I assume that learning to identify intervals by ear is easier than learning to identifying notes by ear.
So if one is capable of playing sound of only one note in his head and comparing it to the sound he hears, he can identify the interval between the two tones and calculate the note he hears. Is it really possible?
Yes, in principle.
What you're describing is called "relative pitch": the ability to determine the interval between two notes. Developing relative pitch is a standard part of much music training at the collegiate level, and many people develop the skill earlier.
Typically this is trained by learning the distinct sound of each type of interval, allowing its identification without knowing the specific identity of either pitch. However, the ability to recognize intervals would also mean that, given a known fixed pitch, another pitch could be identified by ear.
Most training courses limit themselves to intervals up to and including an octave. Some go beyond that by a few notes. Intervals larger than an octave — "compound intervals" — are not usually taught, because the sound sufficiently similar to their "simple" counterparts, function musically in the same way, and the goal of relative pitch is interval identification rather than pitch identification.
However, one can learn, at least in principle, to identify compound intervals with specificity, and this is what would allow for the kind of pitch identification being suggested in the question.
There are numerous questions on this site regarding the development of this ability. Search the tag relative-pitch
Yes, it is possible. In fact, that's how I identified notes by ear when I was younger.
Partway through Grade 8, I found I could reliably identify Middle C by ear and reproduce it on command...and no other notes. I essentially had absolute pitch for only Middle C at that point. I had to use my relative pitch to label all the other notes I heard by ear (i.e. I indeed had to do "OK, this note I hear is an octave and a major third above Middle C, so I calculate it's high E").
I think I only developed the ability to identify all 12 notes in the chromatic scale by ear without needing to compare them to Middle C (or another memorized note) in senior high school (Grades 10-12).
There are two main things here - absolute pitch and relative pitch.
Yes, a lot of musos will reach the point where they have relative pitch - which is basically interval knowledge - mostly from learning the sounds of two notes relative to each other, and knowing what that interval is called, but also from just hearing a note, and being able to play or sing the other note in a given interval or key.
I feel your problem is how does that first 'note in his head' get there. Anyone with absolute pitch will have that nailed anyway - and the other note won't be unknown either! Anyone without absolute pitch will have difficulty in naming the 'note in his head' - but if he can find a way to make this happen (I've been trying for years with only some sporadic success) then, yes, what you ask will be easily achievable. Trouble is, getting that 'note in his head' to be accurate and correct before, or while hearing that second note is where the prroble lies...
Yes. Perfect Pitch - recognising any pitch without a reference - is a particular and quite rare skill. But Relative Pitch - 'given that this note is (say) C, what's THIS one?' - is a basic musical skill that anyone can develop. If you can establish the reference pitch internally (i.e. you have limited, one-note Perfect Pitch) all the better!
I quite consistently blow my nose to B♭. This can be useful! (And that wasn't a joke.)
