This continues to be a fascinating thread, getting a peek into other people's minds and seeing how differently we approach the same music sometimes.
OK - let's take a really well known tune, "Happy Birthday to you," "Auld Lang Syne" or "Silent Night" - can you imagine or "hear" the tune in your mind, or sub-vocalise it or even sing it out loud?
No. If I try to "hear in my mind" any of those tunes or hundreds of others, I will "hear" something like the badly-out-of-tune sound I would make if I actually tried to hum or sing it.
What I
can do, for those tunes, is tell immediately if it was right or wrong when I hear it played/sung. For most pieces, this is a yes/no thing: if you play a wrong note I can tell you which note is wrong but not tell you how to fix it. (Likewise I know the version I imagine in my head is wrong but don't know what the right one is. And if I try to 'pick it out by ear' - I know when I play a wrong note, but all I can do is start over again with a different note and a different note again until I find one that passes muster.)
In the relatively rare case that I can actually say "that should have been a fourth not a third" or "that should have been an E not an F", it'll be because it's a piece I have memorized in the past, and I am doing something closer to calling up a picture of the sheet music in my head and following along with it as I listen to you, than comparing how the song sounds in my mind's ear to how it sounds when you play it.
I do have a moderately good ability to look at a piece of sheet music and hear how it is supposed to sound.
Sight-reading with an actual page is sort of like me listening to you play while imagining the sheet music in my head. I can look at the music, try to play it, and if the sound I make doesn't correspond with what's on the page I will know it, and try again to put my finger in the right place. When I have the printed page, I can "rewind" instantly and try again. When I only have a recording, I have to rewind the !@#$ recording again, try again, get it wrong again, repeat again - it can take an hour to get eight bars off a recording when it would take a couple minutes off a printed page.
That's what I mean by knowing a tune. Alternatively do you think a succession of keyboard notes or intervals that when played will reproduce the tune?
That is at least somewhat closer, for me.
Interesting. Can you copy one note at a time? Ear training apps could help you.
With a pen and paper, yes (though I may be off by a note and fix it later when I try to play it. When I did the inevitable exercises in 'taking melodic dictation' in music theory, we were generally given the first and the last note and filled in what went in between -- which often meant working from both ends to get the intervals right and meeting in the middle.) Copy on my instrument, or by singing? No. I've got one chance in twelve of pressing the right button on the first try.
Can you sing along to familiar songs on the radio?
No, and am tempted to fling people out of moving cars if they do it in my presence. (I don't know if that would be different if someone sang along flawlessly: I've not had that happen. The very few professional singers I've been near a radio with have not been sing-alongers. The people I hear singing along can't sing any better than I can, but either like to pretend they do, or just don't care how it sounds and get caught up in the moment. Which is fine, if it gives them pleasure in the shower, but not fine if it annoys the people around them who'd like to hear what is on the radio.)
Perhaps that's a part of your difficulty - perfectionism.
Singing, loudly, quietly, just humming and/or running a melody through your mind are all varieties of 'singing'.
"Perfect" is often the death of joy, especially where near enough is genuinely good enough.
Hm. There certainly are people who enjoy doing things whether they are good at them or not. Good for them. I don't happen to be one of them -- I am nowhere near perfect, but I aim to be and I want to at least be close before I let anyone listen to me play. I mostly-gave-up violin because my left hand wasn't steady enough to play in tune well.
One of the hazards of music is that it isn't very forgiving. Just one tiny little button off on the accordion? Well, darn, that nice arpeggio came out as F#-A-F instead of F#-A-D because you reached one button too far. Or you accompanied that arpeggio with a lovely G major chord in the left hand instead of D. (Or on the violin, got something two-thirds of the way between F and F#.)
Playing in the back of the second violins in an orchestra, as opposed to being a soloist, we learned a whole catalog of devious tricks for when bad stuff happened. Play only the first note of each bar exactly in time, rather than try to play all the notes and be late. Play one of the two pitches in a doublestop rather than attempt both and miss. Play an octave lower if you aren't sure you are going to hit the high note right. There were very specific kinds of non-perfection that you can get away with and not ruin the effect.
In my case, as a listener, I will happily take computer-generated music over sloppily played live music. Or I will turn off the CD player in the car when I can only hear the loud parts but not the quiet parts over the engine noise, preferring to wait until I can hear the intact piece over hearing fragments of it.