When you play a piece of music on an instrument, can you recite all the notes continuously after that?

[Ysmael]

Just after you play a piece of music, can you recite all the exact notes you've played without stopping to think for a moment?

[. . .]

Many of us can mentally practice or review the pieces we are working on. Most of us can also HEAR them playing in our heads. Most of us with education can also auditate - that it, when when see the music, even if it is brand new to us, we can hear the notes in our head, just by viewing the printed music. I have posted before that I was astounded at my son - who is now in his thirties, with a successful teaching and performing career - that when he was a senior in college, one day sat down while visiting us, and wrote out by memory a complex 20th-century Russian piano work, to see if he had indeed memorized it correctly. His dam, also a fine pianist - checked his work. yup - and DANG! There are also people, who having heard a complex orchestral or operatic work once, can site f down years alter and play and SING the whole thing - all parts, original language - perfectly. I believe that Kissin has this gift.

A colleague and I, both flutists, would entertain ourselves in boring staff meetings, by *playing* flute works on a pencil, and expecting the other person to identify them by finger position, This game has long been played at many music conservatories.

Added - agreeing with other poster - yes, this works if you KNOW a piece well. If you have just sight-read something very difficult, then - unless you are at Kissin-level of memory - this is almost impossible to do - that was my point. And it was not a concerto that my son wrote down, but a Shostakovich (maybe Prokofiev? This was about 11 years ago that he did this) fugue - lotsa lotsa notes, and he did have it already memorized for months, and was testing himself. I could not do that.
If you are playing a melody, and you know that work fairly well, you should be able to say the letters or write it down, within reason. I tell my private flute students that when they are working on advanced things, however they learn it NOW will be stuck in their ears, head, and hands (and lips . . ) forever, and they will be able to play the hardest passages from memory - but the easy segues and plainer melodic parts, have required less effort to learn, will not stay with them as well. Many of us professional have literally thousands of things in our memories - jazz and rock players have "head tunes" that they can summon up for improvisation, and classical players have orchestral excerpts (stare down that conductor!!!) and heaps of solo classical literature, including all the wedding stuff, church stuff - and in my case, Viennese waltzes so I can watch the dancers, too! EVERY profession has tons of stuff that you just memorize without specific effort, because you use it every day. Ask your chemistry teacher just how much of the Periodic Table he/she can recite, with atomic weights and numbers, valences, etc. - ask an astronomy teacher the mean distance of all the planets, etc. from the Sun - you get the idea. You work at anything long enough, your head is filled with it - whether your tried to memorize it of not. How many computer password do you have memorized? Most of us do not bother to memorize phone numbers anymore - not needed - but hashtags, email addresses - you see what I mean. What you use every day, sinks in. That is why we all PRACTICE - we know how to play the instrument, but we crave new literature to play.

[Russell E]

I'd say that most musicians would have a hard time doing that. It would require a very high intellect and a fantastic, almost eidetic memory to be able to do that.
A lot, too, would depend on the musical knowledge of the musician.
But, I'd think it would be very hard for say a classical musician who just played a piece from sheet music to recall all the notes they just played. The more familiar with a piece of music they are, the easier that might be.

I'm sure there are prodigies like (...'s) son who wrote down a piano concerto from memory. But he must have played it for quite some time. To have him tell you the notes verbally would probably have been MUCH harder for him to do.