I am teaching an child of 7 who has white key absolute pitch.
In particular, they can sing any notes of the C major scale without a reference tone and can name the pitch of any of the white notes without looking.
However, they cannot currently do either this for the black keys. I put most of this down to their music education so far in which most of the songs are in C, G, or F.
I am looking for suggestions of exercises for them to develop the same ability for the black keys.
It's common for those with absolute pitch to have more trouble with "black keys" than "white keys."
One idea is to play them pieces in these keys. Something like Chopin's "Butterfly" etude, or "Raindrop," will provide them concrete examples of these keys/pitches.
If the child is already fluent on an instrument, having them play things in keys like D-flat and G-flat will certainly help develop that pitch memory.
If the child is learning an instrument and is only up to keys with, say, one or two accidentals, I recommend letting the learning process happen naturally. In other words, let them get to pieces in D-flat when they're ready; don't push them into D-flat too quickly just in the hopes it will improve their pitch memory.
Given my experience gaining absolute pitch (I found that I had pitch memory of Middle C in Grade 8 and could recognize C minor and E flat major music by ear by Grade 10--I'm fairly certain I figured out all 12 notes and 24 major/minor keys by Grade 12), I recommend training the child's relative pitch. Have him/her learn that both Db and C# are 1 semitone above C, both A# and Bb are a minor third above G and 1 semitone below B, and so on. With a strong enough sense of relative pitch, the gaps in absolute pitch can easily be filled in.
Besides, a basic sense of relative pitch is valuable for finding when a melody appears in a different key (this happens in pretty much every genre of music, from Christmas carols to heavy metal to video game music).
Should be straightforward to establish that between E and F, and B and C, there's only a small gap - one semitone. Whereas between other consecutive notes, there are gaps twice as big - a tone.
Drawing it out on paper, if a keyboard isn't available, will graphically illustrate this. Then it should be easy to fill in the notes in between, mentioning that they normally have two names - rather like the child - and it ought to be a good guessing game after the premise is noted : a note higher than say, C, but lower than D will be either C# or Db.
I think it's better to just play a black key and ask them what the note is. Then convince them that they'll figure it out eventually and not help them one speck. Then they might trust that you know what you're talking about and believe they will eventually figure it out and not give up. Then they'll figure out their own method of determining the note based on what they already know how to do of determining any white key note. If you instead try and teach them how to do it, they'll probably just keep struggling to figure out how to understand what you're saying. They'll be like "You're probably right but how? I don't understand why. I don't know what you're trying to tell me." That's because they'll learn that they can't think for themselves because you know better so then when they apply the rule of not thinking for themselves just following to the instructions of how to do it, which they are supposed to think for themselves what you mean, they get all confused.
