Oh, and about the memory thing:
(this will somewhat repeat things I've said elsewhere on the site, in years past)
If you're listening and calculating strictly from note to note, then as Gordon points out, the dead-reckoning drift can accumulate all too rapidly.
But if you have a clear sense of where one or two key pitches are, then you can err slightly when you depart from them, but find them again when you return (even if needing to adjust slightly).
So, in highly diatonic melodies (e.g., Handel, "Where'er you walk"), I can do pretty well staying in tune from start to finish, because I'm remembering most of the notes of the scale (what the cognitive scientists would call a strategy of position-finding, rather than pattern-matching)... above all, I'm always keeping in mind that tonic B-flat.
In more chromatic selections (e.g., the Rakhmaninov "Vokaliz"), I drift, because the melody is constantly resetting the tonal frame of reference, incorporating more chromatic semitones, etc.
When I'm atop my fuzzy-set soapbox, I emphasize that it's a bit silly to talk about EITHER having absolute pitch, OR not having it (as something one is born with, and cannot hope to cultivate). Rather, my experience suggests that there is a whole continuum of short-term to long-term memory. Absolute pitch represents the long-term extreme (i.e., you never forget where each pitch is). But those of us far from that extreme nonetheless can inch closer to it, with practice.
When there's a piece of music I'm studying from day to day, I'll tend to remember pivotal notes (especially the starting pitch). F'rinstance, yesterday I played along with the prelude to Act I of Wagner's [i]Parsifal[/i], and today I poked my nose into the vocal score for Kundry's kiss in Act II.
Just now, to test myself, I tried to find the opening A-flat of the prelude. I tried to start on one pitch, immediately recognized it as the wrong one (about a third or fourth too high), corrected it, and then checked myself with a pitch pipe... self-corrected second attempt turned out to be an A, rather than Ab.
Then I tried to find Parsifal's cry of "Amfortas!" (F-E), and nailed it.
For those of you keeping score at home: that was an error of only a semitone for the items last heard about 24 hours ago, and spot-on for the item last heard about 7 hours ago.
And then there are some pitches that are just burned in... e.g., the singer's opening G-sharp in the first song of Schumann's [i]Dichterliebe[/i], which I just found, even though I haven't sung or played that selection in months, maybe a year or more.
