However, especially in the signing voice, you need to consider sympathetic vibration occuring in chest and sinus cavities and those vibrations will depend on the fundamental of the sound you are voicing.
I don’t know about finding out how others hear themselves, but I know how to go the other way - i.e. hear roughly how you sound to others, without using a tape.
You need to cup your hands over your ears whilst gently folding them forwards. Now, if you speak, it sounds pretty much how you do to others.
Don’t do this when other people may catch you, though. I just did, and got weird looks of an electrician.