OP here: I won’t address all the responses, because others have said what I would have said. Of the counterarguments, I thought that[ B]Lasciel** in particular made some good points in post #25. Other people have said that I am incorrectly assuming that a certain level of ability is innate, and countering with examples of non-innate ability, such as reading or novel-writing. But clearly some relatively sophisticated abilities are innate, such as walking and talking, which infants largely acquire themselves.
But to put my point another way, my contention is that anyone with the following abilities can reproduce a simple melody:
(1) Ability to determine whether two notes are the same.
(2) Ability to reproduce a simple tune, for example by whistling or singing it, or just “hearing” it in your imagination, and so be able to compare the note produced by the instrument to the desired note.
The following are not strictly necessary, but will speed things up no end:
(3) Ability to determine whether one note is higher or lower than another note.
(4) Ability to establish how to produce higher or lower notes with the instrument e.g. on a piano, the notes get higher as you move to the right.
I believe that (1) is an innate ability that requires no training or special aptitude, although I take the point made earlier that the same note can sound different on different instruments.
Some people have suggested that (2) is not universal. OK, how about if, instead of having to recall the tune in your head while finding the notes on the instrument, you have some patient assistant repeatedly sing it or play it to you?
Some people also assert that (3) is not innate. If so, this would go a long way to answering the question. I invite people to try the interval test at Interval Ear Training (requires Flash) - click New Interval and you will hear two nearby notes, either ascending, descending or the same (called “unison” in music-speak). I would have thought that most people could easily distinguish between unison and non-unison. But can “almost anybody” easily tell whether the first note of the pair is higher or lower?
It seems to me that (4) is just common sense. It’s pretty straightforward on a piano, but can be less intuitive on other instruments such as wind instruments. So we’ll stick to piano.
And one more clarification - in the OP I am talking about a very simple tune, a riff really, of ten notes. No chords or harmony, not a Beethoven concerto in multi-part polyphony. The actual tune in question (I’m not going to name in in case the person sees this) is about as simple as Twinkle Twinkle Little Star.
I am also not expecting people to render the tune in the correct key. So, in the case of Twinkle Twinkle Little Star, both C C G G A A G and G G D D E E D would be correct - same tune, different key.